1,1,246,131,2.166676,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","\frac{\left(A\,a+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{10\,A\,a}{3}+\frac{13\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,a}{3}+\frac{116\,C\,a}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{22\,A\,a}{3}+\frac{19\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,C\right)}{4\,\left(A\,a+\frac{3\,C\,a}{4}\right)}\right)\,\left(4\,A+3\,C\right)}{4\,d}-\frac{a\,\left(4\,A+3\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + (13*C*a)/4) + tan(c/2 + (d*x)/2)^9*(A*a + (3*C*a)/4) + tan(c/2 + (d*x)/2)^7*((10*A*a)/3 + (13*C*a)/6) + tan(c/2 + (d*x)/2)^3*((22*A*a)/3 + (19*C*a)/6) + tan(c/2 + (d*x)/2)^5*((20*A*a)/3 + (116*C*a)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(4*A + 3*C))/(4*(A*a + (3*C*a)/4)))*(4*A + 3*C))/(4*d) - (a*(4*A + 3*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
2,1,212,108,1.713453,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","\frac{\left(A\,a+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(5\,A\,a+\frac{49\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(7\,A\,a+\frac{31\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,C\right)}{4\,\left(A\,a+\frac{3\,C\,a}{4}\right)}\right)\,\left(4\,A+3\,C\right)}{4\,d}-\frac{a\,\left(4\,A+3\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + (13*C*a)/4) + tan(c/2 + (d*x)/2)^7*(A*a + (3*C*a)/4) + tan(c/2 + (d*x)/2)^3*(7*A*a + (31*C*a)/12) + tan(c/2 + (d*x)/2)^5*(5*A*a + (49*C*a)/12))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(4*A + 3*C))/(4*(A*a + (3*C*a)/4)))*(4*A + 3*C))/(4*d) - (a*(4*A + 3*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
3,1,67,81,0.875780,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","A\,a\,x+\frac{C\,a\,x}{2}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"A*a*x + (C*a*x)/2 + (A*a*sin(c + d*x))/d + (3*C*a*sin(c + d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(3*c + 3*d*x))/(12*d)","B"
4,1,115,58,0.973197,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x),x)","\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(C*a*sin(c + d*x))/d + (2*A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*sin(2*c + 2*d*x))/(4*d)","B"
5,1,91,42,0.884220,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(C*a*sin(c + d*x))/d + (2*A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*sin(c + d*x))/(d*cos(c + d*x))","B"
6,1,128,58,0.900557,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*sin(c + d*x))/(d*cos(c + d*x)) + (A*a*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
7,1,129,86,2.693452,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^4,x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+2\,C\right)}{d}-\frac{\left(A\,a+2\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A\,a}{3}-4\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+2\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2))*(A + 2*C))/d - (tan(c/2 + (d*x)/2)*(3*A*a + 2*C*a) + tan(c/2 + (d*x)/2)^5*(A*a + 2*C*a) - tan(c/2 + (d*x)/2)^3*((4*A*a)/3 + 4*C*a))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
8,1,166,117,3.345631,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^5,x)","\frac{\left(-\frac{3\,A\,a}{4}-C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{49\,A\,a}{12}+5\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{31\,A\,a}{12}-7\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,A+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + 3*C*a) - tan(c/2 + (d*x)/2)^7*((3*A*a)/4 + C*a) - tan(c/2 + (d*x)/2)^3*((31*A*a)/12 + 7*C*a) + tan(c/2 + (d*x)/2)^5*((49*A*a)/12 + 5*C*a))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atanh(tan(c/2 + (d*x)/2))*(3*A + 4*C))/(4*d)","B"
9,1,315,194,2.235226,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2,x)","\frac{\left(\frac{7\,A\,a^2}{4}+\frac{11\,C\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{119\,A\,a^2}{12}+\frac{187\,C\,a^2}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{43\,A\,a^2}{2}+\frac{331\,C\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{53\,A\,a^2}{2}+\frac{501\,C\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{233\,A\,a^2}{12}+\frac{87\,C\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{25\,A\,a^2}{4}+\frac{53\,C\,a^2}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^2\,\left(14\,A+11\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(14\,A+11\,C\right)}{8\,\left(\frac{7\,A\,a^2}{4}+\frac{11\,C\,a^2}{8}\right)}\right)\,\left(14\,A+11\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + (53*C*a^2)/8) + tan(c/2 + (d*x)/2)^11*((7*A*a^2)/4 + (11*C*a^2)/8) + tan(c/2 + (d*x)/2)^3*((233*A*a^2)/12 + (87*C*a^2)/8) + tan(c/2 + (d*x)/2)^9*((119*A*a^2)/12 + (187*C*a^2)/24) + tan(c/2 + (d*x)/2)^7*((43*A*a^2)/2 + (331*C*a^2)/20) + tan(c/2 + (d*x)/2)^5*((53*A*a^2)/2 + (501*C*a^2)/20))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (a^2*(14*A + 11*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(14*A + 11*C))/(8*((7*A*a^2)/4 + (11*C*a^2)/8)))*(14*A + 11*C))/(8*d)","B"
10,1,277,163,2.102409,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2,x)","\frac{\left(2\,A\,a^2+\frac{3\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{28\,A\,a^2}{3}+7\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{56\,A\,a^2}{3}+\frac{72\,C\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{52\,A\,a^2}{3}+9\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A\,a^2+\frac{13\,C\,a^2}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^2\,\left(4\,A+3\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{2\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,C\right)}{2\,\left(2\,A\,a^2+\frac{3\,C\,a^2}{2}\right)}\right)\,\left(4\,A+3\,C\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(6*A*a^2 + (13*C*a^2)/2) + tan(c/2 + (d*x)/2)^9*(2*A*a^2 + (3*C*a^2)/2) + tan(c/2 + (d*x)/2)^7*((28*A*a^2)/3 + 7*C*a^2) + tan(c/2 + (d*x)/2)^3*((52*A*a^2)/3 + 9*C*a^2) + tan(c/2 + (d*x)/2)^5*((56*A*a^2)/3 + (72*C*a^2)/5))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (a^2*(4*A + 3*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(2*d) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(4*A + 3*C))/(2*(2*A*a^2 + (3*C*a^2)/2)))*(4*A + 3*C))/(2*d)","B"
11,1,117,123,0.918716,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2,x)","\frac{3\,A\,a^2\,x}{2}+\frac{7\,C\,a^2\,x}{8}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{C\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(3*A*a^2*x)/2 + (7*C*a^2*x)/8 + (2*A*a^2*sin(c + d*x))/d + (3*C*a^2*sin(c + d*x))/(2*d) + (A*a^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*sin(3*c + 3*d*x))/(6*d) + (C*a^2*sin(4*c + 4*d*x))/(32*d)","B"
12,1,159,96,1.025977,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x),x)","\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{7\,C\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{4\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(A*a^2*sin(c + d*x))/d + (7*C*a^2*sin(c + d*x))/(4*d) + (4*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*sin(3*c + 3*d*x))/(12*d)","B"
13,1,152,112,0.963288,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(2*C*a^2*sin(c + d*x))/d + (2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
14,1,154,112,0.953324,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^3,x)","\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(C*a^2*sin(c + d*x))/d + (3*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (A*a^2*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
15,1,184,110,0.938370,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^4,x)","\frac{2\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{5\,A\,a^2\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (5*A*a^2*sin(c + d*x))/(3*d*cos(c + d*x)) + (A*a^2*sin(c + d*x))/(d*cos(c + d*x)^2) + (A*a^2*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (C*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
16,1,185,147,3.349068,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\left(-\frac{7\,A\,a^2}{4}-3\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{77\,A\,a^2}{12}+11\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{83\,A\,a^2}{12}-13\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{25\,A\,a^2}{4}+5\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(7\,A+12\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + 5*C*a^2) - tan(c/2 + (d*x)/2)^7*((7*A*a^2)/4 + 3*C*a^2) + tan(c/2 + (d*x)/2)^5*((77*A*a^2)/12 + 11*C*a^2) - tan(c/2 + (d*x)/2)^3*((83*A*a^2)/12 + 13*C*a^2))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a^2*atanh(tan(c/2 + (d*x)/2))*(7*A + 12*C))/(4*d)","B"
17,1,222,178,3.601171,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^6,x)","\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,A}{4}+C\right)}{d}-\frac{\left(\frac{3\,A\,a^2}{2}+2\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-7\,A\,a^2-\frac{28\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{72\,A\,a^2}{5}+\frac{56\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-9\,A\,a^2-\frac{52\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a^2}{2}+6\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a^2*atanh(tan(c/2 + (d*x)/2))*((3*A)/4 + C))/d - (tan(c/2 + (d*x)/2)*((13*A*a^2)/2 + 6*C*a^2) + tan(c/2 + (d*x)/2)^9*((3*A*a^2)/2 + 2*C*a^2) - tan(c/2 + (d*x)/2)^7*(7*A*a^2 + (28*C*a^2)/3) - tan(c/2 + (d*x)/2)^3*(9*A*a^2 + (52*C*a^2)/3) + tan(c/2 + (d*x)/2)^5*((72*A*a^2)/5 + (56*C*a^2)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
18,1,353,237,2.275094,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3,x)","\frac{\left(\frac{13\,A\,a^3}{4}+\frac{21\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{65\,A\,a^3}{3}+\frac{35\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{3679\,A\,a^3}{60}+\frac{1981\,C\,a^3}{40}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{464\,A\,a^3}{5}+\frac{2608\,C\,a^3}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{5089\,A\,a^3}{60}+\frac{3011\,C\,a^3}{40}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{143\,A\,a^3}{3}+\frac{61\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,A\,a^3}{4}+\frac{107\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^3\,\left(26\,A+21\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(26\,A+21\,C\right)}{8\,\left(\frac{13\,A\,a^3}{4}+\frac{21\,C\,a^3}{8}\right)}\right)\,\left(26\,A+21\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (107*C*a^3)/8) + tan(c/2 + (d*x)/2)^13*((13*A*a^3)/4 + (21*C*a^3)/8) + tan(c/2 + (d*x)/2)^11*((65*A*a^3)/3 + (35*C*a^3)/2) + tan(c/2 + (d*x)/2)^3*((143*A*a^3)/3 + (61*C*a^3)/2) + tan(c/2 + (d*x)/2)^7*((464*A*a^3)/5 + (2608*C*a^3)/35) + tan(c/2 + (d*x)/2)^9*((3679*A*a^3)/60 + (1981*C*a^3)/40) + tan(c/2 + (d*x)/2)^5*((5089*A*a^3)/60 + (3011*C*a^3)/40))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) - (a^3*(26*A + 21*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(26*A + 21*C))/(8*((13*A*a^3)/4 + (21*C*a^3)/8)))*(26*A + 21*C))/(8*d)","B"
19,1,315,188,2.227939,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3,x)","\frac{\left(\frac{15\,A\,a^3}{4}+\frac{23\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{85\,A\,a^3}{4}+\frac{391\,C\,a^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{99\,A\,a^3}{2}+\frac{759\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{125\,A\,a^3}{2}+\frac{969\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{171\,A\,a^3}{4}+\frac{211\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{49\,A\,a^3}{4}+\frac{105\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^3\,\left(30\,A+23\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(30\,A+23\,C\right)}{8\,\left(\frac{15\,A\,a^3}{4}+\frac{23\,C\,a^3}{8}\right)}\right)\,\left(30\,A+23\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((49*A*a^3)/4 + (105*C*a^3)/8) + tan(c/2 + (d*x)/2)^11*((15*A*a^3)/4 + (23*C*a^3)/8) + tan(c/2 + (d*x)/2)^3*((171*A*a^3)/4 + (211*C*a^3)/8) + tan(c/2 + (d*x)/2)^9*((85*A*a^3)/4 + (391*C*a^3)/24) + tan(c/2 + (d*x)/2)^7*((99*A*a^3)/2 + (759*C*a^3)/20) + tan(c/2 + (d*x)/2)^5*((125*A*a^3)/2 + (969*C*a^3)/20))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (a^3*(30*A + 23*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(30*A + 23*C))/(8*((15*A*a^3)/4 + (23*C*a^3)/8)))*(30*A + 23*C))/(8*d)","B"
20,1,277,148,2.152367,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3,x)","\frac{\left(5\,A\,a^3+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{70\,A\,a^3}{3}+\frac{91\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{128\,A\,a^3}{3}+\frac{416\,C\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{106\,A\,a^3}{3}+\frac{133\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A\,a^3+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^3\,\left(20\,A+13\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,A+13\,C\right)}{4\,\left(5\,A\,a^3+\frac{13\,C\,a^3}{4}\right)}\right)\,\left(20\,A+13\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(11*A*a^3 + (51*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*(5*A*a^3 + (13*C*a^3)/4) + tan(c/2 + (d*x)/2)^7*((70*A*a^3)/3 + (91*C*a^3)/6) + tan(c/2 + (d*x)/2)^3*((106*A*a^3)/3 + (133*C*a^3)/6) + tan(c/2 + (d*x)/2)^5*((128*A*a^3)/3 + (416*C*a^3)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (a^3*(20*A + 13*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(20*A + 13*C))/(4*(5*A*a^3 + (13*C*a^3)/4)))*(20*A + 13*C))/(4*d)","B"
21,1,195,147,1.156855,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x),x)","\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{13\,C\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{7\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{15\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(3*A*a^3*sin(c + d*x))/d + (13*C*a^3*sin(c + d*x))/(4*d) + (7*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (15*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (A*a^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(2*c + 2*d*x))/d + (C*a^3*sin(3*c + 3*d*x))/(4*d) + (C*a^3*sin(4*c + 4*d*x))/(32*d)","B"
22,1,189,145,0.995649,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{11\,C\,a^3\,\sin\left(c+d\,x\right)}{3\,d}+\frac{6\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{5\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{3\,C\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(A*a^3*sin(c + d*x))/d + (11*C*a^3*sin(c + d*x))/(3*d) + (6*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (5*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^3*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (3*C*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
23,1,207,160,1.037482,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^3,x)","\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(3*C*a^3*sin(c + d*x))/d + (2*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*A*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (A*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (C*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
24,1,199,156,1.040928,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^4,x)","\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{11\,A\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(C*a^3*sin(c + d*x))/d + (5*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (11*A*a^3*sin(c + d*x))/(3*d*cos(c + d*x)) + (3*A*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (A*a^3*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (C*a^3*sin(c + d*x))/(d*cos(c + d*x))","B"
25,1,231,169,1.044885,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{15\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,A\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{15\,A\,a^3\,\sin\left(c+d\,x\right)}{8\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^3}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{4\,d\,{\cos\left(c+d\,x\right)}^4}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(15*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*A*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (15*A*a^3*sin(c + d*x))/(8*d*cos(c + d*x)^2) + (A*a^3*sin(c + d*x))/(d*cos(c + d*x)^3) + (A*a^3*sin(c + d*x))/(4*d*cos(c + d*x)^4) + (3*C*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
26,1,224,194,3.492769,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^6,x)","\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(13\,A+20\,C\right)}{4\,d}-\frac{\left(\frac{13\,A\,a^3}{4}+5\,C\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{91\,A\,a^3}{6}-\frac{70\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,A\,a^3}{15}+\frac{128\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{133\,A\,a^3}{6}-\frac{106\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,A\,a^3}{4}+11\,C\,a^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^3*atanh(tan(c/2 + (d*x)/2))*(13*A + 20*C))/(4*d) - (tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + 11*C*a^3) + tan(c/2 + (d*x)/2)^9*((13*A*a^3)/4 + 5*C*a^3) - tan(c/2 + (d*x)/2)^7*((91*A*a^3)/6 + (70*C*a^3)/3) - tan(c/2 + (d*x)/2)^3*((133*A*a^3)/6 + (106*C*a^3)/3) + tan(c/2 + (d*x)/2)^5*((416*A*a^3)/15 + (128*C*a^3)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
27,1,262,225,3.588947,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^7,x)","\frac{\left(-\frac{23\,A\,a^3}{8}-\frac{15\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{391\,A\,a^3}{24}+\frac{85\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{759\,A\,a^3}{20}-\frac{99\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{969\,A\,a^3}{20}+\frac{125\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{211\,A\,a^3}{8}-\frac{171\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{105\,A\,a^3}{8}+\frac{49\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(23\,A+30\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((105*A*a^3)/8 + (49*C*a^3)/4) - tan(c/2 + (d*x)/2)^11*((23*A*a^3)/8 + (15*C*a^3)/4) - tan(c/2 + (d*x)/2)^3*((211*A*a^3)/8 + (171*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*((391*A*a^3)/24 + (85*C*a^3)/4) - tan(c/2 + (d*x)/2)^7*((759*A*a^3)/20 + (99*C*a^3)/2) + tan(c/2 + (d*x)/2)^5*((969*A*a^3)/20 + (125*C*a^3)/2))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^3*atanh(tan(c/2 + (d*x)/2))*(23*A + 30*C))/(8*d)","B"
28,1,391,279,2.415553,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4,x)","\frac{\left(\frac{49\,A\,a^4}{8}+\frac{323\,C\,a^4}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+\left(\frac{1127\,A\,a^4}{24}+\frac{7429\,C\,a^4}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{18767\,A\,a^4}{120}+\frac{123709\,C\,a^4}{960}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{35371\,A\,a^4}{120}+\frac{1632119\,C\,a^4}{6720}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{40661\,A\,a^4}{120}+\frac{624003\,C\,a^4}{2240}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{29617\,A\,a^4}{120}+\frac{68673\,C\,a^4}{320}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{2713\,A\,a^4}{24}+\frac{5033\,C\,a^4}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{207\,A\,a^4}{8}+\frac{1725\,C\,a^4}{64}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^4\,\left(392\,A+323\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{64\,d}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A+323\,C\right)}{64\,\left(\frac{49\,A\,a^4}{8}+\frac{323\,C\,a^4}{64}\right)}\right)\,\left(392\,A+323\,C\right)}{64\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + (1725*C*a^4)/64) + tan(c/2 + (d*x)/2)^15*((49*A*a^4)/8 + (323*C*a^4)/64) + tan(c/2 + (d*x)/2)^3*((2713*A*a^4)/24 + (5033*C*a^4)/64) + tan(c/2 + (d*x)/2)^13*((1127*A*a^4)/24 + (7429*C*a^4)/192) + tan(c/2 + (d*x)/2)^5*((29617*A*a^4)/120 + (68673*C*a^4)/320) + tan(c/2 + (d*x)/2)^11*((18767*A*a^4)/120 + (123709*C*a^4)/960) + tan(c/2 + (d*x)/2)^7*((40661*A*a^4)/120 + (624003*C*a^4)/2240) + tan(c/2 + (d*x)/2)^9*((35371*A*a^4)/120 + (1632119*C*a^4)/6720))/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) - (a^4*(392*A + 323*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(64*d) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(392*A + 323*C))/(64*((49*A*a^4)/8 + (323*C*a^4)/64)))*(392*A + 323*C))/(64*d)","B"
29,1,353,219,2.295232,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4,x)","\frac{\left(7\,A\,a^4+\frac{11\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{140\,A\,a^4}{3}+\frac{110\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{1981\,A\,a^4}{15}+\frac{3113\,C\,a^4}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{1024\,A\,a^4}{5}+\frac{5632\,C\,a^4}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{2851\,A\,a^4}{15}+\frac{1501\,C\,a^4}{10}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{308\,A\,a^4}{3}+70\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{53\,C\,a^4}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^4\,\left(14\,A+11\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{2\,d}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(14\,A+11\,C\right)}{2\,\left(7\,A\,a^4+\frac{11\,C\,a^4}{2}\right)}\right)\,\left(14\,A+11\,C\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(25*A*a^4 + (53*C*a^4)/2) + tan(c/2 + (d*x)/2)^13*(7*A*a^4 + (11*C*a^4)/2) + tan(c/2 + (d*x)/2)^11*((140*A*a^4)/3 + (110*C*a^4)/3) + tan(c/2 + (d*x)/2)^3*((308*A*a^4)/3 + 70*C*a^4) + tan(c/2 + (d*x)/2)^5*((2851*A*a^4)/15 + (1501*C*a^4)/10) + tan(c/2 + (d*x)/2)^9*((1981*A*a^4)/15 + (3113*C*a^4)/30) + tan(c/2 + (d*x)/2)^7*((1024*A*a^4)/5 + (5632*C*a^4)/35))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) - (a^4*(14*A + 11*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(2*d) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(14*A + 11*C))/(2*(7*A*a^4 + (11*C*a^4)/2)))*(14*A + 11*C))/(2*d)","B"
30,1,316,179,2.340807,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4,x)","\frac{\left(\frac{35\,A\,a^4}{4}+\frac{49\,C\,a^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{595\,A\,a^4}{12}+\frac{833\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{231\,A\,a^4}{2}+\frac{1617\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{281\,A\,a^4}{2}+\frac{1967\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{1069\,A\,a^4}{12}+\frac{1471\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{93\,A\,a^4}{4}+\frac{207\,C\,a^4}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{7\,a^4\,\left(10\,A+7\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}+\frac{7\,a^4\,\mathrm{atan}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,A+7\,C\right)}{8\,\left(\frac{35\,A\,a^4}{4}+\frac{49\,C\,a^4}{8}\right)}\right)\,\left(10\,A+7\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((93*A*a^4)/4 + (207*C*a^4)/8) + tan(c/2 + (d*x)/2)^11*((35*A*a^4)/4 + (49*C*a^4)/8) + tan(c/2 + (d*x)/2)^9*((595*A*a^4)/12 + (833*C*a^4)/24) + tan(c/2 + (d*x)/2)^7*((231*A*a^4)/2 + (1617*C*a^4)/20) + tan(c/2 + (d*x)/2)^5*((281*A*a^4)/2 + (1967*C*a^4)/20) + tan(c/2 + (d*x)/2)^3*((1069*A*a^4)/12 + (1471*C*a^4)/24))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (7*a^4*(10*A + 7*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) + (7*a^4*atan((7*a^4*tan(c/2 + (d*x)/2)*(10*A + 7*C))/(8*((35*A*a^4)/4 + (49*C*a^4)/8)))*(10*A + 7*C))/(8*d)","B"
31,1,202,177,1.518700,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x),x)","\frac{12\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+7\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{12}+2\,C\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{29\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48}+\frac{C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{80}+\frac{27\,A\,a^4\,\sin\left(c+d\,x\right)}{4}+\frac{49\,C\,a^4\,\sin\left(c+d\,x\right)}{8}}{d}","Not used",1,"(12*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 7*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + A*a^4*sin(2*c + 2*d*x) + (A*a^4*sin(3*c + 3*d*x))/12 + 2*C*a^4*sin(2*c + 2*d*x) + (29*C*a^4*sin(3*c + 3*d*x))/48 + (C*a^4*sin(4*c + 4*d*x))/8 + (C*a^4*sin(5*c + 5*d*x))/80 + (27*A*a^4*sin(c + d*x))/4 + (49*C*a^4*sin(c + d*x))/8)/d","B"
32,1,234,181,1.090909,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x)^2,x)","\frac{4\,A\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{20\,C\,a^4\,\sin\left(c+d\,x\right)}{3\,d}+\frac{13\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{8\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{35\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{4\,C\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{C\,a^4\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{27\,C\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}","Not used",1,"(4*A*a^4*sin(c + d*x))/d + (20*C*a^4*sin(c + d*x))/(3*d) + (13*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (35*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (A*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (4*C*a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (C*a^4*cos(c + d*x)^3*sin(c + d*x))/(4*d) + (A*a^4*cos(c + d*x)*sin(c + d*x))/(2*d) + (27*C*a^4*cos(c + d*x)*sin(c + d*x))/(8*d)","B"
33,1,244,186,1.143658,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x)^3,x)","\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{20\,C\,a^4\,\sin\left(c+d\,x\right)}{3\,d}+\frac{8\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{13\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{12\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,A\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{2\,C\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(A*a^4*sin(c + d*x))/d + (20*C*a^4*sin(c + d*x))/(3*d) + (8*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (12*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*A*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (A*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (C*a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (2*C*a^4*cos(c + d*x)*sin(c + d*x))/d","B"
34,1,252,198,1.115575,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x)^4,x)","\frac{4\,C\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{12\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{13\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{8\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(4*C*a^4*sin(c + d*x))/d + (2*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (12*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (20*A*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (2*A*a^4*sin(c + d*x))/(d*cos(c + d*x)^2) + (A*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (C*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^4*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
35,1,246,200,1.099023,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x)^5,x)","\frac{C\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{35\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{8\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{13\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{27\,A\,a^4\,\sin\left(c+d\,x\right)}{8\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{4\,A\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{4\,d\,{\cos\left(c+d\,x\right)}^4}+\frac{4\,C\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(C*a^4*sin(c + d*x))/d + (35*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (8*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (20*A*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (27*A*a^4*sin(c + d*x))/(8*d*cos(c + d*x)^2) + (4*A*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (A*a^4*sin(c + d*x))/(4*d*cos(c + d*x)^4) + (4*C*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
36,1,277,207,1.053955,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x)^6,x)","\frac{7\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{12\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{83\,A\,a^4\,\sin\left(c+d\,x\right)}{15\,d\,\cos\left(c+d\,x\right)}+\frac{7\,A\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{34\,A\,a^4\,\sin\left(c+d\,x\right)}{15\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^4}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{5\,d\,{\cos\left(c+d\,x\right)}^5}+\frac{20\,C\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(7*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (12*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (83*A*a^4*sin(c + d*x))/(15*d*cos(c + d*x)) + (7*A*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (34*A*a^4*sin(c + d*x))/(15*d*cos(c + d*x)^3) + (A*a^4*sin(c + d*x))/(d*cos(c + d*x)^4) + (A*a^4*sin(c + d*x))/(5*d*cos(c + d*x)^5) + (20*C*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (2*C*a^4*sin(c + d*x))/(d*cos(c + d*x)^2) + (C*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
37,1,262,232,3.598032,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x)^7,x)","\frac{\left(-\frac{49\,A\,a^4}{8}-\frac{35\,C\,a^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{833\,A\,a^4}{24}+\frac{595\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{1617\,A\,a^4}{20}-\frac{231\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{1967\,A\,a^4}{20}+\frac{281\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{1471\,A\,a^4}{24}-\frac{1069\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{207\,A\,a^4}{8}+\frac{93\,C\,a^4}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{7\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(7\,A+10\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + (93*C*a^4)/4) - tan(c/2 + (d*x)/2)^11*((49*A*a^4)/8 + (35*C*a^4)/4) + tan(c/2 + (d*x)/2)^9*((833*A*a^4)/24 + (595*C*a^4)/12) - tan(c/2 + (d*x)/2)^7*((1617*A*a^4)/20 + (231*C*a^4)/2) + tan(c/2 + (d*x)/2)^5*((1967*A*a^4)/20 + (281*C*a^4)/2) - tan(c/2 + (d*x)/2)^3*((1471*A*a^4)/24 + (1069*C*a^4)/12))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (7*a^4*atanh(tan(c/2 + (d*x)/2))*(7*A + 10*C))/(8*d)","B"
38,1,301,263,3.698559,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^4)/cos(c + d*x)^8,x)","\frac{a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(11\,A+14\,C\right)}{2\,d}-\frac{\left(\frac{11\,A\,a^4}{2}+7\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(-\frac{110\,A\,a^4}{3}-\frac{140\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{3113\,A\,a^4}{30}+\frac{1981\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{5632\,A\,a^4}{35}-\frac{1024\,C\,a^4}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{1501\,A\,a^4}{10}+\frac{2851\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-70\,A\,a^4-\frac{308\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{53\,A\,a^4}{2}+25\,C\,a^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^4*atanh(tan(c/2 + (d*x)/2))*(11*A + 14*C))/(2*d) - (tan(c/2 + (d*x)/2)*((53*A*a^4)/2 + 25*C*a^4) + tan(c/2 + (d*x)/2)^13*((11*A*a^4)/2 + 7*C*a^4) - tan(c/2 + (d*x)/2)^11*((110*A*a^4)/3 + (140*C*a^4)/3) - tan(c/2 + (d*x)/2)^3*(70*A*a^4 + (308*C*a^4)/3) + tan(c/2 + (d*x)/2)^5*((1501*A*a^4)/10 + (2851*C*a^4)/15) + tan(c/2 + (d*x)/2)^9*((3113*A*a^4)/30 + (1981*C*a^4)/15) - tan(c/2 + (d*x)/2)^7*((5632*A*a^4)/35 + (1024*C*a^4)/5))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
39,1,153,156,1.000869,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{3\,A\,x}{2\,a}+\frac{15\,C\,x}{8\,a}-\frac{A\,\sin\left(c+d\,x\right)}{a\,d}-\frac{7\,C\,\sin\left(c+d\,x\right)}{4\,a\,d}+\frac{A\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}+\frac{C\,\sin\left(2\,c+2\,d\,x\right)}{2\,a\,d}-\frac{C\,\sin\left(3\,c+3\,d\,x\right)}{12\,a\,d}+\frac{C\,\sin\left(4\,c+4\,d\,x\right)}{32\,a\,d}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(3*A*x)/(2*a) + (15*C*x)/(8*a) - (A*sin(c + d*x))/(a*d) - (7*C*sin(c + d*x))/(4*a*d) + (A*sin(2*c + 2*d*x))/(4*a*d) - (A*tan(c/2 + (d*x)/2))/(a*d) + (C*sin(2*c + 2*d*x))/(2*a*d) - (C*sin(3*c + 3*d*x))/(12*a*d) + (C*sin(4*c + 4*d*x))/(32*a*d) - (C*tan(c/2 + (d*x)/2))/(a*d)","B"
40,1,114,124,0.939053,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{A\,\sin\left(c+d\,x\right)}{a\,d}-\frac{3\,C\,x}{2\,a}-\frac{A\,x}{a}+\frac{7\,C\,\sin\left(c+d\,x\right)}{4\,a\,d}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}-\frac{C\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d}+\frac{C\,\sin\left(3\,c+3\,d\,x\right)}{12\,a\,d}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(A*sin(c + d*x))/(a*d) - (3*C*x)/(2*a) - (A*x)/a + (7*C*sin(c + d*x))/(4*a*d) + (A*tan(c/2 + (d*x)/2))/(a*d) - (C*sin(2*c + 2*d*x))/(4*a*d) + (C*sin(3*c + 3*d*x))/(12*a*d) + (C*tan(c/2 + (d*x)/2))/(a*d)","B"
41,1,83,98,0.938151,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{A\,x}{a}+\frac{3\,C\,x}{2\,a}-\frac{C\,\sin\left(c+d\,x\right)}{a\,d}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}+\frac{C\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(A*x)/a + (3*C*x)/(2*a) - (C*sin(c + d*x))/(a*d) - (A*tan(c/2 + (d*x)/2))/(a*d) + (C*sin(2*c + 2*d*x))/(4*a*d) - (C*tan(c/2 + (d*x)/2))/(a*d)","B"
42,1,59,48,0.902435,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x)),x)","\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{C\,x}{a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(2*C*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2)) - (C*x)/a + (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
43,1,101,48,0.992135,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))),x)","\frac{2\,A\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(2*A*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) - (A*sin(c/2 + (d*x)/2) + C*sin(c/2 + (d*x)/2))/(a*d*cos(c/2 + (d*x)/2))","B"
44,1,72,61,0.924939,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))),x)","\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(2*A*tan(c/2 + (d*x)/2))/(d*(a - a*tan(c/2 + (d*x)/2)^2)) - (2*A*atanh(tan(c/2 + (d*x)/2)))/(a*d) + (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
45,1,106,105,1.013635,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,A}{2}+C\right)}{a\,d}-\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*((3*A)/2 + C))/(a*d) - (A*tan(c/2 + (d*x)/2) - 3*A*tan(c/2 + (d*x)/2)^3)/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) - (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
46,1,150,133,1.322006,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))),x)","\frac{\left(5\,A+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,A}{2}+C\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(5*A + 2*C) - tan(c/2 + (d*x)/2)^3*((16*A)/3 + 4*C) + tan(c/2 + (d*x)/2)*(3*A + 2*C))/(d*(a - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6)) - (2*atanh(tan(c/2 + (d*x)/2))*((3*A)/2 + C))/(a*d) + (tan(c/2 + (d*x)/2)*(A + C))/(a*d)","B"
47,1,220,191,1.035939,"\text{Not used}","int((cos(c + d*x)^4*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{x\,\left(28\,A+55\,C\right)}{8\,a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{2\,a^2}+\frac{2\,A+6\,C}{2\,a^2}\right)}{d}-\frac{\left(5\,A+\frac{65\,C}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(13\,A+\frac{395\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(11\,A+\frac{341\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A+\frac{31\,C}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(x*(28*A + 55*C))/(8*a^2) - (tan(c/2 + (d*x)/2)*((5*(A + C))/(2*a^2) + (2*A + 6*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^7*(5*A + (65*C)/4) + tan(c/2 + (d*x)/2)^3*(11*A + (341*C)/12) + tan(c/2 + (d*x)/2)^5*(13*A + (395*C)/12) + tan(c/2 + (d*x)/2)*(3*A + (31*C)/4))/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 + 6*a^2*tan(c/2 + (d*x)/2)^4 + 4*a^2*tan(c/2 + (d*x)/2)^6 + a^2*tan(c/2 + (d*x)/2)^8 + a^2)) + (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
48,1,181,163,1.008703,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{\left(2\,A+10\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A+\frac{40\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A+6\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{x\,\left(2\,A+5\,C\right)}{a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(A+C\right)}{a^2}+\frac{A+5\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(2*A + 10*C) + tan(c/2 + (d*x)/2)^3*(4*A + (40*C)/3) + tan(c/2 + (d*x)/2)*(2*A + 6*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2)) - (x*(2*A + 5*C))/a^2 + (tan(c/2 + (d*x)/2)*((2*(A + C))/a^2 + (A + 5*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
49,1,134,141,0.963781,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{x\,\left(2\,A+7\,C\right)}{2\,a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^2}+\frac{2\,C}{a^2}\right)}{d}-\frac{5\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(x*(2*A + 7*C))/(2*a^2) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^2) + (2*C)/a^2))/d - (3*C*tan(c/2 + (d*x)/2) + 5*C*tan(c/2 + (d*x)/2)^3)/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + a^2*tan(c/2 + (d*x)/2)^4 + a^2)) + (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
50,1,97,90,0.906686,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{a^2}-\frac{A-3\,C}{2\,a^2}\right)}{d}-\frac{2\,C\,x}{a^2}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A + C)/a^2 - (A - 3*C)/(2*a^2)))/d - (2*C*x)/a^2 + (2*C*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
51,1,64,66,0.891614,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^2,x)","\frac{3\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,C\,d\,x}{6\,a^2\,d}","Not used",1,"(3*A*tan(c/2 + (d*x)/2) - 9*C*tan(c/2 + (d*x)/2) + A*tan(c/2 + (d*x)/2)^3 + C*tan(c/2 + (d*x)/2)^3 + 6*C*d*x)/(6*a^2*d)","B"
52,1,77,77,0.882194,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^2),x)","\frac{2\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{2\,a^2}+\frac{2\,A-2\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)*((A + C)/(2*a^2) + (2*A - 2*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
53,1,113,91,0.945501,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{a^2}+\frac{3\,A-C}{2\,a^2}\right)}{d}-\frac{4\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A + C)/a^2 + (3*A - C)/(2*a^2)))/d - (4*A*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (2*A*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2)) + (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
54,1,144,146,0.959485,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^2),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{7\,A}{2}+C\right)}{a^2\,d}-\frac{3\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^2}+\frac{2\,A}{a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*((7*A)/2 + C))/(a^2*d) - (3*A*tan(c/2 + (d*x)/2) - 5*A*tan(c/2 + (d*x)/2)^3)/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^2) + (2*A)/a^2))/d - (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
55,1,197,172,1.017552,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(A+C\right)}{a^2}+\frac{5\,A+C}{2\,a^2}\right)}{d}-\frac{\left(10\,A+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{40\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(5\,A+2\,C\right)}{a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((2*(A + C))/a^2 + (5*A + C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^5*(10*A + 2*C) - tan(c/2 + (d*x)/2)^3*((40*A)/3 + 4*C) + tan(c/2 + (d*x)/2)*(6*A + 2*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 - 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 - a^2)) - (2*atanh(tan(c/2 + (d*x)/2))*(5*A + 2*C))/(a^2*d) + (tan(c/2 + (d*x)/2)^3*(A + C))/(6*a^2*d)","B"
56,1,229,216,1.123210,"\text{Not used}","int((cos(c + d*x)^4*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{\left(2\,A+17\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A+\frac{76\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A+11\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{x\,\left(6\,A+23\,C\right)}{2\,a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{3\,a^3}+\frac{2\,A+6\,C}{12\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{2\,a^3}-\frac{A-15\,C}{4\,a^3}+\frac{2\,A+6\,C}{a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(2*A + 17*C) + tan(c/2 + (d*x)/2)^3*(4*A + (76*C)/3) + tan(c/2 + (d*x)/2)*(2*A + 11*C))/(d*(3*a^3*tan(c/2 + (d*x)/2)^2 + 3*a^3*tan(c/2 + (d*x)/2)^4 + a^3*tan(c/2 + (d*x)/2)^6 + a^3)) - (x*(6*A + 23*C))/(2*a^3) - (tan(c/2 + (d*x)/2)^3*((A + C)/(3*a^3) + (2*A + 6*C)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)*((5*(A + C))/(2*a^3) - (A - 15*C)/(4*a^3) + (2*A + 6*C)/a^3))/d + (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
57,1,184,189,1.041492,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^3}+\frac{A+5\,C}{12\,a^3}\right)}{d}+\frac{x\,\left(2\,A+13\,C\right)}{2\,a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^3}+\frac{3\,\left(A+5\,C\right)}{4\,a^3}-\frac{2\,A-10\,C}{4\,a^3}\right)}{d}-\frac{7\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^3) + (A + 5*C)/(12*a^3)))/d + (x*(2*A + 13*C))/(2*a^3) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^3) + (3*(A + 5*C))/(4*a^3) - (2*A - 10*C)/(4*a^3)))/d - (5*C*tan(c/2 + (d*x)/2) + 7*C*tan(c/2 + (d*x)/2)^3)/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + a^3*tan(c/2 + (d*x)/2)^4 + a^3)) - (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
58,1,153,136,1.002436,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{\left(\frac{7\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+\frac{24\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{4\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}-\frac{3\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{20}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{20}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}-\frac{3\,C\,x}{a^3}+\frac{2\,C\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}","Not used",1,"((A*sin(c/2 + (d*x)/2))/20 + (C*sin(c/2 + (d*x)/2))/20 - cos(c/2 + (d*x)/2)^2*((4*A*sin(c/2 + (d*x)/2))/15 + (3*C*sin(c/2 + (d*x)/2))/5) + cos(c/2 + (d*x)/2)^4*((7*A*sin(c/2 + (d*x)/2))/15 + (24*C*sin(c/2 + (d*x)/2))/5))/(a^3*d*cos(c/2 + (d*x)/2)^5) - (3*C*x)/a^3 + (2*C*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^3*d)","B"
59,1,116,114,1.016754,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{C\,x}{a^3}+\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{7\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)-\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{C\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(C*x)/a^3 + (cos(c/2 + (d*x)/2)^4*((A*sin(c/2 + (d*x)/2))/4 - (7*C*sin(c/2 + (d*x)/2))/4) - (A*sin(c/2 + (d*x)/2)^5)/20 - (C*sin(c/2 + (d*x)/2)^5)/20 + (C*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^3)/3)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
60,1,69,98,0.892494,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{4\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-2\,C\right)}{12\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A + C))/(4*a^3*d) + (tan(c/2 + (d*x)/2)^3*(2*A - 2*C))/(12*a^3*d) + (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
61,1,114,115,0.886604,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^3),x)","\frac{2\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{12\,a^3}+\frac{3\,A-C}{12\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{4\,a^3}+\frac{3\,A-C}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (tan(c/2 + (d*x)/2)^3*((A + C)/(12*a^3) + (3*A - C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)*((A + C)/(4*a^3) + (3*A - C)/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
62,1,150,129,0.893351,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{6\,a^3}+\frac{A}{3\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{4\,a^3}+\frac{2\,A}{a^3}+\frac{6\,A-2\,C}{4\,a^3}\right)}{d}-\frac{6\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A + C)/(6*a^3) + A/(3*a^3)))/d + (tan(c/2 + (d*x)/2)*((3*(A + C))/(4*a^3) + (2*A)/a^3 + (6*A - 2*C)/(4*a^3)))/d - (6*A*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (2*A*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3)) + (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
63,1,195,192,0.911538,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^3),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{13\,A}{2}+C\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+C\right)}{2\,a^3}+\frac{3\,\left(5\,A+C\right)}{4\,a^3}+\frac{10\,A-2\,C}{4\,a^3}\right)}{d}-\frac{5\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-7\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^3}+\frac{5\,A+C}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*((13*A)/2 + C))/(a^3*d) - (tan(c/2 + (d*x)/2)*((3*(A + C))/(2*a^3) + (3*(5*A + C))/(4*a^3) + (10*A - 2*C)/(4*a^3)))/d - (5*A*tan(c/2 + (d*x)/2) - 7*A*tan(c/2 + (d*x)/2)^3)/(d*(a^3*tan(c/2 + (d*x)/2)^4 - 2*a^3*tan(c/2 + (d*x)/2)^2 + a^3)) - (tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^3) + (5*A + C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
64,1,246,225,0.922383,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{3\,a^3}+\frac{6\,A+2\,C}{12\,a^3}\right)}{d}-\frac{\left(17\,A+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{76\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{2\,a^3}+\frac{6\,A+2\,C}{a^3}+\frac{15\,A-C}{4\,a^3}\right)}{d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(23\,A+6\,C\right)}{a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A + C)/(3*a^3) + (6*A + 2*C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(17*A + 2*C) - tan(c/2 + (d*x)/2)^3*((76*A)/3 + 4*C) + tan(c/2 + (d*x)/2)*(11*A + 2*C))/(d*(3*a^3*tan(c/2 + (d*x)/2)^2 - 3*a^3*tan(c/2 + (d*x)/2)^4 + a^3*tan(c/2 + (d*x)/2)^6 - a^3)) + (tan(c/2 + (d*x)/2)*((5*(A + C))/(2*a^3) + (6*A + 2*C)/a^3 + (15*A - C)/(4*a^3)))/d - (atanh(tan(c/2 + (d*x)/2))*(23*A + 6*C))/(a^3*d) + (tan(c/2 + (d*x)/2)^5*(A + C))/(20*a^3*d)","B"
65,1,245,223,0.951871,"\text{Not used}","int((cos(c + d*x)^4*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","\frac{x\,\left(2\,A+21\,C\right)}{2\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{4\,a^4}-\frac{3\,\left(A-15\,C\right)}{8\,a^4}+\frac{3\,\left(2\,A+6\,C\right)}{4\,a^4}-\frac{4\,A-20\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,\left(A+C\right)}{40\,a^4}+\frac{2\,A+6\,C}{40\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^4}-\frac{A-15\,C}{24\,a^4}+\frac{2\,A+6\,C}{8\,a^4}\right)}{d}-\frac{9\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+7\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(x*(2*A + 21*C))/(2*a^4) - (tan(c/2 + (d*x)/2)*((5*(A + C))/(4*a^4) - (3*(A - 15*C))/(8*a^4) + (3*(2*A + 6*C))/(4*a^4) - (4*A - 20*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((3*(A + C))/(40*a^4) + (2*A + 6*C)/(40*a^4)))/d + (tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^4) - (A - 15*C)/(24*a^4) + (2*A + 6*C)/(8*a^4)))/d - (7*C*tan(c/2 + (d*x)/2) + 9*C*tan(c/2 + (d*x)/2)^3)/(d*(2*a^4*tan(c/2 + (d*x)/2)^2 + a^4*tan(c/2 + (d*x)/2)^4 + a^4)) + (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
66,1,192,174,0.990367,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","\frac{2\,C\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4\,d}-\frac{\left(-\frac{12\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}-\frac{764\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{23\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{70}+\frac{143\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{9\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{70}-\frac{8\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}-\frac{4\,C\,x}{a^4}","Not used",1,"(2*C*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^4*d) - ((A*sin(c/2 + (d*x)/2))/56 + (C*sin(c/2 + (d*x)/2))/56 - cos(c/2 + (d*x)/2)^2*((9*A*sin(c/2 + (d*x)/2))/70 + (8*C*sin(c/2 + (d*x)/2))/35) + cos(c/2 + (d*x)/2)^4*((23*A*sin(c/2 + (d*x)/2))/70 + (143*C*sin(c/2 + (d*x)/2))/105) - cos(c/2 + (d*x)/2)^6*((12*A*sin(c/2 + (d*x)/2))/35 + (764*C*sin(c/2 + (d*x)/2))/105))/(a^4*d*cos(c/2 + (d*x)/2)^7) - (4*C*x)/a^4","B"
67,1,162,152,0.967354,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","\frac{C\,x}{a^4}+\frac{\left(\frac{13\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}-\frac{52\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{13\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{210}+\frac{16\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{11\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{140}-\frac{5\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{28}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}+\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(C*x)/a^4 + ((A*sin(c/2 + (d*x)/2))/56 + (C*sin(c/2 + (d*x)/2))/56 - cos(c/2 + (d*x)/2)^2*((11*A*sin(c/2 + (d*x)/2))/140 + (5*C*sin(c/2 + (d*x)/2))/28) + cos(c/2 + (d*x)/2)^6*((13*A*sin(c/2 + (d*x)/2))/105 - (52*C*sin(c/2 + (d*x)/2))/21) + cos(c/2 + (d*x)/2)^4*((13*A*sin(c/2 + (d*x)/2))/210 + (16*C*sin(c/2 + (d*x)/2))/21))/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
68,1,84,138,0.894217,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-3\,C\right)}{24\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-3\,C\right)}{40\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{8\,a^4}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4) - (tan(c/2 + (d*x)/2)^3*(A - 3*C))/(24*a^4) + (tan(c/2 + (d*x)/2)^5*(A - 3*C))/(40*a^4) - (tan(c/2 + (d*x)/2)*(A + C))/(8*a^4))/d","B"
69,1,87,136,0.881158,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+C\right)}{8\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A-C\right)}{24\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A-C\right)}{40\,a^4}}{d}","Not used",1,"((tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4) + (tan(c/2 + (d*x)/2)*(A + C))/(8*a^4) + (tan(c/2 + (d*x)/2)^3*(3*A - C))/(24*a^4) + (tan(c/2 + (d*x)/2)^5*(3*A - C))/(40*a^4))/d","B"
70,1,156,145,0.895427,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^4),x)","\frac{2\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{8\,a^4}+\frac{A}{a^4}+\frac{6\,A-2\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{24\,a^4}+\frac{A}{6\,a^4}+\frac{6\,A-2\,C}{24\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A+C}{40\,a^4}+\frac{A}{10\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (tan(c/2 + (d*x)/2)*((A + C)/(8*a^4) + A/a^4 + (6*A - 2*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((A + C)/(24*a^4) + A/(6*a^4) + (6*A - 2*C)/(24*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((A + C)/(40*a^4) + A/(10*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
71,1,204,161,0.885017,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A+C}{20\,a^4}+\frac{5\,A+C}{40\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A+C}{2\,a^4}+\frac{3\,\left(5\,A+C\right)}{8\,a^4}+\frac{3\,\left(10\,A-2\,C\right)}{8\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{8\,a^4}+\frac{5\,A+C}{12\,a^4}+\frac{10\,A-2\,C}{24\,a^4}\right)}{d}-\frac{8\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*((A + C)/(20*a^4) + (5*A + C)/(40*a^4)))/d + (tan(c/2 + (d*x)/2)*((A + C)/(2*a^4) + (3*(5*A + C))/(8*a^4) + (3*(10*A - 2*C))/(8*a^4)))/d + (tan(c/2 + (d*x)/2)^3*((A + C)/(8*a^4) + (5*A + C)/(12*a^4) + (10*A - 2*C)/(24*a^4)))/d - (8*A*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (2*A*tan(c/2 + (d*x)/2))/(d*(a^4*tan(c/2 + (d*x)/2)^2 - a^4)) + (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
72,1,260,224,0.915908,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^4),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{21\,A}{2}+C\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,\left(A+C\right)}{40\,a^4}+\frac{6\,A+2\,C}{40\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{4\,a^4}+\frac{3\,\left(6\,A+2\,C\right)}{4\,a^4}+\frac{3\,\left(15\,A-C\right)}{8\,a^4}+\frac{20\,A-4\,C}{8\,a^4}\right)}{d}-\frac{7\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A+C}{4\,a^4}+\frac{6\,A+2\,C}{8\,a^4}+\frac{15\,A-C}{24\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2))*((21*A)/2 + C))/(a^4*d) - (tan(c/2 + (d*x)/2)^5*((3*(A + C))/(40*a^4) + (6*A + 2*C)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)*((5*(A + C))/(4*a^4) + (3*(6*A + 2*C))/(4*a^4) + (3*(15*A - C))/(8*a^4) + (20*A - 4*C)/(8*a^4)))/d - (7*A*tan(c/2 + (d*x)/2) - 9*A*tan(c/2 + (d*x)/2)^3)/(d*(a^4*tan(c/2 + (d*x)/2)^4 - 2*a^4*tan(c/2 + (d*x)/2)^2 + a^4)) - (tan(c/2 + (d*x)/2)^3*((A + C)/(4*a^4) + (6*A + 2*C)/(8*a^4) + (15*A - C)/(24*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
73,1,303,257,0.940082,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^4),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A+C\right)}{2\,a^4}+\frac{21\,A+C}{2\,a^4}+\frac{5\,\left(7\,A+3\,C\right)}{4\,a^4}+\frac{35\,A-5\,C}{8\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A+C}{10\,a^4}+\frac{7\,A+3\,C}{40\,a^4}\right)}{d}-\frac{\left(26\,A+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{124\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(18\,A+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,\left(A+C\right)}{12\,a^4}+\frac{21\,A+C}{24\,a^4}+\frac{7\,A+3\,C}{6\,a^4}\right)}{d}-\frac{4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(11\,A+2\,C\right)}{a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*(A + C))/(2*a^4) + (21*A + C)/(2*a^4) + (5*(7*A + 3*C))/(4*a^4) + (35*A - 5*C)/(8*a^4)))/d + (tan(c/2 + (d*x)/2)^5*((A + C)/(10*a^4) + (7*A + 3*C)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)^5*(26*A + 2*C) - tan(c/2 + (d*x)/2)^3*((124*A)/3 + 4*C) + tan(c/2 + (d*x)/2)*(18*A + 2*C))/(d*(3*a^4*tan(c/2 + (d*x)/2)^2 - 3*a^4*tan(c/2 + (d*x)/2)^4 + a^4*tan(c/2 + (d*x)/2)^6 - a^4)) + (tan(c/2 + (d*x)/2)^3*((5*(A + C))/(12*a^4) + (21*A + C)/(24*a^4) + (7*A + 3*C)/(6*a^4)))/d - (4*atanh(tan(c/2 + (d*x)/2))*(11*A + 2*C))/(a^4*d) + (tan(c/2 + (d*x)/2)^7*(A + C))/(56*a^4*d)","B"
74,0,-1,223,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^3*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2), x)","F"
75,0,-1,180,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2), x)","F"
76,0,-1,137,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2), x)","F"
77,0,-1,95,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2), x)","F"
78,0,-1,96,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
79,0,-1,94,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
80,0,-1,110,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
81,0,-1,153,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^4, x)","F"
82,0,-1,196,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^5,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^5, x)","F"
83,0,-1,225,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2), x)","F"
84,0,-1,174,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2), x)","F"
85,0,-1,132,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2), x)","F"
86,0,-1,133,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
87,0,-1,136,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
88,0,-1,147,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
89,0,-1,155,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^4, x)","F"
90,0,-1,200,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^5,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^5, x)","F"
91,0,-1,245,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^6,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^6, x)","F"
92,0,-1,273,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2), x)","F"
93,0,-1,211,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2), x)","F"
94,0,-1,169,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2), x)","F"
95,0,-1,170,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
96,0,-1,173,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
97,0,-1,184,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^3, x)","F"
98,0,-1,192,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^4, x)","F"
99,0,-1,200,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^5,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^5, x)","F"
100,0,-1,245,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^6,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^6, x)","F"
101,0,-1,290,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^7,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^7} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^7, x)","F"
102,0,-1,236,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
103,0,-1,193,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
104,0,-1,152,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
105,1,139,109,1.044165,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,C\,\sin\left(c+d\,x\right)\,\left(a+a\,\cos\left(c+d\,x\right)\right)+3\,\sqrt{2}\,A\,a\,\sqrt{\frac{a+a\,\cos\left(c+d\,x\right)}{a}}\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)-4\,\sqrt{2}\,C\,a\,\sqrt{\frac{a+a\,\cos\left(c+d\,x\right)}{a}}\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)+3\,\sqrt{2}\,C\,a\,\sqrt{\frac{a+a\,\cos\left(c+d\,x\right)}{a}}\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)}{3\,a\,d\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*C*sin(c + d*x)*(a + a*cos(c + d*x)) + 3*2^(1/2)*A*a*((a + a*cos(c + d*x))/a)^(1/2)*ellipticF(c/2 + (d*x)/2, 1) - 4*2^(1/2)*C*a*((a + a*cos(c + d*x))/a)^(1/2)*ellipticE(c/2 + (d*x)/2, 1) + 3*2^(1/2)*C*a*((a + a*cos(c + d*x))/a)^(1/2)*ellipticF(c/2 + (d*x)/2, 1))/(3*a*d*(a + a*cos(c + d*x))^(1/2))","B"
106,0,-1,115,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\cos\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)), x)","F"
107,0,-1,113,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)), x)","F"
108,0,-1,159,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)), x)","F"
109,0,-1,200,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2)), x)","F"
110,0,-1,243,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^5*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^5\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^5*(a + a*cos(c + d*x))^(1/2)), x)","F"
111,0,-1,259,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
112,0,-1,214,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
113,0,-1,169,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
114,0,-1,114,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(3/2), x)","F"
115,0,-1,125,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)), x)","F"
116,0,-1,158,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)), x)","F"
117,0,-1,217,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)), x)","F"
118,0,-1,266,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(3/2)), x)","F"
119,0,-1,259,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
120,0,-1,212,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
121,0,-1,165,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
122,0,-1,124,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(5/2), x)","F"
123,0,-1,162,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)), x)","F"
124,0,-1,199,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)), x)","F"
125,0,-1,262,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2)), x)","F"
126,1,177,196,1.757777,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
127,1,166,165,1.181706,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
128,1,139,134,0.393556,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
129,1,112,101,1.093922,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
130,1,112,95,1.401779,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
131,1,123,95,1.800749,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^(5/2),x)","\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
132,1,150,132,2.016708,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
133,1,177,165,2.317908,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^(9/2),x)","\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
134,1,266,230,1.722994,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (4*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
135,1,242,197,1.700459,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
136,1,177,164,1.578685,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(1/2),x)","\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (4*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
137,1,188,160,1.818355,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(3/2),x)","\frac{2\,C\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
138,1,161,156,2.024937,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(5/2),x)","\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
139,1,202,156,2.625383,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(7/2),x)","\frac{6\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,A\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*A*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*A*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
140,1,229,197,2.828831,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(9/2),x)","\frac{30\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,A\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,A\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(30*A*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 84*A*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 70*A*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
141,1,482,230,3.110957,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(11/2),x)","\frac{4\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{4\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{3\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{7\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{16\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{64\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{21\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{81\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{16\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(4*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((4*A*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (3*A*a^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (7*C*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2))))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((16*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((64*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (21*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^2*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (81*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (16*A*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
142,1,360,279,1.903645,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3,x)","\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(15/2)*sin(c + d*x)*hypergeom([1/2, 15/4], 19/4, cos(c + d*x)^2))/(15*d*(sin(c + d*x)^2)^(1/2))","B"
143,1,332,246,1.733284,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3,x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + A*a^3*ellipticF(c/2 + (d*x)/2, 2) + A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
144,1,283,213,1.672491,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(1/2),x)","\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (2*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
145,1,269,217,1.631252,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(3/2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + C*a^3*ellipticF(c/2 + (d*x)/2, 2) + C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
146,1,237,211,2.018527,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(5/2),x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
147,1,279,213,2.452552,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(7/2),x)","\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
148,1,279,213,3.352572,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(9/2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+\frac{6\,A\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,A\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,A\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + ((2*A*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + (6*A*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*A*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 2*A*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
149,1,308,246,3.454082,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(11/2),x)","\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{70\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,A\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,A\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,A\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (70*A*a^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 270*A*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 210*A*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*A*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
150,1,621,279,3.778995,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(13/2),x)","\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{42\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{7\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{11\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{231\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{10\,A\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{40\,A\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{15\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{51\,C\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{15\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{168\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{119\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{21\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{11/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{275\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{33\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{231\,d}","Not used",1,"(8*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2)*((42*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (7*A*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (11*C*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2))))/(231*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((10*A*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((40*A*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (15*A*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^3*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (51*C*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(15*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((168*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (119*A*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (21*A*a^3*sin(c + d*x))/(cos(c + d*x)^(11/2)*(1 - cos(c + d*x)^2)^(1/2)) + (275*C*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (33*C*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))))/(231*d)","B"
151,0,-1,192,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
152,0,-1,159,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
153,0,-1,122,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
154,0,-1,83,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))), x)","F"
155,0,-1,113,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))), x)","F"
156,0,-1,150,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))), x)","F"
157,0,-1,192,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))), x)","F"
158,0,-1,196,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
159,0,-1,161,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
160,0,-1,126,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
161,0,-1,125,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
162,0,-1,155,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
163,0,-1,189,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
164,0,-1,250,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
165,0,-1,209,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
166,0,-1,178,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
167,0,-1,180,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
168,0,-1,184,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
169,0,-1,219,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
170,0,-1,242,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
171,0,-1,214,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2), x)","F"
172,0,-1,169,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2), x)","F"
173,0,-1,124,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
174,0,-1,117,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
175,0,-1,116,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2), x)","F"
176,1,170,123,3.486084,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2),x)","\frac{2\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(28\,A\,\sin\left(c+d\,x\right)+30\,C\,\sin\left(c+d\,x\right)+16\,A\,\sin\left(2\,c+2\,d\,x\right)+36\,A\,\sin\left(3\,c+3\,d\,x\right)+8\,A\,\sin\left(4\,c+4\,d\,x\right)+8\,A\,\sin\left(5\,c+5\,d\,x\right)+45\,C\,\sin\left(3\,c+3\,d\,x\right)+15\,C\,\sin\left(5\,c+5\,d\,x\right)\right)}{15\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\left(10\,\cos\left(c+d\,x\right)+8\,\cos\left(2\,c+2\,d\,x\right)+5\,\cos\left(3\,c+3\,d\,x\right)+2\,\cos\left(4\,c+4\,d\,x\right)+\cos\left(5\,c+5\,d\,x\right)+6\right)}","Not used",1,"(2*(a*(cos(c + d*x) + 1))^(1/2)*(28*A*sin(c + d*x) + 30*C*sin(c + d*x) + 16*A*sin(2*c + 2*d*x) + 36*A*sin(3*c + 3*d*x) + 8*A*sin(4*c + 4*d*x) + 8*A*sin(5*c + 5*d*x) + 45*C*sin(3*c + 3*d*x) + 15*C*sin(5*c + 5*d*x)))/(15*d*cos(c + d*x)^(1/2)*(10*cos(c + d*x) + 8*cos(2*c + 2*d*x) + 5*cos(3*c + 3*d*x) + 2*cos(4*c + 4*d*x) + cos(5*c + 5*d*x) + 6))","B"
177,1,479,168,6.683762,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(9/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{\left(96\,A+140\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,4{}\mathrm{i}}{3\,d}+\frac{C\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,4{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(96\,A+140\,C\right)\,1{}\mathrm{i}}{105\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(336\,A+280\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(336\,A+280\,C\right)\,1{}\mathrm{i}}{105\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((96*A + 140*C)*1i)/(105*d) - (C*exp(c*3i + d*x*3i)*4i)/(3*d) + (C*exp(c*4i + d*x*4i)*4i)/(3*d) - (exp(c*7i + d*x*7i)*(96*A + 140*C)*1i)/(105*d) + (exp(c*2i + d*x*2i)*(336*A + 280*C)*1i)/(105*d) - (exp(c*5i + d*x*5i)*(336*A + 280*C)*1i)/(105*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
178,1,611,213,7.743923,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(11/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{\left(256\,A+336\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}+\frac{C\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(256\,A+336\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(1152\,A+1512\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(1152\,A+1512\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(2016\,A+2016\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(2016\,A+2016\,C\right)\,1{}\mathrm{i}}{315\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((256*A + 336*C)*1i)/(315*d) - (C*exp(c*3i + d*x*3i)*8i)/(3*d) + (C*exp(c*6i + d*x*6i)*8i)/(3*d) - (exp(c*9i + d*x*9i)*(256*A + 336*C)*1i)/(315*d) + (exp(c*2i + d*x*2i)*(1152*A + 1512*C)*1i)/(315*d) - (exp(c*7i + d*x*7i)*(1152*A + 1512*C)*1i)/(315*d) + (exp(c*4i + d*x*4i)*(2016*A + 2016*C)*1i)/(315*d) - (exp(c*5i + d*x*5i)*(2016*A + 2016*C)*1i)/(315*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
179,0,-1,265,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2), x)","F"
180,0,-1,218,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2), x)","F"
181,0,-1,171,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
182,0,-1,175,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
183,0,-1,161,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2), x)","F"
184,0,-1,163,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2), x)","F"
185,1,264,172,7.758431,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(9/2),x)","-\frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(\frac{4\,C\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{d}-\frac{52\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(4\,A+5\,C\right)}{15\,d}+\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+11\,C\right)}{3\,d}-\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(104\,A+175\,C\right)}{105\,d}\right)}{6\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}","Not used",1,"-((a + a*cos(c + d*x))^(1/2)*((4*C*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((5*c)/2 + (5*d*x)/2))/d - (52*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((3*c)/2 + (3*d*x)/2)*(4*A + 5*C))/(15*d) + (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin(c/2 + (d*x)/2)*(4*A + 11*C))/(3*d) - (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((7*c)/2 + (7*d*x)/2)*(104*A + 175*C))/(105*d)))/(6*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos(c/2 + (d*x)/2) + 6*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos((3*c)/2 + (3*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos((7*c)/2 + (7*d*x)/2))","B"
186,1,293,219,8.393527,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(11/2),x)","\frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(-\frac{8\,C\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A+13\,C\right)}{5\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(68\,A+77\,C\right)}{35\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(136\,A+189\,C\right)}{315\,d}\right)}{12\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+8\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}","Not used",1,"((a + a*cos(c + d*x))^(1/2)*((8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2)*(12*A + 13*C))/(5*d) - (8*C*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((3*c)/2 + (3*d*x)/2))/d + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2)*(68*A + 77*C))/(35*d) + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2)*(136*A + 189*C))/(315*d)))/(12*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos(c/2 + (d*x)/2) + 8*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((3*c)/2 + (3*d*x)/2) + 8*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((9*c)/2 + (9*d*x)/2))","B"
187,1,356,266,7.923472,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(13/2),x)","\frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(-\frac{16\,C\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{3\,d}-\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A+23\,C\right)}{15\,d}+\frac{48\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(28\,A+27\,C\right)}{35\,d}+\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(112\,A+143\,C\right)}{105\,d}+\frac{32\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(112\,A+143\,C\right)}{1155\,d}\right)}{20\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+20\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+10\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+10\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}","Not used",1,"((a + a*cos(c + d*x))^(1/2)*((48*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((3*c)/2 + (3*d*x)/2)*(28*A + 27*C))/(35*d) - (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin(c/2 + (d*x)/2)*(12*A + 23*C))/(15*d) - (16*C*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((5*c)/2 + (5*d*x)/2))/(3*d) + (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((7*c)/2 + (7*d*x)/2)*(112*A + 143*C))/(105*d) + (32*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((11*c)/2 + (11*d*x)/2)*(112*A + 143*C))/(1155*d)))/(20*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos(c/2 + (d*x)/2) + 20*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((3*c)/2 + (3*d*x)/2) + 10*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((5*c)/2 + (5*d*x)/2) + 10*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((9*c)/2 + (9*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((11*c)/2 + (11*d*x)/2))","B"
188,0,-1,312,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2), x)","F"
189,0,-1,265,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2), x)","F"
190,0,-1,218,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
191,0,-1,222,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
192,0,-1,218,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
193,0,-1,210,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2), x)","F"
194,0,-1,210,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2), x)","F"
195,1,685,219,9.774385,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(11/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{a^2\,\left(584\,A+903\,C\right)\,2{}\mathrm{i}}{315\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(8\,A+11\,C\right)\,12{}\mathrm{i}}{5\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(8\,A+11\,C\right)\,12{}\mathrm{i}}{5\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(73\,A+91\,C\right)\,8{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(73\,A+91\,C\right)\,8{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(584\,A+903\,C\right)\,2{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\left(A+5\,C\right)\,8{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\left(A+5\,C\right)\,8{}\mathrm{i}}{3\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,2{}\mathrm{i}}{d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(584*A + 903*C)*2i)/(315*d) + (a^2*exp(c*4i + d*x*4i)*(8*A + 11*C)*12i)/(5*d) - (a^2*exp(c*5i + d*x*5i)*(8*A + 11*C)*12i)/(5*d) + (a^2*exp(c*2i + d*x*2i)*(73*A + 91*C)*8i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(73*A + 91*C)*8i)/(35*d) - (a^2*exp(c*9i + d*x*9i)*(584*A + 903*C)*2i)/(315*d) - (a^2*exp(c*3i + d*x*3i)*(A + 5*C)*8i)/(3*d) + (a^2*exp(c*6i + d*x*6i)*(A + 5*C)*8i)/(3*d) - (C*a^2*exp(c*1i + d*x*1i)*2i)/d + (C*a^2*exp(c*8i + d*x*8i)*2i)/d))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
196,1,773,266,8.350500,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(13/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{a^2\,\left(568\,A+759\,C\right)\,4{}\mathrm{i}}{693\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(3\,A+5\,C\right)\,16{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\left(3\,A+5\,C\right)\,16{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(32\,A+33\,C\right)\,8{}\mathrm{i}}{7\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(32\,A+33\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(71\,A+87\,C\right)\,16{}\mathrm{i}}{63\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(71\,A+87\,C\right)\,16{}\mathrm{i}}{63\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\left(568\,A+759\,C\right)\,4{}\mathrm{i}}{693\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,20{}\mathrm{i}}{3\,d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,20{}\mathrm{i}}{3\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(568*A + 759*C)*4i)/(693*d) - (a^2*exp(c*5i + d*x*5i)*(3*A + 5*C)*16i)/(3*d) + (a^2*exp(c*6i + d*x*6i)*(3*A + 5*C)*16i)/(3*d) + (a^2*exp(c*4i + d*x*4i)*(32*A + 33*C)*8i)/(7*d) - (a^2*exp(c*7i + d*x*7i)*(32*A + 33*C)*8i)/(7*d) + (a^2*exp(c*2i + d*x*2i)*(71*A + 87*C)*16i)/(63*d) - (a^2*exp(c*9i + d*x*9i)*(71*A + 87*C)*16i)/(63*d) - (a^2*exp(c*11i + d*x*11i)*(568*A + 759*C)*4i)/(693*d) - (C*a^2*exp(c*3i + d*x*3i)*20i)/(3*d) + (C*a^2*exp(c*8i + d*x*8i)*20i)/(3*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*10i + d*x*10i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*11i + d*x*11i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
197,1,911,313,8.200484,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(15/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{a^2\,\left(8368\,A+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(6\,A+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\left(6\,A+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\left(348\,A+379\,C\right)\,16{}\mathrm{i}}{105\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(348\,A+379\,C\right)\,16{}\mathrm{i}}{105\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(523\,A+554\,C\right)\,32{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(523\,A+554\,C\right)\,32{}\mathrm{i}}{315\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(8368\,A+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\left(8368\,A+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}\,\left(8368\,A+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+20\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+20\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,12{}\mathrm{i}+d\,x\,12{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(8368*A + 10439*C)*16i)/(45045*d) - (a^2*exp(c*5i + d*x*5i)*(6*A + 23*C)*16i)/(15*d) + (a^2*exp(c*8i + d*x*8i)*(6*A + 23*C)*16i)/(15*d) + (a^2*exp(c*6i + d*x*6i)*(348*A + 379*C)*16i)/(105*d) - (a^2*exp(c*7i + d*x*7i)*(348*A + 379*C)*16i)/(105*d) + (a^2*exp(c*4i + d*x*4i)*(523*A + 554*C)*32i)/(315*d) - (a^2*exp(c*9i + d*x*9i)*(523*A + 554*C)*32i)/(315*d) + (a^2*exp(c*2i + d*x*2i)*(8368*A + 10439*C)*8i)/(3465*d) - (a^2*exp(c*11i + d*x*11i)*(8368*A + 10439*C)*8i)/(3465*d) - (a^2*exp(c*13i + d*x*13i)*(8368*A + 10439*C)*16i)/(45045*d) - (C*a^2*exp(c*3i + d*x*3i)*8i)/(3*d) + (C*a^2*exp(c*10i + d*x*10i)*8i)/(3*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 20*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 20*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*10i + d*x*10i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*11i + d*x*11i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*12i + d*x*12i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*13i + d*x*13i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
198,0,-1,226,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
199,0,-1,183,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
200,0,-1,133,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
201,0,-1,135,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
202,0,-1,136,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
203,0,-1,181,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
204,0,-1,224,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
205,0,-1,245,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
206,0,-1,188,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
207,0,-1,145,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
208,0,-1,152,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
209,0,-1,201,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
210,0,-1,248,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
211,0,-1,237,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
212,0,-1,192,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
213,0,-1,154,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
214,0,-1,199,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
215,0,-1,246,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
216,1,115,92,4.628279,"\text{Not used}","int(cos(c + d*x)^3*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{3\,B\,x}{8}+\frac{\left(2\,C-\frac{5\,B}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,C}{3}-\frac{B}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{116\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\left(\frac{B}{2}+\frac{8\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,B}{4}+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*B*x)/8 + (tan(c/2 + (d*x)/2)^3*(B/2 + (8*C)/3) - tan(c/2 + (d*x)/2)^9*((5*B)/4 - 2*C) - tan(c/2 + (d*x)/2)^7*(B/2 - (8*C)/3) + (116*C*tan(c/2 + (d*x)/2)^5)/15 + tan(c/2 + (d*x)/2)*((5*B)/4 + 2*C))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
217,1,75,76,1.070611,"\text{Not used}","int(cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{3\,C\,x}{8}+\frac{2\,B\,\sin\left(c+d\,x\right)}{3\,d}+\frac{3\,C\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{B\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{C\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(3*C*x)/8 + (2*B*sin(c + d*x))/(3*d) + (3*C*cos(c + d*x)*sin(c + d*x))/(8*d) + (B*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (C*cos(c + d*x)^3*sin(c + d*x))/(4*d)","B"
218,1,55,54,1.069655,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{B\,x}{2}+\frac{2\,C\,\sin\left(c+d\,x\right)}{3\,d}+\frac{B\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{C\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(B*x)/2 + (2*C*sin(c + d*x))/(3*d) + (B*cos(c + d*x)*sin(c + d*x))/(2*d) + (C*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
219,1,31,38,1.027968,"\text{Not used}","int(B*cos(c + d*x) + C*cos(c + d*x)^2,x)","\frac{C\,x}{2}+\frac{C\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(C*x)/2 + (C*sin(2*c + 2*d*x))/(4*d) + (B*sin(c + d*x))/d","B"
220,1,17,15,0.977714,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x),x)","\frac{C\,\sin\left(c+d\,x\right)+B\,d\,x}{d}","Not used",1,"(C*sin(c + d*x) + B*d*x)/d","B"
221,1,57,16,1.030510,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^2,x)","\frac{2\,B\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(2*B*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
222,1,47,24,1.026843,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^3,x)","\frac{2\,C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*C*atanh(tan(c/2 + (d*x)/2)))/d - (2*B*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
223,1,81,47,1.623328,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^4,x)","\frac{\left(B-2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(B + 2*C) + tan(c/2 + (d*x)/2)^3*(B - 2*C))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (B*atanh(tan(c/2 + (d*x)/2)))/d","B"
224,1,111,63,2.905952,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^5,x)","\frac{C\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\left(2\,B-C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{4\,B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\left(2\,B+C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(C*atanh(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)^5*(2*B - C) + tan(c/2 + (d*x)/2)*(2*B + C) - (4*B*tan(c/2 + (d*x)/2)^3)/3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
225,1,150,85,3.531391,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^6,x)","\frac{\left(\frac{5\,B}{4}-2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,B}{4}+\frac{10\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,B}{4}-\frac{10\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,B}{4}+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*((5*B)/4 - 2*C) + tan(c/2 + (d*x)/2)^3*((3*B)/4 - (10*C)/3) + tan(c/2 + (d*x)/2)^5*((3*B)/4 + (10*C)/3) + tan(c/2 + (d*x)/2)*((5*B)/4 + 2*C))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (3*B*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
226,1,236,125,2.292505,"\text{Not used}","int(cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","\frac{\left(\frac{3\,B\,a}{4}+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{29\,B\,a}{6}+\frac{13\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,B\,a}{3}+\frac{116\,C\,a}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{35\,B\,a}{6}+\frac{19\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,B\,a}{4}+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,a\,\mathrm{atan}\left(\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B+C\right)}{4\,\left(\frac{3\,B\,a}{4}+\frac{3\,C\,a}{4}\right)}\right)\,\left(B+C\right)}{4\,d}-\frac{3\,a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(B+C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*B*a)/4 + (13*C*a)/4) + tan(c/2 + (d*x)/2)^9*((3*B*a)/4 + (3*C*a)/4) + tan(c/2 + (d*x)/2)^7*((29*B*a)/6 + (13*C*a)/6) + tan(c/2 + (d*x)/2)^3*((35*B*a)/6 + (19*C*a)/6) + tan(c/2 + (d*x)/2)^5*((20*B*a)/3 + (116*C*a)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (3*a*atan((3*a*tan(c/2 + (d*x)/2)*(B + C))/(4*((3*B*a)/4 + (3*C*a)/4)))*(B + C))/(4*d) - (3*a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(B + C))/(4*d)","B"
227,1,212,97,2.119565,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","\frac{\left(B\,a+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{7\,B\,a}{3}+\frac{49\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{13\,B\,a}{3}+\frac{31\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B+3\,C\right)}{4\,\left(B\,a+\frac{3\,C\,a}{4}\right)}\right)\,\left(4\,B+3\,C\right)}{4\,d}-\frac{a\,\left(4\,B+3\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*B*a + (13*C*a)/4) + tan(c/2 + (d*x)/2)^7*(B*a + (3*C*a)/4) + tan(c/2 + (d*x)/2)^3*((13*B*a)/3 + (31*C*a)/12) + tan(c/2 + (d*x)/2)^5*((7*B*a)/3 + (49*C*a)/12))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(4*B + 3*C))/(4*(B*a + (3*C*a)/4)))*(4*B + 3*C))/(4*d) - (a*(4*B + 3*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
228,1,84,85,1.113487,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)),x)","\frac{B\,a\,x}{2}+\frac{C\,a\,x}{2}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(B*a*x)/2 + (C*a*x)/2 + (B*a*sin(c + d*x))/d + (3*C*a*sin(c + d*x))/(4*d) + (B*a*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(3*c + 3*d*x))/(12*d)","B"
229,1,50,47,1.051933,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x),x)","B\,a\,x+\frac{C\,a\,x}{2}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"B*a*x + (C*a*x)/2 + (B*a*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (C*a*sin(2*c + 2*d*x))/(4*d)","B"
230,1,100,32,1.152400,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(C*a*sin(c + d*x))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
231,1,100,32,1.172529,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{B\,a\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,B\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(B*a*tan(c + d*x))/d + (2*B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
232,1,94,56,1.694772,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^4,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B\,a+2\,C\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a+2\,C\,a\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B+2\,C\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*B*a + 2*C*a) - tan(c/2 + (d*x)/2)^3*(B*a + 2*C*a))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (a*atanh(tan(c/2 + (d*x)/2))*(B + 2*C))/d","B"
233,1,126,86,2.983846,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^5,x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B+C\right)}{d}-\frac{\left(B\,a+C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,B\,a}{3}-4\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B\,a+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2))*(B + C))/d - (tan(c/2 + (d*x)/2)*(3*B*a + 3*C*a) + tan(c/2 + (d*x)/2)^5*(B*a + C*a) - tan(c/2 + (d*x)/2)^3*((4*B*a)/3 + 4*C*a))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
234,1,166,106,3.543758,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/cos(c + d*x)^6,x)","\frac{\left(-\frac{3\,B\,a}{4}-C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{49\,B\,a}{12}+\frac{7\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{31\,B\,a}{12}-\frac{13\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,B\,a}{4}+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,B+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*B*a)/4 + 3*C*a) - tan(c/2 + (d*x)/2)^7*((3*B*a)/4 + C*a) - tan(c/2 + (d*x)/2)^3*((31*B*a)/12 + (13*C*a)/3) + tan(c/2 + (d*x)/2)^5*((49*B*a)/12 + (7*C*a)/3))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atanh(tan(c/2 + (d*x)/2))*(3*B + 4*C))/(4*d)","B"
235,1,277,160,2.359235,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2,x)","\frac{\left(\frac{7\,B\,a^2}{4}+\frac{3\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{49\,B\,a^2}{6}+7\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{40\,B\,a^2}{3}+\frac{72\,C\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{79\,B\,a^2}{6}+9\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{25\,B\,a^2}{4}+\frac{13\,C\,a^2}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,B+6\,C\right)}{4\,\left(\frac{7\,B\,a^2}{4}+\frac{3\,C\,a^2}{2}\right)}\right)\,\left(7\,B+6\,C\right)}{4\,d}-\frac{a^2\,\left(7\,B+6\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((25*B*a^2)/4 + (13*C*a^2)/2) + tan(c/2 + (d*x)/2)^9*((7*B*a^2)/4 + (3*C*a^2)/2) + tan(c/2 + (d*x)/2)^7*((49*B*a^2)/6 + 7*C*a^2) + tan(c/2 + (d*x)/2)^3*((79*B*a^2)/6 + 9*C*a^2) + tan(c/2 + (d*x)/2)^5*((40*B*a^2)/3 + (72*C*a^2)/5))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(7*B + 6*C))/(4*((7*B*a^2)/4 + (3*C*a^2)/2)))*(7*B + 6*C))/(4*d) - (a^2*(7*B + 6*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
236,1,134,129,1.168361,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2,x)","B\,a^2\,x+\frac{7\,C\,a^2\,x}{8}+\frac{7\,B\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{C\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"B*a^2*x + (7*C*a^2*x)/8 + (7*B*a^2*sin(c + d*x))/(4*d) + (3*C*a^2*sin(c + d*x))/(2*d) + (B*a^2*sin(2*c + 2*d*x))/(2*d) + (B*a^2*sin(3*c + 3*d*x))/(12*d) + (C*a^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*sin(3*c + 3*d*x))/(6*d) + (C*a^2*sin(4*c + 4*d*x))/(32*d)","B"
237,1,98,94,1.092290,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x),x)","\frac{3\,B\,a^2\,x}{2}+C\,a^2\,x+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{7\,C\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(3*B*a^2*x)/2 + C*a^2*x + (2*B*a^2*sin(c + d*x))/d + (7*C*a^2*sin(c + d*x))/(4*d) + (B*a^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*sin(3*c + 3*d*x))/(12*d)","B"
238,1,141,82,1.175155,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{4\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(B*a^2*sin(c + d*x))/d + (2*C*a^2*sin(c + d*x))/d + (4*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a^2*sin(2*c + 2*d*x))/(4*d)","B"
239,1,161,74,1.138958,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^3,x)","\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(C*a^2*sin(c + d*x))/d + (2*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
240,1,162,88,1.118093,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^4,x)","\frac{3\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(3*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^2*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (C*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
241,1,145,113,2.893243,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B+\frac{3\,C}{2}\right)}{d}-\frac{\left(2\,B\,a^2+3\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,B\,a^2}{3}-8\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,B\,a^2+5\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a^2*atanh(tan(c/2 + (d*x)/2))*(B + (3*C)/2))/d - (tan(c/2 + (d*x)/2)*(6*B*a^2 + 5*C*a^2) + tan(c/2 + (d*x)/2)^5*(2*B*a^2 + 3*C*a^2) - tan(c/2 + (d*x)/2)^3*((16*B*a^2)/3 + 8*C*a^2))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
242,1,183,144,3.567539,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^6,x)","\frac{\left(-\frac{7\,B\,a^2}{4}-2\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{77\,B\,a^2}{12}+\frac{22\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{83\,B\,a^2}{12}-\frac{34\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{25\,B\,a^2}{4}+6\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{7\,B}{8}+C\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((25*B*a^2)/4 + 6*C*a^2) - tan(c/2 + (d*x)/2)^7*((7*B*a^2)/4 + 2*C*a^2) + tan(c/2 + (d*x)/2)^5*((77*B*a^2)/12 + (22*C*a^2)/3) - tan(c/2 + (d*x)/2)^3*((83*B*a^2)/12 + (34*C*a^2)/3))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (2*a^2*atanh(tan(c/2 + (d*x)/2))*((7*B)/8 + C))/d","B"
243,1,224,169,3.724984,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/cos(c + d*x)^7,x)","\frac{a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(6\,B+7\,C\right)}{4\,d}-\frac{\left(\frac{3\,B\,a^2}{2}+\frac{7\,C\,a^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-7\,B\,a^2-\frac{49\,C\,a^2}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{72\,B\,a^2}{5}+\frac{40\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-9\,B\,a^2-\frac{79\,C\,a^2}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,B\,a^2}{2}+\frac{25\,C\,a^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^2*atanh(tan(c/2 + (d*x)/2))*(6*B + 7*C))/(4*d) - (tan(c/2 + (d*x)/2)*((13*B*a^2)/2 + (25*C*a^2)/4) + tan(c/2 + (d*x)/2)^9*((3*B*a^2)/2 + (7*C*a^2)/4) - tan(c/2 + (d*x)/2)^7*(7*B*a^2 + (49*C*a^2)/6) - tan(c/2 + (d*x)/2)^3*(9*B*a^2 + (79*C*a^2)/6) + tan(c/2 + (d*x)/2)^5*((72*B*a^2)/5 + (40*C*a^2)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
244,1,315,201,2.495487,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3,x)","\frac{\left(\frac{13\,B\,a^3}{4}+\frac{23\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{221\,B\,a^3}{12}+\frac{391\,C\,a^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{429\,B\,a^3}{10}+\frac{759\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{499\,B\,a^3}{10}+\frac{969\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{419\,B\,a^3}{12}+\frac{211\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,B\,a^3}{4}+\frac{105\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(26\,B+23\,C\right)}{8\,\left(\frac{13\,B\,a^3}{4}+\frac{23\,C\,a^3}{8}\right)}\right)\,\left(26\,B+23\,C\right)}{8\,d}-\frac{a^3\,\left(26\,B+23\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((51*B*a^3)/4 + (105*C*a^3)/8) + tan(c/2 + (d*x)/2)^11*((13*B*a^3)/4 + (23*C*a^3)/8) + tan(c/2 + (d*x)/2)^3*((419*B*a^3)/12 + (211*C*a^3)/8) + tan(c/2 + (d*x)/2)^9*((221*B*a^3)/12 + (391*C*a^3)/24) + tan(c/2 + (d*x)/2)^7*((429*B*a^3)/10 + (759*C*a^3)/20) + tan(c/2 + (d*x)/2)^5*((499*B*a^3)/10 + (969*C*a^3)/20))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(26*B + 23*C))/(8*((13*B*a^3)/4 + (23*C*a^3)/8)))*(26*B + 23*C))/(8*d) - (a^3*(26*B + 23*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d)","B"
245,1,277,154,2.361503,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3,x)","\frac{\left(\frac{15\,B\,a^3}{4}+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{35\,B\,a^3}{2}+\frac{91\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(32\,B\,a^3+\frac{416\,C\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{61\,B\,a^3}{2}+\frac{133\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{49\,B\,a^3}{4}+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,B+13\,C\right)}{4\,\left(\frac{15\,B\,a^3}{4}+\frac{13\,C\,a^3}{4}\right)}\right)\,\left(15\,B+13\,C\right)}{4\,d}-\frac{a^3\,\left(15\,B+13\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((49*B*a^3)/4 + (51*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*((15*B*a^3)/4 + (13*C*a^3)/4) + tan(c/2 + (d*x)/2)^7*((35*B*a^3)/2 + (91*C*a^3)/6) + tan(c/2 + (d*x)/2)^3*((61*B*a^3)/2 + (133*C*a^3)/6) + tan(c/2 + (d*x)/2)^5*(32*B*a^3 + (416*C*a^3)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(15*B + 13*C))/(4*((15*B*a^3)/4 + (13*C*a^3)/4)))*(15*B + 13*C))/(4*d) - (a^3*(15*B + 13*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
246,1,134,116,1.160462,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x),x)","\frac{5\,B\,a^3\,x}{2}+\frac{15\,C\,a^3\,x}{8}+\frac{15\,B\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{13\,C\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(5*B*a^3*x)/2 + (15*C*a^3*x)/8 + (15*B*a^3*sin(c + d*x))/(4*d) + (13*C*a^3*sin(c + d*x))/(4*d) + (3*B*a^3*sin(2*c + 2*d*x))/(4*d) + (B*a^3*sin(3*c + 3*d*x))/(12*d) + (C*a^3*sin(2*c + 2*d*x))/d + (C*a^3*sin(3*c + 3*d*x))/(4*d) + (C*a^3*sin(4*c + 4*d*x))/(32*d)","B"
247,1,178,111,1.307630,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{15\,C\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{7\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{5\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(3*B*a^3*sin(c + d*x))/d + (15*C*a^3*sin(c + d*x))/(4*d) + (7*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (5*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^3*sin(2*c + 2*d*x))/(4*d) + (3*C*a^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(3*c + 3*d*x))/(12*d)","B"
248,1,197,110,1.254514,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^3,x)","\frac{B\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{6\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(B*a^3*sin(c + d*x))/d + (3*C*a^3*sin(c + d*x))/d + (6*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
249,1,207,114,1.246897,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^4,x)","\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(C*a^3*sin(c + d*x))/d + (2*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*B*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (C*a^3*sin(c + d*x))/(d*cos(c + d*x))","B"
250,1,209,125,1.201758,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{5\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{7\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{11\,B\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(5*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (7*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (11*B*a^3*sin(c + d*x))/(3*d*cos(c + d*x)) + (3*B*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (B*a^3*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (3*C*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
251,1,185,154,3.628685,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^6,x)","\frac{\left(-\frac{15\,B\,a^3}{4}-5\,C\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{55\,B\,a^3}{4}+\frac{55\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{73\,B\,a^3}{4}-\frac{73\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{49\,B\,a^3}{4}+11\,C\,a^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{5\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,B+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((49*B*a^3)/4 + 11*C*a^3) - tan(c/2 + (d*x)/2)^7*((15*B*a^3)/4 + 5*C*a^3) + tan(c/2 + (d*x)/2)^5*((55*B*a^3)/4 + (55*C*a^3)/3) - tan(c/2 + (d*x)/2)^3*((73*B*a^3)/4 + (73*C*a^3)/3))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (5*a^3*atanh(tan(c/2 + (d*x)/2))*(3*B + 4*C))/(4*d)","B"
252,1,224,185,3.736928,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/cos(c + d*x)^7,x)","\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(13\,B+15\,C\right)}{4\,d}-\frac{\left(\frac{13\,B\,a^3}{4}+\frac{15\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{91\,B\,a^3}{6}-\frac{35\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,B\,a^3}{15}+32\,C\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{133\,B\,a^3}{6}-\frac{61\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,B\,a^3}{4}+\frac{49\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^3*atanh(tan(c/2 + (d*x)/2))*(13*B + 15*C))/(4*d) - (tan(c/2 + (d*x)/2)*((51*B*a^3)/4 + (49*C*a^3)/4) + tan(c/2 + (d*x)/2)^9*((13*B*a^3)/4 + (15*C*a^3)/4) - tan(c/2 + (d*x)/2)^7*((91*B*a^3)/6 + (35*C*a^3)/2) - tan(c/2 + (d*x)/2)^3*((133*B*a^3)/6 + (61*C*a^3)/2) + tan(c/2 + (d*x)/2)^5*((416*B*a^3)/15 + 32*C*a^3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
253,1,138,122,2.219331,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{3\,x\,\left(B-C\right)}{2\,a}-\frac{\left(3\,B-5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,B-\frac{16\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B-3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(3*x*(B - C))/(2*a) - (tan(c/2 + (d*x)/2)^5*(3*B - 5*C) + tan(c/2 + (d*x)/2)^3*(4*B - (16*C)/3) + tan(c/2 + (d*x)/2)*(B - 3*C))/(d*(a + 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 + a*tan(c/2 + (d*x)/2)^6)) - (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
254,1,107,99,1.370009,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{\left(2\,B-3\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B-C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{x\,\left(2\,B-3\,C\right)}{2\,a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(2*B - 3*C) + tan(c/2 + (d*x)/2)*(2*B - C))/(d*(a + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) - (x*(2*B - 3*C))/(2*a) + (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
255,1,65,54,1.131151,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x)),x)","\frac{x\,\left(B-C\right)}{a}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(x*(B - C))/a + (2*C*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2)) - (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
256,1,30,34,1.064322,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a}+\frac{C\,d\,x}{a}}{d}","Not used",1,"((tan(c/2 + (d*x)/2)*(B - C))/a + (C*d*x)/a)/d","B"
257,1,42,44,1.066380,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))),x)","\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(2*B*atanh(tan(c/2 + (d*x)/2)))/(a*d) - (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
258,1,78,69,1.158123,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))),x)","\frac{2\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-C\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(2*B*tan(c/2 + (d*x)/2))/(d*(a - a*tan(c/2 + (d*x)/2)^2)) - (2*atanh(tan(c/2 + (d*x)/2))*(B - C))/(a*d) + (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
259,1,119,107,1.250985,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,B-2\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-2\,C\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,B}{2}-C\right)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(3*B - 2*C) - tan(c/2 + (d*x)/2)*(B - 2*C))/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) + (2*atanh(tan(c/2 + (d*x)/2))*((3*B)/2 - C))/(a*d) - (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
260,1,152,131,1.509158,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^5*(a + a*cos(c + d*x))),x)","\frac{\left(5\,B-3\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,C-\frac{16\,B}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B-C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B-C\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B-C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(5*B - 3*C) - tan(c/2 + (d*x)/2)^3*((16*B)/3 - 4*C) + tan(c/2 + (d*x)/2)*(3*B - C))/(d*(a - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6)) - (3*atanh(tan(c/2 + (d*x)/2))*(B - C))/(a*d) + (tan(c/2 + (d*x)/2)*(B - C))/(a*d)","B"
261,1,189,170,1.197962,"\text{Not used}","int((cos(c + d*x)^3*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{x\,\left(7\,B-10\,C\right)}{2\,a^2}-\frac{\left(5\,B-10\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,B-\frac{40\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,B-6\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\left(B-C\right)}{a^2}+\frac{3\,B-5\,C}{2\,a^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}","Not used",1,"(x*(7*B - 10*C))/(2*a^2) - (tan(c/2 + (d*x)/2)^5*(5*B - 10*C) + tan(c/2 + (d*x)/2)^3*(8*B - (40*C)/3) + tan(c/2 + (d*x)/2)*(3*B - 6*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2)) - (tan(c/2 + (d*x)/2)*((2*(B - C))/a^2 + (3*B - 5*C)/(2*a^2)))/d + (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d)","B"
262,1,152,147,1.147085,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^2}+\frac{2\,B-4\,C}{2\,a^2}\right)}{d}-\frac{x\,\left(4\,B-7\,C\right)}{2\,a^2}+\frac{\left(2\,B-5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B-3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^2) + (2*B - 4*C)/(2*a^2)))/d - (x*(4*B - 7*C))/(2*a^2) + (tan(c/2 + (d*x)/2)^3*(2*B - 5*C) + tan(c/2 + (d*x)/2)*(2*B - 3*C))/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + a^2*tan(c/2 + (d*x)/2)^4 + a^2)) - (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d)","B"
263,1,105,99,1.120952,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{x\,\left(B-2\,C\right)}{a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B-C}{a^2}+\frac{B-3\,C}{2\,a^2}\right)}{d}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}","Not used",1,"(x*(B - 2*C))/a^2 - (tan(c/2 + (d*x)/2)*((B - C)/a^2 + (B - 3*C)/(2*a^2)))/d + (2*C*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2)) + (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d)","B"
264,1,65,70,1.083969,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^2,x)","\frac{3\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,C\,d\,x}{6\,a^2\,d}","Not used",1,"(3*B*tan(c/2 + (d*x)/2) - 9*C*tan(c/2 + (d*x)/2) - B*tan(c/2 + (d*x)/2)^3 + C*tan(c/2 + (d*x)/2)^3 + 6*C*d*x)/(6*a^2*d)","B"
265,1,45,65,1.050177,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B+C\right)}{2\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d) + (tan(c/2 + (d*x)/2)*(B + C))/(2*a^2*d)","B"
266,1,74,79,1.082295,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^2),x)","\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B}{a^2}+\frac{B-C}{2\,a^2}\right)}{d}","Not used",1,"(2*B*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d) - (tan(c/2 + (d*x)/2)*(B/a^2 + (B - C)/(2*a^2)))/d","B"
267,1,123,107,1.140550,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B-C}{a^2}+\frac{3\,B-C}{2\,a^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}-\frac{2\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,B-C\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((B - C)/a^2 + (3*B - C)/(2*a^2)))/d + (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d) - (2*B*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2)) - (2*atanh(tan(c/2 + (d*x)/2))*(2*B - C))/(a^2*d)","B"
268,1,165,152,1.167426,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,B-2\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B-2\,C\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^2}+\frac{4\,B-2\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-C\right)}{6\,a^2\,d}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(7\,B-4\,C\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(5*B - 2*C) - tan(c/2 + (d*x)/2)*(3*B - 2*C))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^2) + (4*B - 2*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(B - C))/(6*a^2*d) + (atanh(tan(c/2 + (d*x)/2))*(7*B - 4*C))/(a^2*d)","B"
269,1,203,193,1.118896,"\text{Not used}","int((cos(c + d*x)^3*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^3}+\frac{3\,\left(3\,B-5\,C\right)}{4\,a^3}+\frac{2\,B-10\,C}{4\,a^3}\right)}{d}-\frac{x\,\left(6\,B-13\,C\right)}{2\,a^3}+\frac{\left(2\,B-7\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B-5\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{4\,a^3}+\frac{3\,B-5\,C}{12\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^3) + (3*(3*B - 5*C))/(4*a^3) + (2*B - 10*C)/(4*a^3)))/d - (x*(6*B - 13*C))/(2*a^3) + (tan(c/2 + (d*x)/2)^3*(2*B - 7*C) + tan(c/2 + (d*x)/2)*(2*B - 5*C))/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + a^3*tan(c/2 + (d*x)/2)^4 + a^3)) - (tan(c/2 + (d*x)/2)^3*((B - C)/(4*a^3) + (3*B - 5*C)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d)","B"
270,1,152,147,1.129016,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{6\,a^3}+\frac{2\,B-4\,C}{12\,a^3}\right)}{d}+\frac{x\,\left(B-3\,C\right)}{a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{4\,a^3}-\frac{3\,C}{2\,a^3}+\frac{2\,B-4\,C}{2\,a^3}\right)}{d}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((B - C)/(6*a^3) + (2*B - 4*C)/(12*a^3)))/d + (x*(B - 3*C))/a^3 - (tan(c/2 + (d*x)/2)*((3*(B - C))/(4*a^3) - (3*C)/(2*a^3) + (2*B - 4*C)/(2*a^3)))/d + (2*C*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 + a^3)) - (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d)","B"
271,1,134,116,1.244962,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{C\,x}{a^3}-\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}-\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{7\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(C*x)/a^3 - (cos(c/2 + (d*x)/2)^2*((B*sin(c/2 + (d*x)/2)^3)/6 - (C*sin(c/2 + (d*x)/2)^3)/3) - cos(c/2 + (d*x)/2)^4*((B*sin(c/2 + (d*x)/2))/4 - (7*C*sin(c/2 + (d*x)/2))/4) - (B*sin(c/2 + (d*x)/2)^5)/20 + (C*sin(c/2 + (d*x)/2)^5)/20)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
272,1,66,102,1.069869,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,B+15\,C-3\,B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(15*B + 15*C - 3*B*tan(c/2 + (d*x)/2)^4 - 10*C*tan(c/2 + (d*x)/2)^2 + 3*C*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
273,1,66,102,1.086129,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(15\,B+15\,C+10\,B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,C\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(15*B + 15*C + 10*B*tan(c/2 + (d*x)/2)^2 + 3*B*tan(c/2 + (d*x)/2)^4 - 3*C*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
274,1,130,117,1.112211,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^3),x)","\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B-C}{4\,a^3}+\frac{3\,B+C}{4\,a^3}+\frac{3\,B-C}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{12\,a^3}+\frac{3\,B-C}{12\,a^3}\right)}{d}","Not used",1,"(2*B*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (tan(c/2 + (d*x)/2)*((B - C)/(4*a^3) + (3*B + C)/(4*a^3) + (3*B - C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d) - (tan(c/2 + (d*x)/2)^3*((B - C)/(12*a^3) + (3*B - C)/(12*a^3)))/d","B"
275,1,168,145,1.134907,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{6\,a^3}+\frac{4\,B-2\,C}{12\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,B}{2\,a^3}+\frac{3\,\left(B-C\right)}{4\,a^3}+\frac{4\,B-2\,C}{2\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}-\frac{2\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,B-C\right)}{a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((B - C)/(6*a^3) + (4*B - 2*C)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)*((3*B)/(2*a^3) + (3*(B - C))/(4*a^3) + (4*B - 2*C)/(2*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d) - (2*B*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3)) - (2*atanh(tan(c/2 + (d*x)/2))*(3*B - C))/(a^3*d)","B"
276,1,216,196,1.087625,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,B-2\,C\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,B-2\,C\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(B-C\right)}{2\,a^3}+\frac{3\,\left(5\,B-3\,C\right)}{4\,a^3}+\frac{10\,B-2\,C}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{B-C}{4\,a^3}+\frac{5\,B-3\,C}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-C\right)}{20\,a^3\,d}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(13\,B-6\,C\right)}{a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(7*B - 2*C) - tan(c/2 + (d*x)/2)*(5*B - 2*C))/(d*(a^3*tan(c/2 + (d*x)/2)^4 - 2*a^3*tan(c/2 + (d*x)/2)^2 + a^3)) - (tan(c/2 + (d*x)/2)*((3*(B - C))/(2*a^3) + (3*(5*B - 3*C))/(4*a^3) + (10*B - 2*C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((B - C)/(4*a^3) + (5*B - 3*C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(B - C))/(20*a^3*d) + (atanh(tan(c/2 + (d*x)/2))*(13*B - 6*C))/(a^3*d)","B"
277,0,-1,101,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2), x)","F"
278,0,-1,138,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2), x)","F"
279,0,-1,175,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2), x)","F"
280,1,160,118,0.353958,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,B\,\left(2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)-\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)\right)\,\sqrt{\frac{a+a\,\cos\left(c+d\,x\right)}{2\,a}}}{d\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,a\,d}-\frac{2\,C\,\left(4\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)-3\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)\right)\,\sqrt{\frac{a+a\,\cos\left(c+d\,x\right)}{2\,a}}}{3\,a^2\,d\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*B*(2*ellipticE(c/2 + (d*x)/2, 1) - ellipticF(c/2 + (d*x)/2, 1))*((a + a*cos(c + d*x))/(2*a))^(1/2))/(d*(a + a*cos(c + d*x))^(1/2)) + (2*C*sin(c + d*x)*(a + a*cos(c + d*x))^(1/2))/(3*a*d) - (2*C*(4*a^2*ellipticE(c/2 + (d*x)/2, 1) - 3*a^2*ellipticF(c/2 + (d*x)/2, 1))*((a + a*cos(c + d*x))/(2*a))^(1/2))/(3*a^2*d*(a + a*cos(c + d*x))^(1/2))","B"
281,0,-1,118,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(3/2), x)","F"
282,0,-1,126,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(5/2), x)","F"
283,1,87,111,1.364288,"\text{Not used}","int(cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","-\frac{2\,B\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*B*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
284,1,80,87,1.138917,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,B\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,C\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*B*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*C*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
285,1,53,61,1.059508,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(1/2),x)","\frac{2\,B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*B*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
286,1,33,35,1.116138,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(3/2),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*ellipticE(c/2 + (d*x)/2, 2))/d","B"
287,1,60,57,1.354954,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(5/2),x)","\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
288,1,87,83,1.594522,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(7/2),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
289,1,87,111,1.739593,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(9/2),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
290,1,126,132,1.187587,"\text{Not used}","int(cos(c + d*x)^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{3\,A\,x}{8}+\frac{5\,C\,x}{16}+\frac{A\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{5\,B\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{B\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{15\,C\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,C\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{C\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{5\,B\,\sin\left(c+d\,x\right)}{8\,d}","Not used",1,"(3*A*x)/8 + (5*C*x)/16 + (A*sin(2*c + 2*d*x))/(4*d) + (A*sin(4*c + 4*d*x))/(32*d) + (5*B*sin(3*c + 3*d*x))/(48*d) + (B*sin(5*c + 5*d*x))/(80*d) + (15*C*sin(2*c + 2*d*x))/(64*d) + (3*C*sin(4*c + 4*d*x))/(64*d) + (C*sin(6*c + 6*d*x))/(192*d) + (5*B*sin(c + d*x))/(8*d)","B"
291,1,104,113,1.154413,"\text{Not used}","int(cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{3\,B\,x}{8}+\frac{A\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{5\,C\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{C\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{3\,A\,\sin\left(c+d\,x\right)}{4\,d}+\frac{5\,C\,\sin\left(c+d\,x\right)}{8\,d}","Not used",1,"(3*B*x)/8 + (A*sin(3*c + 3*d*x))/(12*d) + (B*sin(2*c + 2*d*x))/(4*d) + (B*sin(4*c + 4*d*x))/(32*d) + (5*C*sin(3*c + 3*d*x))/(48*d) + (C*sin(5*c + 5*d*x))/(80*d) + (3*A*sin(c + d*x))/(4*d) + (5*C*sin(c + d*x))/(8*d)","B"
292,1,81,88,1.100267,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{A\,x}{2}+\frac{3\,C\,x}{8}+\frac{A\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(A*x)/2 + (3*C*x)/8 + (A*sin(2*c + 2*d*x))/(4*d) + (B*sin(3*c + 3*d*x))/(12*d) + (C*sin(2*c + 2*d*x))/(4*d) + (C*sin(4*c + 4*d*x))/(32*d) + (3*B*sin(c + d*x))/(4*d)","B"
293,1,66,69,1.080273,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{B\,x}{2}+\frac{A\,\sin\left(c+d\,x\right)}{d}+\frac{2\,C\,\sin\left(c+d\,x\right)}{3\,d}+\frac{B\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{C\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(B*x)/2 + (A*sin(c + d*x))/d + (2*C*sin(c + d*x))/(3*d) + (B*cos(c + d*x)*sin(c + d*x))/(2*d) + (C*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
294,1,34,41,1.064833,"\text{Not used}","int(A + B*cos(c + d*x) + C*cos(c + d*x)^2,x)","A\,x+\frac{C\,x}{2}+\frac{C\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,\sin\left(c+d\,x\right)}{d}","Not used",1,"A*x + (C*x)/2 + (C*sin(2*c + 2*d*x))/(4*d) + (B*sin(c + d*x))/d","B"
295,1,68,27,1.080825,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x),x)","\frac{2\,A\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(2*A*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*sin(c + d*x))/d","B"
296,1,161,27,1.074897,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^2,x)","\frac{2\,B\,\mathrm{atanh}\left(\frac{64\,B^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,B^3+64\,B\,C^2}+\frac{64\,B\,C^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,B^3+64\,B\,C^2}\right)}{d}+\frac{2\,C\,\mathrm{atan}\left(\frac{64\,C^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,B^2\,C+64\,C^3}+\frac{64\,B^2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,B^2\,C+64\,C^3}\right)}{d}-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*B*atanh((64*B^3*tan(c/2 + (d*x)/2))/(64*B*C^2 + 64*B^3) + (64*B*C^2*tan(c/2 + (d*x)/2))/(64*B*C^2 + 64*B^3)))/d + (2*C*atan((64*C^3*tan(c/2 + (d*x)/2))/(64*B^2*C + 64*C^3) + (64*B^2*C*tan(c/2 + (d*x)/2))/(64*B^2*C + 64*C^3)))/d - (2*A*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
297,1,85,51,1.684838,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^3,x)","\frac{\left(A-2\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A+2\,B\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+2\,C\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A + 2*B) + tan(c/2 + (d*x)/2)^3*(A - 2*B))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (atanh(tan(c/2 + (d*x)/2))*(A + 2*C))/d","B"
298,1,123,78,3.074817,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^4,x)","\frac{B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\left(2\,A-B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A+B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(B*atanh(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)*(2*A + B + 2*C) - tan(c/2 + (d*x)/2)^3*((4*A)/3 + 4*C) + tan(c/2 + (d*x)/2)^5*(2*A - B + 2*C))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
299,1,160,97,3.560064,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^5,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,A}{4}+C\right)}{d}+\frac{\left(\frac{5\,A}{4}-2\,B+C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A}{4}+\frac{10\,B}{3}-C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,A}{4}-\frac{10\,B}{3}-C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A}{4}+2\,B+C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((3*A)/4 + C))/d + (tan(c/2 + (d*x)/2)*((5*A)/4 + 2*B + C) + tan(c/2 + (d*x)/2)^7*((5*A)/4 - 2*B + C) - tan(c/2 + (d*x)/2)^3*((10*B)/3 - (3*A)/4 + C) + tan(c/2 + (d*x)/2)^5*((3*A)/4 + (10*B)/3 - C))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
300,1,197,122,3.757429,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^6,x)","\frac{3\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\left(2\,A-\frac{5\,B}{4}+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{B}{2}-\frac{8\,A}{3}-\frac{16\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A}{15}+\frac{20\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A}{3}-\frac{B}{2}-\frac{16\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A+\frac{5\,B}{4}+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(3*B*atanh(tan(c/2 + (d*x)/2)))/(4*d) - (tan(c/2 + (d*x)/2)^5*((116*A)/15 + (20*C)/3) + tan(c/2 + (d*x)/2)*(2*A + (5*B)/4 + 2*C) + tan(c/2 + (d*x)/2)^9*(2*A - (5*B)/4 + 2*C) - tan(c/2 + (d*x)/2)^3*((8*A)/3 + B/2 + (16*C)/3) - tan(c/2 + (d*x)/2)^7*((8*A)/3 - B/2 + (16*C)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
301,1,279,143,2.556873,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(A\,a+\frac{3\,B\,a}{4}+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{10\,A\,a}{3}+\frac{29\,B\,a}{6}+\frac{13\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,a}{3}+\frac{20\,B\,a}{3}+\frac{116\,C\,a}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{22\,A\,a}{3}+\frac{35\,B\,a}{6}+\frac{19\,C\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,B\,a}{4}+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(4\,A+3\,B+3\,C\right)}{4\,d}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,B+3\,C\right)}{4\,\left(A\,a+\frac{3\,B\,a}{4}+\frac{3\,C\,a}{4}\right)}\right)\,\left(4\,A+3\,B+3\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + (13*B*a)/4 + (13*C*a)/4) + tan(c/2 + (d*x)/2)^9*(A*a + (3*B*a)/4 + (3*C*a)/4) + tan(c/2 + (d*x)/2)^7*((10*A*a)/3 + (29*B*a)/6 + (13*C*a)/6) + tan(c/2 + (d*x)/2)^3*((22*A*a)/3 + (35*B*a)/6 + (19*C*a)/6) + tan(c/2 + (d*x)/2)^5*((20*A*a)/3 + (20*B*a)/3 + (116*C*a)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(4*A + 3*B + 3*C))/(4*d) + (a*atan((a*tan(c/2 + (d*x)/2)*(4*A + 3*B + 3*C))/(4*(A*a + (3*B*a)/4 + (3*C*a)/4)))*(4*A + 3*B + 3*C))/(4*d)","B"
302,1,240,118,2.275108,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(A\,a+B\,a+\frac{3\,C\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(5\,A\,a+\frac{7\,B\,a}{3}+\frac{49\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(7\,A\,a+\frac{13\,B\,a}{3}+\frac{31\,C\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+3\,B\,a+\frac{13\,C\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(4\,A+4\,B+3\,C\right)}{4\,d}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+4\,B+3\,C\right)}{4\,\left(A\,a+B\,a+\frac{3\,C\,a}{4}\right)}\right)\,\left(4\,A+4\,B+3\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + 3*B*a + (13*C*a)/4) + tan(c/2 + (d*x)/2)^7*(A*a + B*a + (3*C*a)/4) + tan(c/2 + (d*x)/2)^3*(7*A*a + (13*B*a)/3 + (31*C*a)/12) + tan(c/2 + (d*x)/2)^5*(5*A*a + (7*B*a)/3 + (49*C*a)/12))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(4*A + 4*B + 3*C))/(4*d) + (a*atan((a*tan(c/2 + (d*x)/2)*(4*A + 4*B + 3*C))/(4*(A*a + B*a + (3*C*a)/4)))*(4*A + 4*B + 3*C))/(4*d)","B"
303,1,100,91,1.123582,"\text{Not used}","int((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","A\,a\,x+\frac{B\,a\,x}{2}+\frac{C\,a\,x}{2}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"A*a*x + (B*a*x)/2 + (C*a*x)/2 + (A*a*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (3*C*a*sin(c + d*x))/(4*d) + (B*a*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(3*c + 3*d*x))/(12*d)","B"
304,1,159,63,1.445945,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(B*a*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (2*A*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (A*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*sin(2*c + 2*d*x))/(4*d)","B"
305,1,153,46,1.438298,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{A\,a\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}","Not used",1,"(A*a*tan(c + d*x))/d + (2*A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*sin(2*c + 2*d*x))/(2*d*cos(c + d*x))","B"
306,1,176,62,1.633727,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{\frac{A\,a\,\sin\left(c+d\,x\right)}{2}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{2\,\left(\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2}+B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}-C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}\right)}{d}","Not used",1,"((A*a*sin(c + d*x))/2 + (A*a*sin(2*c + 2*d*x))/2 + (B*a*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*((A*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/2 + B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i - C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i))/d","B"
307,1,165,91,4.013986,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\frac{a\,\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B+2\,C\right)}{2\,A\,a+2\,B\,a+4\,C\,a}\right)\,\left(A+B+2\,C\right)}{d}-\frac{\left(A\,a+B\,a+2\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A\,a}{3}-4\,B\,a-4\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+3\,B\,a+2\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*atanh((2*a*tan(c/2 + (d*x)/2)*(A + B + 2*C))/(2*A*a + 2*B*a + 4*C*a))*(A + B + 2*C))/d - (tan(c/2 + (d*x)/2)*(3*A*a + 3*B*a + 2*C*a) + tan(c/2 + (d*x)/2)^5*(A*a + B*a + 2*C*a) - tan(c/2 + (d*x)/2)^3*((4*A*a)/3 + 4*B*a + 4*C*a))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
308,1,211,125,4.555948,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{\left(-\frac{3\,A\,a}{4}-B\,a-C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{49\,A\,a}{12}+\frac{7\,B\,a}{3}+5\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{31\,A\,a}{12}-\frac{13\,B\,a}{3}-7\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+3\,B\,a+3\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A+4\,B+4\,C\right)}{2\,\left(\frac{3\,A\,a}{2}+2\,B\,a+2\,C\,a\right)}\right)\,\left(3\,A+4\,B+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + 3*B*a + 3*C*a) - tan(c/2 + (d*x)/2)^7*((3*A*a)/4 + B*a + C*a) - tan(c/2 + (d*x)/2)^3*((31*A*a)/12 + (13*B*a)/3 + 7*C*a) + tan(c/2 + (d*x)/2)^5*((49*A*a)/12 + (7*B*a)/3 + 5*C*a))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atanh((a*tan(c/2 + (d*x)/2)*(3*A + 4*B + 4*C))/(2*((3*A*a)/2 + 2*B*a + 2*C*a)))*(3*A + 4*B + 4*C))/(4*d)","B"
309,1,366,213,2.766592,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(\frac{7\,A\,a^2}{4}+\frac{3\,B\,a^2}{2}+\frac{11\,C\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{119\,A\,a^2}{12}+\frac{17\,B\,a^2}{2}+\frac{187\,C\,a^2}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{43\,A\,a^2}{2}+\frac{107\,B\,a^2}{5}+\frac{331\,C\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{53\,A\,a^2}{2}+\frac{117\,B\,a^2}{5}+\frac{501\,C\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{233\,A\,a^2}{12}+\frac{31\,B\,a^2}{2}+\frac{87\,C\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{25\,A\,a^2}{4}+\frac{13\,B\,a^2}{2}+\frac{53\,C\,a^2}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(14\,A+12\,B+11\,C\right)}{8\,\left(\frac{7\,A\,a^2}{4}+\frac{3\,B\,a^2}{2}+\frac{11\,C\,a^2}{8}\right)}\right)\,\left(14\,A+12\,B+11\,C\right)}{8\,d}-\frac{a^2\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(14\,A+12\,B+11\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*((7*A*a^2)/4 + (3*B*a^2)/2 + (11*C*a^2)/8) + tan(c/2 + (d*x)/2)^9*((119*A*a^2)/12 + (17*B*a^2)/2 + (187*C*a^2)/24) + tan(c/2 + (d*x)/2)^3*((233*A*a^2)/12 + (31*B*a^2)/2 + (87*C*a^2)/8) + tan(c/2 + (d*x)/2)^7*((43*A*a^2)/2 + (107*B*a^2)/5 + (331*C*a^2)/20) + tan(c/2 + (d*x)/2)^5*((53*A*a^2)/2 + (117*B*a^2)/5 + (501*C*a^2)/20) + tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + (13*B*a^2)/2 + (53*C*a^2)/8))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(14*A + 12*B + 11*C))/(8*((7*A*a^2)/4 + (3*B*a^2)/2 + (11*C*a^2)/8)))*(14*A + 12*B + 11*C))/(8*d) - (a^2*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(14*A + 12*B + 11*C))/(8*d)","B"
310,1,322,181,2.597375,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(2\,A\,a^2+\frac{7\,B\,a^2}{4}+\frac{3\,C\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{28\,A\,a^2}{3}+\frac{49\,B\,a^2}{6}+7\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{56\,A\,a^2}{3}+\frac{40\,B\,a^2}{3}+\frac{72\,C\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{52\,A\,a^2}{3}+\frac{79\,B\,a^2}{6}+9\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A\,a^2+\frac{25\,B\,a^2}{4}+\frac{13\,C\,a^2}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A+7\,B+6\,C\right)}{4\,\left(2\,A\,a^2+\frac{7\,B\,a^2}{4}+\frac{3\,C\,a^2}{2}\right)}\right)\,\left(8\,A+7\,B+6\,C\right)}{4\,d}-\frac{a^2\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(8\,A+7\,B+6\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(2*A*a^2 + (7*B*a^2)/4 + (3*C*a^2)/2) + tan(c/2 + (d*x)/2)^7*((28*A*a^2)/3 + (49*B*a^2)/6 + 7*C*a^2) + tan(c/2 + (d*x)/2)^3*((52*A*a^2)/3 + (79*B*a^2)/6 + 9*C*a^2) + tan(c/2 + (d*x)/2)^5*((56*A*a^2)/3 + (40*B*a^2)/3 + (72*C*a^2)/5) + tan(c/2 + (d*x)/2)*(6*A*a^2 + (25*B*a^2)/4 + (13*C*a^2)/2))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(8*A + 7*B + 6*C))/(4*(2*A*a^2 + (7*B*a^2)/4 + (3*C*a^2)/2)))*(8*A + 7*B + 6*C))/(4*d) - (a^2*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(8*A + 7*B + 6*C))/(4*d)","B"
311,1,174,138,1.257721,"\text{Not used}","int((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{3\,A\,a^2\,x}{2}+B\,a^2\,x+\frac{7\,C\,a^2\,x}{8}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{7\,B\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{C\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(3*A*a^2*x)/2 + B*a^2*x + (7*C*a^2*x)/8 + (2*A*a^2*sin(c + d*x))/d + (7*B*a^2*sin(c + d*x))/(4*d) + (3*C*a^2*sin(c + d*x))/(2*d) + (A*a^2*sin(2*c + 2*d*x))/(4*d) + (B*a^2*sin(2*c + 2*d*x))/(2*d) + (B*a^2*sin(3*c + 3*d*x))/(12*d) + (C*a^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*sin(3*c + 3*d*x))/(6*d) + (C*a^2*sin(4*c + 4*d*x))/(32*d)","B"
312,1,226,120,1.633266,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{7\,C\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{4\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}-\frac{A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(A*a^2*sin(c + d*x))/d + (2*B*a^2*sin(c + d*x))/d + (7*C*a^2*sin(c + d*x))/(4*d) + (4*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (A*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (3*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*a^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*sin(3*c + 3*d*x))/(12*d)","B"
313,1,232,121,1.813504,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{2\,A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+4\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+3\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}-B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}+\frac{\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+C\,a^2\,\sin\left(2\,c+2\,d\,x\right)+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{8}+A\,a^2\,\sin\left(c+d\,x\right)+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{8}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - A*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i + 4*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + 3*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + ((B*a^2*sin(2*c + 2*d*x))/2 + C*a^2*sin(2*c + 2*d*x) + (C*a^2*sin(3*c + 3*d*x))/8 + A*a^2*sin(c + d*x) + (C*a^2*sin(c + d*x))/8)/(d*cos(c + d*x))","B"
314,1,244,123,1.945614,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{2}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{4}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{2\,\left(\frac{A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}-B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}-2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}\right)}{d}","Not used",1,"(A*a^2*sin(2*c + 2*d*x) + (B*a^2*sin(2*c + 2*d*x))/2 + (C*a^2*sin(3*c + 3*d*x))/4 + (A*a^2*sin(c + d*x))/2 + (C*a^2*sin(c + d*x))/4)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*((A*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 - B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i - 2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i))/d","B"
315,1,440,134,2.201941,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\frac{\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{5\,A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,A\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{2}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{4}-\frac{A\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}-\frac{B\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{4}+\frac{3\,C\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-C\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}-\frac{A\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{2}-\frac{B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{4}+\frac{C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((A*a^2*sin(2*c + 2*d*x))/2 + (5*A*a^2*sin(3*c + 3*d*x))/12 + (B*a^2*sin(2*c + 2*d*x))/4 + (B*a^2*sin(3*c + 3*d*x))/2 + (C*a^2*sin(3*c + 3*d*x))/4 + (3*A*a^2*sin(c + d*x))/4 + (B*a^2*sin(c + d*x))/2 + (C*a^2*sin(c + d*x))/4 - (A*a^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 - (B*a^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/4 + (3*C*a^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - C*a^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i - (A*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/2 - (B*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/4 + (C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - C*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
316,1,245,160,4.660143,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{2\,a^2\,\mathrm{atanh}\left(\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7\,A}{8}+B+\frac{3\,C}{2}\right)}{\frac{7\,A\,a^2}{2}+4\,B\,a^2+6\,C\,a^2}\right)\,\left(\frac{7\,A}{8}+B+\frac{3\,C}{2}\right)}{d}-\frac{\left(\frac{7\,A\,a^2}{4}+2\,B\,a^2+3\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-\frac{77\,A\,a^2}{12}-\frac{22\,B\,a^2}{3}-11\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{83\,A\,a^2}{12}+\frac{34\,B\,a^2}{3}+13\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{25\,A\,a^2}{4}-6\,B\,a^2-5\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(2*a^2*atanh((4*a^2*tan(c/2 + (d*x)/2)*((7*A)/8 + B + (3*C)/2))/((7*A*a^2)/2 + 4*B*a^2 + 6*C*a^2))*((7*A)/8 + B + (3*C)/2))/d - (tan(c/2 + (d*x)/2)^7*((7*A*a^2)/4 + 2*B*a^2 + 3*C*a^2) - tan(c/2 + (d*x)/2)^5*((77*A*a^2)/12 + (22*B*a^2)/3 + 11*C*a^2) + tan(c/2 + (d*x)/2)^3*((83*A*a^2)/12 + (34*B*a^2)/3 + 13*C*a^2) - tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + 6*B*a^2 + 5*C*a^2))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
317,1,286,196,2.195328,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{3\,A}{4}+\frac{7\,B}{8}+C\right)}{d}-\frac{\left(\frac{3\,A\,a^2}{2}+\frac{7\,B\,a^2}{4}+2\,C\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-7\,A\,a^2-\frac{49\,B\,a^2}{6}-\frac{28\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{72\,A\,a^2}{5}+\frac{40\,B\,a^2}{3}+\frac{56\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-9\,A\,a^2-\frac{79\,B\,a^2}{6}-\frac{52\,C\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a^2}{2}+\frac{25\,B\,a^2}{4}+6\,C\,a^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(6\,A+7\,B+8\,C\right)}{8\,d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2) + 1)*((3*A)/4 + (7*B)/8 + C))/d - (tan(c/2 + (d*x)/2)^9*((3*A*a^2)/2 + (7*B*a^2)/4 + 2*C*a^2) - tan(c/2 + (d*x)/2)^7*(7*A*a^2 + (49*B*a^2)/6 + (28*C*a^2)/3) - tan(c/2 + (d*x)/2)^3*(9*A*a^2 + (79*B*a^2)/6 + (52*C*a^2)/3) + tan(c/2 + (d*x)/2)^5*((72*A*a^2)/5 + (40*B*a^2)/3 + (56*C*a^2)/3) + tan(c/2 + (d*x)/2)*((13*A*a^2)/2 + (25*B*a^2)/4 + 6*C*a^2))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) - (a^2*log(tan(c/2 + (d*x)/2) - 1)*(6*A + 7*B + 8*C))/(8*d)","B"
318,1,410,265,2.910545,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(\frac{13\,A\,a^3}{4}+\frac{23\,B\,a^3}{8}+\frac{21\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{65\,A\,a^3}{3}+\frac{115\,B\,a^3}{6}+\frac{35\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{3679\,A\,a^3}{60}+\frac{6509\,B\,a^3}{120}+\frac{1981\,C\,a^3}{40}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{464\,A\,a^3}{5}+\frac{432\,B\,a^3}{5}+\frac{2608\,C\,a^3}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{5089\,A\,a^3}{60}+\frac{2993\,B\,a^3}{40}+\frac{3011\,C\,a^3}{40}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{143\,A\,a^3}{3}+\frac{79\,B\,a^3}{2}+\frac{61\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,A\,a^3}{4}+\frac{105\,B\,a^3}{8}+\frac{107\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(26\,A+23\,B+21\,C\right)}{8\,\left(\frac{13\,A\,a^3}{4}+\frac{23\,B\,a^3}{8}+\frac{21\,C\,a^3}{8}\right)}\right)\,\left(26\,A+23\,B+21\,C\right)}{8\,d}-\frac{a^3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(26\,A+23\,B+21\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^13*((13*A*a^3)/4 + (23*B*a^3)/8 + (21*C*a^3)/8) + tan(c/2 + (d*x)/2)^11*((65*A*a^3)/3 + (115*B*a^3)/6 + (35*C*a^3)/2) + tan(c/2 + (d*x)/2)^3*((143*A*a^3)/3 + (79*B*a^3)/2 + (61*C*a^3)/2) + tan(c/2 + (d*x)/2)^7*((464*A*a^3)/5 + (432*B*a^3)/5 + (2608*C*a^3)/35) + tan(c/2 + (d*x)/2)^5*((5089*A*a^3)/60 + (2993*B*a^3)/40 + (3011*C*a^3)/40) + tan(c/2 + (d*x)/2)^9*((3679*A*a^3)/60 + (6509*B*a^3)/120 + (1981*C*a^3)/40) + tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (105*B*a^3)/8 + (107*C*a^3)/8))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(26*A + 23*B + 21*C))/(8*((13*A*a^3)/4 + (23*B*a^3)/8 + (21*C*a^3)/8)))*(26*A + 23*B + 21*C))/(8*d) - (a^3*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(26*A + 23*B + 21*C))/(8*d)","B"
319,1,366,207,2.721815,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(\frac{15\,A\,a^3}{4}+\frac{13\,B\,a^3}{4}+\frac{23\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{85\,A\,a^3}{4}+\frac{221\,B\,a^3}{12}+\frac{391\,C\,a^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{99\,A\,a^3}{2}+\frac{429\,B\,a^3}{10}+\frac{759\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{125\,A\,a^3}{2}+\frac{499\,B\,a^3}{10}+\frac{969\,C\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{171\,A\,a^3}{4}+\frac{419\,B\,a^3}{12}+\frac{211\,C\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{49\,A\,a^3}{4}+\frac{51\,B\,a^3}{4}+\frac{105\,C\,a^3}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(30\,A+26\,B+23\,C\right)}{8\,\left(\frac{15\,A\,a^3}{4}+\frac{13\,B\,a^3}{4}+\frac{23\,C\,a^3}{8}\right)}\right)\,\left(30\,A+26\,B+23\,C\right)}{8\,d}-\frac{a^3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(30\,A+26\,B+23\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*((15*A*a^3)/4 + (13*B*a^3)/4 + (23*C*a^3)/8) + tan(c/2 + (d*x)/2)^9*((85*A*a^3)/4 + (221*B*a^3)/12 + (391*C*a^3)/24) + tan(c/2 + (d*x)/2)^3*((171*A*a^3)/4 + (419*B*a^3)/12 + (211*C*a^3)/8) + tan(c/2 + (d*x)/2)^7*((99*A*a^3)/2 + (429*B*a^3)/10 + (759*C*a^3)/20) + tan(c/2 + (d*x)/2)^5*((125*A*a^3)/2 + (499*B*a^3)/10 + (969*C*a^3)/20) + tan(c/2 + (d*x)/2)*((49*A*a^3)/4 + (51*B*a^3)/4 + (105*C*a^3)/8))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(30*A + 26*B + 23*C))/(8*((15*A*a^3)/4 + (13*B*a^3)/4 + (23*C*a^3)/8)))*(30*A + 26*B + 23*C))/(8*d) - (a^3*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(30*A + 26*B + 23*C))/(8*d)","B"
320,1,322,166,2.655852,"\text{Not used}","int((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(5\,A\,a^3+\frac{15\,B\,a^3}{4}+\frac{13\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{70\,A\,a^3}{3}+\frac{35\,B\,a^3}{2}+\frac{91\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{128\,A\,a^3}{3}+32\,B\,a^3+\frac{416\,C\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{106\,A\,a^3}{3}+\frac{61\,B\,a^3}{2}+\frac{133\,C\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A\,a^3+\frac{49\,B\,a^3}{4}+\frac{51\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^3\,\mathrm{atan}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,A+15\,B+13\,C\right)}{4\,\left(5\,A\,a^3+\frac{15\,B\,a^3}{4}+\frac{13\,C\,a^3}{4}\right)}\right)\,\left(20\,A+15\,B+13\,C\right)}{4\,d}-\frac{a^3\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(20\,A+15\,B+13\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(5*A*a^3 + (15*B*a^3)/4 + (13*C*a^3)/4) + tan(c/2 + (d*x)/2)^7*((70*A*a^3)/3 + (35*B*a^3)/2 + (91*C*a^3)/6) + tan(c/2 + (d*x)/2)^3*((106*A*a^3)/3 + (61*B*a^3)/2 + (133*C*a^3)/6) + tan(c/2 + (d*x)/2)^5*((128*A*a^3)/3 + 32*B*a^3 + (416*C*a^3)/15) + tan(c/2 + (d*x)/2)*(11*A*a^3 + (49*B*a^3)/4 + (51*C*a^3)/4))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(20*A + 15*B + 13*C))/(4*(5*A*a^3 + (15*B*a^3)/4 + (13*C*a^3)/4)))*(20*A + 15*B + 13*C))/(4*d) - (a^3*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(20*A + 15*B + 13*C))/(4*d)","B"
321,1,242,162,1.814941,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{7\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+5\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{15\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12}+C\,a^3\,\sin\left(2\,c+2\,d\,x\right)+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32}+3\,A\,a^3\,\sin\left(c+d\,x\right)+\frac{15\,B\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{13\,C\,a^3\,\sin\left(c+d\,x\right)}{4}}{d}","Not used",1,"(7*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 5*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (15*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (A*a^3*sin(2*c + 2*d*x))/4 + (3*B*a^3*sin(2*c + 2*d*x))/4 + (B*a^3*sin(3*c + 3*d*x))/12 + C*a^3*sin(2*c + 2*d*x) + (C*a^3*sin(3*c + 3*d*x))/4 + (C*a^3*sin(4*c + 4*d*x))/32 + 3*A*a^3*sin(c + d*x) + (15*B*a^3*sin(c + d*x))/4 + (13*C*a^3*sin(c + d*x))/4)/d","B"
322,1,290,156,1.983799,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{6\,A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+7\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+5\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}-B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}+\frac{\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{23\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{3\,C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{24}+A\,a^3\,\sin\left(c+d\,x\right)+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{8}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{8}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(6*A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - A*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i + 7*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + 5*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + ((A*a^3*sin(2*c + 2*d*x))/2 + (3*B*a^3*sin(2*c + 2*d*x))/2 + (B*a^3*sin(3*c + 3*d*x))/8 + (23*C*a^3*sin(2*c + 2*d*x))/12 + (3*C*a^3*sin(3*c + 3*d*x))/8 + (C*a^3*sin(4*c + 4*d*x))/24 + A*a^3*sin(c + d*x) + (B*a^3*sin(c + d*x))/8 + (3*C*a^3*sin(c + d*x))/8)/(d*cos(c + d*x))","B"
323,1,319,175,2.219521,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{2\,\left(A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{7\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+3\,B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+3\,B\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{7\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{3\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{3\,C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{4}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(A*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (7*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 3*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 3*B*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (7*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((3*A*a^3*sin(2*c + 2*d*x))/2 + (B*a^3*sin(2*c + 2*d*x))/2 + (B*a^3*sin(3*c + 3*d*x))/4 + (C*a^3*sin(2*c + 2*d*x))/8 + (3*C*a^3*sin(3*c + 3*d*x))/4 + (C*a^3*sin(4*c + 4*d*x))/16 + (A*a^3*sin(c + d*x))/2 + (B*a^3*sin(c + d*x))/4 + (3*C*a^3*sin(c + d*x))/4)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
324,1,541,169,2.578666,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\frac{\frac{3\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{11\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{5\,A\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{4}-\frac{A\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,15{}\mathrm{i}}{4}+\frac{3\,B\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{B\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,21{}\mathrm{i}}{4}+\frac{9\,C\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{C\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{2}-\frac{A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,5{}\mathrm{i}}{4}+\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,7{}\mathrm{i}}{4}+\frac{3\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{2}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((3*A*a^3*sin(2*c + 2*d*x))/4 + (11*A*a^3*sin(3*c + 3*d*x))/12 + (B*a^3*sin(2*c + 2*d*x))/4 + (3*B*a^3*sin(3*c + 3*d*x))/4 + (C*a^3*sin(2*c + 2*d*x))/4 + (C*a^3*sin(3*c + 3*d*x))/4 + (C*a^3*sin(4*c + 4*d*x))/8 + (5*A*a^3*sin(c + d*x))/4 + (3*B*a^3*sin(c + d*x))/4 + (C*a^3*sin(c + d*x))/4 - (A*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*15i)/4 + (3*B*a^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (B*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*21i)/4 + (9*C*a^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (C*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/2 - (A*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*5i)/4 + (B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*7i)/4 + (3*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/2)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
325,1,636,183,3.023578,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{\frac{3\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}-\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,15{}\mathrm{i}}{8}-\frac{A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,45{}\mathrm{i}}{32}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,21{}\mathrm{i}}{8}+\frac{5\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{15\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{32}+\frac{3\,A\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{13\,B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{3\,B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{11\,B\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{24}+\frac{3\,C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{3\,C\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{23\,A\,a^3\,\sin\left(c+d\,x\right)}{32}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{8}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{8}-\frac{A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,15{}\mathrm{i}}{8}-\frac{A\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)\,15{}\mathrm{i}}{32}-\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,5{}\mathrm{i}}{2}-\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)\,5{}\mathrm{i}}{8}+C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,7{}\mathrm{i}}{2}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)\,7{}\mathrm{i}}{8}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((3*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - (B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*15i)/8 - (A*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*45i)/32 - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*21i)/8 + (5*A*a^3*sin(2*c + 2*d*x))/4 + (15*A*a^3*sin(3*c + 3*d*x))/32 + (3*A*a^3*sin(4*c + 4*d*x))/8 + (13*B*a^3*sin(2*c + 2*d*x))/12 + (3*B*a^3*sin(3*c + 3*d*x))/8 + (11*B*a^3*sin(4*c + 4*d*x))/24 + (3*C*a^3*sin(2*c + 2*d*x))/4 + (C*a^3*sin(3*c + 3*d*x))/8 + (3*C*a^3*sin(4*c + 4*d*x))/8 + (23*A*a^3*sin(c + d*x))/32 + (3*B*a^3*sin(c + d*x))/8 + (C*a^3*sin(c + d*x))/8 - (A*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*15i)/8 - (A*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x)*15i)/32 - (B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*5i)/2 - (B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x)*5i)/8 + C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/4 - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*7i)/2 - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x)*7i)/8)/(d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
326,1,292,212,4.725219,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\frac{a^3\,\mathrm{atanh}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,A+15\,B+20\,C\right)}{2\,\left(\frac{13\,A\,a^3}{2}+\frac{15\,B\,a^3}{2}+10\,C\,a^3\right)}\right)\,\left(13\,A+15\,B+20\,C\right)}{4\,d}-\frac{\left(\frac{13\,A\,a^3}{4}+\frac{15\,B\,a^3}{4}+5\,C\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{91\,A\,a^3}{6}-\frac{35\,B\,a^3}{2}-\frac{70\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,A\,a^3}{15}+32\,B\,a^3+\frac{128\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{133\,A\,a^3}{6}-\frac{61\,B\,a^3}{2}-\frac{106\,C\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{51\,A\,a^3}{4}+\frac{49\,B\,a^3}{4}+11\,C\,a^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^3*atanh((a^3*tan(c/2 + (d*x)/2)*(13*A + 15*B + 20*C))/(2*((13*A*a^3)/2 + (15*B*a^3)/2 + 10*C*a^3)))*(13*A + 15*B + 20*C))/(4*d) - (tan(c/2 + (d*x)/2)^9*((13*A*a^3)/4 + (15*B*a^3)/4 + 5*C*a^3) - tan(c/2 + (d*x)/2)^7*((91*A*a^3)/6 + (35*B*a^3)/2 + (70*C*a^3)/3) - tan(c/2 + (d*x)/2)^3*((133*A*a^3)/6 + (61*B*a^3)/2 + (106*C*a^3)/3) + tan(c/2 + (d*x)/2)^5*((416*A*a^3)/15 + 32*B*a^3 + (128*C*a^3)/3) + tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (49*B*a^3)/4 + 11*C*a^3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
327,1,337,244,4.707224,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^7,x)","\frac{a^3\,\mathrm{atanh}\left(\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,A+26\,B+30\,C\right)}{4\,\left(\frac{23\,A\,a^3}{4}+\frac{13\,B\,a^3}{2}+\frac{15\,C\,a^3}{2}\right)}\right)\,\left(23\,A+26\,B+30\,C\right)}{8\,d}-\frac{\left(\frac{23\,A\,a^3}{8}+\frac{13\,B\,a^3}{4}+\frac{15\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(-\frac{391\,A\,a^3}{24}-\frac{221\,B\,a^3}{12}-\frac{85\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{759\,A\,a^3}{20}+\frac{429\,B\,a^3}{10}+\frac{99\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-\frac{969\,A\,a^3}{20}-\frac{499\,B\,a^3}{10}-\frac{125\,C\,a^3}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{211\,A\,a^3}{8}+\frac{419\,B\,a^3}{12}+\frac{171\,C\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{105\,A\,a^3}{8}-\frac{51\,B\,a^3}{4}-\frac{49\,C\,a^3}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a^3*atanh((a^3*tan(c/2 + (d*x)/2)*(23*A + 26*B + 30*C))/(4*((23*A*a^3)/4 + (13*B*a^3)/2 + (15*C*a^3)/2)))*(23*A + 26*B + 30*C))/(8*d) - (tan(c/2 + (d*x)/2)^11*((23*A*a^3)/8 + (13*B*a^3)/4 + (15*C*a^3)/4) - tan(c/2 + (d*x)/2)^9*((391*A*a^3)/24 + (221*B*a^3)/12 + (85*C*a^3)/4) + tan(c/2 + (d*x)/2)^3*((211*A*a^3)/8 + (419*B*a^3)/12 + (171*C*a^3)/4) + tan(c/2 + (d*x)/2)^7*((759*A*a^3)/20 + (429*B*a^3)/10 + (99*C*a^3)/2) - tan(c/2 + (d*x)/2)^5*((969*A*a^3)/20 + (499*B*a^3)/10 + (125*C*a^3)/2) - tan(c/2 + (d*x)/2)*((105*A*a^3)/8 + (51*B*a^3)/4 + (49*C*a^3)/4))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
328,1,454,304,3.108469,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(\frac{49\,A\,a^4}{8}+\frac{11\,B\,a^4}{2}+\frac{323\,C\,a^4}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+\left(\frac{1127\,A\,a^4}{24}+\frac{253\,B\,a^4}{6}+\frac{7429\,C\,a^4}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{18767\,A\,a^4}{120}+\frac{4213\,B\,a^4}{30}+\frac{123709\,C\,a^4}{960}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{35371\,A\,a^4}{120}+\frac{55583\,B\,a^4}{210}+\frac{1632119\,C\,a^4}{6720}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{40661\,A\,a^4}{120}+\frac{21771\,B\,a^4}{70}+\frac{624003\,C\,a^4}{2240}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{29617\,A\,a^4}{120}+\frac{2201\,B\,a^4}{10}+\frac{68673\,C\,a^4}{320}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{2713\,A\,a^4}{24}+\frac{193\,B\,a^4}{2}+\frac{5033\,C\,a^4}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{207\,A\,a^4}{8}+\frac{53\,B\,a^4}{2}+\frac{1725\,C\,a^4}{64}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(392\,A+352\,B+323\,C\right)}{64\,\left(\frac{49\,A\,a^4}{8}+\frac{11\,B\,a^4}{2}+\frac{323\,C\,a^4}{64}\right)}\right)\,\left(392\,A+352\,B+323\,C\right)}{64\,d}-\frac{a^4\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(392\,A+352\,B+323\,C\right)}{64\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^15*((49*A*a^4)/8 + (11*B*a^4)/2 + (323*C*a^4)/64) + tan(c/2 + (d*x)/2)^3*((2713*A*a^4)/24 + (193*B*a^4)/2 + (5033*C*a^4)/64) + tan(c/2 + (d*x)/2)^13*((1127*A*a^4)/24 + (253*B*a^4)/6 + (7429*C*a^4)/192) + tan(c/2 + (d*x)/2)^5*((29617*A*a^4)/120 + (2201*B*a^4)/10 + (68673*C*a^4)/320) + tan(c/2 + (d*x)/2)^11*((18767*A*a^4)/120 + (4213*B*a^4)/30 + (123709*C*a^4)/960) + tan(c/2 + (d*x)/2)^7*((40661*A*a^4)/120 + (21771*B*a^4)/70 + (624003*C*a^4)/2240) + tan(c/2 + (d*x)/2)^9*((35371*A*a^4)/120 + (55583*B*a^4)/210 + (1632119*C*a^4)/6720) + tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + (53*B*a^4)/2 + (1725*C*a^4)/64))/(d*(8*tan(c/2 + (d*x)/2)^2 + 28*tan(c/2 + (d*x)/2)^4 + 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 + 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(392*A + 352*B + 323*C))/(64*((49*A*a^4)/8 + (11*B*a^4)/2 + (323*C*a^4)/64)))*(392*A + 352*B + 323*C))/(64*d) - (a^4*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(392*A + 352*B + 323*C))/(64*d)","B"
329,1,410,243,2.968869,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(7\,A\,a^4+\frac{49\,B\,a^4}{8}+\frac{11\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{140\,A\,a^4}{3}+\frac{245\,B\,a^4}{6}+\frac{110\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{1981\,A\,a^4}{15}+\frac{13867\,B\,a^4}{120}+\frac{3113\,C\,a^4}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{1024\,A\,a^4}{5}+\frac{896\,B\,a^4}{5}+\frac{5632\,C\,a^4}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{2851\,A\,a^4}{15}+\frac{19157\,B\,a^4}{120}+\frac{1501\,C\,a^4}{10}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{308\,A\,a^4}{3}+\frac{523\,B\,a^4}{6}+70\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{207\,B\,a^4}{8}+\frac{53\,C\,a^4}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(56\,A+49\,B+44\,C\right)}{8\,\left(7\,A\,a^4+\frac{49\,B\,a^4}{8}+\frac{11\,C\,a^4}{2}\right)}\right)\,\left(56\,A+49\,B+44\,C\right)}{8\,d}-\frac{a^4\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(56\,A+49\,B+44\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^13*(7*A*a^4 + (49*B*a^4)/8 + (11*C*a^4)/2) + tan(c/2 + (d*x)/2)^11*((140*A*a^4)/3 + (245*B*a^4)/6 + (110*C*a^4)/3) + tan(c/2 + (d*x)/2)^3*((308*A*a^4)/3 + (523*B*a^4)/6 + 70*C*a^4) + tan(c/2 + (d*x)/2)^7*((1024*A*a^4)/5 + (896*B*a^4)/5 + (5632*C*a^4)/35) + tan(c/2 + (d*x)/2)^9*((1981*A*a^4)/15 + (13867*B*a^4)/120 + (3113*C*a^4)/30) + tan(c/2 + (d*x)/2)^5*((2851*A*a^4)/15 + (19157*B*a^4)/120 + (1501*C*a^4)/10) + tan(c/2 + (d*x)/2)*(25*A*a^4 + (207*B*a^4)/8 + (53*C*a^4)/2))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(56*A + 49*B + 44*C))/(8*(7*A*a^4 + (49*B*a^4)/8 + (11*C*a^4)/2)))*(56*A + 49*B + 44*C))/(8*d) - (a^4*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(56*A + 49*B + 44*C))/(8*d)","B"
330,1,334,200,4.235751,"\text{Not used}","int((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\left(\frac{35\,A\,a^4}{4}+7\,B\,a^4+\frac{49\,C\,a^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{595\,A\,a^4}{12}+\frac{119\,B\,a^4}{3}+\frac{833\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{231\,A\,a^4}{2}+\frac{462\,B\,a^4}{5}+\frac{1617\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{281\,A\,a^4}{2}+\frac{562\,B\,a^4}{5}+\frac{1967\,C\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{1069\,A\,a^4}{12}+\frac{233\,B\,a^4}{3}+\frac{1471\,C\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{93\,A\,a^4}{4}+25\,B\,a^4+\frac{207\,C\,a^4}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{7\,a^4\,\mathrm{atan}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,A+8\,B+7\,C\right)}{8\,\left(\frac{35\,A\,a^4}{4}+7\,B\,a^4+\frac{49\,C\,a^4}{8}\right)}\right)\,\left(10\,A+8\,B+7\,C\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*((35*A*a^4)/4 + 7*B*a^4 + (49*C*a^4)/8) + tan(c/2 + (d*x)/2)^9*((595*A*a^4)/12 + (119*B*a^4)/3 + (833*C*a^4)/24) + tan(c/2 + (d*x)/2)^7*((231*A*a^4)/2 + (462*B*a^4)/5 + (1617*C*a^4)/20) + tan(c/2 + (d*x)/2)^3*((1069*A*a^4)/12 + (233*B*a^4)/3 + (1471*C*a^4)/24) + tan(c/2 + (d*x)/2)^5*((281*A*a^4)/2 + (562*B*a^4)/5 + (1967*C*a^4)/20) + tan(c/2 + (d*x)/2)*((93*A*a^4)/4 + 25*B*a^4 + (207*C*a^4)/8))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (7*a^4*atan((7*a^4*tan(c/2 + (d*x)/2)*(10*A + 8*B + 7*C))/(8*((35*A*a^4)/4 + 7*B*a^4 + (49*C*a^4)/8)))*(10*A + 8*B + 7*C))/(8*d)","B"
331,1,1151,195,2.516084,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\left(10\,A\,a^4+\frac{35\,B\,a^4}{4}+7\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{136\,A\,a^4}{3}+\frac{245\,B\,a^4}{6}+\frac{98\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{236\,A\,a^4}{3}+\frac{224\,B\,a^4}{3}+\frac{896\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{184\,A\,a^4}{3}+\frac{395\,B\,a^4}{6}+\frac{158\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(18\,A\,a^4+\frac{93\,B\,a^4}{4}+25\,C\,a^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{A\,a^4\,\mathrm{atan}\left(\frac{A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)+A\,a^4\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\right)\,1{}\mathrm{i}+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)-A\,a^4\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\right)\,1{}\mathrm{i}}{1920\,A^3\,a^{12}+1225\,A\,B^2\,a^{12}+3080\,A^2\,B\,a^{12}+784\,A\,C^2\,a^{12}+2464\,A^2\,C\,a^{12}+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)+A\,a^4\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\right)-A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)-A\,a^4\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\right)+1960\,A\,B\,C\,a^{12}}\right)\,2{}\mathrm{i}}{d}-\frac{a^4\,\mathrm{atan}\left(\frac{\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)-\frac{a^4\,\left(48\,A+35\,B+28\,C\right)\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(48\,A+35\,B+28\,C\right)}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)+\frac{a^4\,\left(48\,A+35\,B+28\,C\right)\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(48\,A+35\,B+28\,C\right)}{8}}{1920\,A^3\,a^{12}+1225\,A\,B^2\,a^{12}+3080\,A^2\,B\,a^{12}+784\,A\,C^2\,a^{12}+2464\,A^2\,C\,a^{12}+1960\,A\,B\,C\,a^{12}-\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)-\frac{a^4\,\left(48\,A+35\,B+28\,C\right)\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(48\,A+35\,B+28\,C\right)\,1{}\mathrm{i}}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1184\,A^2\,a^8+1680\,A\,B\,a^8+1344\,A\,C\,a^8+\frac{1225\,B^2\,a^8}{2}+980\,B\,C\,a^8+392\,C^2\,a^8\right)+\frac{a^4\,\left(48\,A+35\,B+28\,C\right)\,\left(224\,A\,a^4+140\,B\,a^4+112\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(48\,A+35\,B+28\,C\right)\,1{}\mathrm{i}}{8}}\right)\,\left(48\,A+35\,B+28\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(10*A*a^4 + (35*B*a^4)/4 + 7*C*a^4) + tan(c/2 + (d*x)/2)^7*((136*A*a^4)/3 + (245*B*a^4)/6 + (98*C*a^4)/3) + tan(c/2 + (d*x)/2)^3*((184*A*a^4)/3 + (395*B*a^4)/6 + (158*C*a^4)/3) + tan(c/2 + (d*x)/2)^5*((236*A*a^4)/3 + (224*B*a^4)/3 + (896*C*a^4)/15) + tan(c/2 + (d*x)/2)*(18*A*a^4 + (93*B*a^4)/4 + 25*C*a^4))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (A*a^4*atan((A*a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) + A*a^4*(224*A*a^4 + 140*B*a^4 + 112*C*a^4))*1i + A*a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) - A*a^4*(224*A*a^4 + 140*B*a^4 + 112*C*a^4))*1i)/(1920*A^3*a^12 + 1225*A*B^2*a^12 + 3080*A^2*B*a^12 + 784*A*C^2*a^12 + 2464*A^2*C*a^12 + A*a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) + A*a^4*(224*A*a^4 + 140*B*a^4 + 112*C*a^4)) - A*a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) - A*a^4*(224*A*a^4 + 140*B*a^4 + 112*C*a^4)) + 1960*A*B*C*a^12))*2i)/d - (a^4*atan(((a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) - (a^4*(48*A + 35*B + 28*C)*(224*A*a^4 + 140*B*a^4 + 112*C*a^4)*1i)/8)*(48*A + 35*B + 28*C))/8 + (a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) + (a^4*(48*A + 35*B + 28*C)*(224*A*a^4 + 140*B*a^4 + 112*C*a^4)*1i)/8)*(48*A + 35*B + 28*C))/8)/(1920*A^3*a^12 + 1225*A*B^2*a^12 + 3080*A^2*B*a^12 + 784*A*C^2*a^12 + 2464*A^2*C*a^12 - (a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) - (a^4*(48*A + 35*B + 28*C)*(224*A*a^4 + 140*B*a^4 + 112*C*a^4)*1i)/8)*(48*A + 35*B + 28*C)*1i)/8 + (a^4*(tan(c/2 + (d*x)/2)*(1184*A^2*a^8 + (1225*B^2*a^8)/2 + 392*C^2*a^8 + 1680*A*B*a^8 + 1344*A*C*a^8 + 980*B*C*a^8) + (a^4*(48*A + 35*B + 28*C)*(224*A*a^4 + 140*B*a^4 + 112*C*a^4)*1i)/8)*(48*A + 35*B + 28*C)*1i)/8 + 1960*A*B*C*a^12))*(48*A + 35*B + 28*C))/(4*d)","B"
332,1,1244,196,2.633853,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","-\frac{\left(5\,A\,a^4+10\,B\,a^4+\frac{35\,C\,a^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(8\,A\,a^4+\frac{76\,B\,a^4}{3}+\frac{70\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(8\,B\,a^4-10\,A\,a^4+\frac{21\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-24\,A\,a^4-\frac{76\,B\,a^4}{3}-\frac{58\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-11\,A\,a^4-18\,B\,a^4-\frac{93\,C\,a^4}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^4\,\mathrm{atan}\left(\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)+a^4\,\left(4\,A+B\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\right)\,\left(4\,A+B\right)\,1{}\mathrm{i}+a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)-a^4\,\left(4\,A+B\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\right)\,\left(4\,A+B\right)\,1{}\mathrm{i}}{4160\,A^3\,a^{12}+1920\,B^3\,a^{12}+10720\,A\,B^2\,a^{12}+13200\,A^2\,B\,a^{12}+4900\,A\,C^2\,a^{12}+10080\,A^2\,C\,a^{12}+1225\,B\,C^2\,a^{12}+3080\,B^2\,C\,a^{12}+a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)+a^4\,\left(4\,A+B\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\right)\,\left(4\,A+B\right)-a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)-a^4\,\left(4\,A+B\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\right)\,\left(4\,A+B\right)+14840\,A\,B\,C\,a^{12}}\right)\,\left(4\,A+B\right)\,2{}\mathrm{i}}{d}-\frac{a^4\,\mathrm{atan}\left(\frac{\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)-\frac{a^4\,\left(52\,A+48\,B+35\,C\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(52\,A+48\,B+35\,C\right)}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)+\frac{a^4\,\left(52\,A+48\,B+35\,C\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(52\,A+48\,B+35\,C\right)}{8}}{4160\,A^3\,a^{12}+1920\,B^3\,a^{12}+10720\,A\,B^2\,a^{12}+13200\,A^2\,B\,a^{12}+4900\,A\,C^2\,a^{12}+10080\,A^2\,C\,a^{12}+1225\,B\,C^2\,a^{12}+3080\,B^2\,C\,a^{12}+14840\,A\,B\,C\,a^{12}-\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)-\frac{a^4\,\left(52\,A+48\,B+35\,C\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(52\,A+48\,B+35\,C\right)\,1{}\mathrm{i}}{8}+\frac{a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1864\,A^2\,a^8+2752\,A\,B\,a^8+1820\,A\,C\,a^8+1184\,B^2\,a^8+1680\,B\,C\,a^8+\frac{1225\,C^2\,a^8}{2}\right)+\frac{a^4\,\left(52\,A+48\,B+35\,C\right)\,\left(336\,A\,a^4+224\,B\,a^4+140\,C\,a^4\right)\,1{}\mathrm{i}}{8}\right)\,\left(52\,A+48\,B+35\,C\right)\,1{}\mathrm{i}}{8}}\right)\,\left(52\,A+48\,B+35\,C\right)}{4\,d}","Not used",1,"- (tan(c/2 + (d*x)/2)^5*(8*B*a^4 - 10*A*a^4 + (21*C*a^4)/2) + tan(c/2 + (d*x)/2)^9*(5*A*a^4 + 10*B*a^4 + (35*C*a^4)/4) - tan(c/2 + (d*x)/2)^3*(24*A*a^4 + (76*B*a^4)/3 + (58*C*a^4)/3) + tan(c/2 + (d*x)/2)^7*(8*A*a^4 + (76*B*a^4)/3 + (70*C*a^4)/3) - tan(c/2 + (d*x)/2)*(11*A*a^4 + 18*B*a^4 + (93*C*a^4)/4))/(d*(3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^10 + 1)) - (a^4*atan((a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) + a^4*(4*A + B)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4))*(4*A + B)*1i + a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) - a^4*(4*A + B)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4))*(4*A + B)*1i)/(4160*A^3*a^12 + 1920*B^3*a^12 + 10720*A*B^2*a^12 + 13200*A^2*B*a^12 + 4900*A*C^2*a^12 + 10080*A^2*C*a^12 + 1225*B*C^2*a^12 + 3080*B^2*C*a^12 + a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) + a^4*(4*A + B)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4))*(4*A + B) - a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) - a^4*(4*A + B)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4))*(4*A + B) + 14840*A*B*C*a^12))*(4*A + B)*2i)/d - (a^4*atan(((a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) - (a^4*(52*A + 48*B + 35*C)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4)*1i)/8)*(52*A + 48*B + 35*C))/8 + (a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) + (a^4*(52*A + 48*B + 35*C)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4)*1i)/8)*(52*A + 48*B + 35*C))/8)/(4160*A^3*a^12 + 1920*B^3*a^12 + 10720*A*B^2*a^12 + 13200*A^2*B*a^12 + 4900*A*C^2*a^12 + 10080*A^2*C*a^12 + 1225*B*C^2*a^12 + 3080*B^2*C*a^12 - (a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) - (a^4*(52*A + 48*B + 35*C)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4)*1i)/8)*(52*A + 48*B + 35*C)*1i)/8 + (a^4*(tan(c/2 + (d*x)/2)*(1864*A^2*a^8 + 1184*B^2*a^8 + (1225*C^2*a^8)/2 + 2752*A*B*a^8 + 1820*A*C*a^8 + 1680*B*C*a^8) + (a^4*(52*A + 48*B + 35*C)*(336*A*a^4 + 224*B*a^4 + 140*C*a^4)*1i)/8)*(52*A + 48*B + 35*C)*1i)/8 + 14840*A*B*C*a^12))*(52*A + 48*B + 35*C))/(4*d)","B"
333,1,373,206,2.714511,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{2\,\left(4\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,13{}\mathrm{i}}{2}+\frac{13\,B\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-B\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}+6\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}\right)}{d}+\frac{2\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{5\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{8}+B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{C\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{83\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48}+\frac{C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{48}+\frac{3\,A\,a^4\,\sin\left(c+d\,x\right)}{4}+B\,a^4\,\sin\left(c+d\,x\right)+\frac{41\,C\,a^4\,\sin\left(c+d\,x\right)}{24}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*(4*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (A*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*13i)/2 + (13*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - B*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i + 6*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - C*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i))/d + (2*A*a^4*sin(2*c + 2*d*x) + (A*a^4*sin(3*c + 3*d*x))/4 + (5*B*a^4*sin(2*c + 2*d*x))/8 + B*a^4*sin(3*c + 3*d*x) + (B*a^4*sin(4*c + 4*d*x))/16 + (C*a^4*sin(2*c + 2*d*x))/2 + (83*C*a^4*sin(3*c + 3*d*x))/48 + (C*a^4*sin(4*c + 4*d*x))/4 + (C*a^4*sin(5*c + 5*d*x))/48 + (3*A*a^4*sin(c + d*x))/4 + B*a^4*sin(c + d*x) + (41*C*a^4*sin(c + d*x))/24)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
334,1,625,219,3.198514,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\frac{3\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+5\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{3\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+3\,B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{3\,B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+3\,C\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{33\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{32}+\frac{3\,C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{2}+\frac{3\,C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{32}+6\,A\,a^4\,\sin\left(c+d\,x\right)+3\,B\,a^4\,\sin\left(c+d\,x\right)+\frac{15\,C\,a^4\,\sin\left(c+d\,x\right)}{16}+\frac{9\,A\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+27\,A\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+18\,B\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{117\,B\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{117\,C\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+18\,C\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{3\,A\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+9\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)+6\,B\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)+\frac{39\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{39\,C\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+6\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{3\,d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"(3*A*a^4*sin(2*c + 2*d*x) + 5*A*a^4*sin(3*c + 3*d*x) + (3*B*a^4*sin(2*c + 2*d*x))/2 + 3*B*a^4*sin(3*c + 3*d*x) + (3*B*a^4*sin(4*c + 4*d*x))/8 + 3*C*a^4*sin(2*c + 2*d*x) + (33*C*a^4*sin(3*c + 3*d*x))/32 + (3*C*a^4*sin(4*c + 4*d*x))/2 + (3*C*a^4*sin(5*c + 5*d*x))/32 + 6*A*a^4*sin(c + d*x) + 3*B*a^4*sin(c + d*x) + (15*C*a^4*sin(c + d*x))/16 + (9*A*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 27*A*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 18*B*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (117*B*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (117*C*a^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + 18*C*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (3*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + 9*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) + 6*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) + (39*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (39*C*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + 6*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/(3*d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
335,1,1342,217,2.970045,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{\frac{105\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{32}+\frac{9\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{39\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{7\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{3}+\frac{27\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{32}+\frac{5\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{6}+\frac{11\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{6}+\frac{B\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{5\,B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{6}+C\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{5\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{2}+\frac{C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{16}+\frac{3\,B\,a^4\,\mathrm{atan}\left(\frac{1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1225\,A^2+3360\,A\,B+3640\,A\,C+2368\,B^2+5504\,B\,C+3728\,C^2\right)}\right)}{4}+3\,C\,a^4\,\mathrm{atan}\left(\frac{1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1225\,A^2+3360\,A\,B+3640\,A\,C+2368\,B^2+5504\,B\,C+3728\,C^2\right)}\right)+\frac{35\,A\,a^4\,\sin\left(c+d\,x\right)}{32}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{2}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{4}+B\,a^4\,\mathrm{atan}\left(\frac{1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1225\,A^2+3360\,A\,B+3640\,A\,C+2368\,B^2+5504\,B\,C+3728\,C^2\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{B\,a^4\,\mathrm{atan}\left(\frac{1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1225\,A^2+3360\,A\,B+3640\,A\,C+2368\,B^2+5504\,B\,C+3728\,C^2\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}+4\,C\,a^4\,\mathrm{atan}\left(\frac{1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1225\,A^2+3360\,A\,B+3640\,A\,C+2368\,B^2+5504\,B\,C+3728\,C^2\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+C\,a^4\,\mathrm{atan}\left(\frac{1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+3640\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+5504\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+3728\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1225\,A^2+3360\,A\,B+3640\,A\,C+2368\,B^2+5504\,B\,C+3728\,C^2\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+\frac{35\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{8}+\frac{35\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{32}+6\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{3\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{2}+\frac{13\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{13\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((105*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/32 + (9*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (39*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (7*A*a^4*sin(2*c + 2*d*x))/3 + (27*A*a^4*sin(3*c + 3*d*x))/32 + (5*A*a^4*sin(4*c + 4*d*x))/6 + (11*B*a^4*sin(2*c + 2*d*x))/6 + (B*a^4*sin(3*c + 3*d*x))/2 + (5*B*a^4*sin(4*c + 4*d*x))/6 + C*a^4*sin(2*c + 2*d*x) + (5*C*a^4*sin(3*c + 3*d*x))/16 + (C*a^4*sin(4*c + 4*d*x))/2 + (C*a^4*sin(5*c + 5*d*x))/16 + (3*B*a^4*atan((1225*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 3728*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 5504*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(1225*A^2 + 2368*B^2 + 3728*C^2 + 3360*A*B + 3640*A*C + 5504*B*C))))/4 + 3*C*a^4*atan((1225*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 3728*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 5504*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(1225*A^2 + 2368*B^2 + 3728*C^2 + 3360*A*B + 3640*A*C + 5504*B*C))) + (35*A*a^4*sin(c + d*x))/32 + (B*a^4*sin(c + d*x))/2 + (C*a^4*sin(c + d*x))/4 + B*a^4*atan((1225*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 3728*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 5504*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(1225*A^2 + 2368*B^2 + 3728*C^2 + 3360*A*B + 3640*A*C + 5504*B*C)))*cos(2*c + 2*d*x) + (B*a^4*atan((1225*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 3728*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 5504*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(1225*A^2 + 2368*B^2 + 3728*C^2 + 3360*A*B + 3640*A*C + 5504*B*C)))*cos(4*c + 4*d*x))/4 + 4*C*a^4*atan((1225*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 3728*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 5504*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(1225*A^2 + 2368*B^2 + 3728*C^2 + 3360*A*B + 3640*A*C + 5504*B*C)))*cos(2*c + 2*d*x) + C*a^4*atan((1225*A^2*sin(c/2 + (d*x)/2) + 2368*B^2*sin(c/2 + (d*x)/2) + 3728*C^2*sin(c/2 + (d*x)/2) + 3360*A*B*sin(c/2 + (d*x)/2) + 3640*A*C*sin(c/2 + (d*x)/2) + 5504*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(1225*A^2 + 2368*B^2 + 3728*C^2 + 3360*A*B + 3640*A*C + 5504*B*C)))*cos(4*c + 4*d*x) + (35*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/8 + (35*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/32 + 6*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (3*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/2 + (13*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (13*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8)/(d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
336,1,995,225,2.795502,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\frac{\frac{11\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{77\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{48}+\frac{7\,A\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{83\,A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{240}+\frac{31\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{32}+\frac{19\,B\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{12}+\frac{27\,B\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{64}+\frac{5\,B\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{12}+\frac{C\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{4\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{3}+\frac{C\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{5\,C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{12}+\frac{35\,A\,a^4\,\sin\left(c+d\,x\right)}{24}+\frac{7\,B\,a^4\,\sin\left(c+d\,x\right)}{6}+\frac{11\,C\,a^4\,\sin\left(c+d\,x\right)}{12}+\frac{5\,C\,a^4\,\mathrm{atan}\left(\frac{784\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+1960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+2688\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(784\,A^2+1960\,A\,B+2688\,A\,C+1225\,B^2+3360\,B\,C+2368\,C^2\right)}\right)\,\cos\left(c+d\,x\right)}{4}+\frac{5\,C\,a^4\,\mathrm{atan}\left(\frac{784\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+1960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+2688\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(784\,A^2+1960\,A\,B+2688\,A\,C+1225\,B^2+3360\,B\,C+2368\,C^2\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{8}+\frac{C\,a^4\,\mathrm{atan}\left(\frac{784\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2+1960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B+2688\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C+1225\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2+3360\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(784\,A^2+1960\,A\,B+2688\,A\,C+1225\,B^2+3360\,B\,C+2368\,C^2\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{8}+\frac{35\,A\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{175\,B\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{32}+\frac{15\,C\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{35\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{7\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{16}+\frac{175\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{64}+\frac{35\,B\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{64}+\frac{15\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{4}}{d\,\left(\frac{5\,\cos\left(c+d\,x\right)}{8}+\frac{5\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{\cos\left(5\,c+5\,d\,x\right)}{16}\right)}","Not used",1,"((11*A*a^4*sin(2*c + 2*d*x))/8 + (77*A*a^4*sin(3*c + 3*d*x))/48 + (7*A*a^4*sin(4*c + 4*d*x))/16 + (83*A*a^4*sin(5*c + 5*d*x))/240 + (31*B*a^4*sin(2*c + 2*d*x))/32 + (19*B*a^4*sin(3*c + 3*d*x))/12 + (27*B*a^4*sin(4*c + 4*d*x))/64 + (5*B*a^4*sin(5*c + 5*d*x))/12 + (C*a^4*sin(2*c + 2*d*x))/2 + (4*C*a^4*sin(3*c + 3*d*x))/3 + (C*a^4*sin(4*c + 4*d*x))/4 + (5*C*a^4*sin(5*c + 5*d*x))/12 + (35*A*a^4*sin(c + d*x))/24 + (7*B*a^4*sin(c + d*x))/6 + (11*C*a^4*sin(c + d*x))/12 + (5*C*a^4*atan((784*A^2*sin(c/2 + (d*x)/2) + 1225*B^2*sin(c/2 + (d*x)/2) + 2368*C^2*sin(c/2 + (d*x)/2) + 1960*A*B*sin(c/2 + (d*x)/2) + 2688*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(784*A^2 + 1225*B^2 + 2368*C^2 + 1960*A*B + 2688*A*C + 3360*B*C)))*cos(c + d*x))/4 + (5*C*a^4*atan((784*A^2*sin(c/2 + (d*x)/2) + 1225*B^2*sin(c/2 + (d*x)/2) + 2368*C^2*sin(c/2 + (d*x)/2) + 1960*A*B*sin(c/2 + (d*x)/2) + 2688*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(784*A^2 + 1225*B^2 + 2368*C^2 + 1960*A*B + 2688*A*C + 3360*B*C)))*cos(3*c + 3*d*x))/8 + (C*a^4*atan((784*A^2*sin(c/2 + (d*x)/2) + 1225*B^2*sin(c/2 + (d*x)/2) + 2368*C^2*sin(c/2 + (d*x)/2) + 1960*A*B*sin(c/2 + (d*x)/2) + 2688*A*C*sin(c/2 + (d*x)/2) + 3360*B*C*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(784*A^2 + 1225*B^2 + 2368*C^2 + 1960*A*B + 2688*A*C + 3360*B*C)))*cos(5*c + 5*d*x))/8 + (35*A*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (175*B*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/32 + (15*C*a^4*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (35*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/16 + (7*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/16 + (175*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/64 + (35*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/64 + (15*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (3*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/4)/(d*((5*cos(c + d*x))/8 + (5*cos(3*c + 3*d*x))/16 + cos(5*c + 5*d*x)/16))","B"
337,1,338,253,4.709467,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^7,x)","\frac{7\,a^4\,\mathrm{atanh}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,A+8\,B+10\,C\right)}{4\,\left(\frac{49\,A\,a^4}{4}+14\,B\,a^4+\frac{35\,C\,a^4}{2}\right)}\right)\,\left(7\,A+8\,B+10\,C\right)}{8\,d}-\frac{\left(\frac{49\,A\,a^4}{8}+7\,B\,a^4+\frac{35\,C\,a^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(-\frac{833\,A\,a^4}{24}-\frac{119\,B\,a^4}{3}-\frac{595\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{1617\,A\,a^4}{20}+\frac{462\,B\,a^4}{5}+\frac{231\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-\frac{1967\,A\,a^4}{20}-\frac{562\,B\,a^4}{5}-\frac{281\,C\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{1471\,A\,a^4}{24}+\frac{233\,B\,a^4}{3}+\frac{1069\,C\,a^4}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{207\,A\,a^4}{8}-25\,B\,a^4-\frac{93\,C\,a^4}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(7*a^4*atanh((7*a^4*tan(c/2 + (d*x)/2)*(7*A + 8*B + 10*C))/(4*((49*A*a^4)/4 + 14*B*a^4 + (35*C*a^4)/2)))*(7*A + 8*B + 10*C))/(8*d) - (tan(c/2 + (d*x)/2)^11*((49*A*a^4)/8 + 7*B*a^4 + (35*C*a^4)/4) - tan(c/2 + (d*x)/2)^9*((833*A*a^4)/24 + (119*B*a^4)/3 + (595*C*a^4)/12) + tan(c/2 + (d*x)/2)^7*((1617*A*a^4)/20 + (462*B*a^4)/5 + (231*C*a^4)/2) + tan(c/2 + (d*x)/2)^3*((1471*A*a^4)/24 + (233*B*a^4)/3 + (1069*C*a^4)/12) - tan(c/2 + (d*x)/2)^5*((1967*A*a^4)/20 + (562*B*a^4)/5 + (281*C*a^4)/2) - tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + 25*B*a^4 + (93*C*a^4)/4))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
338,1,381,287,4.774397,"\text{Not used}","int(((a + a*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^8,x)","\frac{a^4\,\mathrm{atanh}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(44\,A+49\,B+56\,C\right)}{4\,\left(11\,A\,a^4+\frac{49\,B\,a^4}{4}+14\,C\,a^4\right)}\right)\,\left(44\,A+49\,B+56\,C\right)}{8\,d}-\frac{\left(\frac{11\,A\,a^4}{2}+\frac{49\,B\,a^4}{8}+7\,C\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(-\frac{110\,A\,a^4}{3}-\frac{245\,B\,a^4}{6}-\frac{140\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{3113\,A\,a^4}{30}+\frac{13867\,B\,a^4}{120}+\frac{1981\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{5632\,A\,a^4}{35}-\frac{896\,B\,a^4}{5}-\frac{1024\,C\,a^4}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{1501\,A\,a^4}{10}+\frac{19157\,B\,a^4}{120}+\frac{2851\,C\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-70\,A\,a^4-\frac{523\,B\,a^4}{6}-\frac{308\,C\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{53\,A\,a^4}{2}+\frac{207\,B\,a^4}{8}+25\,C\,a^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a^4*atanh((a^4*tan(c/2 + (d*x)/2)*(44*A + 49*B + 56*C))/(4*(11*A*a^4 + (49*B*a^4)/4 + 14*C*a^4)))*(44*A + 49*B + 56*C))/(8*d) - (tan(c/2 + (d*x)/2)^13*((11*A*a^4)/2 + (49*B*a^4)/8 + 7*C*a^4) - tan(c/2 + (d*x)/2)^11*((110*A*a^4)/3 + (245*B*a^4)/6 + (140*C*a^4)/3) - tan(c/2 + (d*x)/2)^3*(70*A*a^4 + (523*B*a^4)/6 + (308*C*a^4)/3) - tan(c/2 + (d*x)/2)^7*((5632*A*a^4)/35 + (896*B*a^4)/5 + (1024*C*a^4)/5) + tan(c/2 + (d*x)/2)^9*((3113*A*a^4)/30 + (13867*B*a^4)/120 + (1981*C*a^4)/15) + tan(c/2 + (d*x)/2)^5*((1501*A*a^4)/10 + (19157*B*a^4)/120 + (2851*C*a^4)/15) + tan(c/2 + (d*x)/2)*((53*A*a^4)/2 + (207*B*a^4)/8 + 25*C*a^4))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
339,1,189,174,3.025760,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{3\,x\,\left(4\,A-4\,B+5\,C\right)}{8\,a}-\frac{\left(3\,A-5\,B+\frac{25\,C}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(7\,A-\frac{31\,B}{3}+\frac{115\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(5\,A-\frac{25\,B}{3}+\frac{109\,C}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A-3\,B+\frac{7\,C}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}","Not used",1,"(3*x*(4*A - 4*B + 5*C))/(8*a) - (tan(c/2 + (d*x)/2)*(A - 3*B + (7*C)/4) + tan(c/2 + (d*x)/2)^7*(3*A - 5*B + (25*C)/4) + tan(c/2 + (d*x)/2)^3*(5*A - (25*B)/3 + (109*C)/12) + tan(c/2 + (d*x)/2)^5*(7*A - (31*B)/3 + (115*C)/12))/(d*(a + 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 + 4*a*tan(c/2 + (d*x)/2)^6 + a*tan(c/2 + (d*x)/2)^8)) - (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d)","B"
340,1,153,139,2.531519,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{\left(2\,A-3\,B+5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A-4\,B+\frac{16\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-B+3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{x\,\left(2\,A-3\,B+3\,C\right)}{2\,a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A - B + 3*C) + tan(c/2 + (d*x)/2)^5*(2*A - 3*B + 5*C) + tan(c/2 + (d*x)/2)^3*(4*A - 4*B + (16*C)/3))/(d*(a + 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 + a*tan(c/2 + (d*x)/2)^6)) - (x*(2*A - 3*B + 3*C))/(2*a) + (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d)","B"
341,1,112,110,1.472901,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\frac{\left(2\,B-3\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B-C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}+\frac{x\,\left(2\,A-2\,B+3\,C\right)}{2\,a}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(2*B - 3*C) + tan(c/2 + (d*x)/2)*(2*B - C))/(d*(a + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) + (x*(2*A - 2*B + 3*C))/(2*a) - (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d)","B"
342,1,65,54,1.165879,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x)),x)","\frac{x\,\left(B-C\right)}{a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(x*(B - C))/a + (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) + (2*C*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2))","B"
343,1,113,51,1.215749,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))),x)","\frac{2\,A\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(2*A*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) - (A*sin(c/2 + (d*x)/2) - B*sin(c/2 + (d*x)/2) + C*sin(c/2 + (d*x)/2))/(a*d*cos(c/2 + (d*x)/2))","B"
344,1,79,71,1.187480,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}+\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A-B\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) + (2*A*tan(c/2 + (d*x)/2))/(d*(a - a*tan(c/2 + (d*x)/2)^2)) - (2*atanh(tan(c/2 + (d*x)/2))*(A - B))/(a*d)","B"
345,1,143,117,1.346797,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A-2\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-2\,B\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}+\frac{2\,\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A}{2}-B+C\right)}{3\,A-2\,B+2\,C}\right)\,\left(\frac{3\,A}{2}-B+C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(3*A - 2*B) - tan(c/2 + (d*x)/2)*(A - 2*B))/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) - (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) + (2*atanh((2*tan(c/2 + (d*x)/2)*((3*A)/2 - B + C))/(3*A - 2*B + 2*C))*((3*A)/2 - B + C))/(a*d)","B"
346,1,187,148,1.768975,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))),x)","\frac{\left(5\,A-3\,B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,B-\frac{16\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A-B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B+C\right)}{a\,d}-\frac{2\,\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A}{2}-\frac{3\,B}{2}+C\right)}{3\,A-3\,B+2\,C}\right)\,\left(\frac{3\,A}{2}-\frac{3\,B}{2}+C\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A - B + 2*C) + tan(c/2 + (d*x)/2)^5*(5*A - 3*B + 2*C) - tan(c/2 + (d*x)/2)^3*((16*A)/3 - 4*B + 4*C))/(d*(a - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6)) + (tan(c/2 + (d*x)/2)*(A - B + C))/(a*d) - (2*atanh((2*tan(c/2 + (d*x)/2)*((3*A)/2 - (3*B)/2 + C))/(3*A - 3*B + 2*C))*((3*A)/2 - (3*B)/2 + C))/(a*d)","B"
347,1,202,185,1.288330,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{\left(2\,A-5\,B+10\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A-8\,B+\frac{40\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-3\,B+6\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{x\,\left(4\,A-7\,B+10\,C\right)}{2\,a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-3\,B+5\,C}{2\,a^2}+\frac{2\,\left(A-B+C\right)}{a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A - 3*B + 6*C) + tan(c/2 + (d*x)/2)^5*(2*A - 5*B + 10*C) + tan(c/2 + (d*x)/2)^3*(4*A - 8*B + (40*C)/3))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 + 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 + a^2)) - (x*(4*A - 7*B + 10*C))/(2*a^2) + (tan(c/2 + (d*x)/2)*((A - 3*B + 5*C)/(2*a^2) + (2*(A - B + C))/a^2))/d - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
348,1,158,160,1.262862,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{\left(2\,B-5\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B-3\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B+C\right)}{2\,a^2}-\frac{2\,B-4\,C}{2\,a^2}\right)}{d}+\frac{x\,\left(2\,A-4\,B+7\,C\right)}{2\,a^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(2*B - 5*C) + tan(c/2 + (d*x)/2)*(2*B - 3*C))/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 + a^2*tan(c/2 + (d*x)/2)^4 + a^2)) - (tan(c/2 + (d*x)/2)*((3*(A - B + C))/(2*a^2) - (2*B - 4*C)/(2*a^2)))/d + (x*(2*A - 4*B + 7*C))/(2*a^2) + (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
349,1,107,103,1.205734,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{a^2}-\frac{A+B-3\,C}{2\,a^2}\right)}{d}+\frac{x\,\left(B-2\,C\right)}{a^2}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A - B + C)/a^2 - (A + B - 3*C)/(2*a^2)))/d + (x*(B - 2*C))/a^2 + (2*C*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
350,1,113,72,1.296385,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^2,x)","\frac{\frac{3\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{A\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}+B\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)-\frac{3\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}-\frac{5\,C\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{2}+\frac{9\,C\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(c+d\,x\right)}{2}+\frac{3\,C\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(c+d\,x\right)}{2}}{6\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"((3*A*sin(c/2 + (d*x)/2))/2 + (A*sin((3*c)/2 + (3*d*x)/2))/2 + B*sin((3*c)/2 + (3*d*x)/2) - (3*C*sin(c/2 + (d*x)/2))/2 - (5*C*sin((3*c)/2 + (3*d*x)/2))/2 + (9*C*cos(c/2 + (d*x)/2)*(c + d*x))/2 + (3*C*cos((3*c)/2 + (3*d*x)/2)*(c + d*x))/2)/(6*a^2*d*cos(c/2 + (d*x)/2)^3)","B"
351,1,83,83,1.170033,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^2),x)","\frac{2\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{2\,a^2}+\frac{2\,A-2\,C}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)*((A - B + C)/(2*a^2) + (2*A - 2*C)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
352,1,124,109,1.222060,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{a^2}-\frac{B-3\,A+C}{2\,a^2}\right)}{d}-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,A-B\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((A - B + C)/a^2 - (B - 3*A + C)/(2*a^2)))/d - (2*A*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2)) + (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d) - (2*atanh(tan(c/2 + (d*x)/2))*(2*A - B))/(a^2*d)","B"
353,1,191,165,1.238784,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,A-2\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A-2\,B\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B+C\right)}{2\,a^2}+\frac{4\,A-2\,B}{2\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}+\frac{2\,\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7\,A}{2}-2\,B+C\right)}{7\,A-4\,B+2\,C}\right)\,\left(\frac{7\,A}{2}-2\,B+C\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(5*A - 2*B) - tan(c/2 + (d*x)/2)*(3*A - 2*B))/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (tan(c/2 + (d*x)/2)*((3*(A - B + C))/(2*a^2) + (4*A - 2*B)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d) + (2*atanh((2*tan(c/2 + (d*x)/2)*((7*A)/2 - 2*B + C))/(7*A - 4*B + 2*C))*((7*A)/2 - 2*B + C))/(a^2*d)","B"
354,1,218,194,1.291257,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^2),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,A-3\,B+C}{2\,a^2}+\frac{2\,\left(A-B+C\right)}{a^2}\right)}{d}-\frac{\left(10\,A-5\,B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,B-\frac{40\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A-3\,B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(10\,A-7\,B+4\,C\right)}{a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B+C\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A - 3*B + C)/(2*a^2) + (2*(A - B + C))/a^2))/d - (tan(c/2 + (d*x)/2)*(6*A - 3*B + 2*C) + tan(c/2 + (d*x)/2)^5*(10*A - 5*B + 2*C) - tan(c/2 + (d*x)/2)^3*((40*A)/3 - 8*B + 4*C))/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 - 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 - a^2)) - (atanh(tan(c/2 + (d*x)/2))*(10*A - 7*B + 4*C))/(a^2*d) + (tan(c/2 + (d*x)/2)^3*(A - B + C))/(6*a^2*d)","B"
355,1,259,237,1.277534,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{\left(2\,A-7\,B+17\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A-12\,B+\frac{76\,C}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-5\,B+11\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,A-4\,B+6\,C}{a^3}-\frac{A+5\,B-15\,C}{4\,a^3}+\frac{5\,\left(A-B+C\right)}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,A-4\,B+6\,C}{12\,a^3}+\frac{A-B+C}{3\,a^3}\right)}{d}-\frac{x\,\left(6\,A-13\,B+23\,C\right)}{2\,a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A - 5*B + 11*C) + tan(c/2 + (d*x)/2)^5*(2*A - 7*B + 17*C) + tan(c/2 + (d*x)/2)^3*(4*A - 12*B + (76*C)/3))/(d*(3*a^3*tan(c/2 + (d*x)/2)^2 + 3*a^3*tan(c/2 + (d*x)/2)^4 + a^3*tan(c/2 + (d*x)/2)^6 + a^3)) + (tan(c/2 + (d*x)/2)*((2*A - 4*B + 6*C)/a^3 - (A + 5*B - 15*C)/(4*a^3) + (5*(A - B + C))/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((2*A - 4*B + 6*C)/(12*a^3) + (A - B + C)/(3*a^3)))/d - (x*(6*A - 13*B + 23*C))/(2*a^3) + (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
356,1,214,207,1.228363,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-3\,B+5\,C}{12\,a^3}+\frac{A-B+C}{4\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-3\,B+5\,C\right)}{4\,a^3}-\frac{2\,A+2\,B-10\,C}{4\,a^3}+\frac{3\,\left(A-B+C\right)}{2\,a^3}\right)}{d}+\frac{\left(2\,B-7\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B-5\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{x\,\left(2\,A-6\,B+13\,C\right)}{2\,a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A - 3*B + 5*C)/(12*a^3) + (A - B + C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)*((3*(A - 3*B + 5*C))/(4*a^3) - (2*A + 2*B - 10*C)/(4*a^3) + (3*(A - B + C))/(2*a^3)))/d + (tan(c/2 + (d*x)/2)^3*(2*B - 7*C) + tan(c/2 + (d*x)/2)*(2*B - 5*C))/(d*(2*a^3*tan(c/2 + (d*x)/2)^2 + a^3*tan(c/2 + (d*x)/2)^4 + a^3)) + (x*(2*A - 6*B + 13*C))/(2*a^3) - (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
357,1,162,152,1.237389,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{x\,\left(B-3\,C\right)}{a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,A-6\,C}{4\,a^3}-\frac{3\,\left(A-B+C\right)}{4\,a^3}+\frac{2\,B-4\,C}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B+C}{6\,a^3}-\frac{2\,B-4\,C}{12\,a^3}\right)}{d}+\frac{2\,C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(x*(B - 3*C))/a^3 - (tan(c/2 + (d*x)/2)*((2*A - 6*C)/(4*a^3) - (3*(A - B + C))/(4*a^3) + (2*B - 4*C)/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((A - B + C)/(6*a^3) - (2*B - 4*C)/(12*a^3)))/d + (2*C*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 + a^3)) + (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
358,1,160,123,1.395911,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\frac{C\,x}{a^3}-\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}-\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}+\frac{B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}-\frac{7\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}\right)+\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(C*x)/a^3 - (cos(c/2 + (d*x)/2)^2*((B*sin(c/2 + (d*x)/2)^3)/6 - (C*sin(c/2 + (d*x)/2)^3)/3) - cos(c/2 + (d*x)/2)^4*((A*sin(c/2 + (d*x)/2))/4 + (B*sin(c/2 + (d*x)/2))/4 - (7*C*sin(c/2 + (d*x)/2))/4) + (A*sin(c/2 + (d*x)/2)^5)/20 - (B*sin(c/2 + (d*x)/2)^5)/20 + (C*sin(c/2 + (d*x)/2)^5)/20)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
359,1,73,109,1.206956,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A-2\,C\right)}{12\,a^3\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B+C\right)}{4\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d) + (tan(c/2 + (d*x)/2)^3*(2*A - 2*C))/(12*a^3*d) + (tan(c/2 + (d*x)/2)*(A + B + C))/(4*a^3*d)","B"
360,1,134,124,1.225233,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^3),x)","\frac{2\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B+C}{12\,a^3}-\frac{B-3\,A+C}{12\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A+B-C}{4\,a^3}+\frac{A-B+C}{4\,a^3}-\frac{B-3\,A+C}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (tan(c/2 + (d*x)/2)^3*((A - B + C)/(12*a^3) - (B - 3*A + C)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)*((3*A + B - C)/(4*a^3) + (A - B + C)/(4*a^3) - (B - 3*A + C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
361,1,177,150,1.216074,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B+C}{6\,a^3}+\frac{4\,A-2\,B}{12\,a^3}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B+C\right)}{4\,a^3}+\frac{4\,A-2\,B}{2\,a^3}+\frac{6\,A-2\,C}{4\,a^3}\right)}{d}-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,A-B\right)}{a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A - B + C)/(6*a^3) + (4*A - 2*B)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)*((3*(A - B + C))/(4*a^3) + (4*A - 2*B)/(2*a^3) + (6*A - 2*C)/(4*a^3)))/d - (2*A*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3)) + (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d) - (2*atanh(tan(c/2 + (d*x)/2))*(3*A - B))/(a^3*d)","B"
362,1,248,210,1.209853,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,A-2\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A-2\,B\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(5\,A-3\,B+C\right)}{4\,a^3}-\frac{2\,B-10\,A+2\,C}{4\,a^3}+\frac{3\,\left(A-B+C\right)}{2\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,A-3\,B+C}{12\,a^3}+\frac{A-B+C}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}+\frac{2\,\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{13\,A}{2}-3\,B+C\right)}{13\,A-6\,B+2\,C}\right)\,\left(\frac{13\,A}{2}-3\,B+C\right)}{a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(7*A - 2*B) - tan(c/2 + (d*x)/2)*(5*A - 2*B))/(d*(a^3*tan(c/2 + (d*x)/2)^4 - 2*a^3*tan(c/2 + (d*x)/2)^2 + a^3)) - (tan(c/2 + (d*x)/2)*((3*(5*A - 3*B + C))/(4*a^3) - (2*B - 10*A + 2*C)/(4*a^3) + (3*(A - B + C))/(2*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((5*A - 3*B + C)/(12*a^3) + (A - B + C)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d) + (2*atanh((2*tan(c/2 + (d*x)/2)*((13*A)/2 - 3*B + C))/(13*A - 6*B + 2*C))*((13*A)/2 - 3*B + C))/(a^3*d)","B"
363,1,274,246,1.223581,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{6\,A-4\,B+2\,C}{a^3}-\frac{5\,B-15\,A+C}{4\,a^3}+\frac{5\,\left(A-B+C\right)}{2\,a^3}\right)}{d}-\frac{\left(17\,A-7\,B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(12\,B-\frac{76\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(11\,A-5\,B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{6\,A-4\,B+2\,C}{12\,a^3}+\frac{A-B+C}{3\,a^3}\right)}{d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(23\,A-13\,B+6\,C\right)}{a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B+C\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((6*A - 4*B + 2*C)/a^3 - (5*B - 15*A + C)/(4*a^3) + (5*(A - B + C))/(2*a^3)))/d - (tan(c/2 + (d*x)/2)*(11*A - 5*B + 2*C) + tan(c/2 + (d*x)/2)^5*(17*A - 7*B + 2*C) - tan(c/2 + (d*x)/2)^3*((76*A)/3 - 12*B + 4*C))/(d*(3*a^3*tan(c/2 + (d*x)/2)^2 - 3*a^3*tan(c/2 + (d*x)/2)^4 + a^3*tan(c/2 + (d*x)/2)^6 - a^3)) + (tan(c/2 + (d*x)/2)^3*((6*A - 4*B + 2*C)/(12*a^3) + (A - B + C)/(3*a^3)))/d - (atanh(tan(c/2 + (d*x)/2))*(23*A - 13*B + 6*C))/(a^3*d) + (tan(c/2 + (d*x)/2)^5*(A - B + C))/(20*a^3*d)","B"
364,1,283,245,1.213822,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A+5\,B-15\,C\right)}{8\,a^4}-\frac{3\,\left(2\,A-4\,B+6\,C\right)}{4\,a^4}-\frac{5\,\left(A-B+C\right)}{4\,a^4}+\frac{4\,A-20\,C}{8\,a^4}\right)}{d}+\frac{\left(2\,B-9\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B-7\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{2\,A-4\,B+6\,C}{40\,a^4}+\frac{3\,\left(A-B+C\right)}{40\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,A-4\,B+6\,C}{8\,a^4}-\frac{A+5\,B-15\,C}{24\,a^4}+\frac{A-B+C}{4\,a^4}\right)}{d}+\frac{x\,\left(2\,A-8\,B+21\,C\right)}{2\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(A + 5*B - 15*C))/(8*a^4) - (3*(2*A - 4*B + 6*C))/(4*a^4) - (5*(A - B + C))/(4*a^4) + (4*A - 20*C)/(8*a^4)))/d + (tan(c/2 + (d*x)/2)^3*(2*B - 9*C) + tan(c/2 + (d*x)/2)*(2*B - 7*C))/(d*(2*a^4*tan(c/2 + (d*x)/2)^2 + a^4*tan(c/2 + (d*x)/2)^4 + a^4)) - (tan(c/2 + (d*x)/2)^5*((2*A - 4*B + 6*C)/(40*a^4) + (3*(A - B + C))/(40*a^4)))/d + (tan(c/2 + (d*x)/2)^3*((2*A - 4*B + 6*C)/(8*a^4) - (A + 5*B - 15*C)/(24*a^4) + (A - B + C)/(4*a^4)))/d + (x*(2*A - 8*B + 21*C))/(2*a^4) + (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d)","B"
365,1,248,195,1.368788,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","\frac{B\,d\,x-4\,C\,d\,x}{a^4\,d}+\frac{\left(\frac{12\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}-\frac{52\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}+\frac{764\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{16\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}-\frac{23\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{70}-\frac{143\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{9\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{70}-\frac{5\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{28}+\frac{8\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{35}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}+\frac{B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}-\frac{C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{56}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}+\frac{2\,C\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4\,d}","Not used",1,"(B*d*x - 4*C*d*x)/(a^4*d) + (cos(c/2 + (d*x)/2)^2*((9*A*sin(c/2 + (d*x)/2))/70 - (5*B*sin(c/2 + (d*x)/2))/28 + (8*C*sin(c/2 + (d*x)/2))/35) - cos(c/2 + (d*x)/2)^4*((23*A*sin(c/2 + (d*x)/2))/70 - (16*B*sin(c/2 + (d*x)/2))/21 + (143*C*sin(c/2 + (d*x)/2))/105) + cos(c/2 + (d*x)/2)^6*((12*A*sin(c/2 + (d*x)/2))/35 - (52*B*sin(c/2 + (d*x)/2))/21 + (764*C*sin(c/2 + (d*x)/2))/105) - (A*sin(c/2 + (d*x)/2))/56 + (B*sin(c/2 + (d*x)/2))/56 - (C*sin(c/2 + (d*x)/2))/56)/(a^4*d*cos(c/2 + (d*x)/2)^7) + (2*C*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^4*d)","B"
366,1,229,164,1.614290,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","\frac{C\,x}{a^4}+\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}-\frac{15\,C\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}-\frac{11\,C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}-\frac{3\,B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8}\right)+\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56}-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56}+\frac{C\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(C*x)/a^4 + (cos(c/2 + (d*x)/2)^6*((A*sin(c/2 + (d*x)/2))/8 + (B*sin(c/2 + (d*x)/2))/8 - (15*C*sin(c/2 + (d*x)/2))/8) - cos(c/2 + (d*x)/2)^4*((A*sin(c/2 + (d*x)/2)^3)/24 + (B*sin(c/2 + (d*x)/2)^3)/8 - (11*C*sin(c/2 + (d*x)/2)^3)/24) - cos(c/2 + (d*x)/2)^2*((A*sin(c/2 + (d*x)/2)^5)/40 - (3*B*sin(c/2 + (d*x)/2)^5)/40 + (C*sin(c/2 + (d*x)/2)^5)/8) + (A*sin(c/2 + (d*x)/2)^7)/56 - (B*sin(c/2 + (d*x)/2)^7)/56 + (C*sin(c/2 + (d*x)/2)^7)/56)/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
367,1,99,148,1.161376,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^4,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B+C\right)}{8\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+B-3\,C\right)}{40\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B-A+3\,C\right)}{24\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A + B + C))/(8*a^4*d) - (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d) - (tan(c/2 + (d*x)/2)^5*(A + B - 3*C))/(40*a^4*d) - (tan(c/2 + (d*x)/2)^3*(B - A + 3*C))/(24*a^4*d)","B"
368,1,99,148,1.180370,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(B-3\,A+C\right)}{40\,a^4\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B+C\right)}{8\,a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A+B-C\right)}{24\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d) - (tan(c/2 + (d*x)/2)^5*(B - 3*A + C))/(40*a^4*d) + (tan(c/2 + (d*x)/2)*(A + B + C))/(8*a^4*d) + (tan(c/2 + (d*x)/2)^3*(3*A + B - C))/(24*a^4*d)","B"
369,1,199,157,1.141200,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^4),x)","\frac{2\,A\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B+C}{8\,a^4}+\frac{4\,A-2\,B}{8\,a^4}+\frac{4\,A+2\,B}{8\,a^4}+\frac{6\,A-2\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B+C}{24\,a^4}+\frac{4\,A-2\,B}{24\,a^4}+\frac{6\,A-2\,C}{24\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A-B+C}{40\,a^4}+\frac{4\,A-2\,B}{40\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (tan(c/2 + (d*x)/2)*((A - B + C)/(8*a^4) + (4*A - 2*B)/(8*a^4) + (4*A + 2*B)/(8*a^4) + (6*A - 2*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((A - B + C)/(24*a^4) + (4*A - 2*B)/(24*a^4) + (6*A - 2*C)/(24*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((A - B + C)/(40*a^4) + (4*A - 2*B)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d)","B"
370,1,252,185,1.206994,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{5\,A-3\,B+C}{40\,a^4}+\frac{A-B+C}{20\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,A-3\,B+C}{12\,a^4}-\frac{2\,B-10\,A+2\,C}{24\,a^4}+\frac{A-B+C}{8\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(5\,A-3\,B+C\right)}{8\,a^4}-\frac{2\,B-10\,A+2\,C}{4\,a^4}+\frac{10\,A+2\,B-2\,C}{8\,a^4}+\frac{A-B+C}{2\,a^4}\right)}{d}-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A-B\right)}{a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*((5*A - 3*B + C)/(40*a^4) + (A - B + C)/(20*a^4)))/d + (tan(c/2 + (d*x)/2)^3*((5*A - 3*B + C)/(12*a^4) - (2*B - 10*A + 2*C)/(24*a^4) + (A - B + C)/(8*a^4)))/d + (tan(c/2 + (d*x)/2)*((3*(5*A - 3*B + C))/(8*a^4) - (2*B - 10*A + 2*C)/(4*a^4) + (10*A + 2*B - 2*C)/(8*a^4) + (A - B + C)/(2*a^4)))/d - (2*A*tan(c/2 + (d*x)/2))/(d*(a^4*tan(c/2 + (d*x)/2)^2 - a^4)) + (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d) - (2*atanh(tan(c/2 + (d*x)/2))*(4*A - B))/(a^4*d)","B"
371,1,318,248,1.226950,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,A-2\,B\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,A-2\,B\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(6\,A-4\,B+2\,C\right)}{4\,a^4}-\frac{3\,\left(5\,B-15\,A+C\right)}{8\,a^4}+\frac{5\,\left(A-B+C\right)}{4\,a^4}+\frac{20\,A-4\,C}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{6\,A-4\,B+2\,C}{40\,a^4}+\frac{3\,\left(A-B+C\right)}{40\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{6\,A-4\,B+2\,C}{8\,a^4}-\frac{5\,B-15\,A+C}{24\,a^4}+\frac{A-B+C}{4\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}+\frac{2\,\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{21\,A}{2}-4\,B+C\right)}{21\,A-8\,B+2\,C}\right)\,\left(\frac{21\,A}{2}-4\,B+C\right)}{a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(9*A - 2*B) - tan(c/2 + (d*x)/2)*(7*A - 2*B))/(d*(a^4*tan(c/2 + (d*x)/2)^4 - 2*a^4*tan(c/2 + (d*x)/2)^2 + a^4)) - (tan(c/2 + (d*x)/2)*((3*(6*A - 4*B + 2*C))/(4*a^4) - (3*(5*B - 15*A + C))/(8*a^4) + (5*(A - B + C))/(4*a^4) + (20*A - 4*C)/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((6*A - 4*B + 2*C)/(40*a^4) + (3*(A - B + C))/(40*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((6*A - 4*B + 2*C)/(8*a^4) - (5*B - 15*A + C)/(24*a^4) + (A - B + C)/(4*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d) + (2*atanh((2*tan(c/2 + (d*x)/2)*((21*A)/2 - 4*B + C))/(21*A - 8*B + 2*C))*((21*A)/2 - 4*B + C))/(a^4*d)","B"
372,1,345,287,1.241698,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^4),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{7\,A-5\,B+3\,C}{40\,a^4}+\frac{A-B+C}{10\,a^4}\right)}{d}-\frac{\left(26\,A-9\,B+2\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(16\,B-\frac{124\,A}{3}-4\,C\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(18\,A-7\,B+2\,C\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{21\,A-9\,B+C}{24\,a^4}+\frac{7\,A-5\,B+3\,C}{6\,a^4}+\frac{5\,\left(A-B+C\right)}{12\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{21\,A-9\,B+C}{2\,a^4}+\frac{5\,\left(7\,A-5\,B+3\,C\right)}{4\,a^4}-\frac{5\,B-35\,A+5\,C}{8\,a^4}+\frac{5\,\left(A-B+C\right)}{2\,a^4}\right)}{d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(44\,A-21\,B+8\,C\right)}{a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B+C\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*((7*A - 5*B + 3*C)/(40*a^4) + (A - B + C)/(10*a^4)))/d - (tan(c/2 + (d*x)/2)*(18*A - 7*B + 2*C) + tan(c/2 + (d*x)/2)^5*(26*A - 9*B + 2*C) - tan(c/2 + (d*x)/2)^3*((124*A)/3 - 16*B + 4*C))/(d*(3*a^4*tan(c/2 + (d*x)/2)^2 - 3*a^4*tan(c/2 + (d*x)/2)^4 + a^4*tan(c/2 + (d*x)/2)^6 - a^4)) + (tan(c/2 + (d*x)/2)^3*((21*A - 9*B + C)/(24*a^4) + (7*A - 5*B + 3*C)/(6*a^4) + (5*(A - B + C))/(12*a^4)))/d + (tan(c/2 + (d*x)/2)*((21*A - 9*B + C)/(2*a^4) + (5*(7*A - 5*B + 3*C))/(4*a^4) - (5*B - 35*A + 5*C)/(8*a^4) + (5*(A - B + C))/(2*a^4)))/d - (atanh(tan(c/2 + (d*x)/2))*(44*A - 21*B + 8*C))/(a^4*d) + (tan(c/2 + (d*x)/2)^7*(A - B + C))/(56*a^4*d)","B"
373,0,-1,239,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
374,0,-1,193,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
375,0,-1,147,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
376,0,-1,104,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
377,0,-1,100,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x), x)","F"
378,0,-1,98,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
379,0,-1,117,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
380,0,-1,163,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4, x)","F"
381,0,-1,209,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5, x)","F"
382,0,-1,243,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
383,0,-1,187,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
384,0,-1,144,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
385,0,-1,142,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x), x)","F"
386,0,-1,144,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
387,0,-1,159,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
388,0,-1,165,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4, x)","F"
389,0,-1,215,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5, x)","F"
390,0,-1,263,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6, x)","F"
391,0,-1,294,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
392,0,-1,229,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
393,0,-1,184,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
394,0,-1,182,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x), x)","F"
395,0,-1,184,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
396,0,-1,199,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
397,0,-1,207,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4, x)","F"
398,0,-1,215,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5, x)","F"
399,0,-1,261,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6, x)","F"
400,0,-1,311,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^7,x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^7} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^7, x)","F"
401,0,-1,254,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
402,0,-1,208,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
403,0,-1,164,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
404,1,206,118,1.425740,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,B\,\left(2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)-\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)\right)\,\sqrt{\frac{a+a\,\cos\left(c+d\,x\right)}{2\,a}}}{d\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}+\frac{A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)\,\sqrt{\frac{2\,\left(a+a\,\cos\left(c+d\,x\right)\right)}{a}}}{d\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,a\,d}-\frac{2\,C\,\left(4\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)-3\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|1\right)\right)\,\sqrt{\frac{a+a\,\cos\left(c+d\,x\right)}{2\,a}}}{3\,a^2\,d\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*B*(2*ellipticE(c/2 + (d*x)/2, 1) - ellipticF(c/2 + (d*x)/2, 1))*((a + a*cos(c + d*x))/(2*a))^(1/2))/(d*(a + a*cos(c + d*x))^(1/2)) + (A*ellipticF(c/2 + (d*x)/2, 1)*((2*(a + a*cos(c + d*x)))/a)^(1/2))/(d*(a + a*cos(c + d*x))^(1/2)) + (2*C*sin(c + d*x)*(a + a*cos(c + d*x))^(1/2))/(3*a*d) - (2*C*(4*a^2*ellipticE(c/2 + (d*x)/2, 1) - 3*a^2*ellipticF(c/2 + (d*x)/2, 1))*((a + a*cos(c + d*x))/(2*a))^(1/2))/(3*a^2*d*(a + a*cos(c + d*x))^(1/2))","B"
405,0,-1,118,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\cos\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)), x)","F"
406,0,-1,120,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)), x)","F"
407,0,-1,169,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)), x)","F"
408,0,-1,213,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2)), x)","F"
409,0,-1,259,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^5*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^5\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^5*(a + a*cos(c + d*x))^(1/2)), x)","F"
410,0,-1,277,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
411,0,-1,229,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
412,0,-1,181,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
413,0,-1,120,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(3/2), x)","F"
414,0,-1,131,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)), x)","F"
415,0,-1,173,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)), x)","F"
416,0,-1,232,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)), x)","F"
417,0,-1,284,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^4\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(3/2)), x)","F"
418,0,-1,277,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
419,0,-1,227,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
420,0,-1,179,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
421,0,-1,133,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + a*cos(c + d*x))^(5/2), x)","F"
422,0,-1,171,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)), x)","F"
423,0,-1,217,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)), x)","F"
424,0,-1,280,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^3\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2)), x)","F"
425,1,123,123,1.498287,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,A\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,B\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*A*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*B*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
426,1,96,93,1.288659,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,B\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,C\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*B*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*C*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
427,1,69,65,0.247158,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(1/2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,C\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*C*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
428,1,76,61,1.568067,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(3/2),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
429,1,103,87,1.836635,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(5/2),x)","\frac{2\,C\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
430,1,108,123,2.113594,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/cos(c + d*x)^(7/2),x)","\frac{6\,A\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 10*B*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*C*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
431,1,265,211,2.265827,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
432,1,254,177,1.611857,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
433,1,216,144,1.502445,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*B*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
434,1,162,107,0.452633,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{2\,B\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
435,1,146,101,1.763552,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
436,1,184,100,2.406670,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\frac{2\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
437,1,217,139,2.753501,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{6\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*C*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
438,1,223,177,3.150548,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{6\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{30\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,C\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+42\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*C*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (30*A*a*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*C*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 42*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
439,1,404,251,2.469832,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{4\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (4*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
440,1,369,215,2.382430,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,A\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*A*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
441,1,280,179,2.314032,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{2\,B\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a^2*ellipticE(c/2 + (d*x)/2, 2))/d - (2*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
442,1,237,172,2.505165,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{2\,C\,a^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
443,1,245,172,2.877897,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + 6*ellipticE(c/2 + (d*x)/2, 2) + 4*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
444,1,313,174,3.637289,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{6\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,A\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*A*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*A*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*B*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*B*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
445,1,346,215,3.863116,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{30\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,A\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,A\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,B\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,B\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(30*A*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 84*A*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 70*A*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*B*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*B*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*B*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
446,1,688,251,4.326759,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{8\,\left(\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{16\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{18\,B\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{64\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{21\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{72\,B\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{18\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{81\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{8\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{11\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{3\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{14\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{21\,d}","Not used",1,"(8*((2*A*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (B*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)))*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((16*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (18*B*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((64*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (21*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^2*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (72*B*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (18*B*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (81*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((8*A*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*A*a^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (11*B*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (3*B*a^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (14*C*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2))))/(21*d)","B"
447,1,544,303,2.760539,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(15/2)*sin(c + d*x)*hypergeom([1/2, 15/4], 19/4, cos(c + d*x)^2))/(15*d*(sin(c + d*x)^2)^(1/2))","B"
448,1,507,267,2.545464,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{B\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{6\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + A*a^3*ellipticF(c/2 + (d*x)/2, 2) + A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (B*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (6*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
449,1,430,231,2.412740,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{2\,\left(B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{2\,A\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^3*ellipticE(c/2 + (d*x)/2, 2) + B*a^3*ellipticF(c/2 + (d*x)/2, 2) + B*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (2*A*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
450,1,376,229,2.250695,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{A\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + C*a^3*ellipticF(c/2 + (d*x)/2, 2) + C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (A*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*B*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*B*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
451,1,358,227,2.729424,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{B\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (B*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*B*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
452,1,408,230,3.670505,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{2\,\left(B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*B*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
453,1,436,231,4.672437,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{2\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+\frac{6\,A\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,A\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,A\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + ((2*A*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + (6*A*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*A*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 2*A*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
454,1,457,267,4.847740,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{70\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,A\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,A\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,A\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+\frac{6\,B\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,B\,a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,B\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (70*A*a^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 270*A*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 210*A*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*A*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + ((2*B*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + (6*B*a^3*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*B*a^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 2*B*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
455,1,893,303,5.357024,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(13/2),x)","\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{120\,A\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{45\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{15\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{136\,B\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{39\,B\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,B\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{153\,C\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{27\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{42\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{7\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{33\,B\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{11\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{231\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{168\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{119\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{21\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{11/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{209\,B\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{99\,B\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{275\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{33\,C\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{231\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{30\,A\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{15\,A\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{34\,B\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,B\,a^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{27\,C\,a^3\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{135\,d}","Not used",1,"(2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((120*A*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (45*A*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (15*A*a^3*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (136*B*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (39*B*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*B*a^3*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (153*C*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (27*C*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (8*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2)*((42*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (7*A*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (33*B*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (11*C*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2))))/(231*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((168*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (119*A*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (21*A*a^3*sin(c + d*x))/(cos(c + d*x)^(11/2)*(1 - cos(c + d*x)^2)^(1/2)) + (209*B*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (99*B*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (275*C*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (33*C*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))))/(231*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((30*A*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (15*A*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (34*B*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*B*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (27*C*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2))))/(135*d)","B"
456,0,-1,210,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
457,0,-1,174,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
458,0,-1,134,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
459,0,-1,90,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))), x)","F"
460,0,-1,125,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))), x)","F"
461,0,-1,165,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))), x)","F"
462,0,-1,210,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))), x)","F"
463,0,-1,214,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
464,0,-1,180,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
465,0,-1,139,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
466,0,-1,133,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
467,0,-1,175,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
468,0,-1,211,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
469,0,-1,273,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
470,0,-1,232,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
471,0,-1,195,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
472,0,-1,191,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
473,0,-1,193,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
474,0,-1,237,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
475,0,-1,270,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
476,0,-1,227,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
477,0,-1,179,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
478,0,-1,131,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
479,0,-1,121,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
480,0,-1,120,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
481,1,227,130,4.465578,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{2\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(28\,A\,\sin\left(c+d\,x\right)+20\,B\,\sin\left(c+d\,x\right)+30\,C\,\sin\left(c+d\,x\right)+16\,A\,\sin\left(2\,c+2\,d\,x\right)+36\,A\,\sin\left(3\,c+3\,d\,x\right)+8\,A\,\sin\left(4\,c+4\,d\,x\right)+8\,A\,\sin\left(5\,c+5\,d\,x\right)+20\,B\,\sin\left(2\,c+2\,d\,x\right)+30\,B\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(4\,c+4\,d\,x\right)+10\,B\,\sin\left(5\,c+5\,d\,x\right)+45\,C\,\sin\left(3\,c+3\,d\,x\right)+15\,C\,\sin\left(5\,c+5\,d\,x\right)\right)}{15\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\left(10\,\cos\left(c+d\,x\right)+8\,\cos\left(2\,c+2\,d\,x\right)+5\,\cos\left(3\,c+3\,d\,x\right)+2\,\cos\left(4\,c+4\,d\,x\right)+\cos\left(5\,c+5\,d\,x\right)+6\right)}","Not used",1,"(2*(a*(cos(c + d*x) + 1))^(1/2)*(28*A*sin(c + d*x) + 20*B*sin(c + d*x) + 30*C*sin(c + d*x) + 16*A*sin(2*c + 2*d*x) + 36*A*sin(3*c + 3*d*x) + 8*A*sin(4*c + 4*d*x) + 8*A*sin(5*c + 5*d*x) + 20*B*sin(2*c + 2*d*x) + 30*B*sin(3*c + 3*d*x) + 10*B*sin(4*c + 4*d*x) + 10*B*sin(5*c + 5*d*x) + 45*C*sin(3*c + 3*d*x) + 15*C*sin(5*c + 5*d*x)))/(15*d*cos(c + d*x)^(1/2)*(10*cos(c + d*x) + 8*cos(2*c + 2*d*x) + 5*cos(3*c + 3*d*x) + 2*cos(4*c + 4*d*x) + cos(5*c + 5*d*x) + 6))","B"
482,1,503,178,7.200027,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{\left(96\,A+112\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(96\,A+112\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(336\,A+392\,B+280\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(336\,A+392\,B+280\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\left(280\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(280\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+3\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((96*A + 112*B + 140*C)*1i)/(105*d) - (exp(c*7i + d*x*7i)*(96*A + 112*B + 140*C)*1i)/(105*d) + (exp(c*2i + d*x*2i)*(336*A + 392*B + 280*C)*1i)/(105*d) - (exp(c*5i + d*x*5i)*(336*A + 392*B + 280*C)*1i)/(105*d) - (exp(c*3i + d*x*3i)*(280*B + 140*C)*1i)/(105*d) + (exp(c*4i + d*x*4i)*(280*B + 140*C)*1i)/(105*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 3*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
483,1,629,226,7.696927,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{\left(256\,A+288\,B+336\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}+\frac{C\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(256\,A+288\,B+336\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(1152\,A+1296\,B+1512\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(1152\,A+1296\,B+1512\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(2016\,A+1008\,B+2016\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(2016\,A+1008\,B+2016\,C\right)\,1{}\mathrm{i}}{315\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((256*A + 288*B + 336*C)*1i)/(315*d) - (C*exp(c*3i + d*x*3i)*8i)/(3*d) + (C*exp(c*6i + d*x*6i)*8i)/(3*d) - (exp(c*9i + d*x*9i)*(256*A + 288*B + 336*C)*1i)/(315*d) + (exp(c*2i + d*x*2i)*(1152*A + 1296*B + 1512*C)*1i)/(315*d) - (exp(c*7i + d*x*7i)*(1152*A + 1296*B + 1512*C)*1i)/(315*d) + (exp(c*4i + d*x*4i)*(2016*A + 1008*B + 2016*C)*1i)/(315*d) - (exp(c*5i + d*x*5i)*(2016*A + 1008*B + 2016*C)*1i)/(315*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
484,0,-1,283,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
485,0,-1,233,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
486,0,-1,181,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
487,0,-1,181,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
488,0,-1,171,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
489,0,-1,172,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2), x)","F"
490,1,273,184,9.353128,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","-\frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(\frac{4\,C\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{d}+\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+6\,B+11\,C\right)}{3\,d}-\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(52\,A+48\,B+65\,C\right)}{15\,d}-\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(104\,A+126\,B+175\,C\right)}{105\,d}\right)}{6\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}","Not used",1,"-((a + a*cos(c + d*x))^(1/2)*((4*C*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((5*c)/2 + (5*d*x)/2))/d + (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin(c/2 + (d*x)/2)*(4*A + 6*B + 11*C))/(3*d) - (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((3*c)/2 + (3*d*x)/2)*(52*A + 48*B + 65*C))/(15*d) - (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((7*c)/2 + (7*d*x)/2)*(104*A + 126*B + 175*C))/(105*d)))/(6*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos(c/2 + (d*x)/2) + 6*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos((3*c)/2 + (3*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*7i)/2 + (d*x*7i)/2)*cos((7*c)/2 + (7*d*x)/2))","B"
491,1,308,232,8.748432,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A+12\,B+13\,C\right)}{5\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(68\,A+78\,B+77\,C\right)}{35\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(136\,A+156\,B+189\,C\right)}{315\,d}-\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(2\,B+3\,C\right)}{3\,d}\right)}{12\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+8\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}","Not used",1,"((a + a*cos(c + d*x))^(1/2)*((8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2)*(12*A + 12*B + 13*C))/(5*d) + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2)*(68*A + 78*B + 77*C))/(35*d) + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2)*(136*A + 156*B + 189*C))/(315*d) - (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((3*c)/2 + (3*d*x)/2)*(2*B + 3*C))/(3*d)))/(12*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos(c/2 + (d*x)/2) + 8*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((3*c)/2 + (3*d*x)/2) + 8*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((9*c)/2 + (9*d*x)/2))","B"
492,1,368,284,8.273470,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(13/2),x)","\frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(-\frac{16\,C\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{3\,d}-\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A+18\,B+23\,C\right)}{15\,d}+\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(84\,A+76\,B+81\,C\right)}{35\,d}+\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(336\,A+374\,B+429\,C\right)}{315\,d}+\frac{32\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(336\,A+374\,B+429\,C\right)}{3465\,d}\right)}{20\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+20\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+10\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+10\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}","Not used",1,"((a + a*cos(c + d*x))^(1/2)*((16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((3*c)/2 + (3*d*x)/2)*(84*A + 76*B + 81*C))/(35*d) - (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin(c/2 + (d*x)/2)*(12*A + 18*B + 23*C))/(15*d) - (16*C*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((5*c)/2 + (5*d*x)/2))/(3*d) + (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((7*c)/2 + (7*d*x)/2)*(336*A + 374*B + 429*C))/(315*d) + (32*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((11*c)/2 + (11*d*x)/2)*(336*A + 374*B + 429*C))/(3465*d)))/(20*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos(c/2 + (d*x)/2) + 20*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((3*c)/2 + (3*d*x)/2) + 10*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((5*c)/2 + (5*d*x)/2) + 10*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((9*c)/2 + (9*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*11i)/2 + (d*x*11i)/2)*cos((11*c)/2 + (11*d*x)/2))","B"
493,0,-1,333,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
494,0,-1,281,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
495,0,-1,233,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
496,0,-1,231,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
497,0,-1,233,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
498,0,-1,223,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2), x)","F"
499,0,-1,222,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2), x)","F"
500,1,713,234,8.887170,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{a^2\,\left(584\,A+690\,B+903\,C\right)\,2{}\mathrm{i}}{315\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,2{}\mathrm{i}}{d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\left(2\,A+5\,B+10\,C\right)\,4{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\left(2\,A+5\,B+10\,C\right)\,4{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(24\,A+25\,B+33\,C\right)\,4{}\mathrm{i}}{5\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(24\,A+25\,B+33\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(146\,A+155\,B+182\,C\right)\,4{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(146\,A+155\,B+182\,C\right)\,4{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(584\,A+690\,B+903\,C\right)\,2{}\mathrm{i}}{315\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(584*A + 690*B + 903*C)*2i)/(315*d) - (C*a^2*exp(c*1i + d*x*1i)*2i)/d + (C*a^2*exp(c*8i + d*x*8i)*2i)/d - (a^2*exp(c*3i + d*x*3i)*(2*A + 5*B + 10*C)*4i)/(3*d) + (a^2*exp(c*6i + d*x*6i)*(2*A + 5*B + 10*C)*4i)/(3*d) + (a^2*exp(c*4i + d*x*4i)*(24*A + 25*B + 33*C)*4i)/(5*d) - (a^2*exp(c*5i + d*x*5i)*(24*A + 25*B + 33*C)*4i)/(5*d) + (a^2*exp(c*2i + d*x*2i)*(146*A + 155*B + 182*C)*4i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(146*A + 155*B + 182*C)*4i)/(35*d) - (a^2*exp(c*9i + d*x*9i)*(584*A + 690*B + 903*C)*2i)/(315*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 4*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
501,1,809,284,8.968256,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(13/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{a^2\,\left(2840\,A+3212\,B+3795\,C\right)\,4{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\left(2\,B+5\,C\right)\,4{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\left(2\,B+5\,C\right)\,4{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(30\,A+41\,B+50\,C\right)\,8{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\left(30\,A+41\,B+50\,C\right)\,8{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(160\,A+157\,B+165\,C\right)\,8{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(160\,A+157\,B+165\,C\right)\,8{}\mathrm{i}}{35\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(710\,A+803\,B+870\,C\right)\,8{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(710\,A+803\,B+870\,C\right)\,8{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\left(2840\,A+3212\,B+3795\,C\right)\,4{}\mathrm{i}}{3465\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+10\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+5\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(2840*A + 3212*B + 3795*C)*4i)/(3465*d) - (a^2*exp(c*3i + d*x*3i)*(2*B + 5*C)*4i)/(3*d) + (a^2*exp(c*8i + d*x*8i)*(2*B + 5*C)*4i)/(3*d) - (a^2*exp(c*5i + d*x*5i)*(30*A + 41*B + 50*C)*8i)/(15*d) + (a^2*exp(c*6i + d*x*6i)*(30*A + 41*B + 50*C)*8i)/(15*d) + (a^2*exp(c*4i + d*x*4i)*(160*A + 157*B + 165*C)*8i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(160*A + 157*B + 165*C)*8i)/(35*d) + (a^2*exp(c*2i + d*x*2i)*(710*A + 803*B + 870*C)*8i)/(315*d) - (a^2*exp(c*9i + d*x*9i)*(710*A + 803*B + 870*C)*8i)/(315*d) - (a^2*exp(c*11i + d*x*11i)*(2840*A + 3212*B + 3795*C)*4i)/(3465*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 10*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 5*exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*10i + d*x*10i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*11i + d*x*11i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
502,1,941,334,9.085387,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(15/2),x)","\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{a^2\,\left(8368\,A+9230\,B+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(6\,A+15\,B+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\left(6\,A+15\,B+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\left(348\,A+345\,B+379\,C\right)\,16{}\mathrm{i}}{105\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(348\,A+345\,B+379\,C\right)\,16{}\mathrm{i}}{105\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(1046\,A+1075\,B+1108\,C\right)\,16{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(1046\,A+1075\,B+1108\,C\right)\,16{}\mathrm{i}}{315\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(8368\,A+9230\,B+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\left(8368\,A+9230\,B+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}\,\left(8368\,A+9230\,B+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}\right)}{\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+20\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+20\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+15\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+6\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,12{}\mathrm{i}+d\,x\,12{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}+{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}\,\sqrt{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}","Not used",1,"((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(8368*A + 9230*B + 10439*C)*16i)/(45045*d) - (C*a^2*exp(c*3i + d*x*3i)*8i)/(3*d) + (C*a^2*exp(c*10i + d*x*10i)*8i)/(3*d) - (a^2*exp(c*5i + d*x*5i)*(6*A + 15*B + 23*C)*16i)/(15*d) + (a^2*exp(c*8i + d*x*8i)*(6*A + 15*B + 23*C)*16i)/(15*d) + (a^2*exp(c*6i + d*x*6i)*(348*A + 345*B + 379*C)*16i)/(105*d) - (a^2*exp(c*7i + d*x*7i)*(348*A + 345*B + 379*C)*16i)/(105*d) + (a^2*exp(c*4i + d*x*4i)*(1046*A + 1075*B + 1108*C)*16i)/(315*d) - (a^2*exp(c*9i + d*x*9i)*(1046*A + 1075*B + 1108*C)*16i)/(315*d) + (a^2*exp(c*2i + d*x*2i)*(8368*A + 9230*B + 10439*C)*8i)/(3465*d) - (a^2*exp(c*11i + d*x*11i)*(8368*A + 9230*B + 10439*C)*8i)/(3465*d) - (a^2*exp(c*13i + d*x*13i)*(8368*A + 9230*B + 10439*C)*16i)/(45045*d)))/((exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*1i + d*x*1i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*2i + d*x*2i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*3i + d*x*3i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*4i + d*x*4i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*5i + d*x*5i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 20*exp(c*6i + d*x*6i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 20*exp(c*7i + d*x*7i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*8i + d*x*8i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 15*exp(c*9i + d*x*9i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*10i + d*x*10i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + 6*exp(c*11i + d*x*11i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*12i + d*x*12i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2) + exp(c*13i + d*x*13i)*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2)^(1/2))","B"
503,0,-1,241,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
504,0,-1,195,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
505,0,-1,141,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
506,0,-1,138,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
507,0,-1,143,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
508,0,-1,191,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
509,0,-1,237,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
510,0,-1,213,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(B\,b\,{\cos\left(c+d\,x\right)}^2+\left(A\,b+B\,a\right)\,\cos\left(c+d\,x\right)+A\,a\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
511,0,-1,260,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
512,0,-1,202,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
513,0,-1,149,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
514,0,-1,161,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
515,0,-1,213,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
516,0,-1,263,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
517,0,-1,254,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
518,0,-1,201,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
519,0,-1,163,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
520,0,-1,211,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
521,0,-1,261,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
522,1,279,131,2.528559,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\frac{\left(2\,A\,b-A\,a-\frac{5\,C\,a}{4}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{16\,A\,b}{3}-2\,A\,a-\frac{C\,a}{2}+\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b}{3}+\frac{116\,C\,b}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,A\,a+\frac{16\,A\,b}{3}+\frac{C\,a}{2}+\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a+2\,A\,b+\frac{5\,C\,a}{4}+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,C\right)}{4\,\left(A\,a+\frac{3\,C\,a}{4}\right)}\right)\,\left(4\,A+3\,C\right)}{4\,d}-\frac{a\,\left(4\,A+3\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A*a + 2*A*b + (5*C*a)/4 + 2*C*b) + tan(c/2 + (d*x)/2)^5*((20*A*b)/3 + (116*C*b)/15) - tan(c/2 + (d*x)/2)^9*(A*a - 2*A*b + (5*C*a)/4 - 2*C*b) + tan(c/2 + (d*x)/2)^3*(2*A*a + (16*A*b)/3 + (C*a)/2 + (8*C*b)/3) - tan(c/2 + (d*x)/2)^7*(2*A*a - (16*A*b)/3 + (C*a)/2 - (8*C*b)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(4*A + 3*C))/(4*(A*a + (3*C*a)/4)))*(4*A + 3*C))/(4*d) - (a*(4*A + 3*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
523,1,243,108,2.439741,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\frac{\left(2\,A\,a-A\,b+2\,C\,a-\frac{5\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a-A\,b+\frac{10\,C\,a}{3}+\frac{3\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,a+A\,b+\frac{10\,C\,a}{3}-\frac{3\,C\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+A\,b+2\,C\,a+\frac{5\,C\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,C\right)}{4\,\left(A\,b+\frac{3\,C\,b}{4}\right)}\right)\,\left(4\,A+3\,C\right)}{4\,d}-\frac{b\,\left(4\,A+3\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a + A*b + 2*C*a + (5*C*b)/4) + tan(c/2 + (d*x)/2)^7*(2*A*a - A*b + 2*C*a - (5*C*b)/4) + tan(c/2 + (d*x)/2)^3*(6*A*a + A*b + (10*C*a)/3 - (3*C*b)/4) + tan(c/2 + (d*x)/2)^5*(6*A*a - A*b + (10*C*a)/3 + (3*C*b)/4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (b*atan((b*tan(c/2 + (d*x)/2)*(4*A + 3*C))/(4*(A*b + (3*C*b)/4)))*(4*A + 3*C))/(4*d) - (b*(4*A + 3*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
524,1,67,96,1.281864,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","A\,a\,x+\frac{C\,a\,x}{2}+\frac{A\,b\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"A*a*x + (C*a*x)/2 + (A*b*sin(c + d*x))/d + (3*C*b*sin(c + d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d) + (C*b*sin(3*c + 3*d*x))/(12*d)","B"
525,1,115,58,1.488099,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x),x)","\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(C*a*sin(c + d*x))/d + (2*A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b*sin(2*c + 2*d*x))/(4*d)","B"
526,1,91,42,1.278383,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{C\,b\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(C*b*sin(c + d*x))/d + (2*A*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*sin(c + d*x))/(d*cos(c + d*x))","B"
527,1,135,58,1.398249,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{2\,C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{A\,a\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{A\,b\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(2*C*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (A*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d + (A*a*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (A*b*sin(c + d*x))/(d*cos(c + d*x))","B"
528,1,137,86,3.290028,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^4,x)","\frac{b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+2\,C\right)}{d}-\frac{\left(2\,A\,a-A\,b+2\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A\,a}{3}-4\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+A\,b+2\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(b*atanh(tan(c/2 + (d*x)/2))*(A + 2*C))/d - (tan(c/2 + (d*x)/2)*(2*A*a + A*b + 2*C*a) - tan(c/2 + (d*x)/2)^3*((4*A*a)/3 + 4*C*a) + tan(c/2 + (d*x)/2)^5*(2*A*a - A*b + 2*C*a))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
529,1,195,117,4.739463,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^5,x)","\frac{\left(\frac{5\,A\,a}{4}-2\,A\,b+C\,a-2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a}{4}+\frac{10\,A\,b}{3}-C\,a+6\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,A\,a}{4}-\frac{10\,A\,b}{3}-C\,a-6\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a}{4}+2\,A\,b+C\,a+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,A+4\,C\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*a)/4 + 2*A*b + C*a + 2*C*b) + tan(c/2 + (d*x)/2)^7*((5*A*a)/4 - 2*A*b + C*a - 2*C*b) - tan(c/2 + (d*x)/2)^3*((10*A*b)/3 - (3*A*a)/4 + C*a + 6*C*b) + tan(c/2 + (d*x)/2)^5*((3*A*a)/4 + (10*A*b)/3 - C*a + 6*C*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (a*atanh(tan(c/2 + (d*x)/2))*(3*A + 4*C))/(4*d)","B"
530,1,233,140,4.829253,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^6,x)","\frac{b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,A+4\,C\right)}{4\,d}-\frac{\left(2\,A\,a-\frac{5\,A\,b}{4}+2\,C\,a-C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b}{2}-\frac{8\,A\,a}{3}-\frac{16\,C\,a}{3}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a}{15}+\frac{20\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a}{3}-\frac{A\,b}{2}-\frac{16\,C\,a}{3}-2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+\frac{5\,A\,b}{4}+2\,C\,a+C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(b*atanh(tan(c/2 + (d*x)/2))*(3*A + 4*C))/(4*d) - (tan(c/2 + (d*x)/2)*(2*A*a + (5*A*b)/4 + 2*C*a + C*b) + tan(c/2 + (d*x)/2)^5*((116*A*a)/15 + (20*C*a)/3) + tan(c/2 + (d*x)/2)^9*(2*A*a - (5*A*b)/4 + 2*C*a - C*b) - tan(c/2 + (d*x)/2)^3*((8*A*a)/3 + (A*b)/2 + (16*C*a)/3 + 2*C*b) - tan(c/2 + (d*x)/2)^7*((8*A*a)/3 - (A*b)/2 + (16*C*a)/3 - 2*C*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
531,1,252,214,1.660183,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\frac{A\,a^2\,x}{2}+\frac{3\,A\,b^2\,x}{8}+\frac{3\,C\,a^2\,x}{8}+\frac{5\,C\,b^2\,x}{16}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{15\,C\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,C\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{C\,b^2\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{3\,A\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{5\,C\,a\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{5\,C\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{24\,d}+\frac{C\,a\,b\,\sin\left(5\,c+5\,d\,x\right)}{40\,d}","Not used",1,"(A*a^2*x)/2 + (3*A*b^2*x)/8 + (3*C*a^2*x)/8 + (5*C*b^2*x)/16 + (A*a^2*sin(2*c + 2*d*x))/(4*d) + (A*b^2*sin(2*c + 2*d*x))/(4*d) + (A*b^2*sin(4*c + 4*d*x))/(32*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(4*c + 4*d*x))/(32*d) + (15*C*b^2*sin(2*c + 2*d*x))/(64*d) + (3*C*b^2*sin(4*c + 4*d*x))/(64*d) + (C*b^2*sin(6*c + 6*d*x))/(192*d) + (3*A*a*b*sin(c + d*x))/(2*d) + (5*C*a*b*sin(c + d*x))/(4*d) + (A*a*b*sin(3*c + 3*d*x))/(6*d) + (5*C*a*b*sin(3*c + 3*d*x))/(24*d) + (C*a*b*sin(5*c + 5*d*x))/(40*d)","B"
532,1,371,178,2.545592,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\frac{\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2-2\,A\,a\,b-\frac{5\,C\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(8\,A\,a^2+\frac{16\,A\,b^2}{3}+\frac{16\,C\,a^2}{3}+\frac{8\,C\,b^2}{3}-4\,A\,a\,b-C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,A\,a^2+\frac{20\,A\,b^2}{3}+\frac{20\,C\,a^2}{3}+\frac{116\,C\,b^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,A\,a^2+\frac{16\,A\,b^2}{3}+\frac{16\,C\,a^2}{3}+\frac{8\,C\,b^2}{3}+4\,A\,a\,b+C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2+2\,A\,a\,b+\frac{5\,C\,a\,b}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+3\,C\right)}{2\,\left(2\,A\,a\,b+\frac{3\,C\,a\,b}{2}\right)}\right)\,\left(4\,A+3\,C\right)}{2\,d}-\frac{a\,b\,\left(4\,A+3\,C\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 - 2*A*a*b - (5*C*a*b)/2) + tan(c/2 + (d*x)/2)^3*(8*A*a^2 + (16*A*b^2)/3 + (16*C*a^2)/3 + (8*C*b^2)/3 + 4*A*a*b + C*a*b) + tan(c/2 + (d*x)/2)^7*(8*A*a^2 + (16*A*b^2)/3 + (16*C*a^2)/3 + (8*C*b^2)/3 - 4*A*a*b - C*a*b) + tan(c/2 + (d*x)/2)^5*(12*A*a^2 + (20*A*b^2)/3 + (20*C*a^2)/3 + (116*C*b^2)/15) + tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 + 2*A*a*b + (5*C*a*b)/2))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*b*atan((a*b*tan(c/2 + (d*x)/2)*(4*A + 3*C))/(2*(2*A*a*b + (3*C*a*b)/2)))*(4*A + 3*C))/(2*d) - (a*b*(4*A + 3*C)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(2*d)","B"
533,1,145,161,1.393336,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","A\,a^2\,x+\frac{A\,b^2\,x}{2}+\frac{C\,a^2\,x}{2}+\frac{3\,C\,b^2\,x}{8}+\frac{A\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{2\,A\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{C\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}","Not used",1,"A*a^2*x + (A*b^2*x)/2 + (C*a^2*x)/2 + (3*C*b^2*x)/8 + (A*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d) + (C*b^2*sin(2*c + 2*d*x))/(4*d) + (C*b^2*sin(4*c + 4*d*x))/(32*d) + (2*A*a*b*sin(c + d*x))/d + (3*C*a*b*sin(c + d*x))/(2*d) + (C*a*b*sin(3*c + 3*d*x))/(6*d)","B"
534,1,170,103,1.638653,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x),x)","\frac{A\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{2\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{4\,A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(A*b^2*sin(c + d*x))/d + (C*a^2*sin(c + d*x))/d + (3*C*b^2*sin(c + d*x))/(4*d) + (2*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b^2*sin(3*c + 3*d*x))/(12*d) + (4*A*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*b*sin(2*c + 2*d*x))/(2*d)","B"
535,1,193,109,1.519361,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,C\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{C\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}-\frac{A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}-\frac{A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}","Not used",1,"(A*a^2*sin(c + d*x))/(d*cos(c + d*x)) - (C*a^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d - (A*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (2*C*a*b*sin(c + d*x))/d - (A*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (C*b^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
536,1,188,103,1.931969,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^3,x)","\frac{2\,\left(\frac{A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{C\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{2}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{4}+A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + A*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((C*b^2*sin(3*c + 3*d*x))/4 + (A*a^2*sin(c + d*x))/2 + (C*b^2*sin(c + d*x))/4 + A*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
537,1,209,112,1.471784,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^4,x)","\frac{2\,C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{A\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{A\,a\,b\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}-\frac{A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}","Not used",1,"(2*C*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*a^2*sin(c + d*x))/(3*d*cos(c + d*x)) + (A*a^2*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (A*b^2*sin(c + d*x))/(d*cos(c + d*x)) + (C*a^2*sin(c + d*x))/(d*cos(c + d*x)) - (A*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (A*a*b*sin(c + d*x))/(d*cos(c + d*x)^2)","B"
538,1,307,154,4.762702,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\left(\frac{5\,A\,a^2}{4}+A\,b^2+C\,a^2-4\,A\,a\,b-4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a^2}{4}-A\,b^2-C\,a^2+\frac{20\,A\,a\,b}{3}+12\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,A\,a^2}{4}-A\,b^2-C\,a^2-\frac{20\,A\,a\,b}{3}-12\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a^2}{4}+A\,b^2+C\,a^2+4\,A\,a\,b+4\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A\,a^2}{8}+\frac{A\,b^2}{2}+\frac{C\,a^2}{2}+C\,b^2\right)}{\frac{3\,A\,a^2}{2}+2\,A\,b^2+2\,C\,a^2+4\,C\,b^2}\right)\,\left(\frac{3\,A\,a^2}{4}+A\,b^2+C\,a^2+2\,C\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*a^2)/4 + A*b^2 + C*a^2 + 4*A*a*b + 4*C*a*b) + tan(c/2 + (d*x)/2)^7*((5*A*a^2)/4 + A*b^2 + C*a^2 - 4*A*a*b - 4*C*a*b) - tan(c/2 + (d*x)/2)^3*(A*b^2 - (3*A*a^2)/4 + C*a^2 + (20*A*a*b)/3 + 12*C*a*b) + tan(c/2 + (d*x)/2)^5*((3*A*a^2)/4 - A*b^2 - C*a^2 + (20*A*a*b)/3 + 12*C*a*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*((3*A*a^2)/8 + (A*b^2)/2 + (C*a^2)/2 + C*b^2))/((3*A*a^2)/2 + 2*A*b^2 + 2*C*a^2 + 4*C*b^2))*((3*A*a^2)/4 + A*b^2 + C*a^2 + 2*C*b^2))/d","B"
539,1,322,187,4.813407,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^6,x)","\frac{a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,A+4\,C\right)}{2\,d}-\frac{\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2-\frac{5\,A\,a\,b}{2}-2\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(A\,a\,b-\frac{16\,A\,b^2}{3}-\frac{16\,C\,a^2}{3}-8\,C\,b^2-\frac{8\,A\,a^2}{3}+4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^2}{15}+\frac{20\,A\,b^2}{3}+\frac{20\,C\,a^2}{3}+12\,C\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a^2}{3}-\frac{16\,A\,b^2}{3}-\frac{16\,C\,a^2}{3}-8\,C\,b^2-A\,a\,b-4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+2\,C\,b^2+\frac{5\,A\,a\,b}{2}+2\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*b*atanh(tan(c/2 + (d*x)/2))*(3*A + 4*C))/(2*d) - (tan(c/2 + (d*x)/2)^9*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 - (5*A*a*b)/2 - 2*C*a*b) - tan(c/2 + (d*x)/2)^3*((8*A*a^2)/3 + (16*A*b^2)/3 + (16*C*a^2)/3 + 8*C*b^2 + A*a*b + 4*C*a*b) - tan(c/2 + (d*x)/2)^7*((8*A*a^2)/3 + (16*A*b^2)/3 + (16*C*a^2)/3 + 8*C*b^2 - A*a*b - 4*C*a*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^2)/15 + (20*A*b^2)/3 + (20*C*a^2)/3 + 12*C*b^2) + tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + 2*C*b^2 + (5*A*a*b)/2 + 2*C*a*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
540,1,617,264,2.919441,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3,x)","\frac{\left(2\,A\,a^3-\frac{5\,A\,b^3}{4}+2\,C\,a^3-\frac{11\,C\,b^3}{8}+6\,A\,a\,b^2-3\,A\,a^2\,b+6\,C\,a\,b^2-\frac{15\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(10\,A\,a^3-\frac{7\,A\,b^3}{4}+\frac{22\,C\,a^3}{3}+\frac{5\,C\,b^3}{24}+22\,A\,a\,b^2-9\,A\,a^2\,b+14\,C\,a\,b^2-\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(20\,A\,a^3-\frac{A\,b^3}{2}+12\,C\,a^3-\frac{15\,C\,b^3}{4}+36\,A\,a\,b^2-6\,A\,a^2\,b+\frac{156\,C\,a\,b^2}{5}-\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(20\,A\,a^3+\frac{A\,b^3}{2}+12\,C\,a^3+\frac{15\,C\,b^3}{4}+36\,A\,a\,b^2+6\,A\,a^2\,b+\frac{156\,C\,a\,b^2}{5}+\frac{3\,C\,a^2\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(10\,A\,a^3+\frac{7\,A\,b^3}{4}+\frac{22\,C\,a^3}{3}-\frac{5\,C\,b^3}{24}+22\,A\,a\,b^2+9\,A\,a^2\,b+14\,C\,a\,b^2+\frac{21\,C\,a^2\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+\frac{5\,A\,b^3}{4}+2\,C\,a^3+\frac{11\,C\,b^3}{8}+6\,A\,a\,b^2+3\,A\,a^2\,b+6\,C\,a\,b^2+\frac{15\,C\,a^2\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{b\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(24\,A\,a^2+6\,A\,b^2+18\,C\,a^2+5\,C\,b^2\right)}{8\,d}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,A\,a^2+6\,A\,b^2+18\,C\,a^2+5\,C\,b^2\right)}{8\,\left(\frac{3\,A\,b^3}{4}+\frac{5\,C\,b^3}{8}+3\,A\,a^2\,b+\frac{9\,C\,a^2\,b}{4}\right)}\right)\,\left(24\,A\,a^2+6\,A\,b^2+18\,C\,a^2+5\,C\,b^2\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^3 + (5*A*b^3)/4 + 2*C*a^3 + (11*C*b^3)/8 + 6*A*a*b^2 + 3*A*a^2*b + 6*C*a*b^2 + (15*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^11*(2*A*a^3 - (5*A*b^3)/4 + 2*C*a^3 - (11*C*b^3)/8 + 6*A*a*b^2 - 3*A*a^2*b + 6*C*a*b^2 - (15*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^3*(10*A*a^3 + (7*A*b^3)/4 + (22*C*a^3)/3 - (5*C*b^3)/24 + 22*A*a*b^2 + 9*A*a^2*b + 14*C*a*b^2 + (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^9*(10*A*a^3 - (7*A*b^3)/4 + (22*C*a^3)/3 + (5*C*b^3)/24 + 22*A*a*b^2 - 9*A*a^2*b + 14*C*a*b^2 - (21*C*a^2*b)/4) + tan(c/2 + (d*x)/2)^5*(20*A*a^3 + (A*b^3)/2 + 12*C*a^3 + (15*C*b^3)/4 + 36*A*a*b^2 + 6*A*a^2*b + (156*C*a*b^2)/5 + (3*C*a^2*b)/2) + tan(c/2 + (d*x)/2)^7*(20*A*a^3 - (A*b^3)/2 + 12*C*a^3 - (15*C*b^3)/4 + 36*A*a*b^2 - 6*A*a^2*b + (156*C*a*b^2)/5 - (3*C*a^2*b)/2))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (b*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(24*A*a^2 + 6*A*b^2 + 18*C*a^2 + 5*C*b^2))/(8*d) + (b*atan((b*tan(c/2 + (d*x)/2)*(24*A*a^2 + 6*A*b^2 + 18*C*a^2 + 5*C*b^2))/(8*((3*A*b^3)/4 + (5*C*b^3)/8 + 3*A*a^2*b + (9*C*a^2*b)/4)))*(24*A*a^2 + 6*A*b^2 + 18*C*a^2 + 5*C*b^2))/(8*d)","B"
541,1,488,225,2.863411,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3,x)","\frac{\left(2\,A\,b^3-C\,a^3+2\,C\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{16\,A\,b^3}{3}-2\,C\,a^3+\frac{8\,C\,b^3}{3}-6\,A\,a\,b^2+24\,A\,a^2\,b-\frac{3\,C\,a\,b^2}{2}+16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b^3}{3}+\frac{116\,C\,b^3}{15}+36\,A\,a^2\,b+20\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,A\,b^3}{3}+2\,C\,a^3+\frac{8\,C\,b^3}{3}+6\,A\,a\,b^2+24\,A\,a^2\,b+\frac{3\,C\,a\,b^2}{2}+16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b^3+C\,a^3+2\,C\,b^3+3\,A\,a\,b^2+6\,A\,a^2\,b+\frac{15\,C\,a\,b^2}{4}+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(8\,A\,a^2+12\,A\,b^2+4\,C\,a^2+9\,C\,b^2\right)}{4\,d}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A\,a^2+12\,A\,b^2+4\,C\,a^2+9\,C\,b^2\right)}{4\,\left(2\,A\,a^3+C\,a^3+3\,A\,a\,b^2+\frac{9\,C\,a\,b^2}{4}\right)}\right)\,\left(8\,A\,a^2+12\,A\,b^2+4\,C\,a^2+9\,C\,b^2\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^9*(2*A*b^3 - C*a^3 + 2*C*b^3 - 3*A*a*b^2 + 6*A*a^2*b - (15*C*a*b^2)/4 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*((16*A*b^3)/3 + 2*C*a^3 + (8*C*b^3)/3 + 6*A*a*b^2 + 24*A*a^2*b + (3*C*a*b^2)/2 + 16*C*a^2*b) + tan(c/2 + (d*x)/2)^7*((16*A*b^3)/3 - 2*C*a^3 + (8*C*b^3)/3 - 6*A*a*b^2 + 24*A*a^2*b - (3*C*a*b^2)/2 + 16*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((20*A*b^3)/3 + (116*C*b^3)/15 + 36*A*a^2*b + 20*C*a^2*b) + tan(c/2 + (d*x)/2)*(2*A*b^3 + C*a^3 + 2*C*b^3 + 3*A*a*b^2 + 6*A*a^2*b + (15*C*a*b^2)/4 + 6*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(8*A*a^2 + 12*A*b^2 + 4*C*a^2 + 9*C*b^2))/(4*d) + (a*atan((a*tan(c/2 + (d*x)/2)*(8*A*a^2 + 12*A*b^2 + 4*C*a^2 + 9*C*b^2))/(4*(2*A*a^3 + C*a^3 + 3*A*a*b^2 + (9*C*a*b^2)/4)))*(8*A*a^2 + 12*A*b^2 + 4*C*a^2 + 9*C*b^2))/(4*d)","B"
542,1,2008,167,3.017874,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x),x)","\frac{\left(2\,C\,a^3-A\,b^3-\frac{5\,C\,b^3}{4}+6\,A\,a\,b^2+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,C\,a^3-A\,b^3+\frac{3\,C\,b^3}{4}+18\,A\,a\,b^2+10\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(A\,b^3+6\,C\,a^3-\frac{3\,C\,b^3}{4}+18\,A\,a\,b^2+10\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,b^3+2\,C\,a^3+\frac{5\,C\,b^3}{4}+6\,A\,a\,b^2+6\,C\,a\,b^2+3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-\frac{b\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\,1{}\mathrm{i}}{8}\right)\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)}{8}+\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+\frac{b\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\,1{}\mathrm{i}}{8}\right)\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)}{8}}{16\,A^3\,a^3\,b^6-192\,A^3\,a^8\,b+192\,A^3\,a^5\,b^4-32\,A^3\,a^6\,b^3+576\,A^3\,a^7\,b^2-96\,A^2\,C\,a^8\,b+9\,A\,C^2\,a^3\,b^6+72\,A\,C^2\,a^5\,b^4+144\,A\,C^2\,a^7\,b^2+24\,A^2\,C\,a^3\,b^6+240\,A^2\,C\,a^5\,b^4-24\,A^2\,C\,a^6\,b^3+576\,A^2\,C\,a^7\,b^2-\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-\frac{b\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\,1{}\mathrm{i}}{8}\right)\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)\,1{}\mathrm{i}}{8}+\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+\frac{b\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\,1{}\mathrm{i}}{8}\right)\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)\,1{}\mathrm{i}}{8}}\right)\,\left(24\,A\,a^2+4\,A\,b^2+12\,C\,a^2+3\,C\,b^2\right)}{4\,d}-\frac{A\,a^3\,\mathrm{atan}\left(\frac{A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\right)\,1{}\mathrm{i}+A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\right)\,1{}\mathrm{i}}{A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\right)-192\,A^3\,a^8\,b-A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+12\,C\,b^3+96\,A\,a^2\,b+48\,C\,a^2\,b\right)\right)+16\,A^3\,a^3\,b^6+192\,A^3\,a^5\,b^4-32\,A^3\,a^6\,b^3+576\,A^3\,a^7\,b^2-96\,A^2\,C\,a^8\,b+9\,A\,C^2\,a^3\,b^6+72\,A\,C^2\,a^5\,b^4+144\,A\,C^2\,a^7\,b^2+24\,A^2\,C\,a^3\,b^6+240\,A^2\,C\,a^5\,b^4-24\,A^2\,C\,a^6\,b^3+576\,A^2\,C\,a^7\,b^2}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A*b^3 + 2*C*a^3 + (5*C*b^3)/4 + 6*A*a*b^2 + 6*C*a*b^2 + 3*C*a^2*b) - tan(c/2 + (d*x)/2)^7*(A*b^3 - 2*C*a^3 + (5*C*b^3)/4 - 6*A*a*b^2 - 6*C*a*b^2 + 3*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(A*b^3 + 6*C*a^3 - (3*C*b^3)/4 + 18*A*a*b^2 + 10*C*a*b^2 + 3*C*a^2*b) + tan(c/2 + (d*x)/2)^5*(6*C*a^3 - A*b^3 + (3*C*b^3)/4 + 18*A*a*b^2 + 10*C*a*b^2 - 3*C*a^2*b))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (b*atan(((b*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) - (b*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2)*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b)*1i)/8)*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2))/8 + (b*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) + (b*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2)*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b)*1i)/8)*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2))/8)/((b*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) + (b*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2)*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b)*1i)/8)*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2)*1i)/8 - (b*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) - (b*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2)*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b)*1i)/8)*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2)*1i)/8 - 192*A^3*a^8*b + 16*A^3*a^3*b^6 + 192*A^3*a^5*b^4 - 32*A^3*a^6*b^3 + 576*A^3*a^7*b^2 - 96*A^2*C*a^8*b + 9*A*C^2*a^3*b^6 + 72*A*C^2*a^5*b^4 + 144*A*C^2*a^7*b^2 + 24*A^2*C*a^3*b^6 + 240*A^2*C*a^5*b^4 - 24*A^2*C*a^6*b^3 + 576*A^2*C*a^7*b^2))*(24*A*a^2 + 4*A*b^2 + 12*C*a^2 + 3*C*b^2))/(4*d) - (A*a^3*atan((A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) + A*a^3*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b))*1i + A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) - A*a^3*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b))*1i)/(A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) + A*a^3*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b)) - 192*A^3*a^8*b - A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2) - A*a^3*(32*A*a^3 + 16*A*b^3 + 12*C*b^3 + 96*A*a^2*b + 48*C*a^2*b)) + 16*A^3*a^3*b^6 + 192*A^3*a^5*b^4 - 32*A^3*a^6*b^3 + 576*A^3*a^7*b^2 - 96*A^2*C*a^8*b + 9*A*C^2*a^3*b^6 + 72*A*C^2*a^5*b^4 + 144*A*C^2*a^7*b^2 + 24*A^2*C*a^3*b^6 + 240*A^2*C*a^5*b^4 - 24*A^2*C*a^6*b^3 + 576*A^2*C*a^7*b^2))*2i)/d","B"
543,1,238,167,2.283290,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+6\,A\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+3\,C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-A\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}+\frac{\frac{A\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{5\,C\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{12}+\frac{C\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{24}+A\,a^3\,\sin\left(c+d\,x\right)+\frac{3\,C\,a\,b^2\,\sin\left(c+d\,x\right)}{8}+\frac{3\,C\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,C\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{8}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*A*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - A*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i + 3*C*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + ((A*b^3*sin(2*c + 2*d*x))/2 + (5*C*b^3*sin(2*c + 2*d*x))/12 + (C*b^3*sin(4*c + 4*d*x))/24 + A*a^3*sin(c + d*x) + (3*C*a*b^2*sin(c + d*x))/8 + (3*C*a^2*b*sin(2*c + 2*d*x))/2 + (3*C*a*b^2*sin(3*c + 3*d*x))/8)/(d*cos(c + d*x))","B"
544,1,282,168,2.986293,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^3,x)","\frac{2\,\left(\frac{A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+A\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{C\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+3\,A\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+3\,C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{C\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{C\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,C\,a\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,A\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,C\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + A*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (C*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 3*A*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 3*C*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((C*b^3*sin(2*c + 2*d*x))/8 + (C*b^3*sin(4*c + 4*d*x))/16 + (A*a^3*sin(c + d*x))/2 + (3*C*a*b^2*sin(c + d*x))/4 + (3*A*a^2*b*sin(2*c + 2*d*x))/2 + (3*C*a*b^2*sin(3*c + 3*d*x))/4)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
545,1,464,163,2.804083,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^4,x)","\frac{\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{C\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{4}+\frac{3\,A\,a\,b^2\,\sin\left(c+d\,x\right)}{4}-\frac{A\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}+\frac{3\,A\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,A\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}-\frac{A\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{2}-\frac{A\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{4}+\frac{3\,C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{2}-\frac{A\,a^2\,b\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{4}+\frac{9\,C\,a\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}-\frac{C\,a^2\,b\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{2}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((A*a^3*sin(3*c + 3*d*x))/6 + (C*a^3*sin(3*c + 3*d*x))/4 + (C*b^3*sin(2*c + 2*d*x))/4 + (C*b^3*sin(4*c + 4*d*x))/8 + (A*a^3*sin(c + d*x))/2 + (C*a^3*sin(c + d*x))/4 + (3*A*a*b^2*sin(c + d*x))/4 - (A*b^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 + (3*A*a^2*b*sin(2*c + 2*d*x))/4 + (3*A*a*b^2*sin(3*c + 3*d*x))/4 - (A*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/2 - (A*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/4 + (3*C*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (C*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/2 - (A*a^2*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/4 + (9*C*a*b^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (C*a^2*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/2)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
546,1,1547,182,3.514967,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{\frac{3\,C\,b^3\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+72\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+240\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6+192\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^6+72\,A^2\,a^4\,b^2+144\,A^2\,a^2\,b^4+24\,A\,C\,a^6+240\,A\,C\,a^4\,b^2+576\,A\,C\,a^2\,b^4+16\,C^2\,a^6+192\,C^2\,a^4\,b^2+576\,C^2\,a^2\,b^4+64\,C^2\,b^6\right)}\right)}{4}+\frac{9\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{32}+\frac{3\,C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{3\,A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{32}+\frac{A\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{A\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{11\,A\,a^3\,\sin\left(c+d\,x\right)}{32}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{8}+\frac{3\,A\,a\,b^2\,\sin\left(c+d\,x\right)}{8}+\frac{9\,A\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+\frac{9\,C\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+A\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)+\frac{3\,A\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{A\,a^2\,b\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\sin\left(4\,c+4\,d\,x\right)}{8}+C\,b^3\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+72\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+240\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6+192\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^6+72\,A^2\,a^4\,b^2+144\,A^2\,a^2\,b^4+24\,A\,C\,a^6+240\,A\,C\,a^4\,b^2+576\,A\,C\,a^2\,b^4+16\,C^2\,a^6+192\,C^2\,a^4\,b^2+576\,C^2\,a^2\,b^4+64\,C^2\,b^6\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{C\,b^3\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+72\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+240\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6+192\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+576\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^6+72\,A^2\,a^4\,b^2+144\,A^2\,a^2\,b^4+24\,A\,C\,a^6+240\,A\,C\,a^4\,b^2+576\,A\,C\,a^2\,b^4+16\,C^2\,a^6+192\,C^2\,a^4\,b^2+576\,C^2\,a^2\,b^4+64\,C^2\,b^6\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}+\frac{3\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{8}+\frac{3\,A\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{32}+\frac{C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3\,A\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,A\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+3\,C\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{3\,C\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{4}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((3*C*b^3*atan((9*A^2*a^6*sin(c/2 + (d*x)/2) + 16*C^2*a^6*sin(c/2 + (d*x)/2) + 64*C^2*b^6*sin(c/2 + (d*x)/2) + 144*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 72*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 576*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 192*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^6*sin(c/2 + (d*x)/2) + 576*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 240*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^6 + 16*C^2*a^6 + 64*C^2*b^6 + 144*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 576*C^2*a^2*b^4 + 192*C^2*a^4*b^2 + 24*A*C*a^6 + 576*A*C*a^2*b^4 + 240*A*C*a^4*b^2))))/4 + (9*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/32 + (3*C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (3*A*a^3*sin(3*c + 3*d*x))/32 + (A*b^3*sin(2*c + 2*d*x))/4 + (A*b^3*sin(4*c + 4*d*x))/8 + (C*a^3*sin(3*c + 3*d*x))/8 + (11*A*a^3*sin(c + d*x))/32 + (C*a^3*sin(c + d*x))/8 + (3*A*a*b^2*sin(c + d*x))/8 + (9*A*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + (9*C*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + A*a^2*b*sin(2*c + 2*d*x) + (3*A*a*b^2*sin(3*c + 3*d*x))/8 + (A*a^2*b*sin(4*c + 4*d*x))/4 + (3*C*a^2*b*sin(2*c + 2*d*x))/4 + (3*C*a^2*b*sin(4*c + 4*d*x))/8 + C*b^3*atan((9*A^2*a^6*sin(c/2 + (d*x)/2) + 16*C^2*a^6*sin(c/2 + (d*x)/2) + 64*C^2*b^6*sin(c/2 + (d*x)/2) + 144*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 72*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 576*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 192*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^6*sin(c/2 + (d*x)/2) + 576*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 240*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^6 + 16*C^2*a^6 + 64*C^2*b^6 + 144*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 576*C^2*a^2*b^4 + 192*C^2*a^4*b^2 + 24*A*C*a^6 + 576*A*C*a^2*b^4 + 240*A*C*a^4*b^2)))*cos(2*c + 2*d*x) + (C*b^3*atan((9*A^2*a^6*sin(c/2 + (d*x)/2) + 16*C^2*a^6*sin(c/2 + (d*x)/2) + 64*C^2*b^6*sin(c/2 + (d*x)/2) + 144*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 72*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 576*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 192*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^6*sin(c/2 + (d*x)/2) + 576*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 240*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^6 + 16*C^2*a^6 + 64*C^2*b^6 + 144*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 576*C^2*a^2*b^4 + 192*C^2*a^4*b^2 + 24*A*C*a^6 + 576*A*C*a^2*b^4 + 240*A*C*a^4*b^2)))*cos(4*c + 4*d*x))/4 + (3*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/8 + (3*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/32 + (C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (C*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8 + (3*A*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (3*A*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8 + 3*C*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (3*C*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/4)/(d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
547,1,445,227,4.818054,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^6,x)","\frac{b\,\mathrm{atanh}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A\,a^2+4\,A\,b^2+12\,C\,a^2+8\,C\,b^2\right)}{2\,\left(2\,A\,b^3+4\,C\,b^3+\frac{9\,A\,a^2\,b}{2}+6\,C\,a^2\,b\right)}\right)\,\left(9\,A\,a^2+4\,A\,b^2+12\,C\,a^2+8\,C\,b^2\right)}{4\,d}-\frac{\left(2\,A\,a^3-A\,b^3+2\,C\,a^3+6\,A\,a\,b^2-\frac{15\,A\,a^2\,b}{4}+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,A\,b^3-\frac{8\,A\,a^3}{3}-\frac{16\,C\,a^3}{3}-16\,A\,a\,b^2+\frac{3\,A\,a^2\,b}{2}-24\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^3}{15}+\frac{20\,C\,a^3}{3}+20\,A\,a\,b^2+36\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a^3}{3}-2\,A\,b^3-\frac{16\,C\,a^3}{3}-16\,A\,a\,b^2-\frac{3\,A\,a^2\,b}{2}-24\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+A\,b^3+2\,C\,a^3+6\,A\,a\,b^2+\frac{15\,A\,a^2\,b}{4}+6\,C\,a\,b^2+3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(b*atanh((b*tan(c/2 + (d*x)/2)*(9*A*a^2 + 4*A*b^2 + 12*C*a^2 + 8*C*b^2))/(2*(2*A*b^3 + 4*C*b^3 + (9*A*a^2*b)/2 + 6*C*a^2*b)))*(9*A*a^2 + 4*A*b^2 + 12*C*a^2 + 8*C*b^2))/(4*d) - (tan(c/2 + (d*x)/2)^9*(2*A*a^3 - A*b^3 + 2*C*a^3 + 6*A*a*b^2 - (15*A*a^2*b)/4 + 6*C*a*b^2 - 3*C*a^2*b) - tan(c/2 + (d*x)/2)^3*((8*A*a^3)/3 + 2*A*b^3 + (16*C*a^3)/3 + 16*A*a*b^2 + (3*A*a^2*b)/2 + 24*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^7*((8*A*a^3)/3 - 2*A*b^3 + (16*C*a^3)/3 + 16*A*a*b^2 - (3*A*a^2*b)/2 + 24*C*a*b^2 - 6*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^3)/15 + (20*C*a^3)/3 + 20*A*a*b^2 + 36*C*a*b^2) + tan(c/2 + (d*x)/2)*(2*A*a^3 + A*b^3 + 2*C*a^3 + 6*A*a*b^2 + (15*A*a^2*b)/4 + 6*C*a*b^2 + 3*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
548,1,572,273,4.674021,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^7,x)","\frac{\left(\frac{11\,A\,a^3}{8}-2\,A\,b^3+\frac{5\,C\,a^3}{4}-2\,C\,b^3+\frac{15\,A\,a\,b^2}{4}-6\,A\,a^2\,b+3\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{5\,A\,a^3}{24}+\frac{22\,A\,b^3}{3}-\frac{7\,C\,a^3}{4}+10\,C\,b^3-\frac{21\,A\,a\,b^2}{4}+14\,A\,a^2\,b-9\,C\,a\,b^2+22\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{15\,A\,a^3}{4}-12\,A\,b^3+\frac{C\,a^3}{2}-20\,C\,b^3+\frac{3\,A\,a\,b^2}{2}-\frac{156\,A\,a^2\,b}{5}+6\,C\,a\,b^2-36\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{15\,A\,a^3}{4}+12\,A\,b^3+\frac{C\,a^3}{2}+20\,C\,b^3+\frac{3\,A\,a\,b^2}{2}+\frac{156\,A\,a^2\,b}{5}+6\,C\,a\,b^2+36\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,A\,a^3}{24}-\frac{22\,A\,b^3}{3}-\frac{7\,C\,a^3}{4}-10\,C\,b^3-\frac{21\,A\,a\,b^2}{4}-14\,A\,a^2\,b-9\,C\,a\,b^2-22\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,A\,a^3}{8}+2\,A\,b^3+\frac{5\,C\,a^3}{4}+2\,C\,b^3+\frac{15\,A\,a\,b^2}{4}+6\,A\,a^2\,b+3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atanh}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A\,a^2+18\,A\,b^2+6\,C\,a^2+24\,C\,b^2\right)}{4\,\left(\frac{5\,A\,a^3}{4}+\frac{3\,C\,a^3}{2}+\frac{9\,A\,a\,b^2}{2}+6\,C\,a\,b^2\right)}\right)\,\left(5\,A\,a^2+18\,A\,b^2+6\,C\,a^2+24\,C\,b^2\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((11*A*a^3)/8 + 2*A*b^3 + (5*C*a^3)/4 + 2*C*b^3 + (15*A*a*b^2)/4 + 6*A*a^2*b + 3*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^11*((11*A*a^3)/8 - 2*A*b^3 + (5*C*a^3)/4 - 2*C*b^3 + (15*A*a*b^2)/4 - 6*A*a^2*b + 3*C*a*b^2 - 6*C*a^2*b) - tan(c/2 + (d*x)/2)^3*((22*A*b^3)/3 - (5*A*a^3)/24 + (7*C*a^3)/4 + 10*C*b^3 + (21*A*a*b^2)/4 + 14*A*a^2*b + 9*C*a*b^2 + 22*C*a^2*b) + tan(c/2 + (d*x)/2)^9*((5*A*a^3)/24 + (22*A*b^3)/3 - (7*C*a^3)/4 + 10*C*b^3 - (21*A*a*b^2)/4 + 14*A*a^2*b - 9*C*a*b^2 + 22*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((15*A*a^3)/4 + 12*A*b^3 + (C*a^3)/2 + 20*C*b^3 + (3*A*a*b^2)/2 + (156*A*a^2*b)/5 + 6*C*a*b^2 + 36*C*a^2*b) + tan(c/2 + (d*x)/2)^7*((15*A*a^3)/4 - 12*A*b^3 + (C*a^3)/2 - 20*C*b^3 + (3*A*a*b^2)/2 - (156*A*a^2*b)/5 + 6*C*a*b^2 - 36*C*a^2*b))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a*atanh((a*tan(c/2 + (d*x)/2)*(5*A*a^2 + 18*A*b^2 + 6*C*a^2 + 24*C*b^2))/(4*((5*A*a^3)/4 + (3*C*a^3)/2 + (9*A*a*b^2)/2 + 6*C*a*b^2)))*(5*A*a^2 + 18*A*b^2 + 6*C*a^2 + 24*C*b^2))/(8*d)","B"
549,1,798,345,3.063437,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4,x)","\frac{\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2-5\,A\,a\,b^3-4\,A\,a^3\,b-\frac{11\,C\,a\,b^3}{2}-5\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(12\,A\,a^4+\frac{20\,A\,b^4}{3}+\frac{28\,C\,a^4}{3}+4\,C\,b^4+56\,A\,a^2\,b^2+40\,C\,a^2\,b^2-12\,A\,a\,b^3-16\,A\,a^3\,b-\frac{14\,C\,a\,b^3}{3}-12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(30\,A\,a^4+\frac{226\,A\,b^4}{15}+\frac{58\,C\,a^4}{3}+\frac{86\,C\,b^4}{5}+116\,A\,a^2\,b^2+\frac{452\,C\,a^2\,b^2}{5}-9\,A\,a\,b^3-20\,A\,a^3\,b-\frac{85\,C\,a\,b^3}{6}-9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(40\,A\,a^4+\frac{104\,A\,b^4}{5}+24\,C\,a^4+\frac{424\,C\,b^4}{35}+144\,A\,a^2\,b^2+\frac{624\,C\,a^2\,b^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(30\,A\,a^4+\frac{226\,A\,b^4}{15}+\frac{58\,C\,a^4}{3}+\frac{86\,C\,b^4}{5}+116\,A\,a^2\,b^2+\frac{452\,C\,a^2\,b^2}{5}+9\,A\,a\,b^3+20\,A\,a^3\,b+\frac{85\,C\,a\,b^3}{6}+9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(12\,A\,a^4+\frac{20\,A\,b^4}{3}+\frac{28\,C\,a^4}{3}+4\,C\,b^4+56\,A\,a^2\,b^2+40\,C\,a^2\,b^2+12\,A\,a\,b^3+16\,A\,a^3\,b+\frac{14\,C\,a\,b^3}{3}+12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2+5\,A\,a\,b^3+4\,A\,a^3\,b+\frac{11\,C\,a\,b^3}{2}+5\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,b\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(8\,A\,a^2+6\,A\,b^2+6\,C\,a^2+5\,C\,b^2\right)}{2\,d}+\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A\,a^2+6\,A\,b^2+6\,C\,a^2+5\,C\,b^2\right)}{2\,\left(3\,A\,a\,b^3+4\,A\,a^3\,b+\frac{5\,C\,a\,b^3}{2}+3\,C\,a^3\,b\right)}\right)\,\left(8\,A\,a^2+6\,A\,b^2+6\,C\,a^2+5\,C\,b^2\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 + 5*A*a*b^3 + 4*A*a^3*b + (11*C*a*b^3)/2 + 5*C*a^3*b) + tan(c/2 + (d*x)/2)^7*(40*A*a^4 + (104*A*b^4)/5 + 24*C*a^4 + (424*C*b^4)/35 + 144*A*a^2*b^2 + (624*C*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^13*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 - 5*A*a*b^3 - 4*A*a^3*b - (11*C*a*b^3)/2 - 5*C*a^3*b) + tan(c/2 + (d*x)/2)^3*(12*A*a^4 + (20*A*b^4)/3 + (28*C*a^4)/3 + 4*C*b^4 + 56*A*a^2*b^2 + 40*C*a^2*b^2 + 12*A*a*b^3 + 16*A*a^3*b + (14*C*a*b^3)/3 + 12*C*a^3*b) + tan(c/2 + (d*x)/2)^11*(12*A*a^4 + (20*A*b^4)/3 + (28*C*a^4)/3 + 4*C*b^4 + 56*A*a^2*b^2 + 40*C*a^2*b^2 - 12*A*a*b^3 - 16*A*a^3*b - (14*C*a*b^3)/3 - 12*C*a^3*b) + tan(c/2 + (d*x)/2)^5*(30*A*a^4 + (226*A*b^4)/15 + (58*C*a^4)/3 + (86*C*b^4)/5 + 116*A*a^2*b^2 + (452*C*a^2*b^2)/5 + 9*A*a*b^3 + 20*A*a^3*b + (85*C*a*b^3)/6 + 9*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(30*A*a^4 + (226*A*b^4)/15 + (58*C*a^4)/3 + (86*C*b^4)/5 + 116*A*a^2*b^2 + (452*C*a^2*b^2)/5 - 9*A*a*b^3 - 20*A*a^3*b - (85*C*a*b^3)/6 - 9*C*a^3*b))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) - (a*b*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(8*A*a^2 + 6*A*b^2 + 6*C*a^2 + 5*C*b^2))/(2*d) + (a*b*atan((a*b*tan(c/2 + (d*x)/2)*(8*A*a^2 + 6*A*b^2 + 6*C*a^2 + 5*C*b^2))/(2*(3*A*a*b^3 + 4*A*a^3*b + (5*C*a*b^3)/2 + 3*C*a^3*b)))*(8*A*a^2 + 6*A*b^2 + 6*C*a^2 + 5*C*b^2))/(2*d)","B"
550,1,359,301,2.069727,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4,x)","A\,a^4\,x+\frac{3\,A\,b^4\,x}{8}+\frac{C\,a^4\,x}{2}+\frac{5\,C\,b^4\,x}{16}+3\,A\,a^2\,b^2\,x+\frac{9\,C\,a^2\,b^2\,x}{4}+\frac{A\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{15\,C\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,C\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{C\,b^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{A\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{5\,C\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{C\,a\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{20\,d}+\frac{3\,A\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,C\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,C\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{3\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{4\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{d}+\frac{5\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{2\,d}+\frac{3\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"A*a^4*x + (3*A*b^4*x)/8 + (C*a^4*x)/2 + (5*C*b^4*x)/16 + 3*A*a^2*b^2*x + (9*C*a^2*b^2*x)/4 + (A*b^4*sin(2*c + 2*d*x))/(4*d) + (A*b^4*sin(4*c + 4*d*x))/(32*d) + (C*a^4*sin(2*c + 2*d*x))/(4*d) + (15*C*b^4*sin(2*c + 2*d*x))/(64*d) + (3*C*b^4*sin(4*c + 4*d*x))/(64*d) + (C*b^4*sin(6*c + 6*d*x))/(192*d) + (A*a*b^3*sin(3*c + 3*d*x))/(3*d) + (5*C*a*b^3*sin(3*c + 3*d*x))/(12*d) + (C*a^3*b*sin(3*c + 3*d*x))/(3*d) + (C*a*b^3*sin(5*c + 5*d*x))/(20*d) + (3*A*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*C*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*C*a^2*b^2*sin(4*c + 4*d*x))/(16*d) + (3*A*a*b^3*sin(c + d*x))/d + (4*A*a^3*b*sin(c + d*x))/d + (5*C*a*b^3*sin(c + d*x))/(2*d) + (3*C*a^3*b*sin(c + d*x))/d","B"
551,1,2241,227,3.090802,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x),x)","\frac{\left(2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2-4\,A\,a\,b^3-5\,C\,a\,b^3-4\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{16\,A\,b^4}{3}+8\,C\,a^4+\frac{8\,C\,b^4}{3}+48\,A\,a^2\,b^2+32\,C\,a^2\,b^2-8\,A\,a\,b^3-2\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b^4}{3}+12\,C\,a^4+\frac{116\,C\,b^4}{15}+72\,A\,a^2\,b^2+40\,C\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,A\,b^4}{3}+8\,C\,a^4+\frac{8\,C\,b^4}{3}+48\,A\,a^2\,b^2+32\,C\,a^2\,b^2+8\,A\,a\,b^3+2\,C\,a\,b^3+8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2+4\,A\,a\,b^3+5\,C\,a\,b^3+4\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{A\,a^4\,\mathrm{atan}\left(\frac{A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+A\,a^4\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-A\,a^4\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}}{256\,A^3\,a^6\,b^6-256\,A^3\,a^{11}\,b+1024\,A^3\,a^8\,b^4-128\,A^3\,a^9\,b^3+1024\,A^3\,a^{10}\,b^2+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+A\,a^4\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)-A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-A\,a^4\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)-128\,A^2\,C\,a^{11}\,b+144\,A\,C^2\,a^6\,b^6+384\,A\,C^2\,a^8\,b^4+256\,A\,C^2\,a^{10}\,b^2+384\,A^2\,C\,a^6\,b^6+1280\,A^2\,C\,a^8\,b^4-96\,A^2\,C\,a^9\,b^3+1024\,A^2\,C\,a^{10}\,b^2}\right)\,2{}\mathrm{i}}{d}-\frac{a\,b\,\mathrm{atan}\left(\frac{\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-\frac{a\,b\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)}{2}+\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+\frac{a\,b\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)}{2}}{256\,A^3\,a^6\,b^6-256\,A^3\,a^{11}\,b+1024\,A^3\,a^8\,b^4-128\,A^3\,a^9\,b^3+1024\,A^3\,a^{10}\,b^2-128\,A^2\,C\,a^{11}\,b+144\,A\,C^2\,a^6\,b^6+384\,A\,C^2\,a^8\,b^4+256\,A\,C^2\,a^{10}\,b^2+384\,A^2\,C\,a^6\,b^6+1280\,A^2\,C\,a^8\,b^4-96\,A^2\,C\,a^9\,b^3+1024\,A^2\,C\,a^{10}\,b^2-\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-\frac{a\,b\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)\,1{}\mathrm{i}}{2}+\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+\frac{a\,b\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)\,\left(32\,A\,a^4+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)\,1{}\mathrm{i}}{2}}\right)\,\left(8\,A\,a^2+4\,A\,b^2+4\,C\,a^2+3\,C\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 + 4*A*a*b^3 + 5*C*a*b^3 + 4*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((20*A*b^4)/3 + 12*C*a^4 + (116*C*b^4)/15 + 72*A*a^2*b^2 + 40*C*a^2*b^2) + tan(c/2 + (d*x)/2)^9*(2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 - 4*A*a*b^3 - 5*C*a*b^3 - 4*C*a^3*b) + tan(c/2 + (d*x)/2)^3*((16*A*b^4)/3 + 8*C*a^4 + (8*C*b^4)/3 + 48*A*a^2*b^2 + 32*C*a^2*b^2 + 8*A*a*b^3 + 2*C*a*b^3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((16*A*b^4)/3 + 8*C*a^4 + (8*C*b^4)/3 + 48*A*a^2*b^2 + 32*C*a^2*b^2 - 8*A*a*b^3 - 2*C*a*b^3 - 8*C*a^3*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (A*a^4*atan((A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + A*a^4*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*1i + A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - A*a^4*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*1i)/(256*A^3*a^6*b^6 - 256*A^3*a^11*b + 1024*A^3*a^8*b^4 - 128*A^3*a^9*b^3 + 1024*A^3*a^10*b^2 + A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + A*a^4*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)) - A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - A*a^4*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)) - 128*A^2*C*a^11*b + 144*A*C^2*a^6*b^6 + 384*A*C^2*a^8*b^4 + 256*A*C^2*a^10*b^2 + 384*A^2*C*a^6*b^6 + 1280*A^2*C*a^8*b^4 - 96*A^2*C*a^9*b^3 + 1024*A^2*C*a^10*b^2))*2i)/d - (a*b*atan(((a*b*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - (a*b*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2)*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2))/2 + (a*b*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + (a*b*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2)*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2))/2)/(256*A^3*a^6*b^6 - 256*A^3*a^11*b + 1024*A^3*a^8*b^4 - 128*A^3*a^9*b^3 + 1024*A^3*a^10*b^2 - 128*A^2*C*a^11*b + 144*A*C^2*a^6*b^6 + 384*A*C^2*a^8*b^4 + 256*A*C^2*a^10*b^2 + 384*A^2*C*a^6*b^6 + 1280*A^2*C*a^8*b^4 - 96*A^2*C*a^9*b^3 + 1024*A^2*C*a^10*b^2 - (a*b*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - (a*b*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2)*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2)*1i)/2 + (a*b*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + (a*b*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2)*(32*A*a^4 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)*1i)/2)*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2)*1i)/2))*(8*A*a^2 + 4*A*b^2 + 4*C*a^2 + 3*C*b^2))/d","B"
552,1,395,229,2.135655,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^2,x)","\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{C\,b^4\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{4\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{A\,b^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{8\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{3\,d}+\frac{4\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,b^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,C\,a^2\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}+\frac{4\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}-\frac{A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}-\frac{C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{4\,d}-\frac{A\,a^3\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,8{}\mathrm{i}}{d}-\frac{A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,12{}\mathrm{i}}{d}-\frac{C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}","Not used",1,"(A*a^4*sin(c + d*x))/(d*cos(c + d*x)) - (C*a^4*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*b^4*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/(4*d) - (A*a^3*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*8i)/d - (A*b^4*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d + (C*b^4*cos(c + d*x)^3*sin(c + d*x))/(4*d) - (A*a^2*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*12i)/d - (C*a^2*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i)/d + (4*A*a*b^3*sin(c + d*x))/d + (A*b^4*cos(c + d*x)*sin(c + d*x))/(2*d) + (8*C*a*b^3*sin(c + d*x))/(3*d) + (4*C*a^3*b*sin(c + d*x))/d + (3*C*b^4*cos(c + d*x)*sin(c + d*x))/(8*d) + (3*C*a^2*b^2*cos(c + d*x)*sin(c + d*x))/d + (4*C*a*b^3*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
553,1,2658,219,3.233838,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^3,x)","\frac{\left(A\,a^4+2\,A\,b^4+2\,C\,b^4+12\,C\,a^2\,b^2-8\,A\,a^3\,b-4\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(4\,A\,a^4-16\,A\,a^3\,b+8\,C\,a\,b^3-\frac{8\,C\,b^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a^4-4\,A\,b^4+\frac{4\,C\,b^4}{3}-24\,C\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A\,a^4+16\,A\,a^3\,b-8\,C\,a\,b^3-\frac{8\,C\,b^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a^4+2\,A\,b^4+2\,C\,b^4+12\,C\,a^2\,b^2+8\,A\,a^3\,b+4\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)\,1{}\mathrm{i}}{\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)+\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2\right)-256\,C^3\,a^{11}\,b+6144\,A^3\,a^4\,b^8-9216\,A^3\,a^5\,b^7+512\,A^3\,a^6\,b^6-1536\,A^3\,a^7\,b^5-64\,A^3\,a^9\,b^3+256\,C^3\,a^6\,b^6+1024\,C^3\,a^8\,b^4-128\,C^3\,a^9\,b^3+1024\,C^3\,a^{10}\,b^2-256\,A\,C^2\,a^{11}\,b-64\,A^2\,C\,a^{11}\,b+1536\,A\,C^2\,a^4\,b^8+7296\,A\,C^2\,a^6\,b^6-1536\,A\,C^2\,a^7\,b^5+8704\,A\,C^2\,a^8\,b^4-3456\,A\,C^2\,a^9\,b^3+512\,A\,C^2\,a^{10}\,b^2+6144\,A^2\,C\,a^4\,b^8-4608\,A^2\,C\,a^5\,b^7+13824\,A^2\,C\,a^6\,b^6-13056\,A^2\,C\,a^7\,b^5+1024\,A^2\,C\,a^8\,b^4-1824\,A^2\,C\,a^9\,b^3}\right)\,\left(A\,a^4\,1{}\mathrm{i}+C\,a^4\,2{}\mathrm{i}+A\,a^2\,b^2\,12{}\mathrm{i}\right)}{d}+\frac{4\,a\,b\,\mathrm{atan}\left(\frac{2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)+2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)}{256\,C^3\,a^{11}\,b-6144\,A^3\,a^4\,b^8+9216\,A^3\,a^5\,b^7-512\,A^3\,a^6\,b^6+1536\,A^3\,a^7\,b^5+64\,A^3\,a^9\,b^3-256\,C^3\,a^6\,b^6-1024\,C^3\,a^8\,b^4+128\,C^3\,a^9\,b^3-1024\,C^3\,a^{10}\,b^2+256\,A\,C^2\,a^{11}\,b+64\,A^2\,C\,a^{11}\,b-1536\,A\,C^2\,a^4\,b^8-7296\,A\,C^2\,a^6\,b^6+1536\,A\,C^2\,a^7\,b^5-8704\,A\,C^2\,a^8\,b^4+3456\,A\,C^2\,a^9\,b^3-512\,A\,C^2\,a^{10}\,b^2-6144\,A^2\,C\,a^4\,b^8+4608\,A^2\,C\,a^5\,b^7-13824\,A^2\,C\,a^6\,b^6+13056\,A^2\,C\,a^7\,b^5-1024\,A^2\,C\,a^8\,b^4+1824\,A^2\,C\,a^9\,b^3+a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,2{}\mathrm{i}-a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+a\,b\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,\left(16\,A\,a^4+32\,C\,a^4+192\,A\,a^2\,b^2+128\,A\,a\,b^3+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,2{}\mathrm{i}\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)\,2{}\mathrm{i}}\right)\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(6*A*a^4 - 4*A*b^4 + (4*C*b^4)/3 - 24*C*a^2*b^2) + tan(c/2 + (d*x)/2)^3*(4*A*a^4 - (8*C*b^4)/3 + 16*A*a^3*b - 8*C*a*b^3) + tan(c/2 + (d*x)/2)^7*(4*A*a^4 - (8*C*b^4)/3 - 16*A*a^3*b + 8*C*a*b^3) + tan(c/2 + (d*x)/2)*(A*a^4 + 2*A*b^4 + 2*C*b^4 + 12*C*a^2*b^2 + 8*A*a^3*b + 4*C*a*b^3) + tan(c/2 + (d*x)/2)^9*(A*a^4 + 2*A*b^4 + 2*C*b^4 + 12*C*a^2*b^2 - 8*A*a^3*b - 4*C*a*b^3))/(d*(tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (atan(((((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2)*1i - (((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2)*1i)/((((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2) + (((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2) - 256*C^3*a^11*b + 6144*A^3*a^4*b^8 - 9216*A^3*a^5*b^7 + 512*A^3*a^6*b^6 - 1536*A^3*a^7*b^5 - 64*A^3*a^9*b^3 + 256*C^3*a^6*b^6 + 1024*C^3*a^8*b^4 - 128*C^3*a^9*b^3 + 1024*C^3*a^10*b^2 - 256*A*C^2*a^11*b - 64*A^2*C*a^11*b + 1536*A*C^2*a^4*b^8 + 7296*A*C^2*a^6*b^6 - 1536*A*C^2*a^7*b^5 + 8704*A*C^2*a^8*b^4 - 3456*A*C^2*a^9*b^3 + 512*A*C^2*a^10*b^2 + 6144*A^2*C*a^4*b^8 - 4608*A^2*C*a^5*b^7 + 13824*A^2*C*a^6*b^6 - 13056*A^2*C*a^7*b^5 + 1024*A^2*C*a^8*b^4 - 1824*A^2*C*a^9*b^3))*(A*a^4*1i + C*a^4*2i + A*a^2*b^2*12i))/d + (4*a*b*atan((2*a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) - a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*2i)*(2*A*b^2 + 2*C*a^2 + C*b^2) + 2*a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) + a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*2i)*(2*A*b^2 + 2*C*a^2 + C*b^2))/(256*C^3*a^11*b - 6144*A^3*a^4*b^8 + 9216*A^3*a^5*b^7 - 512*A^3*a^6*b^6 + 1536*A^3*a^7*b^5 + 64*A^3*a^9*b^3 - 256*C^3*a^6*b^6 - 1024*C^3*a^8*b^4 + 128*C^3*a^9*b^3 - 1024*C^3*a^10*b^2 + a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) - a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*2i)*(2*A*b^2 + 2*C*a^2 + C*b^2)*2i - a*b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2) + a*b*(2*A*b^2 + 2*C*a^2 + C*b^2)*(16*A*a^4 + 32*C*a^4 + 192*A*a^2*b^2 + 128*A*a*b^3 + 64*C*a*b^3 + 128*C*a^3*b)*2i)*(2*A*b^2 + 2*C*a^2 + C*b^2)*2i + 256*A*C^2*a^11*b + 64*A^2*C*a^11*b - 1536*A*C^2*a^4*b^8 - 7296*A*C^2*a^6*b^6 + 1536*A*C^2*a^7*b^5 - 8704*A*C^2*a^8*b^4 + 3456*A*C^2*a^9*b^3 - 512*A*C^2*a^10*b^2 - 6144*A^2*C*a^4*b^8 + 4608*A^2*C*a^5*b^7 - 13824*A^2*C*a^6*b^6 + 13056*A^2*C*a^7*b^5 - 1024*A^2*C*a^8*b^4 + 1824*A^2*C*a^9*b^3))*(2*A*b^2 + 2*C*a^2 + C*b^2))/d","B"
554,1,2662,251,3.407816,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^4,x)","-\frac{\left(2\,A\,a^4+2\,C\,a^4+C\,b^4+12\,A\,a^2\,b^2-4\,A\,a^3\,b-8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a^4}{3}-8\,A\,a^3\,b+16\,C\,a\,b^3-4\,C\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{4\,A\,a^4}{3}-4\,C\,a^4+6\,C\,b^4-24\,A\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a^4}{3}+8\,A\,a^3\,b-16\,C\,a\,b^3-4\,C\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,C\,a^4+C\,b^4+12\,A\,a^2\,b^2+4\,A\,a^3\,b+8\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)}{2}+\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)}{2}}{256\,A^3\,a\,b^{11}-1024\,A^3\,a^2\,b^{10}+128\,A^3\,a^3\,b^9-1024\,A^3\,a^4\,b^8-256\,A^3\,a^6\,b^6+64\,C^3\,a^3\,b^9+1536\,C^3\,a^5\,b^7-512\,C^3\,a^6\,b^6+9216\,C^3\,a^7\,b^5-6144\,C^3\,a^8\,b^4+64\,A\,C^2\,a\,b^{11}+256\,A^2\,C\,a\,b^{11}+1824\,A\,C^2\,a^3\,b^9-1024\,A\,C^2\,a^4\,b^8+13056\,A\,C^2\,a^5\,b^7-13824\,A\,C^2\,a^6\,b^6+4608\,A\,C^2\,a^7\,b^5-6144\,A\,C^2\,a^8\,b^4-512\,A^2\,C\,a^2\,b^{10}+3456\,A^2\,C\,a^3\,b^9-8704\,A^2\,C\,a^4\,b^8+1536\,A^2\,C\,a^5\,b^7-7296\,A^2\,C\,a^6\,b^6-1536\,A^2\,C\,a^8\,b^4-\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)\,1{}\mathrm{i}}{2}+\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)\,1{}\mathrm{i}}{2}}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2\right)}{d}-\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-2\,a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,2{}\mathrm{i}+a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+2\,a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,2{}\mathrm{i}}{256\,A^3\,a\,b^{11}-1024\,A^3\,a^2\,b^{10}+128\,A^3\,a^3\,b^9-1024\,A^3\,a^4\,b^8-256\,A^3\,a^6\,b^6+64\,C^3\,a^3\,b^9+1536\,C^3\,a^5\,b^7-512\,C^3\,a^6\,b^6+9216\,C^3\,a^7\,b^5-6144\,C^3\,a^8\,b^4-2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-2\,a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)+2\,a\,b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+2\,a\,b\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,\left(32\,A\,b^4+16\,C\,b^4+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,C\,a^3\,b\right)\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)+64\,A\,C^2\,a\,b^{11}+256\,A^2\,C\,a\,b^{11}+1824\,A\,C^2\,a^3\,b^9-1024\,A\,C^2\,a^4\,b^8+13056\,A\,C^2\,a^5\,b^7-13824\,A\,C^2\,a^6\,b^6+4608\,A\,C^2\,a^7\,b^5-6144\,A\,C^2\,a^8\,b^4-512\,A^2\,C\,a^2\,b^{10}+3456\,A^2\,C\,a^3\,b^9-8704\,A^2\,C\,a^4\,b^8+1536\,A^2\,C\,a^5\,b^7-7296\,A^2\,C\,a^6\,b^6-1536\,A^2\,C\,a^8\,b^4}\right)\,\left(A\,a^2+2\,A\,b^2+2\,C\,a^2\right)\,4{}\mathrm{i}}{d}","Not used",1,"- (tan(c/2 + (d*x)/2)^5*((4*A*a^4)/3 - 4*C*a^4 + 6*C*b^4 - 24*A*a^2*b^2) + tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 - 4*C*b^4 + 8*A*a^3*b - 16*C*a*b^3) + tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 - 4*C*b^4 - 8*A*a^3*b + 16*C*a*b^3) + tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 + 4*A*a^3*b + 8*C*a*b^3) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 - 4*A*a^3*b - 8*C*a*b^3))/(d*(tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) - (b^2*atan(((b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2))/2 + (b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2))/2)/(256*A^3*a*b^11 - (b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2)*1i)/2 + (b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2)*1i)/2 - 1024*A^3*a^2*b^10 + 128*A^3*a^3*b^9 - 1024*A^3*a^4*b^8 - 256*A^3*a^6*b^6 + 64*C^3*a^3*b^9 + 1536*C^3*a^5*b^7 - 512*C^3*a^6*b^6 + 9216*C^3*a^7*b^5 - 6144*C^3*a^8*b^4 + 64*A*C^2*a*b^11 + 256*A^2*C*a*b^11 + 1824*A*C^2*a^3*b^9 - 1024*A*C^2*a^4*b^8 + 13056*A*C^2*a^5*b^7 - 13824*A*C^2*a^6*b^6 + 4608*A*C^2*a^7*b^5 - 6144*A*C^2*a^8*b^4 - 512*A^2*C*a^2*b^10 + 3456*A^2*C*a^3*b^9 - 8704*A^2*C*a^4*b^8 + 1536*A^2*C*a^5*b^7 - 7296*A^2*C*a^6*b^6 - 1536*A^2*C*a^8*b^4))*(2*A*b^2 + 12*C*a^2 + C*b^2))/d - (a*b*atan((a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - 2*a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b))*(A*a^2 + 2*A*b^2 + 2*C*a^2)*2i + a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + 2*a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b))*(A*a^2 + 2*A*b^2 + 2*C*a^2)*2i)/(256*A^3*a*b^11 - 1024*A^3*a^2*b^10 + 128*A^3*a^3*b^9 - 1024*A^3*a^4*b^8 - 256*A^3*a^6*b^6 + 64*C^3*a^3*b^9 + 1536*C^3*a^5*b^7 - 512*C^3*a^6*b^6 + 9216*C^3*a^7*b^5 - 6144*C^3*a^8*b^4 - 2*a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) - 2*a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b))*(A*a^2 + 2*A*b^2 + 2*C*a^2) + 2*a*b*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2) + 2*a*b*(A*a^2 + 2*A*b^2 + 2*C*a^2)*(32*A*b^4 + 16*C*b^4 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*C*a^3*b))*(A*a^2 + 2*A*b^2 + 2*C*a^2) + 64*A*C^2*a*b^11 + 256*A^2*C*a*b^11 + 1824*A*C^2*a^3*b^9 - 1024*A*C^2*a^4*b^8 + 13056*A*C^2*a^5*b^7 - 13824*A*C^2*a^6*b^6 + 4608*A*C^2*a^7*b^5 - 6144*A*C^2*a^8*b^4 - 512*A^2*C*a^2*b^10 + 3456*A^2*C*a^3*b^9 - 8704*A^2*C*a^4*b^8 + 1536*A^2*C*a^5*b^7 - 7296*A^2*C*a^6*b^6 - 1536*A^2*C*a^8*b^4))*(A*a^2 + 2*A*b^2 + 2*C*a^2)*4i)/d","B"
555,1,1988,246,3.900341,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^5,x)","\frac{\frac{27\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+9\,A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{9\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{9\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{3\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{9\,C\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{4}+\frac{33\,A\,a^4\,\sin\left(c+d\,x\right)}{8}+\frac{3\,C\,a^4\,\sin\left(c+d\,x\right)}{2}+\frac{3\,C\,b^4\,\sin\left(c+d\,x\right)}{2}+12\,A\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+16\,A\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+6\,A\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)+4\,A\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)+9\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)+12\,C\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+6\,C\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)+36\,C\,a\,b^3\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^8+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^8+480\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+768\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+2304\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^8+144\,A^2\,a^6\,b^2+624\,A^2\,a^4\,b^4+384\,A^2\,a^2\,b^6+64\,A^2\,b^8+24\,A\,C\,a^8+480\,A\,C\,a^6\,b^2+2368\,A\,C\,a^4\,b^4+768\,A\,C\,a^2\,b^6+16\,C^2\,a^8+384\,C^2\,a^6\,b^2+2304\,C^2\,a^4\,b^4+1024\,C^2\,a^2\,b^6\right)}\right)+\frac{9\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{9\,A\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{8}+27\,A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+12\,A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+3\,A\,b^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+6\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+\frac{3\,C\,a^4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{2}+54\,C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+9\,A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)+48\,C\,a\,b^3\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^8+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^8+480\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+768\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+2304\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^8+144\,A^2\,a^6\,b^2+624\,A^2\,a^4\,b^4+384\,A^2\,a^2\,b^6+64\,A^2\,b^8+24\,A\,C\,a^8+480\,A\,C\,a^6\,b^2+2368\,A\,C\,a^4\,b^4+768\,A\,C\,a^2\,b^6+16\,C^2\,a^8+384\,C^2\,a^6\,b^2+2304\,C^2\,a^4\,b^4+1024\,C^2\,a^2\,b^6\right)}\right)+12\,C\,a\,b^3\,\cos\left(4\,c+4\,d\,x\right)\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^8+144\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6\,b^2+624\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^8+480\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2+2368\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+768\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^8+384\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2+2304\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^8+144\,A^2\,a^6\,b^2+624\,A^2\,a^4\,b^4+384\,A^2\,a^2\,b^6+64\,A^2\,b^8+24\,A\,C\,a^8+480\,A\,C\,a^6\,b^2+2368\,A\,C\,a^4\,b^4+768\,A\,C\,a^2\,b^6+16\,C^2\,a^8+384\,C^2\,a^6\,b^2+2304\,C^2\,a^4\,b^4+1024\,C^2\,a^2\,b^6\right)}\right)+36\,A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+9\,A\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)+72\,C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+18\,C\,a^2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(4\,c+4\,d\,x\right)}{12\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{\cos\left(4\,c+4\,d\,x\right)}{8}+\frac{3}{8}\right)}","Not used",1,"((27*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + 9*A*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (9*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (9*A*a^4*sin(3*c + 3*d*x))/8 + (3*C*a^4*sin(3*c + 3*d*x))/2 + (9*C*b^4*sin(3*c + 3*d*x))/4 + (3*C*b^4*sin(5*c + 5*d*x))/4 + (33*A*a^4*sin(c + d*x))/8 + (3*C*a^4*sin(c + d*x))/2 + (3*C*b^4*sin(c + d*x))/2 + 12*A*a*b^3*sin(2*c + 2*d*x) + 16*A*a^3*b*sin(2*c + 2*d*x) + 6*A*a*b^3*sin(4*c + 4*d*x) + 4*A*a^3*b*sin(4*c + 4*d*x) + 9*A*a^2*b^2*sin(c + d*x) + 12*C*a^3*b*sin(2*c + 2*d*x) + 6*C*a^3*b*sin(4*c + 4*d*x) + 36*C*a*b^3*atan((9*A^2*a^8*sin(c/2 + (d*x)/2) + 64*A^2*b^8*sin(c/2 + (d*x)/2) + 16*C^2*a^8*sin(c/2 + (d*x)/2) + 384*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*A^2*a^4*b^4*sin(c/2 + (d*x)/2) + 144*A^2*a^6*b^2*sin(c/2 + (d*x)/2) + 1024*C^2*a^2*b^6*sin(c/2 + (d*x)/2) + 2304*C^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*C^2*a^6*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^8*sin(c/2 + (d*x)/2) + 768*A*C*a^2*b^6*sin(c/2 + (d*x)/2) + 2368*A*C*a^4*b^4*sin(c/2 + (d*x)/2) + 480*A*C*a^6*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^8 + 64*A^2*b^8 + 16*C^2*a^8 + 384*A^2*a^2*b^6 + 624*A^2*a^4*b^4 + 144*A^2*a^6*b^2 + 1024*C^2*a^2*b^6 + 2304*C^2*a^4*b^4 + 384*C^2*a^6*b^2 + 24*A*C*a^8 + 768*A*C*a^2*b^6 + 2368*A*C*a^4*b^4 + 480*A*C*a^6*b^2))) + (9*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2 + (9*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/8 + 27*A*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 12*A*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 3*A*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 6*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + (3*C*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/2 + 54*C*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 9*A*a^2*b^2*sin(3*c + 3*d*x) + 48*C*a*b^3*cos(2*c + 2*d*x)*atan((9*A^2*a^8*sin(c/2 + (d*x)/2) + 64*A^2*b^8*sin(c/2 + (d*x)/2) + 16*C^2*a^8*sin(c/2 + (d*x)/2) + 384*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*A^2*a^4*b^4*sin(c/2 + (d*x)/2) + 144*A^2*a^6*b^2*sin(c/2 + (d*x)/2) + 1024*C^2*a^2*b^6*sin(c/2 + (d*x)/2) + 2304*C^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*C^2*a^6*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^8*sin(c/2 + (d*x)/2) + 768*A*C*a^2*b^6*sin(c/2 + (d*x)/2) + 2368*A*C*a^4*b^4*sin(c/2 + (d*x)/2) + 480*A*C*a^6*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^8 + 64*A^2*b^8 + 16*C^2*a^8 + 384*A^2*a^2*b^6 + 624*A^2*a^4*b^4 + 144*A^2*a^6*b^2 + 1024*C^2*a^2*b^6 + 2304*C^2*a^4*b^4 + 384*C^2*a^6*b^2 + 24*A*C*a^8 + 768*A*C*a^2*b^6 + 2368*A*C*a^4*b^4 + 480*A*C*a^6*b^2))) + 12*C*a*b^3*cos(4*c + 4*d*x)*atan((9*A^2*a^8*sin(c/2 + (d*x)/2) + 64*A^2*b^8*sin(c/2 + (d*x)/2) + 16*C^2*a^8*sin(c/2 + (d*x)/2) + 384*A^2*a^2*b^6*sin(c/2 + (d*x)/2) + 624*A^2*a^4*b^4*sin(c/2 + (d*x)/2) + 144*A^2*a^6*b^2*sin(c/2 + (d*x)/2) + 1024*C^2*a^2*b^6*sin(c/2 + (d*x)/2) + 2304*C^2*a^4*b^4*sin(c/2 + (d*x)/2) + 384*C^2*a^6*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^8*sin(c/2 + (d*x)/2) + 768*A*C*a^2*b^6*sin(c/2 + (d*x)/2) + 2368*A*C*a^4*b^4*sin(c/2 + (d*x)/2) + 480*A*C*a^6*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^8 + 64*A^2*b^8 + 16*C^2*a^8 + 384*A^2*a^2*b^6 + 624*A^2*a^4*b^4 + 144*A^2*a^6*b^2 + 1024*C^2*a^2*b^6 + 2304*C^2*a^4*b^4 + 384*C^2*a^6*b^2 + 24*A*C*a^8 + 768*A*C*a^2*b^6 + 2368*A*C*a^4*b^4 + 480*A*C*a^6*b^2))) + 36*A*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 9*A*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 72*C*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 18*C*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x))/(12*d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
556,1,1738,250,3.955215,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^6,x)","\frac{\frac{A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{A\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{30}+\frac{3\,A\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{A\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{16}+\frac{5\,C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{24}+\frac{C\,a^4\,\sin\left(5\,c+5\,d\,x\right)}{24}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{3}+\frac{A\,b^4\,\sin\left(c+d\,x\right)}{8}+\frac{C\,a^4\,\sin\left(c+d\,x\right)}{6}+\frac{5\,C\,b^4\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+80\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^6+24\,A^2\,a^4\,b^2+16\,A^2\,a^2\,b^4+24\,A\,C\,a^6+80\,A\,C\,a^4\,b^2+64\,A\,C\,a^2\,b^4+16\,C^2\,a^6+64\,C^2\,a^4\,b^2+64\,C^2\,a^2\,b^4+4\,C^2\,b^6\right)}\right)}{4}+\frac{A\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{7\,A\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{A\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{3\,A\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{16}+A\,a^2\,b^2\,\sin\left(c+d\,x\right)+\frac{C\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{3\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{5\,C\,b^4\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+80\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^6+24\,A^2\,a^4\,b^2+16\,A^2\,a^2\,b^4+24\,A\,C\,a^6+80\,A\,C\,a^4\,b^2+64\,A\,C\,a^2\,b^4+16\,C^2\,a^6+64\,C^2\,a^4\,b^2+64\,C^2\,a^2\,b^4+4\,C^2\,b^6\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{8}+\frac{C\,b^4\,\mathrm{atan}\left(\frac{9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^6+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^2+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^4+24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6+80\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^4+16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^2+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^4+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^6}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^6+24\,A^2\,a^4\,b^2+16\,A^2\,a^2\,b^4+24\,A\,C\,a^6+80\,A\,C\,a^4\,b^2+64\,A\,C\,a^2\,b^4+16\,C^2\,a^6+64\,C^2\,a^4\,b^2+64\,C^2\,a^2\,b^4+4\,C^2\,b^6\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{8}+\frac{5\,A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{4}+\frac{9\,C\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{8}+\frac{3\,C\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{8}+\frac{5\,A\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{15\,A\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{A\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{4}+\frac{3\,A\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{16}+\frac{5\,C\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{5\,C\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{2}+\frac{C\,a^3\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(5\,c+5\,d\,x\right)}{4}+\frac{5\,A\,a\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{15\,A\,a^3\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8}+5\,C\,a\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{5\,C\,a^3\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}}{d\,\left(\frac{5\,\cos\left(c+d\,x\right)}{8}+\frac{5\,\cos\left(3\,c+3\,d\,x\right)}{16}+\frac{\cos\left(5\,c+5\,d\,x\right)}{16}\right)}","Not used",1,"((A*a^4*sin(3*c + 3*d*x))/6 + (A*a^4*sin(5*c + 5*d*x))/30 + (3*A*b^4*sin(3*c + 3*d*x))/16 + (A*b^4*sin(5*c + 5*d*x))/16 + (5*C*a^4*sin(3*c + 3*d*x))/24 + (C*a^4*sin(5*c + 5*d*x))/24 + (A*a^4*sin(c + d*x))/3 + (A*b^4*sin(c + d*x))/8 + (C*a^4*sin(c + d*x))/6 + (5*C*b^4*cos(c + d*x)*atan((9*A^2*a^6*sin(c/2 + (d*x)/2) + 16*C^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*b^6*sin(c/2 + (d*x)/2) + 16*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 24*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 64*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 64*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^6*sin(c/2 + (d*x)/2) + 64*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 80*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^6 + 16*C^2*a^6 + 4*C^2*b^6 + 16*A^2*a^2*b^4 + 24*A^2*a^4*b^2 + 64*C^2*a^2*b^4 + 64*C^2*a^4*b^2 + 24*A*C*a^6 + 64*A*C*a^2*b^4 + 80*A*C*a^4*b^2))))/4 + (A*a*b^3*sin(2*c + 2*d*x))/2 + (7*A*a^3*b*sin(2*c + 2*d*x))/8 + (A*a*b^3*sin(4*c + 4*d*x))/4 + (3*A*a^3*b*sin(4*c + 4*d*x))/16 + A*a^2*b^2*sin(c + d*x) + (C*a^3*b*sin(2*c + 2*d*x))/2 + (C*a^3*b*sin(4*c + 4*d*x))/4 + (3*C*a^2*b^2*sin(c + d*x))/4 + (5*C*b^4*atan((9*A^2*a^6*sin(c/2 + (d*x)/2) + 16*C^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*b^6*sin(c/2 + (d*x)/2) + 16*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 24*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 64*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 64*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^6*sin(c/2 + (d*x)/2) + 64*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 80*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^6 + 16*C^2*a^6 + 4*C^2*b^6 + 16*A^2*a^2*b^4 + 24*A^2*a^4*b^2 + 64*C^2*a^2*b^4 + 64*C^2*a^4*b^2 + 24*A*C*a^6 + 64*A*C*a^2*b^4 + 80*A*C*a^4*b^2)))*cos(3*c + 3*d*x))/8 + (C*b^4*atan((9*A^2*a^6*sin(c/2 + (d*x)/2) + 16*C^2*a^6*sin(c/2 + (d*x)/2) + 4*C^2*b^6*sin(c/2 + (d*x)/2) + 16*A^2*a^2*b^4*sin(c/2 + (d*x)/2) + 24*A^2*a^4*b^2*sin(c/2 + (d*x)/2) + 64*C^2*a^2*b^4*sin(c/2 + (d*x)/2) + 64*C^2*a^4*b^2*sin(c/2 + (d*x)/2) + 24*A*C*a^6*sin(c/2 + (d*x)/2) + 64*A*C*a^2*b^4*sin(c/2 + (d*x)/2) + 80*A*C*a^4*b^2*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^6 + 16*C^2*a^6 + 4*C^2*b^6 + 16*A^2*a^2*b^4 + 24*A^2*a^4*b^2 + 64*C^2*a^2*b^4 + 64*C^2*a^4*b^2 + 24*A*C*a^6 + 64*A*C*a^2*b^4 + 80*A*C*a^4*b^2)))*cos(5*c + 5*d*x))/8 + (5*A*a^2*b^2*sin(3*c + 3*d*x))/4 + (A*a^2*b^2*sin(5*c + 5*d*x))/4 + (9*C*a^2*b^2*sin(3*c + 3*d*x))/8 + (3*C*a^2*b^2*sin(5*c + 5*d*x))/8 + (5*A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (15*A*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/16 + (A*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/4 + (3*A*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/16 + (5*C*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (5*C*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (C*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/2 + (C*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(5*c + 5*d*x))/4 + (5*A*a*b^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (15*A*a^3*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 + 5*C*a*b^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (5*C*a^3*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2)/(d*((5*cos(c + d*x))/8 + (5*cos(3*c + 3*d*x))/16 + cos(5*c + 5*d*x)/16))","B"
557,1,690,307,3.968019,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^7,x)","\frac{\left(\frac{11\,A\,a^4}{8}+A\,b^4+\frac{5\,C\,a^4}{4}+\frac{15\,A\,a^2\,b^2}{2}+6\,C\,a^2\,b^2-8\,A\,a\,b^3-8\,A\,a^3\,b-8\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{5\,A\,a^4}{24}-3\,A\,b^4-\frac{7\,C\,a^4}{4}-\frac{21\,A\,a^2\,b^2}{2}-18\,C\,a^2\,b^2+\frac{88\,A\,a\,b^3}{3}+\frac{56\,A\,a^3\,b}{3}+40\,C\,a\,b^3+\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{15\,A\,a^4}{4}+2\,A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+12\,C\,a^2\,b^2-48\,A\,a\,b^3-\frac{208\,A\,a^3\,b}{5}-80\,C\,a\,b^3-48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{15\,A\,a^4}{4}+2\,A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+12\,C\,a^2\,b^2+48\,A\,a\,b^3+\frac{208\,A\,a^3\,b}{5}+80\,C\,a\,b^3+48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,A\,a^4}{24}-3\,A\,b^4-\frac{7\,C\,a^4}{4}-\frac{21\,A\,a^2\,b^2}{2}-18\,C\,a^2\,b^2-\frac{88\,A\,a\,b^3}{3}-\frac{56\,A\,a^3\,b}{3}-40\,C\,a\,b^3-\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,A\,a^4}{8}+A\,b^4+\frac{5\,C\,a^4}{4}+\frac{15\,A\,a^2\,b^2}{2}+6\,C\,a^2\,b^2+8\,A\,a\,b^3+8\,A\,a^3\,b+8\,C\,a\,b^3+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,A\,a^4}{16}+\frac{A\,b^4}{2}+\frac{3\,C\,a^4}{8}+C\,b^4+\frac{9\,A\,a^2\,b^2}{4}+3\,C\,a^2\,b^2\right)}{\frac{5\,A\,a^4}{4}+2\,A\,b^4+\frac{3\,C\,a^4}{2}+4\,C\,b^4+9\,A\,a^2\,b^2+12\,C\,a^2\,b^2}\right)\,\left(\frac{5\,A\,a^4}{8}+A\,b^4+\frac{3\,C\,a^4}{4}+2\,C\,b^4+\frac{9\,A\,a^2\,b^2}{2}+6\,C\,a^2\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((11*A*a^4)/8 + A*b^4 + (5*C*a^4)/4 + (15*A*a^2*b^2)/2 + 6*C*a^2*b^2 + 8*A*a*b^3 + 8*A*a^3*b + 8*C*a*b^3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^11*((11*A*a^4)/8 + A*b^4 + (5*C*a^4)/4 + (15*A*a^2*b^2)/2 + 6*C*a^2*b^2 - 8*A*a*b^3 - 8*A*a^3*b - 8*C*a*b^3 - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^3*(3*A*b^4 - (5*A*a^4)/24 + (7*C*a^4)/4 + (21*A*a^2*b^2)/2 + 18*C*a^2*b^2 + (88*A*a*b^3)/3 + (56*A*a^3*b)/3 + 40*C*a*b^3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^9*((5*A*a^4)/24 - 3*A*b^4 - (7*C*a^4)/4 - (21*A*a^2*b^2)/2 - 18*C*a^2*b^2 + (88*A*a*b^3)/3 + (56*A*a^3*b)/3 + 40*C*a*b^3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^5*((15*A*a^4)/4 + 2*A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 12*C*a^2*b^2 + 48*A*a*b^3 + (208*A*a^3*b)/5 + 80*C*a*b^3 + 48*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((15*A*a^4)/4 + 2*A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 12*C*a^2*b^2 - 48*A*a*b^3 - (208*A*a^3*b)/5 - 80*C*a*b^3 - 48*C*a^3*b))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*((5*A*a^4)/16 + (A*b^4)/2 + (3*C*a^4)/8 + C*b^4 + (9*A*a^2*b^2)/4 + 3*C*a^2*b^2))/((5*A*a^4)/4 + 2*A*b^4 + (3*C*a^4)/2 + 4*C*b^4 + 9*A*a^2*b^2 + 12*C*a^2*b^2))*((5*A*a^4)/8 + A*b^4 + (3*C*a^4)/4 + 2*C*b^4 + (9*A*a^2*b^2)/2 + 6*C*a^2*b^2))/d","B"
558,1,755,355,4.939394,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^8,x)","\frac{a\,b\,\mathrm{atanh}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A\,a^2+6\,A\,b^2+6\,C\,a^2+8\,C\,b^2\right)}{6\,A\,a\,b^3+5\,A\,a^3\,b+8\,C\,a\,b^3+6\,C\,a^3\,b}\right)\,\left(5\,A\,a^2+6\,A\,b^2+6\,C\,a^2+8\,C\,b^2\right)}{2\,d}-\frac{\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2-5\,A\,a\,b^3-\frac{11\,A\,a^3\,b}{2}-4\,C\,a\,b^3-5\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(12\,A\,a\,b^3-\frac{28\,A\,b^4}{3}-\frac{20\,C\,a^4}{3}-12\,C\,b^4-40\,A\,a^2\,b^2-56\,C\,a^2\,b^2-4\,A\,a^4+\frac{14\,A\,a^3\,b}{3}+16\,C\,a\,b^3+12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{86\,A\,a^4}{5}+\frac{58\,A\,b^4}{3}+\frac{226\,C\,a^4}{15}+30\,C\,b^4+\frac{452\,A\,a^2\,b^2}{5}+116\,C\,a^2\,b^2-9\,A\,a\,b^3-\frac{85\,A\,a^3\,b}{6}-20\,C\,a\,b^3-9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{424\,A\,a^4}{35}-24\,A\,b^4-\frac{104\,C\,a^4}{5}-40\,C\,b^4-\frac{624\,A\,a^2\,b^2}{5}-144\,C\,a^2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{86\,A\,a^4}{5}+\frac{58\,A\,b^4}{3}+\frac{226\,C\,a^4}{15}+30\,C\,b^4+\frac{452\,A\,a^2\,b^2}{5}+116\,C\,a^2\,b^2+9\,A\,a\,b^3+\frac{85\,A\,a^3\,b}{6}+20\,C\,a\,b^3+9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,a^4-\frac{28\,A\,b^4}{3}-\frac{20\,C\,a^4}{3}-12\,C\,b^4-40\,A\,a^2\,b^2-56\,C\,a^2\,b^2-12\,A\,a\,b^3-\frac{14\,A\,a^3\,b}{3}-16\,C\,a\,b^3-12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+12\,C\,a^2\,b^2+5\,A\,a\,b^3+\frac{11\,A\,a^3\,b}{2}+4\,C\,a\,b^3+5\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(a*b*atanh((a*b*tan(c/2 + (d*x)/2)*(5*A*a^2 + 6*A*b^2 + 6*C*a^2 + 8*C*b^2))/(6*A*a*b^3 + 5*A*a^3*b + 8*C*a*b^3 + 6*C*a^3*b))*(5*A*a^2 + 6*A*b^2 + 6*C*a^2 + 8*C*b^2))/(2*d) - (tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 + 5*A*a*b^3 + (11*A*a^3*b)/2 + 4*C*a*b^3 + 5*C*a^3*b) - tan(c/2 + (d*x)/2)^7*((424*A*a^4)/35 + 24*A*b^4 + (104*C*a^4)/5 + 40*C*b^4 + (624*A*a^2*b^2)/5 + 144*C*a^2*b^2) + tan(c/2 + (d*x)/2)^13*(2*A*a^4 + 2*A*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 12*C*a^2*b^2 - 5*A*a*b^3 - (11*A*a^3*b)/2 - 4*C*a*b^3 - 5*C*a^3*b) - tan(c/2 + (d*x)/2)^3*(4*A*a^4 + (28*A*b^4)/3 + (20*C*a^4)/3 + 12*C*b^4 + 40*A*a^2*b^2 + 56*C*a^2*b^2 + 12*A*a*b^3 + (14*A*a^3*b)/3 + 16*C*a*b^3 + 12*C*a^3*b) - tan(c/2 + (d*x)/2)^11*(4*A*a^4 + (28*A*b^4)/3 + (20*C*a^4)/3 + 12*C*b^4 + 40*A*a^2*b^2 + 56*C*a^2*b^2 - 12*A*a*b^3 - (14*A*a^3*b)/3 - 16*C*a*b^3 - 12*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((86*A*a^4)/5 + (58*A*b^4)/3 + (226*C*a^4)/15 + 30*C*b^4 + (452*A*a^2*b^2)/5 + 116*C*a^2*b^2 + 9*A*a*b^3 + (85*A*a^3*b)/6 + 20*C*a*b^3 + 9*C*a^3*b) + tan(c/2 + (d*x)/2)^9*((86*A*a^4)/5 + (58*A*b^4)/3 + (226*C*a^4)/15 + 30*C*b^4 + (452*A*a^2*b^2)/5 + 116*C*a^2*b^2 - 9*A*a*b^3 - (85*A*a^3*b)/6 - 20*C*a*b^3 - 9*C*a^3*b))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
559,1,406,183,2.778954,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^4+8\,a^2\,b^2-9\,b^4\right)}{4\,\left(2\,a^5+2\,a^3\,b^2-\frac{9\,a\,b^4}{4}\right)}\right)\,\left(8\,a^4+8\,a^2\,b^2-9\,b^4\right)}{4\,d}-\frac{\left(-6\,a^4\,b+2\,a^3\,b^2+4\,a^2\,b^3-\frac{15\,a\,b^4}{4}+2\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-24\,a^4\,b+4\,a^3\,b^2+\frac{32\,a^2\,b^3}{3}-\frac{3\,a\,b^4}{2}+\frac{8\,b^5}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-36\,a^4\,b+\frac{40\,a^2\,b^3}{3}+\frac{116\,b^5}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-24\,a^4\,b-4\,a^3\,b^2+\frac{32\,a^2\,b^3}{3}+\frac{3\,a\,b^4}{2}+\frac{8\,b^5}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-6\,a^4\,b-2\,a^3\,b^2+4\,a^2\,b^3+\frac{15\,a\,b^4}{4}+2\,b^5\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(8\,a^4+8\,a^2\,b^2-9\,b^4\right)}{4\,d}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(8*a^4 - 9*b^4 + 8*a^2*b^2))/(4*(2*a^5 - (9*a*b^4)/4 + 2*a^3*b^2)))*(8*a^4 - 9*b^4 + 8*a^2*b^2))/(4*d) - (tan(c/2 + (d*x)/2)^5*((116*b^5)/15 - 36*a^4*b + (40*a^2*b^3)/3) + tan(c/2 + (d*x)/2)*((15*a*b^4)/4 - 6*a^4*b + 2*b^5 + 4*a^2*b^3 - 2*a^3*b^2) + tan(c/2 + (d*x)/2)^9*(2*b^5 - 6*a^4*b - (15*a*b^4)/4 + 4*a^2*b^3 + 2*a^3*b^2) + tan(c/2 + (d*x)/2)^3*((3*a*b^4)/2 - 24*a^4*b + (8*b^5)/3 + (32*a^2*b^3)/3 - 4*a^3*b^2) + tan(c/2 + (d*x)/2)^7*((8*b^5)/3 - 24*a^4*b - (3*a*b^4)/2 + (32*a^2*b^3)/3 + 4*a^3*b^2))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (a*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2)*(8*a^4 - 9*b^4 + 8*a^2*b^2))/(4*d)","B"
560,1,107,129,1.345417,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","a^4\,x-\frac{3\,b^4\,x}{8}-\frac{b^4\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}-\frac{4\,a\,b^3\,\sin\left(c+d\,x\right)}{3\,d}+\frac{2\,a^3\,b\,\sin\left(c+d\,x\right)}{d}-\frac{3\,b^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}-\frac{2\,a\,b^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"a^4*x - (3*b^4*x)/8 - (b^4*cos(c + d*x)^3*sin(c + d*x))/(4*d) - (4*a*b^3*sin(c + d*x))/(3*d) + (2*a^3*b*sin(c + d*x))/d - (3*b^4*cos(c + d*x)*sin(c + d*x))/(8*d) - (2*a*b^3*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
561,1,76,92,1.334745,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","a^3\,x-\frac{3\,b^3\,\sin\left(c+d\,x\right)}{4\,d}-\frac{b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}-\frac{a\,b^2\,x}{2}-\frac{a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a^2\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"a^3*x - (3*b^3*sin(c + d*x))/(4*d) - (b^3*sin(3*c + 3*d*x))/(12*d) - (a*b^2*x)/2 - (a*b^2*sin(2*c + 2*d*x))/(4*d) + (a^2*b*sin(c + d*x))/d","B"
562,1,5844,233,7.840154,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,A\,b^3+8\,C\,a^3+5\,C\,b^3+8\,A\,a\,b^2+8\,C\,a\,b^2+4\,C\,a^2\,b\right)}{4\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(72\,C\,a^3-12\,A\,b^3+9\,C\,b^3+72\,A\,a\,b^2+40\,C\,a\,b^2-12\,C\,a^2\,b\right)}{12\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,A\,b^3+72\,C\,a^3-9\,C\,b^3+72\,A\,a\,b^2+40\,C\,a\,b^2+12\,C\,a^2\,b\right)}{12\,b^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3-8\,C\,a^3+5\,C\,b^3-8\,A\,a\,b^2-8\,C\,a\,b^2+4\,C\,a^2\,b\right)}{4\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)\,1{}\mathrm{i}}{b^5}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)\,1{}\mathrm{i}}{b^5}}{\frac{64\,A^3\,a^8\,b^6-96\,A^3\,a^7\,b^7+96\,A^3\,a^6\,b^8-80\,A^3\,a^5\,b^9+32\,A^3\,a^4\,b^{10}-16\,A^3\,a^3\,b^{11}+192\,A^2\,C\,a^{10}\,b^4-288\,A^2\,C\,a^9\,b^5+288\,A^2\,C\,a^8\,b^6-264\,A^2\,C\,a^7\,b^7+168\,A^2\,C\,a^6\,b^8-120\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}-24\,A^2\,C\,a^3\,b^{11}+192\,A\,C^2\,a^{12}\,b^2-288\,A\,C^2\,a^{11}\,b^3+288\,A\,C^2\,a^{10}\,b^4-288\,A\,C^2\,a^9\,b^5+240\,A\,C^2\,a^8\,b^6-192\,A\,C^2\,a^7\,b^7+96\,A\,C^2\,a^6\,b^8-57\,A\,C^2\,a^5\,b^9+18\,A\,C^2\,a^4\,b^{10}-9\,A\,C^2\,a^3\,b^{11}+64\,C^3\,a^{14}-96\,C^3\,a^{13}\,b+96\,C^3\,a^{12}\,b^2-104\,C^3\,a^{11}\,b^3+104\,C^3\,a^{10}\,b^4-88\,C^3\,a^9\,b^5+48\,C^3\,a^8\,b^6-33\,C^3\,a^7\,b^7+18\,C^3\,a^6\,b^8-9\,C^3\,a^5\,b^9}{b^{12}}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{b^5}-\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)}{b^5}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)\right)\,2{}\mathrm{i}}{b^5\,d}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}}{\frac{64\,A^3\,a^8\,b^6-96\,A^3\,a^7\,b^7+96\,A^3\,a^6\,b^8-80\,A^3\,a^5\,b^9+32\,A^3\,a^4\,b^{10}-16\,A^3\,a^3\,b^{11}+192\,A^2\,C\,a^{10}\,b^4-288\,A^2\,C\,a^9\,b^5+288\,A^2\,C\,a^8\,b^6-264\,A^2\,C\,a^7\,b^7+168\,A^2\,C\,a^6\,b^8-120\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}-24\,A^2\,C\,a^3\,b^{11}+192\,A\,C^2\,a^{12}\,b^2-288\,A\,C^2\,a^{11}\,b^3+288\,A\,C^2\,a^{10}\,b^4-288\,A\,C^2\,a^9\,b^5+240\,A\,C^2\,a^8\,b^6-192\,A\,C^2\,a^7\,b^7+96\,A\,C^2\,a^6\,b^8-57\,A\,C^2\,a^5\,b^9+18\,A\,C^2\,a^4\,b^{10}-9\,A\,C^2\,a^3\,b^{11}+64\,C^3\,a^{14}-96\,C^3\,a^{13}\,b+96\,C^3\,a^{12}\,b^2-104\,C^3\,a^{11}\,b^3+104\,C^3\,a^{10}\,b^4-88\,C^3\,a^9\,b^5+48\,C^3\,a^8\,b^6-33\,C^3\,a^7\,b^7+18\,C^3\,a^6\,b^8-9\,C^3\,a^5\,b^9}{b^{12}}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^7-a^2\,b^5\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^7*(4*A*b^3 + 8*C*a^3 + 5*C*b^3 + 8*A*a*b^2 + 8*C*a*b^2 + 4*C*a^2*b))/(4*b^4) + (tan(c/2 + (d*x)/2)^3*(72*C*a^3 - 12*A*b^3 + 9*C*b^3 + 72*A*a*b^2 + 40*C*a*b^2 - 12*C*a^2*b))/(12*b^4) + (tan(c/2 + (d*x)/2)^5*(12*A*b^3 + 72*C*a^3 - 9*C*b^3 + 72*A*a*b^2 + 40*C*a*b^2 + 12*C*a^2*b))/(12*b^4) - (tan(c/2 + (d*x)/2)*(4*A*b^3 - 8*C*a^3 + 5*C*b^3 - 8*A*a*b^2 - 8*C*a*b^2 + 4*C*a^2*b))/(4*b^4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atan(((((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) + (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 - (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8))*1i)/b^5 + (((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) - (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 + (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8))*1i)/b^5)/((64*C^3*a^14 - 96*C^3*a^13*b - 16*A^3*a^3*b^11 + 32*A^3*a^4*b^10 - 80*A^3*a^5*b^9 + 96*A^3*a^6*b^8 - 96*A^3*a^7*b^7 + 64*A^3*a^8*b^6 - 9*C^3*a^5*b^9 + 18*C^3*a^6*b^8 - 33*C^3*a^7*b^7 + 48*C^3*a^8*b^6 - 88*C^3*a^9*b^5 + 104*C^3*a^10*b^4 - 104*C^3*a^11*b^3 + 96*C^3*a^12*b^2 - 9*A*C^2*a^3*b^11 + 18*A*C^2*a^4*b^10 - 57*A*C^2*a^5*b^9 + 96*A*C^2*a^6*b^8 - 192*A*C^2*a^7*b^7 + 240*A*C^2*a^8*b^6 - 288*A*C^2*a^9*b^5 + 288*A*C^2*a^10*b^4 - 288*A*C^2*a^11*b^3 + 192*A*C^2*a^12*b^2 - 24*A^2*C*a^3*b^11 + 48*A^2*C*a^4*b^10 - 120*A^2*C*a^5*b^9 + 168*A^2*C*a^6*b^8 - 264*A^2*C*a^7*b^7 + 288*A^2*C*a^8*b^6 - 288*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4)/b^12 + (((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) + (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 - (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/b^5 - (((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) - (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 + (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8)))/b^5))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8))*2i)/(b^5*d) - (a^3*atan(((a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) + (a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 - (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5))*1i)/(b^7 - a^2*b^5) + (a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) - (a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 + (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5))*1i)/(b^7 - a^2*b^5))/((64*C^3*a^14 - 96*C^3*a^13*b - 16*A^3*a^3*b^11 + 32*A^3*a^4*b^10 - 80*A^3*a^5*b^9 + 96*A^3*a^6*b^8 - 96*A^3*a^7*b^7 + 64*A^3*a^8*b^6 - 9*C^3*a^5*b^9 + 18*C^3*a^6*b^8 - 33*C^3*a^7*b^7 + 48*C^3*a^8*b^6 - 88*C^3*a^9*b^5 + 104*C^3*a^10*b^4 - 104*C^3*a^11*b^3 + 96*C^3*a^12*b^2 - 9*A*C^2*a^3*b^11 + 18*A*C^2*a^4*b^10 - 57*A*C^2*a^5*b^9 + 96*A*C^2*a^6*b^8 - 192*A*C^2*a^7*b^7 + 240*A*C^2*a^8*b^6 - 288*A*C^2*a^9*b^5 + 288*A*C^2*a^10*b^4 - 288*A*C^2*a^11*b^3 + 192*A*C^2*a^12*b^2 - 24*A^2*C*a^3*b^11 + 48*A^2*C*a^4*b^10 - 120*A^2*C*a^5*b^9 + 168*A^2*C*a^6*b^8 - 264*A^2*C*a^7*b^7 + 288*A^2*C*a^8*b^6 - 288*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4)/b^12 + (a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) + (a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 - (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5) - (a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 72*A*C*a*b^10 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2))/(2*b^8) - (a^3*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 12*C*a*b^15)/b^12 + (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*2i)/(d*(b^7 - a^2*b^5))","B"
563,1,3953,177,5.177262,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^2+2\,C\,a^2+2\,C\,b^2+C\,a\,b\right)}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^2+3\,C\,a^2+C\,b^2\right)}{3\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^2+2\,C\,a^2+2\,C\,b^2-C\,a\,b\right)}{b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{b^4}-\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}+\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)}{b^4}+\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^{10}}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)}{b^4}}\right)\,\left(C\,a^3\,1{}\mathrm{i}+\frac{a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}}{2}\right)\,2{}\mathrm{i}}{b^4\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^4-16\,A^2\,a^4\,b^5+12\,A^2\,a^3\,b^6-4\,A^2\,a^2\,b^7+16\,A\,C\,a^7\,b^2-32\,A\,C\,a^6\,b^3+28\,A\,C\,a^5\,b^4-20\,A\,C\,a^4\,b^5+12\,A\,C\,a^3\,b^6-4\,A\,C\,a^2\,b^7+8\,C^2\,a^9-16\,C^2\,a^8\,b+16\,C^2\,a^7\,b^2-16\,C^2\,a^6\,b^3+13\,C^2\,a^5\,b^4-7\,C^2\,a^4\,b^5+3\,C^2\,a^3\,b^6-C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(2*A*b^2 + 2*C*a^2 + 2*C*b^2 + C*a*b))/b^3 + (4*tan(c/2 + (d*x)/2)^3*(3*A*b^2 + 3*C*a^2 + C*b^2))/(3*b^3) + (tan(c/2 + (d*x)/2)*(2*A*b^2 + 2*C*a^2 + 2*C*b^2 - C*a*b))/b^3)/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) - (atan(-((((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2))/b^4 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2)*1i)/b^4 - (((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2))/b^4 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2)*1i)/b^4)/((16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4))/b^9 + (((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2))/b^4 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2))/b^4 + (((((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/b^10)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2))/b^4 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6)*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2))/b^4))*(C*a^3*1i + (a*b^2*(2*A + C)*1i)/2)*2i)/(b^4*d) - (a^2*atan(((a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4) + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 - (a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4))/b^9 + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4) - (a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^9 - 16*C^2*a^8*b - 4*A^2*a^2*b^7 + 12*A^2*a^3*b^6 - 16*A^2*a^4*b^5 + 8*A^2*a^5*b^4 - C^2*a^2*b^7 + 3*C^2*a^3*b^6 - 7*C^2*a^4*b^5 + 13*C^2*a^5*b^4 - 16*C^2*a^6*b^3 + 16*C^2*a^7*b^2 - 4*A*C*a^2*b^7 + 12*A*C*a^3*b^6 - 20*A*C*a^4*b^5 + 28*A*C*a^5*b^4 - 32*A*C*a^6*b^3 + 16*A*C*a^7*b^2))/b^6 - (a^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4))))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*2i)/(d*(b^6 - a^2*b^4))","B"
564,1,2398,128,4.649034,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a-C\,b\right)}{b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a+C\,b\right)}{b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\left(C\,a^3\,\sqrt{b^2-a^2}+A\,a\,b^2\,\sqrt{b^2-a^2}\right)}{b^3\,d\,\left(a^2-b^2\right)}-\frac{a\,\ln\left(\frac{8\,a\,\left(a-b\right)\,\left(4\,A^3\,b^6+12\,A^2\,C\,a^2\,b^4-2\,A^2\,C\,a\,b^5+4\,A^2\,C\,b^6+12\,A\,C^2\,a^4\,b^2-4\,A\,C^2\,a^3\,b^3+8\,A\,C^2\,a^2\,b^4-A\,C^2\,a\,b^5+A\,C^2\,b^6+4\,C^3\,a^6-2\,C^3\,a^5\,b+4\,C^3\,a^4\,b^2-C^3\,a^3\,b^3+C^3\,a^2\,b^4\right)}{b^6}+\frac{a\,\left(C\,a^2+A\,b^2\right)\,\sqrt{b^2-a^2}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-b\right)\,\left(8\,A^2\,a^2\,b^4-8\,A^2\,a\,b^5+4\,A^2\,b^6+16\,A\,C\,a^4\,b^2-16\,A\,C\,a^3\,b^3+12\,A\,C\,a^2\,b^4-8\,A\,C\,a\,b^5+4\,A\,C\,b^6+8\,C^2\,a^6-8\,C^2\,a^5\,b+8\,C^2\,a^4\,b^2-8\,C^2\,a^3\,b^3+5\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{b^4}+\frac{a\,\left(C\,a^2+A\,b^2\right)\,\sqrt{b^2-a^2}\,\left(16\,{\left(a-b\right)}^2\,\left(2\,A\,b^2+2\,C\,a^2+C\,b^2+C\,a\,b\right)+\frac{64\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+A\,b^2\right)\,\sqrt{b^2-a^2}\,{\left(a-b\right)}^2}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)}{d\,\left(b^5-a^2\,b^3\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(4\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+12\,A^2\,C\,a^4\,b^4-14\,A^2\,C\,a^3\,b^5+6\,A^2\,C\,a^2\,b^6-4\,A^2\,C\,a\,b^7+12\,A\,C^2\,a^6\,b^2-16\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4-9\,A\,C^2\,a^3\,b^5+2\,A\,C^2\,a^2\,b^6-A\,C^2\,a\,b^7+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}}\right)\,\left(1{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^3\,d}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(2*C*a - C*b))/b^2 + (tan(c/2 + (d*x)/2)^3*(2*C*a + C*b))/b^2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 + ((C*a^2*1i + b^2*(A*1i + (C*1i)/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2))*1i)/b^3 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 - ((C*a^2*1i + b^2*(A*1i + (C*1i)/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2))*1i)/b^3)/((16*(4*C^3*a^8 - 4*A^3*a*b^7 - 6*C^3*a^7*b + 4*A^3*a^2*b^6 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - A*C^2*a*b^7 - 4*A^2*C*a*b^7 + 2*A*C^2*a^2*b^6 - 9*A*C^2*a^3*b^5 + 12*A*C^2*a^4*b^4 - 16*A*C^2*a^5*b^3 + 12*A*C^2*a^6*b^2 + 6*A^2*C*a^2*b^6 - 14*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4))/b^6 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 + ((C*a^2*1i + b^2*(A*1i + (C*1i)/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2)))/b^3 - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 12*A*C*a*b^6 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2))/b^4 - ((C*a^2*1i + b^2*(A*1i + (C*1i)/2))*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2))*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2)))/b^3))*(C*a^2*1i + b^2*(A*1i + (C*1i)/2))*2i)/(b^3*d) - (log(a*tan(c/2 + (d*x)/2) - b*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(C*a^3*(b^2 - a^2)^(1/2) + A*a*b^2*(b^2 - a^2)^(1/2)))/(b^3*d*(a^2 - b^2)) - (a*log((8*a*(a - b)*(4*A^3*b^6 + 4*C^3*a^6 + A*C^2*b^6 + 4*A^2*C*b^6 - 2*C^3*a^5*b + C^3*a^2*b^4 - C^3*a^3*b^3 + 4*C^3*a^4*b^2 - A*C^2*a*b^5 - 2*A^2*C*a*b^5 + 8*A*C^2*a^2*b^4 - 4*A*C^2*a^3*b^3 + 12*A*C^2*a^4*b^2 + 12*A^2*C*a^2*b^4))/b^6 + (a*(A*b^2 + C*a^2)*(b^2 - a^2)^(1/2)*((8*tan(c/2 + (d*x)/2)*(a - b)*(4*A^2*b^6 + 8*C^2*a^6 + C^2*b^6 - 8*A^2*a*b^5 - 2*C^2*a*b^5 - 8*C^2*a^5*b + 8*A^2*a^2*b^4 + 5*C^2*a^2*b^4 - 8*C^2*a^3*b^3 + 8*C^2*a^4*b^2 + 4*A*C*b^6 - 8*A*C*a*b^5 + 12*A*C*a^2*b^4 - 16*A*C*a^3*b^3 + 16*A*C*a^4*b^2))/b^4 + (a*(A*b^2 + C*a^2)*(b^2 - a^2)^(1/2)*(16*(a - b)^2*(2*A*b^2 + 2*C*a^2 + C*b^2 + C*a*b) + (64*a^2*b^2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2)*(b^2 - a^2)^(1/2)*(a - b)^2)/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2))/(d*(b^5 - a^2*b^3))","B"
565,1,916,86,3.553371,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x)),x)","\frac{C\,\sin\left(c+d\,x\right)}{b\,d}-\frac{2\,C\,a\,\mathrm{atan}\left(\frac{64\,C^3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,C^3\,a^3+128\,A\,C^2\,a^3-\frac{64\,C^3\,a^4}{b}+64\,A^2\,C\,a\,b^2-64\,A^2\,C\,a^2\,b-\frac{128\,A\,C^2\,a^4}{b}}+\frac{64\,C^3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2\,b^2-64\,A^2\,C\,a\,b^3+128\,A\,C^2\,a^4-128\,A\,C^2\,a^3\,b+64\,C^3\,a^4-64\,C^3\,a^3\,b}+\frac{128\,A\,C^2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2\,b^2-64\,A^2\,C\,a\,b^3+128\,A\,C^2\,a^4-128\,A\,C^2\,a^3\,b+64\,C^3\,a^4-64\,C^3\,a^3\,b}+\frac{64\,A^2\,C\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2-\frac{64\,C^3\,a^3}{b}+\frac{64\,C^3\,a^4}{b^2}-64\,A^2\,C\,a\,b-\frac{128\,A\,C^2\,a^3}{b}+\frac{128\,A\,C^2\,a^4}{b^2}}+\frac{128\,A\,C^2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,C^3\,a^3+128\,A\,C^2\,a^3-\frac{64\,C^3\,a^4}{b}+64\,A^2\,C\,a\,b^2-64\,A^2\,C\,a^2\,b-\frac{128\,A\,C^2\,a^4}{b}}-\frac{64\,A^2\,C\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,A^2\,C\,a^2-\frac{64\,C^3\,a^3}{b}+\frac{64\,C^3\,a^4}{b^2}-64\,A^2\,C\,a\,b-\frac{128\,A\,C^2\,a^3}{b}+\frac{128\,A\,C^2\,a^4}{b^2}}\right)}{b^2\,d}-\frac{\ln\left(\frac{\left(C\,a^2+A\,b^2\right)\,\sqrt{b^2-a^2}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-b\right)\,\left(A^2\,b^4+2\,A\,C\,a^2\,b^2+2\,C^2\,a^4-2\,C^2\,a^3\,b+C^2\,a^2\,b^2\right)}{b^2}-\frac{32\,\left(C\,a^2+A\,b^2\right)\,\sqrt{b^2-a^2}\,\left(a-b\right)\,\left(A\,b^4-A\,a^2\,b^2-C\,a\,b^3+C\,a^3\,b+2\,C\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)}{\left(b^4-a^2\,b^2\right)\,\left(a+b\right)}\right)}{b^4-a^2\,b^2}-\frac{32\,C\,a\,\left(a-b\right)\,\left(A^2\,b^3+A\,C\,a^2\,b+A\,C\,a\,b^2+C^2\,a^3\right)}{b^3}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)}{d\,\left(b^4-a^2\,b^2\right)}-\frac{\ln\left(b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\left(A\,b^2\,\sqrt{b^2-a^2}+C\,a^2\,\sqrt{b^2-a^2}\right)}{b^2\,d\,\left(a^2-b^2\right)}","Not used",1,"(C*sin(c + d*x))/(b*d) - (2*C*a*atan((64*C^3*a^3*tan(c/2 + (d*x)/2))/(64*C^3*a^3 + 128*A*C^2*a^3 - (64*C^3*a^4)/b + 64*A^2*C*a*b^2 - 64*A^2*C*a^2*b - (128*A*C^2*a^4)/b) + (64*C^3*a^4*tan(c/2 + (d*x)/2))/(64*C^3*a^4 + 128*A*C^2*a^4 - 64*C^3*a^3*b - 128*A*C^2*a^3*b - 64*A^2*C*a*b^3 + 64*A^2*C*a^2*b^2) + (128*A*C^2*a^4*tan(c/2 + (d*x)/2))/(64*C^3*a^4 + 128*A*C^2*a^4 - 64*C^3*a^3*b - 128*A*C^2*a^3*b - 64*A^2*C*a*b^3 + 64*A^2*C*a^2*b^2) + (64*A^2*C*a^2*tan(c/2 + (d*x)/2))/(64*A^2*C*a^2 - (64*C^3*a^3)/b + (64*C^3*a^4)/b^2 - 64*A^2*C*a*b - (128*A*C^2*a^3)/b + (128*A*C^2*a^4)/b^2) + (128*A*C^2*a^3*tan(c/2 + (d*x)/2))/(64*C^3*a^3 + 128*A*C^2*a^3 - (64*C^3*a^4)/b + 64*A^2*C*a*b^2 - 64*A^2*C*a^2*b - (128*A*C^2*a^4)/b) - (64*A^2*C*a*b*tan(c/2 + (d*x)/2))/(64*A^2*C*a^2 - (64*C^3*a^3)/b + (64*C^3*a^4)/b^2 - 64*A^2*C*a*b - (128*A*C^2*a^3)/b + (128*A*C^2*a^4)/b^2)))/(b^2*d) - (log(((A*b^2 + C*a^2)*(b^2 - a^2)^(1/2)*((32*tan(c/2 + (d*x)/2)*(a - b)*(A^2*b^4 + 2*C^2*a^4 - 2*C^2*a^3*b + C^2*a^2*b^2 + 2*A*C*a^2*b^2))/b^2 - (32*(A*b^2 + C*a^2)*(b^2 - a^2)^(1/2)*(a - b)*(A*b^4 - A*a^2*b^2 - C*a*b^3 + C*a^3*b + 2*C*a^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A*a*b^2*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)))/((b^4 - a^2*b^2)*(a + b))))/(b^4 - a^2*b^2) - (32*C*a*(a - b)*(A^2*b^3 + C^2*a^3 + A*C*a*b^2 + A*C*a^2*b))/b^3)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2))/(d*(b^4 - a^2*b^2)) - (log(b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(A*b^2*(b^2 - a^2)^(1/2) + C*a^2*(b^2 - a^2)^(1/2)))/(b^2*d*(a^2 - b^2))","B"
566,1,2862,88,4.056058,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))),x)","\frac{2\,A\,\mathrm{atanh}\left(\frac{16384\,A^5\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{16384\,A^5\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-16384\,A^5\,a\,b^4+16384\,A^5\,b^5-32768\,A^4\,C\,a\,b^4+32768\,A^4\,C\,b^5-32768\,A^3\,C^2\,a^3\,b^2+32768\,A^3\,C^2\,a^2\,b^3-32768\,A^2\,C^3\,a^3\,b^2+32768\,A^2\,C^3\,a^2\,b^3-16384\,A\,C^4\,a^5+16384\,A\,C^4\,a^4\,b}+\frac{16384\,A\,C^4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^4\,C\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^4\,C\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-16384\,A^5\,a\,b^4+16384\,A^5\,b^5-32768\,A^4\,C\,a\,b^4+32768\,A^4\,C\,b^5-32768\,A^3\,C^2\,a^3\,b^2+32768\,A^3\,C^2\,a^2\,b^3-32768\,A^2\,C^3\,a^3\,b^2+32768\,A^2\,C^3\,a^2\,b^3-16384\,A\,C^4\,a^5+16384\,A\,C^4\,a^4\,b}-\frac{16384\,A\,C^4\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}-\frac{32768\,A^2\,C^3\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}-\frac{32768\,A^3\,C^2\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^2\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}+\frac{32768\,A^3\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4-\frac{16384\,A^5\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A\,C^4\,a^3\,b-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}}\right)}{a\,d}+\frac{2\,C\,\mathrm{atan}\left(\frac{16384\,C^5\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{16384\,C^5\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^4\,C\,a\,b^4-16384\,A^4\,C\,b^5+32768\,A^3\,C^2\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^2\,C^3\,a^2\,b^3+32768\,A\,C^4\,a^5-32768\,A\,C^4\,a^4\,b+16384\,C^5\,a^5-16384\,C^5\,a^4\,b}+\frac{32768\,A\,C^4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{32768\,A\,C^4\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^4\,C\,a\,b^4-16384\,A^4\,C\,b^5+32768\,A^3\,C^2\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^2\,C^3\,a^2\,b^3+32768\,A\,C^4\,a^5-32768\,A\,C^4\,a^4\,b+16384\,C^5\,a^5-16384\,C^5\,a^4\,b}+\frac{16384\,A^4\,C\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}-\frac{16384\,A^4\,C\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}-\frac{32768\,A^2\,C^3\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}-\frac{32768\,A^3\,C^2\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{32768\,A^2\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}+\frac{32768\,A^3\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-16384\,A^4\,C\,a\,b^3-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}}\right)}{b\,d}-\frac{\ln\left(b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)}{d\,\left(a\,b^3-a^3\,b\right)}-\frac{\ln\left(a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\left(A\,b^2\,\sqrt{b^2-a^2}+C\,a^2\,\sqrt{b^2-a^2}\right)}{a\,b\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*A*atanh((16384*A^5*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (16384*A^5*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4) + (16384*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^4*C*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4) - (16384*A*C^4*a^3*b*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) - (32768*A^2*C^3*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) - (32768*A^3*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 - (16384*A^5*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A*C^4*a^3*b - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a)))/(a*d) + (2*C*atan((16384*C^5*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (16384*C^5*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4) + (32768*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (32768*A*C^4*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4) + (16384*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) - (16384*A^4*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) - (32768*A^2*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) - (32768*A^3*C^2*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - 16384*A^4*C*a*b^3 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b)))/(b*d) - (log(b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2))/(d*(a*b^3 - a^3*b)) - (log(a*tan(c/2 + (d*x)/2) - b*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(A*b^2*(b^2 - a^2)^(1/2) + C*a^2*(b^2 - a^2)^(1/2)))/(a*b*d*(a^2 - b^2))","B"
567,1,1328,95,2.877151,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))),x)","\frac{A\,a\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}-\frac{C\,\mathrm{atan}\left(\frac{\left(2\,A^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,C^2\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+C^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,C\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^3\,b^2-A^2\,a\,b^4+2\,A\,C\,a^3\,b^2-2\,A\,C\,a\,b^4+C^2\,a^5-C^2\,a^3\,b^2\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,2{}\mathrm{i}}{d\,\left(a^2-b^2\right)}-\frac{2\,A\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^2-b^2\right)}+\frac{2\,A\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^2\,d\,\left(a^2-b^2\right)}-\frac{A\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{a\,d\,\left(a^2-b^2\right)}-\frac{A\,b^2\,\mathrm{atan}\left(\frac{\left(2\,A^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,C^2\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+C^2\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+A^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,C\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^3\,b^2-A^2\,a\,b^4+2\,A\,C\,a^3\,b^2-2\,A\,C\,a\,b^4+C^2\,a^5-C^2\,a^3\,b^2\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,2{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)}","Not used",1,"(A*a*tan(c + d*x))/(d*(a^2 - b^2)) - (C*atan(((2*A^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + C^2*a^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*C^2*a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + C^2*a^6*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*C*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(C^2*a^5 - A^2*a*b^4 + A^2*a^3*b^2 - C^2*a^3*b^2 - 2*A*C*a*b^4 + 2*A*C*a^3*b^2)))*(-(a + b)*(a - b))^(1/2)*2i)/(d*(a^2 - b^2)) - (2*A*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) + (2*A*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d*(a^2 - b^2)) - (A*b^2*tan(c + d*x))/(a*d*(a^2 - b^2)) - (A*b^2*atan(((2*A^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + C^2*a^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*C^2*a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + C^2*a^6*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + A^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*C*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(C^2*a^5 - A^2*a*b^4 + A^2*a^3*b^2 - C^2*a^3*b^2 - 2*A*C*a*b^4 + 2*A*C*a^3*b^2)))*(-(a + b)*(a - b))^(1/2)*2i)/(a^2*d*(a^2 - b^2))","B"
568,1,3926,137,4.963992,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))),x)","\frac{A\,a\,\sin\left(c+d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{A\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{A\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2\,a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{A\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{A\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2\,a^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{A\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{A\,b^2\,\sin\left(c+d\,x\right)}{2\,a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b\,\mathrm{atan}\left(\frac{\left(A^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,A^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,C\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,A^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+16\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,A\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,A\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4+4\,A\,C\,a^7-4\,A\,C\,a^3\,b^4+4\,C^2\,a^7-4\,C^2\,a^5\,b^2\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{A\,b^3\,\mathrm{atan}\left(\frac{\left(A^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,A^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,C\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,A^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+16\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,A\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,A\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4+4\,A\,C\,a^7-4\,A\,C\,a^3\,b^4+4\,C^2\,a^7-4\,C^2\,a^5\,b^2\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{A\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{2\,a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{A\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{\left(A^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,A^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,C\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,A^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+16\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,A\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,A\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4+4\,A\,C\,a^7-4\,A\,C\,a^3\,b^4+4\,C^2\,a^7-4\,C^2\,a^5\,b^2\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{A\,b^3\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{\left(A^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,A^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,C\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-A^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,A^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,A^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,A^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,A^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,A^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+16\,A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-16\,A\,C\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+20\,A\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,C\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4+4\,A\,C\,a^7-4\,A\,C\,a^3\,b^4+4\,C^2\,a^7-4\,C^2\,a^5\,b^2\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(A*a*sin(c + d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*b*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(2*a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (A*b^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (A*b^3*sin(2*c + 2*d*x))/(2*a^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*b^2*sin(c + d*x))/(2*a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b*atan(((A^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*A^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*C*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*A^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 16*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*A*C*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*A*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(A^2*a^7 + 4*C^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*C^2*a^5*b^2 + 4*A*C*a^7 - 4*A*C*a^3*b^4)))*(-(a + b)*(a - b))^(1/2)*1i)/(a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (A*b^3*atan(((A^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*A^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*C*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*A^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 16*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*A*C*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*A*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(A^2*a^7 + 4*C^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*C^2*a^5*b^2 + 4*A*C*a^7 - 4*A*C*a^3*b^4)))*(-(a + b)*(a - b))^(1/2)*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (A*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(2*a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (A*b^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b*cos(2*c + 2*d*x)*atan(((A^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*A^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*C*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*A^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 16*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*A*C*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*A*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(A^2*a^7 + 4*C^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*C^2*a^5*b^2 + 4*A*C*a^7 - 4*A*C*a^3*b^4)))*(-(a + b)*(a - b))^(1/2)*1i)/(a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (A*b^3*cos(2*c + 2*d*x)*atan(((A^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*A^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*C*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - A^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*A^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*A^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*A^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*A^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*A^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 16*A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 16*A*C*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 20*A*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*C*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(A^2*a^7 + 4*C^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*C^2*a^5*b^2 + 4*A*C*a^7 - 4*A*C*a^3*b^4)))*(-(a + b)*(a - b))^(1/2)*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2))","B"
569,1,3927,184,5.193659,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2+A\,a\,b\right)}{a^3}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^2+3\,A\,b^2+3\,C\,a^2\right)}{3\,a^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^2+2\,A\,b^2+2\,C\,a^2-A\,a\,b\right)}{a^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}\right)\,1{}\mathrm{i}}{a^4}}{\frac{\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}\right)}{a^4}-\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}+\frac{\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}\right)}{a^4}}\right)\,\left(A\,b^3+a^2\,\left(\frac{A\,b}{2}+C\,b\right)\right)\,2{}\mathrm{i}}{a^4\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"(b^2*atan(((b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 + (b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 - (b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2))/((16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4))/a^9 - (b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 + (b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) + (b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6 - (b^2*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2))))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2)*2i)/(d*(a^6 - a^4*b^2)) - (atan((((A*b^3 + a^2*((A*b)/2 + C*b))*((((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(A*b^3 + a^2*((A*b)/2 + C*b))*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3 + a^2*((A*b)/2 + C*b)))/a^4 + (8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6)*1i)/a^4 - ((A*b^3 + a^2*((A*b)/2 + C*b))*((((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(A*b^3 + a^2*((A*b)/2 + C*b))*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3 + a^2*((A*b)/2 + C*b)))/a^4 - (8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6)*1i)/a^4)/(((A*b^3 + a^2*((A*b)/2 + C*b))*((((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(A*b^3 + a^2*((A*b)/2 + C*b))*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3 + a^2*((A*b)/2 + C*b)))/a^4 + (8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6))/a^4 - (16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4))/a^9 + ((A*b^3 + a^2*((A*b)/2 + C*b))*((((8*(4*A*a^8*b^5 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(A*b^3 + a^2*((A*b)/2 + C*b))*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10)*(A*b^3 + a^2*((A*b)/2 + C*b)))/a^4 - (8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - 16*A^2*a*b^8 + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2))/a^6))/a^4))*(A*b^3 + a^2*((A*b)/2 + C*b))*2i)/(a^4*d) - ((tan(c/2 + (d*x)/2)^5*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 + A*a*b))/a^3 - (4*tan(c/2 + (d*x)/2)^3*(A*a^2 + 3*A*b^2 + 3*C*a^2))/(3*a^3) + (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + 2*C*a^2 - A*a*b))/a^3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
570,1,6989,332,10.349224,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^5-36\,C\,a^5-C\,b^5-3\,A\,a^2\,b^3-18\,A\,a^3\,b^2+7\,C\,a^2\,b^3+19\,C\,a^3\,b^2+9\,A\,a\,b^4+8\,C\,a\,b^4-6\,C\,a^4\,b\right)}{3\,b^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(C\,b^5-36\,C\,a^5-3\,A\,b^5+3\,A\,a^2\,b^3-18\,A\,a^3\,b^2-7\,C\,a^2\,b^3+19\,C\,a^3\,b^2+9\,A\,a\,b^4+8\,C\,a\,b^4+6\,C\,a^4\,b\right)}{3\,b^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A\,b^5+4\,C\,a^5+C\,b^5-A\,a^2\,b^3+2\,A\,a^3\,b^2+C\,a^2\,b^3-3\,C\,a^3\,b^2-A\,a\,b^4-2\,C\,a^4\,b\right)}{b^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^5-4\,C\,a^5+C\,b^5-A\,a^2\,b^3-2\,A\,a^3\,b^2+C\,a^2\,b^3+3\,C\,a^3\,b^2+A\,a\,b^4-2\,C\,a^4\,b\right)}{b^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(4\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a+2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)}{b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}-\frac{\left(\frac{\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)}{b^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}}{-\frac{64\,\left(8\,A^3\,a^8\,b^6-4\,A^3\,a^7\,b^7-20\,A^3\,a^6\,b^8+6\,A^3\,a^5\,b^9+12\,A^3\,a^4\,b^{10}+48\,A^2\,C\,a^{10}\,b^4-24\,A^2\,C\,a^9\,b^5-108\,A^2\,C\,a^8\,b^6+36\,A^2\,C\,a^7\,b^7+48\,A^2\,C\,a^6\,b^8-3\,A^2\,C\,a^5\,b^9+12\,A^2\,C\,a^4\,b^{10}+96\,A\,C^2\,a^{12}\,b^2-48\,A\,C^2\,a^{11}\,b^3-192\,A\,C^2\,a^{10}\,b^4+72\,A\,C^2\,a^9\,b^5+54\,A\,C^2\,a^8\,b^6-9\,A\,C^2\,a^7\,b^7+39\,A\,C^2\,a^6\,b^8-3\,A\,C^2\,a^5\,b^9+3\,A\,C^2\,a^4\,b^{10}+64\,C^3\,a^{14}-32\,C^3\,a^{13}\,b-112\,C^3\,a^{12}\,b^2+48\,C^3\,a^{11}\,b^3+12\,C^3\,a^{10}\,b^4-6\,C^3\,a^9\,b^5+31\,C^3\,a^8\,b^6-5\,C^3\,a^7\,b^7+5\,C^3\,a^6\,b^8\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{\left(\frac{\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)}{b^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)}{b^5}+\frac{\left(\frac{\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)}{b^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)}{b^5}}\right)\,\left(C\,a^3\,4{}\mathrm{i}+a\,b^2\,\left(2\,A+C\right)\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^5\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a^2\,\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^2\,\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}{\frac{64\,\left(8\,A^3\,a^8\,b^6-4\,A^3\,a^7\,b^7-20\,A^3\,a^6\,b^8+6\,A^3\,a^5\,b^9+12\,A^3\,a^4\,b^{10}+48\,A^2\,C\,a^{10}\,b^4-24\,A^2\,C\,a^9\,b^5-108\,A^2\,C\,a^8\,b^6+36\,A^2\,C\,a^7\,b^7+48\,A^2\,C\,a^6\,b^8-3\,A^2\,C\,a^5\,b^9+12\,A^2\,C\,a^4\,b^{10}+96\,A\,C^2\,a^{12}\,b^2-48\,A\,C^2\,a^{11}\,b^3-192\,A\,C^2\,a^{10}\,b^4+72\,A\,C^2\,a^9\,b^5+54\,A\,C^2\,a^8\,b^6-9\,A\,C^2\,a^7\,b^7+39\,A\,C^2\,a^6\,b^8-3\,A\,C^2\,a^5\,b^9+3\,A\,C^2\,a^4\,b^{10}+64\,C^3\,a^{14}-32\,C^3\,a^{13}\,b-112\,C^3\,a^{12}\,b^2+48\,C^3\,a^{11}\,b^3+12\,C^3\,a^{10}\,b^4-6\,C^3\,a^9\,b^5+31\,C^3\,a^8\,b^6-5\,C^3\,a^7\,b^7+5\,C^3\,a^6\,b^8\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a^2\,\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8\,b^4-8\,A^2\,a^7\,b^5-16\,A^2\,a^6\,b^6+16\,A^2\,a^5\,b^7+5\,A^2\,a^4\,b^8-8\,A^2\,a^3\,b^9+4\,A^2\,a^2\,b^{10}+32\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3-56\,A\,C\,a^8\,b^4+56\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6-16\,A\,C\,a^5\,b^7+12\,A\,C\,a^4\,b^8-8\,A\,C\,a^3\,b^9+4\,A\,C\,a^2\,b^{10}+32\,C^2\,a^{12}-32\,C^2\,a^{11}\,b-48\,C^2\,a^{10}\,b^2+48\,C^2\,a^9\,b^3+2\,C^2\,a^8\,b^4-2\,C^2\,a^7\,b^5+7\,C^2\,a^6\,b^6-12\,C^2\,a^5\,b^7+7\,C^2\,a^4\,b^8-2\,C^2\,a^3\,b^9+C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^2\,\left(\frac{32\,\left(5\,A\,a^4\,b^{14}-3\,A\,a^3\,b^{15}-3\,A\,a^2\,b^{16}+A\,a^5\,b^{13}-2\,A\,a^6\,b^{12}+C\,a^3\,b^{15}-5\,C\,a^4\,b^{14}-4\,C\,a^5\,b^{13}+9\,C\,a^6\,b^{12}+2\,C\,a^7\,b^{11}-4\,C\,a^8\,b^{10}+2\,A\,a\,b^{17}+C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}","Not used",1,"(atan(((((((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (32*tan(c/2 + (d*x)/2)*(C*a^3*4i + a*b^2*(2*A + C)*1i)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(C*a^3*4i + a*b^2*(2*A + C)*1i))/b^5 + (32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*(C*a^3*4i + a*b^2*(2*A + C)*1i)*1i)/b^5 - (((((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (32*tan(c/2 + (d*x)/2)*(C*a^3*4i + a*b^2*(2*A + C)*1i)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(C*a^3*4i + a*b^2*(2*A + C)*1i))/b^5 - (32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*(C*a^3*4i + a*b^2*(2*A + C)*1i)*1i)/b^5)/((((((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (32*tan(c/2 + (d*x)/2)*(C*a^3*4i + a*b^2*(2*A + C)*1i)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(C*a^3*4i + a*b^2*(2*A + C)*1i))/b^5 + (32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*(C*a^3*4i + a*b^2*(2*A + C)*1i))/b^5 - (64*(64*C^3*a^14 - 32*C^3*a^13*b + 12*A^3*a^4*b^10 + 6*A^3*a^5*b^9 - 20*A^3*a^6*b^8 - 4*A^3*a^7*b^7 + 8*A^3*a^8*b^6 + 5*C^3*a^6*b^8 - 5*C^3*a^7*b^7 + 31*C^3*a^8*b^6 - 6*C^3*a^9*b^5 + 12*C^3*a^10*b^4 + 48*C^3*a^11*b^3 - 112*C^3*a^12*b^2 + 3*A*C^2*a^4*b^10 - 3*A*C^2*a^5*b^9 + 39*A*C^2*a^6*b^8 - 9*A*C^2*a^7*b^7 + 54*A*C^2*a^8*b^6 + 72*A*C^2*a^9*b^5 - 192*A*C^2*a^10*b^4 - 48*A*C^2*a^11*b^3 + 96*A*C^2*a^12*b^2 + 12*A^2*C*a^4*b^10 - 3*A^2*C*a^5*b^9 + 48*A^2*C*a^6*b^8 + 36*A^2*C*a^7*b^7 - 108*A^2*C*a^8*b^6 - 24*A^2*C*a^9*b^5 + 48*A^2*C*a^10*b^4))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (((((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (32*tan(c/2 + (d*x)/2)*(C*a^3*4i + a*b^2*(2*A + C)*1i)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(C*a^3*4i + a*b^2*(2*A + C)*1i))/b^5 - (32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*(C*a^3*4i + a*b^2*(2*A + C)*1i))/b^5))*(C*a^3*4i + a*b^2*(2*A + C)*1i)*2i)/(b^5*d) - ((2*tan(c/2 + (d*x)/2)^3*(3*A*b^5 - 36*C*a^5 - C*b^5 - 3*A*a^2*b^3 - 18*A*a^3*b^2 + 7*C*a^2*b^3 + 19*C*a^3*b^2 + 9*A*a*b^4 + 8*C*a*b^4 - 6*C*a^4*b))/(3*b^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^5*(C*b^5 - 36*C*a^5 - 3*A*b^5 + 3*A*a^2*b^3 - 18*A*a^3*b^2 - 7*C*a^2*b^3 + 19*C*a^3*b^2 + 9*A*a*b^4 + 8*C*a*b^4 + 6*C*a^4*b))/(3*b^4*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)^7*(A*b^5 + 4*C*a^5 + C*b^5 - A*a^2*b^3 + 2*A*a^3*b^2 + C*a^2*b^3 - 3*C*a^3*b^2 - A*a*b^4 - 2*C*a^4*b))/(b^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(A*b^5 - 4*C*a^5 + C*b^5 - A*a^2*b^3 - 2*A*a^3*b^2 + C*a^2*b^3 + 3*C*a^3*b^2 + A*a*b^4 - 2*C*a^4*b))/(b^4*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^8*(a - b) + tan(c/2 + (d*x)/2)^2*(4*a + 2*b) + tan(c/2 + (d*x)/2)^6*(4*a - 2*b) + 6*a*tan(c/2 + (d*x)/2)^4)) - (a^2*atan(((a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^2*((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2)*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) + (a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^2*((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2)*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))/((64*(64*C^3*a^14 - 32*C^3*a^13*b + 12*A^3*a^4*b^10 + 6*A^3*a^5*b^9 - 20*A^3*a^6*b^8 - 4*A^3*a^7*b^7 + 8*A^3*a^8*b^6 + 5*C^3*a^6*b^8 - 5*C^3*a^7*b^7 + 31*C^3*a^8*b^6 - 6*C^3*a^9*b^5 + 12*C^3*a^10*b^4 + 48*C^3*a^11*b^3 - 112*C^3*a^12*b^2 + 3*A*C^2*a^4*b^10 - 3*A*C^2*a^5*b^9 + 39*A*C^2*a^6*b^8 - 9*A*C^2*a^7*b^7 + 54*A*C^2*a^8*b^6 + 72*A*C^2*a^9*b^5 - 192*A*C^2*a^10*b^4 - 48*A*C^2*a^11*b^3 + 96*A*C^2*a^12*b^2 + 12*A^2*C*a^4*b^10 - 3*A^2*C*a^5*b^9 + 48*A^2*C*a^6*b^8 + 36*A^2*C*a^7*b^7 - 108*A^2*C*a^8*b^6 - 24*A^2*C*a^9*b^5 + 48*A^2*C*a^10*b^4))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^2*((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) + (a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*C^2*a^12 - 32*C^2*a^11*b + 4*A^2*a^2*b^10 - 8*A^2*a^3*b^9 + 5*A^2*a^4*b^8 + 16*A^2*a^5*b^7 - 16*A^2*a^6*b^6 - 8*A^2*a^7*b^5 + 8*A^2*a^8*b^4 + C^2*a^2*b^10 - 2*C^2*a^3*b^9 + 7*C^2*a^4*b^8 - 12*C^2*a^5*b^7 + 7*C^2*a^6*b^6 - 2*C^2*a^7*b^5 + 2*C^2*a^8*b^4 + 48*C^2*a^9*b^3 - 48*C^2*a^10*b^2 + 4*A*C*a^2*b^10 - 8*A*C*a^3*b^9 + 12*A*C*a^4*b^8 - 16*A*C*a^5*b^7 + 10*A*C*a^6*b^6 + 56*A*C*a^7*b^5 - 56*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 32*A*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^2*((32*(5*A*a^4*b^14 - 3*A*a^3*b^15 - 3*A*a^2*b^16 + A*a^5*b^13 - 2*A*a^6*b^12 + C*a^3*b^15 - 5*C*a^4*b^14 - 4*C*a^5*b^13 + 9*C*a^6*b^12 + 2*C*a^7*b^11 - 4*C*a^8*b^10 + 2*A*a*b^17 + C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2)*2i)/(d*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))","B"
571,1,6546,262,10.114024,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^4+C\,b^4+2\,A\,a^2\,b^2-5\,C\,a^2\,b^2-3\,C\,a\,b^3+3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^4+C\,b^4+2\,A\,a^2\,b^2-5\,C\,a^2\,b^2+3\,C\,a\,b^3-3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,C\,a^4-C\,b^4+2\,A\,a^2\,b^2-3\,C\,a^2\,b^2\right)}{b\,\left(a\,b^2-b^3\right)\,\left(a+b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(3\,a+b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}\right)}{b^4}+\frac{\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}\right)}{b^4}}\right)\,\left(3{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^4\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"(atan((((C*a^2*3i + b^2*(A*1i + (C*1i)/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2)))/b^4)*1i)/b^4 + ((C*a^2*3i + b^2*(A*1i + (C*1i)/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2)))/b^4)*1i)/b^4)/((16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - ((C*a^2*3i + b^2*(A*1i + (C*1i)/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2)))/b^4))/b^4 + ((C*a^2*3i + b^2*(A*1i + (C*1i)/2))*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2))*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2)))/b^4))/b^4))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2))*2i)/(b^4*d) - ((tan(c/2 + (d*x)/2)*(6*C*a^4 + C*b^4 + 2*A*a^2*b^2 - 5*C*a^2*b^2 - 3*C*a*b^3 + 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(6*C*a^4 + C*b^4 + 2*A*a^2*b^2 - 5*C*a^2*b^2 + 3*C*a*b^3 - 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(6*C*a^4 - C*b^4 + 2*A*a^2*b^2 - 3*C*a^2*b^2))/(b*(a*b^2 - b^3)*(a + b)))/(d*(a + b + tan(c/2 + (d*x)/2)^2*(3*a + b) + tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 8*A*C*a*b^9 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
572,1,4124,144,8.744910,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^3+C\,b^3+A\,a\,b^2-C\,a\,b^2-C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a^3-C\,b^3+A\,a\,b^2-C\,a\,b^2+C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{4\,C\,a\,\mathrm{atan}\left(\frac{\frac{2\,C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)}{b^3}+\frac{2\,C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)}{b^3}}{\frac{64\,\left(2\,A^2\,C\,a\,b^7-4\,A\,C^2\,a^5\,b^3-4\,A\,C^2\,a^4\,b^4+8\,A\,C^2\,a^3\,b^5+4\,A\,C^2\,a^2\,b^6+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)\,2{}\mathrm{i}}{b^3}-\frac{C\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{C\,a\,\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)\,2{}\mathrm{i}}{b^3}}\right)}{b^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(2\,A^2\,C\,a\,b^7-4\,A\,C^2\,a^5\,b^3-4\,A\,C^2\,a^4\,b^4+8\,A\,C^2\,a^3\,b^5+4\,A\,C^2\,a^2\,b^6+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,b^{12}-A\,a^2\,b^{10}+A\,a^3\,b^9+3\,C\,a^2\,b^{10}+3\,C\,a^3\,b^9-5\,C\,a^4\,b^8-C\,a^5\,b^7+2\,C\,a^6\,b^6-A\,a\,b^{11}-2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+3\,C\,a^2\,b^2+A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(2*C*a^3 + C*b^3 + A*a*b^2 - C*a*b^2 - C*a^2*b))/(b^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(2*C*a^3 - C*b^3 + A*a*b^2 - C*a*b^2 + C*a^2*b))/(b^2*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) + 2*a*tan(c/2 + (d*x)/2)^2)) - (4*C*a*atan(((2*C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3))/b^3 + (2*C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3))/b^3)/((64*(8*C^3*a^8 - 4*C^3*a^7*b + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 + 2*A^2*C*a*b^7 + 4*A*C^2*a^2*b^6 + 8*A*C^2*a^3*b^5 - 4*A*C^2*a^4*b^4 - 4*A*C^2*a^5*b^3))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3)*2i)/b^3 - (C*a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (C*a*((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (C*a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3)*2i)/b^3)))/(b^3*d) - (atan(((((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*C^3*a^8 - 4*C^3*a^7*b + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 + 2*A^2*C*a*b^7 + 4*A*C^2*a^2*b^6 + 8*A*C^2*a^3*b^5 - 4*A*C^2*a^4*b^4 - 4*A*C^2*a^5*b^3))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) - (((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*C^2*a^8 - 8*C^2*a^7*b + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*b^12 - A*a^2*b^10 + A*a^3*b^9 + 3*C*a^2*b^10 + 3*C*a^3*b^9 - 5*C*a^4*b^8 - C*a^5*b^7 + 2*C*a^6*b^6 - A*a*b^11 - 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
573,1,3862,126,8.296235,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^2,x)","\frac{2\,C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}-\frac{C\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}}{\frac{64\,\left(A^2\,C\,a^2\,b^3-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}+\frac{C\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}\right)}{b^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-b^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(A^2\,C\,a^2\,b^3-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{a\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^2\,b^7-A\,a^3\,b^6-C\,b^9+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^2-C\,a^2+2\,C\,b^2\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"(2*C*atan(((C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 + (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2 - (C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 - (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2)/((64*(C^3*a^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 + (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2 + (C*((C*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 - (32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2)))/(b^2*d) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2))/(d*(a + b)*(a*b - b^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b))) + (a*atan(((a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(C^3*a^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (a*((32*(A*a^4*b^5 - A*a^2*b^7 - A*a^3*b^6 - C*b^9 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(A*b^2 - C*a^2 + 2*C*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^2 - C*a^2 + 2*C*b^2)*2i)/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))","B"
574,1,3850,134,8.464987,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^2),x)","-\frac{A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)\,1{}\mathrm{i}}{a^2}-\frac{A\,\left(\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)\,1{}\mathrm{i}}{a^2}}{\frac{A\,\left(\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)}{a^2}-\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{A\,\left(\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)}{a^2}}\right)\,2{}\mathrm{i}}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^4\,b^5-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,a^2-A\,b^2+C\,a^2\right)\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"- (A*atan(((A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 - (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2 - (A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 + (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2)/((A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 - (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2 - (64*(A^3*b^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - A^2*C*a*b^4 + A^2*C*a^4*b + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (A*((A*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 + (32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2))*2i)/(a^2*d) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2))/(d*(a + b)*(a*b - a^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b))) - (b*atan(((b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(A^3*b^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - A^2*C*a*b^4 + A^2*C*a^4*b + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*((32*(A*a^4*b^5 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*A*a^2 - A*b^2 + C*a^2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*a^2 - A*b^2 + C*a^2)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))","B"
575,1,4118,180,8.809785,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^2),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^3+2\,A\,b^3-A\,a\,b^2-A\,a^2\,b+C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^3-A\,a^3+A\,a\,b^2-A\,a^2\,b+C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{A\,b\,\mathrm{atan}\left(\frac{\frac{A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{2\,A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{64\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)\,2{}\mathrm{i}}{a^3}+\frac{A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{2\,A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{64\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)\,2{}\mathrm{i}}{a^3}}{\frac{64\,\left(12\,A^3\,a^4\,b^4+6\,A^3\,a^3\,b^5-20\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+8\,A^3\,b^8+4\,A^2\,C\,a^6\,b^2+8\,A^2\,C\,a^5\,b^3-4\,A^2\,C\,a^4\,b^4-4\,A^2\,C\,a^3\,b^5+2\,A\,C^2\,a^7\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{2\,A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{2\,A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{64\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)}{a^3}-\frac{2\,A\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{2\,A\,b\,\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{64\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)}{a^3}}\right)\,4{}\mathrm{i}}{a^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{64\,\left(12\,A^3\,a^4\,b^4+6\,A^3\,a^3\,b^5-20\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+8\,A^3\,b^8+4\,A^2\,C\,a^6\,b^2+8\,A^2\,C\,a^5\,b^3-4\,A^2\,C\,a^4\,b^4-4\,A^2\,C\,a^3\,b^5+2\,A\,C^2\,a^7\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(C\,a^{12}+2\,A\,a^6\,b^6-A\,a^7\,b^5-5\,A\,a^8\,b^4+3\,A\,a^9\,b^3+3\,A\,a^{10}\,b^2+C\,a^9\,b^3-C\,a^{10}\,b^2-2\,A\,a^{11}\,b-C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4+3\,A\,a^2\,b^2-2\,A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(A*a^3 + 2*A*b^3 - A*a*b^2 - A*a^2*b + C*a^2*b))/(a^2*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)*(2*A*b^3 - A*a^3 + A*a*b^2 - A*a^2*b + C*a^2*b))/(a^2*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^4*(a - b) - 2*b*tan(c/2 + (d*x)/2)^2)) + (A*b*atan(((A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (2*A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (64*A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3)*2i)/a^3 + (A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (2*A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (64*A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3)*2i)/a^3)/((64*(8*A^3*b^8 - 4*A^3*a*b^7 - 20*A^3*a^2*b^6 + 6*A^3*a^3*b^5 + 12*A^3*a^4*b^4 + 2*A*C^2*a^7*b - 4*A^2*C*a^3*b^5 - 4*A^2*C*a^4*b^4 + 8*A^2*C*a^5*b^3 + 4*A^2*C*a^6*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (2*A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (2*A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (64*A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3))/a^3 - (2*A*b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (2*A*b*((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (64*A*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3))/a^3))*4i)/(a^3*d) + (atan(((((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((64*(8*A^3*b^8 - 4*A^3*a*b^7 - 20*A^3*a^2*b^6 + 6*A^3*a^3*b^5 + 12*A^3*a^4*b^4 + 2*A*C^2*a^7*b - 4*A^2*C*a^3*b^5 - 4*A^2*C*a^4*b^4 + 8*A^2*C*a^5*b^3 + 4*A^2*C*a^6*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + C^2*a^8 - 8*A^2*a*b^7 - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(C*a^12 + 2*A*a^6*b^6 - A*a^7*b^5 - 5*A*a^8*b^4 + 3*A*a^9*b^3 + 3*A*a^10*b^2 + C*a^9*b^3 - C*a^10*b^2 - 2*A*a^11*b - C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
576,1,6465,265,10.130972,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^2),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^4+6\,A\,b^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2+3\,A\,a\,b^3-3\,A\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A\,a^4+6\,A\,b^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,A\,a\,b^3+3\,A\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^4-6\,A\,b^4+3\,A\,a^2\,b^2-2\,C\,a^2\,b^2\right)}{a\,\left(a^2\,b-a^3\right)\,\left(a+b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-a-3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)}{a^4}+\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)}{a^4}}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+3\,A\,b^2\right)\,2{}\mathrm{i}}{a^4\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(A*a^4 + 6*A*b^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 + 3*A*a*b^3 - 3*A*a^3*b))/((a^3*b - a^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(A*a^4 + 6*A*b^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*A*a*b^3 + 3*A*a^3*b))/((a^3*b - a^4)*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(A*a^4 - 6*A*b^4 + 3*A*a^2*b^2 - 2*C*a^2*b^2))/(a*(a^2*b - a^3)*(a + b)))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) + tan(c/2 + (d*x)/2)^6*(a - b))) - (atan(-(((3*A*b^2 + a^2*(A/2 + C))*(((3*A*b^2 + a^2*(A/2 + C))*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4 - (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*1i)/a^4 - ((3*A*b^2 + a^2*(A/2 + C))*(((3*A*b^2 + a^2*(A/2 + C))*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4 + (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*1i)/a^4)/((16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + ((3*A*b^2 + a^2*(A/2 + C))*(((3*A*b^2 + a^2*(A/2 + C))*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4 - (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))/a^4 + ((3*A*b^2 + a^2*(A/2 + C))*(((3*A*b^2 + a^2*(A/2 + C))*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C))*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4 + (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))/a^4))*(3*A*b^2 + a^2*(A/2 + C))*2i)/(a^4*d) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 8*A*C*a^9*b + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
577,1,6976,335,10.831994,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^2),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^5+36\,A\,b^5-3\,C\,a^5-19\,A\,a^2\,b^3-7\,A\,a^3\,b^2+18\,C\,a^2\,b^3+3\,C\,a^3\,b^2+6\,A\,a\,b^4-8\,A\,a^4\,b-9\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A\,a^5-36\,A\,b^5-3\,C\,a^5+19\,A\,a^2\,b^3-7\,A\,a^3\,b^2-18\,C\,a^2\,b^3+3\,C\,a^3\,b^2+6\,A\,a\,b^4+8\,A\,a^4\,b+9\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A\,a^5+4\,A\,b^5+C\,a^5-3\,A\,a^2\,b^3+A\,a^3\,b^2+2\,C\,a^2\,b^3-C\,a^3\,b^2-2\,A\,a\,b^4-C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^5-4\,A\,b^5+C\,a^5+3\,A\,a^2\,b^3+A\,a^3\,b^2-2\,C\,a^2\,b^3-C\,a^3\,b^2-2\,A\,a\,b^4+C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)}{a^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)}{a^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,1{}\mathrm{i}}{a^5}}{\frac{64\,\left(5\,A^3\,a^8\,b^6-5\,A^3\,a^7\,b^7+31\,A^3\,a^6\,b^8-6\,A^3\,a^5\,b^9+12\,A^3\,a^4\,b^{10}+48\,A^3\,a^3\,b^{11}-112\,A^3\,a^2\,b^{12}-32\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+3\,A^2\,C\,a^{10}\,b^4-3\,A^2\,C\,a^9\,b^5+39\,A^2\,C\,a^8\,b^6-9\,A^2\,C\,a^7\,b^7+54\,A^2\,C\,a^6\,b^8+72\,A^2\,C\,a^5\,b^9-192\,A^2\,C\,a^4\,b^{10}-48\,A^2\,C\,a^3\,b^{11}+96\,A^2\,C\,a^2\,b^{12}+12\,A\,C^2\,a^{10}\,b^4-3\,A\,C^2\,a^9\,b^5+48\,A\,C^2\,a^8\,b^6+36\,A\,C^2\,a^7\,b^7-108\,A\,C^2\,a^6\,b^8-24\,A\,C^2\,a^5\,b^9+48\,A\,C^2\,a^4\,b^{10}+12\,C^3\,a^{10}\,b^4+6\,C^3\,a^9\,b^5-20\,C^3\,a^8\,b^6-4\,C^3\,a^7\,b^7+8\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)}{a^5}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)}{a^5}+\frac{\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(\frac{\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)}{a^5}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)}{a^5}}\right)\,\left(4\,A\,b^3+a^2\,\left(A\,b+2\,C\,b\right)\right)\,2{}\mathrm{i}}{a^5\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}+\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}{\frac{64\,\left(5\,A^3\,a^8\,b^6-5\,A^3\,a^7\,b^7+31\,A^3\,a^6\,b^8-6\,A^3\,a^5\,b^9+12\,A^3\,a^4\,b^{10}+48\,A^3\,a^3\,b^{11}-112\,A^3\,a^2\,b^{12}-32\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+3\,A^2\,C\,a^{10}\,b^4-3\,A^2\,C\,a^9\,b^5+39\,A^2\,C\,a^8\,b^6-9\,A^2\,C\,a^7\,b^7+54\,A^2\,C\,a^6\,b^8+72\,A^2\,C\,a^5\,b^9-192\,A^2\,C\,a^4\,b^{10}-48\,A^2\,C\,a^3\,b^{11}+96\,A^2\,C\,a^2\,b^{12}+12\,A\,C^2\,a^{10}\,b^4-3\,A\,C^2\,a^9\,b^5+48\,A\,C^2\,a^8\,b^6+36\,A\,C^2\,a^7\,b^7-108\,A\,C^2\,a^6\,b^8-24\,A\,C^2\,a^5\,b^9+48\,A\,C^2\,a^4\,b^{10}+12\,C^3\,a^{10}\,b^4+6\,C^3\,a^9\,b^5-20\,C^3\,a^8\,b^6-4\,C^3\,a^7\,b^7+8\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}-\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}\,b^2-2\,A^2\,a^9\,b^3+7\,A^2\,a^8\,b^4-12\,A^2\,a^7\,b^5+7\,A^2\,a^6\,b^6-2\,A^2\,a^5\,b^7+2\,A^2\,a^4\,b^8+48\,A^2\,a^3\,b^9-48\,A^2\,a^2\,b^{10}-32\,A^2\,a\,b^{11}+32\,A^2\,b^{12}+4\,A\,C\,a^{10}\,b^2-8\,A\,C\,a^9\,b^3+12\,A\,C\,a^8\,b^4-16\,A\,C\,a^7\,b^5+10\,A\,C\,a^6\,b^6+56\,A\,C\,a^5\,b^7-56\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+32\,A\,C\,a^2\,b^{10}+4\,C^2\,a^{10}\,b^2-8\,C^2\,a^9\,b^3+5\,C^2\,a^8\,b^4+16\,C^2\,a^7\,b^5-16\,C^2\,a^6\,b^6-8\,C^2\,a^5\,b^7+8\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{32\,\left(2\,A\,a^{11}\,b^7-4\,A\,a^{10}\,b^8+9\,A\,a^{12}\,b^6-4\,A\,a^{13}\,b^5-5\,A\,a^{14}\,b^4+A\,a^{15}\,b^3-2\,C\,a^{12}\,b^6+C\,a^{13}\,b^5+5\,C\,a^{14}\,b^4-3\,C\,a^{15}\,b^3-3\,C\,a^{16}\,b^2+A\,a^{17}\,b+2\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(A*a^5 + 36*A*b^5 - 3*C*a^5 - 19*A*a^2*b^3 - 7*A*a^3*b^2 + 18*C*a^2*b^3 + 3*C*a^3*b^2 + 6*A*a*b^4 - 8*A*a^4*b - 9*C*a^4*b))/(3*a^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^5*(A*a^5 - 36*A*b^5 - 3*C*a^5 + 19*A*a^2*b^3 - 7*A*a^3*b^2 - 18*C*a^2*b^3 + 3*C*a^3*b^2 + 6*A*a*b^4 + 8*A*a^4*b + 9*C*a^4*b))/(3*a^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^7*(A*a^5 + 4*A*b^5 + C*a^5 - 3*A*a^2*b^3 + A*a^3*b^2 + 2*C*a^2*b^3 - C*a^3*b^2 - 2*A*a*b^4 - C*a^4*b))/(a^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(A*a^5 - 4*A*b^5 + C*a^5 + 3*A*a^2*b^3 + A*a^3*b^2 - 2*C*a^2*b^3 - C*a^3*b^2 - 2*A*a*b^4 + C*a^4*b))/(a^4*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^8*(a - b) - tan(c/2 + (d*x)/2)^2*(2*a + 4*b) + tan(c/2 + (d*x)/2)^6*(2*a - 4*b) + 6*b*tan(c/2 + (d*x)/2)^4)) - (atan((((4*A*b^3 + a^2*(A*b + 2*C*b))*((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*tan(c/2 + (d*x)/2)*(4*A*b^3 + a^2*(A*b + 2*C*b))*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 + a^2*(A*b + 2*C*b)))/a^5 - (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*1i)/a^5 - ((4*A*b^3 + a^2*(A*b + 2*C*b))*((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*tan(c/2 + (d*x)/2)*(4*A*b^3 + a^2*(A*b + 2*C*b))*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 + a^2*(A*b + 2*C*b)))/a^5 + (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*1i)/a^5)/((64*(64*A^3*b^14 - 32*A^3*a*b^13 - 112*A^3*a^2*b^12 + 48*A^3*a^3*b^11 + 12*A^3*a^4*b^10 - 6*A^3*a^5*b^9 + 31*A^3*a^6*b^8 - 5*A^3*a^7*b^7 + 5*A^3*a^8*b^6 + 8*C^3*a^6*b^8 - 4*C^3*a^7*b^7 - 20*C^3*a^8*b^6 + 6*C^3*a^9*b^5 + 12*C^3*a^10*b^4 + 48*A*C^2*a^4*b^10 - 24*A*C^2*a^5*b^9 - 108*A*C^2*a^6*b^8 + 36*A*C^2*a^7*b^7 + 48*A*C^2*a^8*b^6 - 3*A*C^2*a^9*b^5 + 12*A*C^2*a^10*b^4 + 96*A^2*C*a^2*b^12 - 48*A^2*C*a^3*b^11 - 192*A^2*C*a^4*b^10 + 72*A^2*C*a^5*b^9 + 54*A^2*C*a^6*b^8 - 9*A^2*C*a^7*b^7 + 39*A^2*C*a^8*b^6 - 3*A^2*C*a^9*b^5 + 3*A^2*C*a^10*b^4))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + ((4*A*b^3 + a^2*(A*b + 2*C*b))*((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*tan(c/2 + (d*x)/2)*(4*A*b^3 + a^2*(A*b + 2*C*b))*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 + a^2*(A*b + 2*C*b)))/a^5 - (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))/a^5 + ((4*A*b^3 + a^2*(A*b + 2*C*b))*((((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*tan(c/2 + (d*x)/2)*(4*A*b^3 + a^2*(A*b + 2*C*b))*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 + a^2*(A*b + 2*C*b)))/a^5 + (32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))/a^5))*(4*A*b^3 + a^2*(A*b + 2*C*b))*2i)/(a^5*d) + (b^2*atan(((b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))/((64*(64*A^3*b^14 - 32*A^3*a*b^13 - 112*A^3*a^2*b^12 + 48*A^3*a^3*b^11 + 12*A^3*a^4*b^10 - 6*A^3*a^5*b^9 + 31*A^3*a^6*b^8 - 5*A^3*a^7*b^7 + 5*A^3*a^8*b^6 + 8*C^3*a^6*b^8 - 4*C^3*a^7*b^7 - 20*C^3*a^8*b^6 + 6*C^3*a^9*b^5 + 12*C^3*a^10*b^4 + 48*A*C^2*a^4*b^10 - 24*A*C^2*a^5*b^9 - 108*A*C^2*a^6*b^8 + 36*A*C^2*a^7*b^7 + 48*A*C^2*a^8*b^6 - 3*A*C^2*a^9*b^5 + 12*A*C^2*a^10*b^4 + 96*A^2*C*a^2*b^12 - 48*A^2*C*a^3*b^11 - 192*A^2*C*a^4*b^10 + 72*A^2*C*a^5*b^9 + 54*A^2*C*a^6*b^8 - 9*A^2*C*a^7*b^7 + 39*A^2*C*a^8*b^6 - 3*A^2*C*a^9*b^5 + 3*A^2*C*a^10*b^4))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) - (b^2*((32*tan(c/2 + (d*x)/2)*(32*A^2*b^12 - 32*A^2*a*b^11 - 48*A^2*a^2*b^10 + 48*A^2*a^3*b^9 + 2*A^2*a^4*b^8 - 2*A^2*a^5*b^7 + 7*A^2*a^6*b^6 - 12*A^2*a^7*b^5 + 7*A^2*a^8*b^4 - 2*A^2*a^9*b^3 + A^2*a^10*b^2 + 8*C^2*a^4*b^8 - 8*C^2*a^5*b^7 - 16*C^2*a^6*b^6 + 16*C^2*a^7*b^5 + 5*C^2*a^8*b^4 - 8*C^2*a^9*b^3 + 4*C^2*a^10*b^2 + 32*A*C*a^2*b^10 - 32*A*C*a^3*b^9 - 56*A*C*a^4*b^8 + 56*A*C*a^5*b^7 + 10*A*C*a^6*b^6 - 16*A*C*a^7*b^5 + 12*A*C*a^8*b^4 - 8*A*C*a^9*b^3 + 4*A*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((32*(2*A*a^11*b^7 - 4*A*a^10*b^8 + 9*A*a^12*b^6 - 4*A*a^13*b^5 - 5*A*a^14*b^4 + A*a^15*b^3 - 2*C*a^12*b^6 + C*a^13*b^5 + 5*C*a^14*b^4 - 3*C*a^15*b^3 - 3*C*a^16*b^2 + A*a^17*b + 2*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2)*2i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
578,1,10483,372,14.461197,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,C\,a^6-C\,b^6-6\,A\,a^2\,b^4+A\,a^3\,b^3+2\,A\,a^4\,b^2+8\,C\,a^2\,b^4-10\,C\,a^3\,b^3-23\,C\,a^4\,b^2+5\,C\,a\,b^5+6\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,C\,a^7+3\,C\,b^7-6\,A\,a^2\,b^5-15\,A\,a^3\,b^4+3\,A\,a^4\,b^3+6\,A\,a^5\,b^2+5\,C\,a^2\,b^5+26\,C\,a^3\,b^4-29\,C\,a^4\,b^3-67\,C\,a^5\,b^2-4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,C\,b^7-36\,C\,a^7-6\,A\,a^2\,b^5+15\,A\,a^3\,b^4+3\,A\,a^4\,b^3-6\,A\,a^5\,b^2+5\,C\,a^2\,b^5-26\,C\,a^3\,b^4-29\,C\,a^4\,b^3+67\,C\,a^5\,b^2+4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(C\,b^6-12\,C\,a^6+6\,A\,a^2\,b^4+A\,a^3\,b^3-2\,A\,a^4\,b^2-8\,C\,a^2\,b^4-10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+5\,C\,a\,b^5+6\,C\,a^5\,b\right)}{\left(a\,b^4-b^5\right)\,{\left(a+b\right)}^2}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)\,1{}\mathrm{i}}{b^5}-\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)\,1{}\mathrm{i}}{b^5}}{-\frac{8\,\left(8\,A^3\,a^9\,b^6-4\,A^3\,a^8\,b^7-36\,A^3\,a^7\,b^8+26\,A^3\,a^6\,b^9+72\,A^3\,a^5\,b^{10}-52\,A^3\,a^4\,b^{11}-68\,A^3\,a^3\,b^{12}+48\,A^3\,a^2\,b^{13}+24\,A^3\,a\,b^{14}+144\,A^2\,C\,a^{11}\,b^4-72\,A^2\,C\,a^{10}\,b^5-636\,A^2\,C\,a^9\,b^6+408\,A^2\,C\,a^8\,b^7+1188\,A^2\,C\,a^7\,b^8-747\,A^2\,C\,a^6\,b^9-1020\,A^2\,C\,a^5\,b^{10}+552\,A^2\,C\,a^4\,b^{11}+300\,A^2\,C\,a^3\,b^{12}+12\,A^2\,C\,a^2\,b^{13}+24\,A^2\,C\,a\,b^{14}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)}{b^5}+\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)}{b^5}}\right)\,\left(6{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^5\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}{\frac{8\,\left(8\,A^3\,a^9\,b^6-4\,A^3\,a^8\,b^7-36\,A^3\,a^7\,b^8+26\,A^3\,a^6\,b^9+72\,A^3\,a^5\,b^{10}-52\,A^3\,a^4\,b^{11}-68\,A^3\,a^3\,b^{12}+48\,A^3\,a^2\,b^{13}+24\,A^3\,a\,b^{14}+144\,A^2\,C\,a^{11}\,b^4-72\,A^2\,C\,a^{10}\,b^5-636\,A^2\,C\,a^9\,b^6+408\,A^2\,C\,a^8\,b^7+1188\,A^2\,C\,a^7\,b^8-747\,A^2\,C\,a^6\,b^9-1020\,A^2\,C\,a^5\,b^{10}+552\,A^2\,C\,a^4\,b^{11}+300\,A^2\,C\,a^3\,b^{12}+12\,A^2\,C\,a^2\,b^{13}+24\,A^2\,C\,a\,b^{14}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}","Not used",1,"(a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))/((8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 20*C*a^2*b^4 - 29*C*a^4*b^2)*1i)/(d*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) - (atan((((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*1i)/b^5 - ((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*1i)/b^5)/(((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))/b^5 - (8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + ((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*6i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2))*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))))/b^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 8*A*C*a*b^13 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))/b^5))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2))*2i)/(b^5*d) - ((tan(c/2 + (d*x)/2)*(12*C*a^6 - C*b^6 - 6*A*a^2*b^4 + A*a^3*b^3 + 2*A*a^4*b^2 + 8*C*a^2*b^4 - 10*C*a^3*b^3 - 23*C*a^4*b^2 + 5*C*a*b^5 + 6*C*a^5*b))/((a + b)*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^3*(36*C*a^7 + 3*C*b^7 - 6*A*a^2*b^5 - 15*A*a^3*b^4 + 3*A*a^4*b^3 + 6*A*a^5*b^2 + 5*C*a^2*b^5 + 26*C*a^3*b^4 - 29*C*a^4*b^3 - 67*C*a^5*b^2 - 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^5*(3*C*b^7 - 36*C*a^7 - 6*A*a^2*b^5 + 15*A*a^3*b^4 + 3*A*a^4*b^3 - 6*A*a^5*b^2 + 5*C*a^2*b^5 - 26*C*a^3*b^4 - 29*C*a^4*b^3 + 67*C*a^5*b^2 + 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^7*(C*b^6 - 12*C*a^6 + 6*A*a^2*b^4 + A*a^3*b^3 - 2*A*a^4*b^2 - 8*C*a^2*b^4 - 10*C*a^3*b^3 + 23*C*a^4*b^2 + 5*C*a*b^5 + 6*C*a^5*b))/((a*b^4 - b^5)*(a + b)^2))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(6*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^2*(4*a*b + 4*a^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 4*a^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
579,1,7216,262,10.934904,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,b^5-6\,C\,a^5+A\,a^2\,b^3-4\,C\,a^2\,b^3+12\,C\,a^3\,b^2+4\,A\,a\,b^4-2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^5+2\,C\,b^5+A\,a^2\,b^3-4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-4\,A\,a\,b^4+2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,b^6-6\,C\,a^6+3\,A\,a^2\,b^4-6\,C\,a^2\,b^4+13\,C\,a^4\,b^2\right)}{b\,\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+2\,a\,b-b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^2+2\,a\,b+b^2\right)\right)}-\frac{6\,C\,a\,\mathrm{atan}\left(\frac{\frac{3\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}+\frac{3\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}}{\frac{16\,\left(3\,A^2\,C\,a^5\,b^7+12\,A^2\,C\,a^3\,b^9+12\,A^2\,C\,a\,b^{11}+18\,A\,C^2\,a^9\,b^3+18\,A\,C^2\,a^8\,b^4-18\,A\,C^2\,a^7\,b^5-54\,A\,C^2\,a^5\,b^7-54\,A\,C^2\,a^4\,b^8+108\,A\,C^2\,a^3\,b^9+36\,A\,C^2\,a^2\,b^{10}+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}-\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,a\,\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}}\right)}{b^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(3\,A^2\,C\,a^5\,b^7+12\,A^2\,C\,a^3\,b^9+12\,A^2\,C\,a\,b^{11}+18\,A\,C^2\,a^9\,b^3+18\,A\,C^2\,a^8\,b^4-18\,A\,C^2\,a^7\,b^5-54\,A\,C^2\,a^5\,b^7-54\,A\,C^2\,a^4\,b^8+108\,A\,C^2\,a^3\,b^9+36\,A\,C^2\,a^2\,b^{10}+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\left(4\,A\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^5*(2*C*b^5 - 6*C*a^5 + A*a^2*b^3 - 4*C*a^2*b^3 + 12*C*a^3*b^2 + 4*A*a*b^4 - 2*C*a*b^4 + 3*C*a^4*b))/((a*b^3 - b^4)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(6*C*a^5 + 2*C*b^5 + A*a^2*b^3 - 4*C*a^2*b^3 - 12*C*a^3*b^2 - 4*A*a*b^4 + 2*C*a*b^4 + 3*C*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) + (2*tan(c/2 + (d*x)/2)^3*(2*C*b^6 - 6*C*a^6 + 3*A*a^2*b^4 - 6*C*a^2*b^4 + 13*C*a^4*b^2))/(b*(a*b^2 - b^3)*(a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) - (6*C*a*atan(((3*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4))/b^4 + (3*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4))/b^4)/((16*(108*C^3*a^12 - 54*C^3*a^11*b + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 + 12*A^2*C*a*b^11 + 36*A*C^2*a^2*b^10 + 108*A*C^2*a^3*b^9 - 54*A*C^2*a^4*b^8 - 54*A*C^2*a^5*b^7 - 18*A*C^2*a^7*b^5 + 18*A*C^2*a^8*b^4 + 18*A*C^2*a^9*b^3 + 12*A^2*C*a^3*b^9 + 3*A^2*C*a^5*b^7))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4)*3i)/b^4 - (C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*a*((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (C*a*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4)*3i)/b^4)))/(b^4*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(108*C^3*a^12 - 54*C^3*a^11*b + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 + 12*A^2*C*a*b^11 + 36*A*C^2*a^2*b^10 + 108*A*C^2*a^3*b^9 - 54*A*C^2*a^4*b^8 - 54*A*C^2*a^5*b^7 - 18*A*C^2*a^7*b^5 + 18*A*C^2*a^8*b^4 + 18*A*C^2*a^9*b^3 + 12*A^2*C*a^3*b^9 + 3*A^2*C*a^5*b^7))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*C^2*a^12 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*(4*A*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 12*C*a^2*b^4 - 15*C*a^4*b^2)*1i)/(d*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
580,1,6587,203,10.419584,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2+6\,C\,a^2\,b^2+A\,a\,b^3+C\,a^3\,b\right)}{\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2+6\,C\,a^2\,b^2-A\,a\,b^3-C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{2\,C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}-\frac{C\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}}{-\frac{16\,\left(9\,A^2\,C\,a^2\,b^7+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{C\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}\right)}{b^3\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(9\,A^2\,C\,a^2\,b^7+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(3\,A\,b^4+2\,C\,a^4+6\,C\,b^4-5\,C\,a^2\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 + 6*C*a^2*b^2 + A*a*b^3 + C*a^3*b))/((a*b^2 - b^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 + 6*C*a^2*b^2 - A*a*b^3 - C*a^3*b))/((a + b)*(b^4 - 2*a*b^3 + a^2*b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (2*C*atan(((C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 - (C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3)/((C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3 - (16*(4*C^3*a^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*((C*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3)))/(b^3*d) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(4*C^3*a^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (a*((8*(4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*(-(a + b)^5*(a - b)^5)^(1/2)*(3*A*b^4 + 2*C*a^4 + 6*C*b^4 - 5*C*a^2*b^2)*1i)/(d*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))","B"
581,1,241,177,4.283695,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^2+C\,a^2-4\,A\,a\,b-4\,C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^2+C\,a^2+4\,A\,a\,b+4\,C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,A\,a^2+A\,b^2+C\,a^2+2\,C\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2 - 4*A*a*b - 4*C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)) - (tan(c/2 + (d*x)/2)^3*(A*b^2 + C*a^2 + 4*A*a*b + 4*C*a*b))/((a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*A*a^2 + A*b^2 + C*a^2 + 2*C*b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
582,1,6574,211,10.092254,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^4-2\,A\,b^4+6\,A\,a^2\,b^2+2\,C\,a^2\,b^2+A\,a\,b^3+C\,a^3\,b\right)}{\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4-6\,A\,a^2\,b^2-2\,C\,a^2\,b^2+A\,a\,b^3+C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)\,1{}\mathrm{i}}{a^3}-\frac{A\,\left(\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)\,1{}\mathrm{i}}{a^3}}{\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,\left(\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)}{a^3}+\frac{A\,\left(\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)}{a^3}}\right)\,2{}\mathrm{i}}{a^3\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,a^4+2\,A\,b^4+3\,C\,a^4-5\,A\,a^2\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"(A*atan(((A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3 - (A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3)/((16*(4*A^3*b^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 + 6*A^2*C*a^8*b + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 + (A*((A*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3))*2i)/(a^3*d) - ((tan(c/2 + (d*x)/2)^3*(2*C*a^4 - 2*A*b^4 + 6*A*a^2*b^2 + 2*C*a^2*b^2 + A*a*b^3 + C*a^3*b))/((a^2*b - a^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 - 6*A*a^2*b^2 - 2*C*a^2*b^2 + A*a*b^3 + C*a^3*b))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((16*(4*A^3*b^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 + 6*A^2*C*a^8*b + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + 9*C^2*a^8*b^2 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(4*A*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*a^4 + 2*A*b^4 + 3*C*a^4 - 5*A*a^2*b^2)*1i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
583,1,7211,275,10.695009,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^5-6\,A\,b^5+12\,A\,a^2\,b^3-4\,A\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4-2\,A\,a^4\,b+4\,C\,a^4\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^5+6\,A\,b^5-12\,A\,a^2\,b^3-4\,A\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4+2\,A\,a^4\,b-4\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a^6-6\,A\,b^6+13\,A\,a^2\,b^4-6\,A\,a^4\,b^2+3\,C\,a^4\,b^2\right)}{a\,\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^2+2\,a\,b+3\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,a\,b-3\,b^2\right)\right)}+\frac{A\,b\,\mathrm{atan}\left(\frac{\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{3\,A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{24\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)\,3{}\mathrm{i}}{a^4}+\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{3\,A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{24\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)\,3{}\mathrm{i}}{a^4}}{\frac{16\,\left(216\,A^3\,a^8\,b^4+216\,A^3\,a^7\,b^5-702\,A^3\,a^6\,b^6-378\,A^3\,a^5\,b^7+864\,A^3\,a^4\,b^8+243\,A^3\,a^3\,b^9-486\,A^3\,a^2\,b^{10}-54\,A^3\,a\,b^{11}+108\,A^3\,b^{12}+36\,A^2\,C\,a^{10}\,b^2+108\,A^2\,C\,a^9\,b^3-54\,A^2\,C\,a^8\,b^4-54\,A^2\,C\,a^7\,b^5-18\,A^2\,C\,a^5\,b^7+18\,A^2\,C\,a^4\,b^8+18\,A^2\,C\,a^3\,b^9+12\,A\,C^2\,a^{11}\,b+12\,A\,C^2\,a^9\,b^3+3\,A\,C^2\,a^7\,b^5\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{3\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{3\,A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{24\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)}{a^4}-\frac{3\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{3\,A\,b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{24\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)}{a^4}}\right)\,6{}\mathrm{i}}{a^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{16\,\left(216\,A^3\,a^8\,b^4+216\,A^3\,a^7\,b^5-702\,A^3\,a^6\,b^6-378\,A^3\,a^5\,b^7+864\,A^3\,a^4\,b^8+243\,A^3\,a^3\,b^9-486\,A^3\,a^2\,b^{10}-54\,A^3\,a\,b^{11}+108\,A^3\,b^{12}+36\,A^2\,C\,a^{10}\,b^2+108\,A^2\,C\,a^9\,b^3-54\,A^2\,C\,a^8\,b^4-54\,A^2\,C\,a^7\,b^5-18\,A^2\,C\,a^5\,b^7+18\,A^2\,C\,a^4\,b^8+18\,A^2\,C\,a^3\,b^9+12\,A\,C^2\,a^{11}\,b+12\,A\,C^2\,a^9\,b^3+3\,A\,C^2\,a^7\,b^5\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}","Not used",1,"(A*b*atan(((A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (3*A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (24*A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4)*3i)/a^4 + (A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (3*A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (24*A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4)*3i)/a^4)/((16*(108*A^3*b^12 - 54*A^3*a*b^11 - 486*A^3*a^2*b^10 + 243*A^3*a^3*b^9 + 864*A^3*a^4*b^8 - 378*A^3*a^5*b^7 - 702*A^3*a^6*b^6 + 216*A^3*a^7*b^5 + 216*A^3*a^8*b^4 + 12*A*C^2*a^11*b + 3*A*C^2*a^7*b^5 + 12*A*C^2*a^9*b^3 + 18*A^2*C*a^3*b^9 + 18*A^2*C*a^4*b^8 - 18*A^2*C*a^5*b^7 - 54*A^2*C*a^7*b^5 - 54*A^2*C*a^8*b^4 + 108*A^2*C*a^9*b^3 + 36*A^2*C*a^10*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (3*A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (3*A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (24*A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4))/a^4 - (3*A*b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (3*A*b*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (24*A*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4))/a^4))*6i)/(a^4*d) - ((tan(c/2 + (d*x)/2)^5*(2*A*a^5 - 6*A*b^5 + 12*A*a^2*b^3 - 4*A*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 - 2*A*a^4*b + 4*C*a^4*b))/((a^3*b - a^4)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*A*a^5 + 6*A*b^5 - 12*A*a^2*b^3 - 4*A*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 + 2*A*a^4*b - 4*C*a^4*b))/((a + b)*(a^5 - 2*a^4*b + a^3*b^2)) + (2*tan(c/2 + (d*x)/2)^3*(2*A*a^6 - 6*A*b^6 + 13*A*a^2*b^4 - 6*A*a^4*b^2 + 3*C*a^4*b^2))/(a*(a^2*b - a^3)*(a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) + (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((16*(108*A^3*b^12 - 54*A^3*a*b^11 - 486*A^3*a^2*b^10 + 243*A^3*a^3*b^9 + 864*A^3*a^4*b^8 - 378*A^3*a^5*b^7 - 702*A^3*a^6*b^6 + 216*A^3*a^7*b^5 + 216*A^3*a^8*b^4 + 12*A*C^2*a^11*b + 3*A*C^2*a^7*b^5 + 12*A*C^2*a^9*b^3 + 18*A^2*C*a^3*b^9 + 18*A^2*C*a^4*b^8 - 18*A^2*C*a^5*b^7 - 54*A^2*C*a^7*b^5 - 54*A^2*C*a^8*b^4 + 108*A^2*C*a^9*b^3 + 36*A^2*C*a^10*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + C*a^4*b^2)*1i)/(d*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))","B"
584,1,10422,378,14.599596,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A\,b^6-A\,a^6-23\,A\,a^2\,b^4-10\,A\,a^3\,b^3+8\,A\,a^4\,b^2+2\,C\,a^2\,b^4+C\,a^3\,b^3-6\,C\,a^4\,b^2+6\,A\,a\,b^5+5\,A\,a^5\,b\right)}{\left(a+b\right)\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^7+36\,A\,b^7-67\,A\,a^2\,b^5-29\,A\,a^3\,b^4+26\,A\,a^4\,b^3+5\,A\,a^5\,b^2+6\,C\,a^2\,b^5+3\,C\,a^3\,b^4-15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6-4\,A\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A\,a^7-36\,A\,b^7+67\,A\,a^2\,b^5-29\,A\,a^3\,b^4-26\,A\,a^4\,b^3+5\,A\,a^5\,b^2-6\,C\,a^2\,b^5+3\,C\,a^3\,b^4+15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6+4\,A\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A\,a^6-12\,A\,b^6+23\,A\,a^2\,b^4-10\,A\,a^3\,b^3-8\,A\,a^4\,b^2-2\,C\,a^2\,b^4+C\,a^3\,b^3+6\,C\,a^4\,b^2+6\,A\,a\,b^5+5\,A\,a^5\,b\right)}{\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^2}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-6\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,b^2+4\,a\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}+\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}}{\frac{8\,\left(20\,A^3\,a^{12}\,b^3-20\,A^3\,a^{11}\,b^4+411\,A^3\,a^{10}\,b^5-11\,A^3\,a^9\,b^6+1314\,A^3\,a^8\,b^7+2326\,A^3\,a^7\,b^8-7829\,A^3\,a^6\,b^9-4770\,A^3\,a^5\,b^{10}+11700\,A^3\,a^4\,b^{11}+3456\,A^3\,a^3\,b^{12}-7344\,A^3\,a^2\,b^{13}-864\,A^3\,a\,b^{14}+1728\,A^3\,b^{15}+6\,A^2\,C\,a^{14}\,b-6\,A^2\,C\,a^{13}\,b^2+207\,A^2\,C\,a^{12}\,b^3+33\,A^2\,C\,a^{11}\,b^4+1158\,A^2\,C\,a^{10}\,b^5+1974\,A^2\,C\,a^9\,b^6-4977\,A^2\,C\,a^8\,b^7-3405\,A^2\,C\,a^7\,b^8+6486\,A^2\,C\,a^6\,b^9+2088\,A^2\,C\,a^5\,b^{10}-3744\,A^2\,C\,a^4\,b^{11}-432\,A^2\,C\,a^3\,b^{12}+864\,A^2\,C\,a^2\,b^{13}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}\right)}{a^5}-\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)}{a^5}\right)}{a^5}}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+6\,A\,b^2\right)\,2{}\mathrm{i}}{a^5\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}{\frac{8\,\left(20\,A^3\,a^{12}\,b^3-20\,A^3\,a^{11}\,b^4+411\,A^3\,a^{10}\,b^5-11\,A^3\,a^9\,b^6+1314\,A^3\,a^8\,b^7+2326\,A^3\,a^7\,b^8-7829\,A^3\,a^6\,b^9-4770\,A^3\,a^5\,b^{10}+11700\,A^3\,a^4\,b^{11}+3456\,A^3\,a^3\,b^{12}-7344\,A^3\,a^2\,b^{13}-864\,A^3\,a\,b^{14}+1728\,A^3\,b^{15}+6\,A^2\,C\,a^{14}\,b-6\,A^2\,C\,a^{13}\,b^2+207\,A^2\,C\,a^{12}\,b^3+33\,A^2\,C\,a^{11}\,b^4+1158\,A^2\,C\,a^{10}\,b^5+1974\,A^2\,C\,a^9\,b^6-4977\,A^2\,C\,a^8\,b^7-3405\,A^2\,C\,a^7\,b^8+6486\,A^2\,C\,a^6\,b^9+2088\,A^2\,C\,a^5\,b^{10}-3744\,A^2\,C\,a^4\,b^{11}-432\,A^2\,C\,a^3\,b^{12}+864\,A^2\,C\,a^2\,b^{13}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(12*A*b^6 - A*a^6 - 23*A*a^2*b^4 - 10*A*a^3*b^3 + 8*A*a^4*b^2 + 2*C*a^2*b^4 + C*a^3*b^3 - 6*C*a^4*b^2 + 6*A*a*b^5 + 5*A*a^5*b))/((a + b)*(a^6 - 2*a^5*b + a^4*b^2)) - (tan(c/2 + (d*x)/2)^3*(3*A*a^7 + 36*A*b^7 - 67*A*a^2*b^5 - 29*A*a^3*b^4 + 26*A*a^4*b^3 + 5*A*a^5*b^2 + 6*C*a^2*b^5 + 3*C*a^3*b^4 - 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 - 4*A*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) - (tan(c/2 + (d*x)/2)^5*(3*A*a^7 - 36*A*b^7 + 67*A*a^2*b^5 - 29*A*a^3*b^4 - 26*A*a^4*b^3 + 5*A*a^5*b^2 - 6*C*a^2*b^5 + 3*C*a^3*b^4 + 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 + 4*A*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) + (tan(c/2 + (d*x)/2)^7*(A*a^6 - 12*A*b^6 + 23*A*a^2*b^4 - 10*A*a^3*b^3 - 8*A*a^4*b^2 - 2*C*a^2*b^4 + C*a^3*b^3 + 6*C*a^4*b^2 + 6*A*a*b^5 + 5*A*a^5*b))/((a^4*b - a^5)*(a + b)^2))/(d*(2*a*b - tan(c/2 + (d*x)/2)^4*(2*a^2 - 6*b^2) - tan(c/2 + (d*x)/2)^2*(4*a*b + 4*b^2) + tan(c/2 + (d*x)/2)^6*(4*a*b - 4*b^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (atan((((6*A*b^2 + a^2*(A/2 + C))*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + ((6*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5)*1i)/a^5 + ((6*A*b^2 + a^2*(A/2 + C))*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - ((6*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5)*1i)/a^5)/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + ((6*A*b^2 + a^2*(A/2 + C))*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + ((6*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5))/a^5 - ((6*A*b^2 + a^2*(A/2 + C))*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - ((6*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C))*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))))/a^5))/a^5))*(6*A*b^2 + a^2*(A/2 + C))*2i)/(a^5*d) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 8*A*C*a^13*b + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 2*C*a^2*b^4 - 5*C*a^4*b^2)*1i)/(d*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))","B"
585,1,14280,514,18.718246,"\text{Not used}","int((cos(c + d*x)^4*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,C\,a^8+C\,b^8+12\,A\,a^2\,b^6-4\,A\,a^3\,b^5-6\,A\,a^4\,b^4+A\,a^5\,b^3+2\,A\,a^6\,b^2-11\,C\,a^2\,b^6+21\,C\,a^3\,b^5+57\,C\,a^4\,b^4-27\,C\,a^5\,b^3-59\,C\,a^6\,b^2-7\,C\,a\,b^7+10\,C\,a^7\,b\right)}{b^5\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(20\,C\,a^8+C\,b^8+12\,A\,a^2\,b^6+4\,A\,a^3\,b^5-6\,A\,a^4\,b^4-A\,a^5\,b^3+2\,A\,a^6\,b^2-11\,C\,a^2\,b^6-21\,C\,a^3\,b^5+57\,C\,a^4\,b^4+27\,C\,a^5\,b^3-59\,C\,a^6\,b^2+7\,C\,a\,b^7-10\,C\,a^7\,b\right)}{b^5\,{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(120\,C\,a^9-6\,C\,b^9+60\,A\,a^3\,b^6-8\,A\,a^4\,b^5-37\,A\,a^5\,b^4+3\,A\,a^6\,b^3+12\,A\,a^7\,b^2-3\,C\,a^2\,b^7-111\,C\,a^3\,b^6+45\,C\,a^4\,b^5+369\,C\,a^5\,b^4-71\,C\,a^6\,b^3-364\,C\,a^7\,b^2+21\,C\,a\,b^8+30\,C\,a^8\,b\right)}{3\,b^5\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(120\,C\,a^9+6\,C\,b^9+60\,A\,a^3\,b^6+8\,A\,a^4\,b^5-37\,A\,a^5\,b^4-3\,A\,a^6\,b^3+12\,A\,a^7\,b^2+3\,C\,a^2\,b^7-111\,C\,a^3\,b^6-45\,C\,a^4\,b^5+369\,C\,a^5\,b^4+71\,C\,a^6\,b^3-364\,C\,a^7\,b^2+21\,C\,a\,b^8-30\,C\,a^8\,b\right)}{3\,b^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(180\,C\,a^{10}+9\,C\,b^{10}-36\,A\,a^2\,b^8+110\,A\,a^4\,b^6-62\,A\,a^6\,b^4+18\,A\,a^8\,b^2+36\,C\,a^2\,b^8-324\,C\,a^4\,b^6+740\,C\,a^6\,b^4-611\,C\,a^8\,b^2\right)}{3\,b^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^3+9\,a^2\,b+3\,a\,b^2-b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-10\,a^3-6\,a^2\,b+6\,a\,b^2+2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-10\,a^3+6\,a^2\,b+6\,a\,b^2-2\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^3-9\,a^2\,b+3\,a\,b^2+b^3\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(10{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{\left(10{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+52\,C\,a^2\,b^{25}-160\,C\,a^3\,b^{24}-316\,C\,a^4\,b^{23}+816\,C\,a^5\,b^{22}+724\,C\,a^6\,b^{21}-1764\,C\,a^7\,b^{20}-896\,C\,a^8\,b^{19}+2076\,C\,a^9\,b^{18}+640\,C\,a^{10}\,b^{17}-1404\,C\,a^{11}\,b^{16}-248\,C\,a^{12}\,b^{15}+516\,C\,a^{13}\,b^{14}+40\,C\,a^{14}\,b^{13}-80\,C\,a^{15}\,b^{12}-32\,A\,a\,b^{26}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}+48\,a^{12}\,b^{14}-48\,a^{11}\,b^{15}-120\,a^{10}\,b^{16}+120\,a^9\,b^{17}+160\,a^8\,b^{18}-160\,a^7\,b^{19}-120\,a^6\,b^{20}+120\,a^5\,b^{21}+48\,a^4\,b^{22}-48\,a^3\,b^{23}-8\,a^2\,b^{24}+8\,a\,b^{25}\right)}{b^6\,\left(-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}\right)}\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^4-8\,A^2\,a^{13}\,b^5-48\,A^2\,a^{12}\,b^6+48\,A^2\,a^{11}\,b^7+117\,A^2\,a^{10}\,b^8-120\,A^2\,a^9\,b^9-164\,A^2\,a^8\,b^{10}+160\,A^2\,a^7\,b^{11}+156\,A^2\,a^6\,b^{12}-120\,A^2\,a^5\,b^{13}-92\,A^2\,a^4\,b^{14}+48\,A^2\,a^3\,b^{15}+44\,A^2\,a^2\,b^{16}-8\,A^2\,a\,b^{17}+4\,A^2\,b^{18}+160\,A\,C\,a^{16}\,b^2-160\,A\,C\,a^{15}\,b^3-952\,A\,C\,a^{14}\,b^4+952\,A\,C\,a^{13}\,b^5+2322\,A\,C\,a^{12}\,b^6-2352\,A\,C\,a^{11}\,b^7-3124\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9+2588\,A\,C\,a^8\,b^{10}-2240\,A\,C\,a^7\,b^{11}-1284\,A\,C\,a^6\,b^{12}+840\,A\,C\,a^5\,b^{13}+276\,A\,C\,a^4\,b^{14}-112\,A\,C\,a^3\,b^{15}+60\,A\,C\,a^2\,b^{16}-8\,A\,C\,a\,b^{17}+4\,A\,C\,b^{18}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}\right)\,1{}\mathrm{i}}{b^6}-\frac{\left(10{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{\left(10{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+52\,C\,a^2\,b^{25}-160\,C\,a^3\,b^{24}-316\,C\,a^4\,b^{23}+816\,C\,a^5\,b^{22}+724\,C\,a^6\,b^{21}-1764\,C\,a^7\,b^{20}-896\,C\,a^8\,b^{19}+2076\,C\,a^9\,b^{18}+640\,C\,a^{10}\,b^{17}-1404\,C\,a^{11}\,b^{16}-248\,C\,a^{12}\,b^{15}+516\,C\,a^{13}\,b^{14}+40\,C\,a^{14}\,b^{13}-80\,C\,a^{15}\,b^{12}-32\,A\,a\,b^{26}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}+48\,a^{12}\,b^{14}-48\,a^{11}\,b^{15}-120\,a^{10}\,b^{16}+120\,a^9\,b^{17}+160\,a^8\,b^{18}-160\,a^7\,b^{19}-120\,a^6\,b^{20}+120\,a^5\,b^{21}+48\,a^4\,b^{22}-48\,a^3\,b^{23}-8\,a^2\,b^{24}+8\,a\,b^{25}\right)}{b^6\,\left(-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}\right)}\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^4-8\,A^2\,a^{13}\,b^5-48\,A^2\,a^{12}\,b^6+48\,A^2\,a^{11}\,b^7+117\,A^2\,a^{10}\,b^8-120\,A^2\,a^9\,b^9-164\,A^2\,a^8\,b^{10}+160\,A^2\,a^7\,b^{11}+156\,A^2\,a^6\,b^{12}-120\,A^2\,a^5\,b^{13}-92\,A^2\,a^4\,b^{14}+48\,A^2\,a^3\,b^{15}+44\,A^2\,a^2\,b^{16}-8\,A^2\,a\,b^{17}+4\,A^2\,b^{18}+160\,A\,C\,a^{16}\,b^2-160\,A\,C\,a^{15}\,b^3-952\,A\,C\,a^{14}\,b^4+952\,A\,C\,a^{13}\,b^5+2322\,A\,C\,a^{12}\,b^6-2352\,A\,C\,a^{11}\,b^7-3124\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9+2588\,A\,C\,a^8\,b^{10}-2240\,A\,C\,a^7\,b^{11}-1284\,A\,C\,a^6\,b^{12}+840\,A\,C\,a^5\,b^{13}+276\,A\,C\,a^4\,b^{14}-112\,A\,C\,a^3\,b^{15}+60\,A\,C\,a^2\,b^{16}-8\,A\,C\,a\,b^{17}+4\,A\,C\,b^{18}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}\right)\,1{}\mathrm{i}}{b^6}}{-\frac{8\,\left(8\,A^3\,a^{13}\,b^6-4\,A^3\,a^{12}\,b^7-52\,A^3\,a^{11}\,b^8+22\,A^3\,a^{10}\,b^9+140\,A^3\,a^9\,b^{10}-68\,A^3\,a^8\,b^{11}-220\,A^3\,a^7\,b^{12}+132\,A^3\,a^6\,b^{13}+220\,A^3\,a^5\,b^{14}-128\,A^3\,a^4\,b^{15}-128\,A^3\,a^3\,b^{16}+96\,A^3\,a^2\,b^{17}+32\,A^3\,a\,b^{18}+240\,A^2\,C\,a^{15}\,b^4-120\,A^2\,C\,a^{14}\,b^5-1548\,A^2\,C\,a^{13}\,b^6+684\,A^2\,C\,a^{12}\,b^7+4152\,A^2\,C\,a^{11}\,b^8-1983\,A^2\,C\,a^{10}\,b^9-6336\,A^2\,C\,a^9\,b^{10}+3448\,A^2\,C\,a^8\,b^{11}+5944\,A^2\,C\,a^7\,b^{12}-3196\,A^2\,C\,a^6\,b^{13}-3156\,A^2\,C\,a^5\,b^{14}+1760\,A^2\,C\,a^4\,b^{15}+672\,A^2\,C\,a^3\,b^{16}+32\,A^2\,C\,a^2\,b^{17}+32\,A^2\,C\,a\,b^{18}+2400\,A\,C^2\,a^{17}\,b^2-1200\,A\,C^2\,a^{16}\,b^3-15360\,A\,C^2\,a^{15}\,b^4+7080\,A\,C^2\,a^{14}\,b^5+41046\,A\,C^2\,a^{13}\,b^6-19233\,A\,C^2\,a^{12}\,b^7-60729\,A\,C^2\,a^{11}\,b^8+29513\,A\,C^2\,a^{10}\,b^9+53039\,A\,C^2\,a^9\,b^{10}-24901\,A\,C^2\,a^8\,b^{11}-25211\,A\,C^2\,a^7\,b^{12}+9657\,A\,C^2\,a^6\,b^{13}+4359\,A\,C^2\,a^5\,b^{14}+192\,A\,C^2\,a^4\,b^{15}+448\,A\,C^2\,a^3\,b^{16}-8\,A\,C^2\,a^2\,b^{17}+8\,A\,C^2\,a\,b^{18}+8000\,C^3\,a^{19}-4000\,C^3\,a^{18}\,b-50800\,C^3\,a^{17}\,b^2+24400\,C^3\,a^{16}\,b^3+135260\,C^3\,a^{15}\,b^4-62030\,C^3\,a^{14}\,b^5-193689\,C^3\,a^{13}\,b^6+82337\,C^3\,a^{12}\,b^7+155991\,C^3\,a^{11}\,b^8-57345\,C^3\,a^{10}\,b^9-64479\,C^3\,a^9\,b^{10}+16999\,C^3\,a^8\,b^{11}+8281\,C^3\,a^7\,b^{12}+204\,C^3\,a^6\,b^{13}+1396\,C^3\,a^5\,b^{14}-40\,C^3\,a^4\,b^{15}+40\,C^3\,a^3\,b^{16}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}+\frac{\left(10{}\mathrm{i}\,C\,a^2+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\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c{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^4-8\,A^2\,a^{13}\,b^5-48\,A^2\,a^{12}\,b^6+48\,A^2\,a^{11}\,b^7+117\,A^2\,a^{10}\,b^8-120\,A^2\,a^9\,b^9-164\,A^2\,a^8\,b^{10}+160\,A^2\,a^7\,b^{11}+156\,A^2\,a^6\,b^{12}-120\,A^2\,a^5\,b^{13}-92\,A^2\,a^4\,b^{14}+48\,A^2\,a^3\,b^{15}+44\,A^2\,a^2\,b^{16}-8\,A^2\,a\,b^{17}+4\,A^2\,b^{18}+160\,A\,C\,a^{16}\,b^2-160\,A\,C\,a^{15}\,b^3-952\,A\,C\,a^{14}\,b^4+952\,A\,C\,a^{13}\,b^5+2322\,A\,C\,a^{12}\,b^6-2352\,A\,C\,a^{11}\,b^7-3124\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9+2588\,A\,C\,a^8\,b^{10}-2240\,A\,C\,a^7\,b^{11}-1284\,A\,C\,a^6\,b^{12}+840\,A\,C\,a^5\,b^{13}+276\,A\,C\,a^4\,b^{14}-112\,A\,C\,a^3\,b^{15}+60\,A\,C\,a^2\,b^{16}-8\,A\,C\,a\,b^{17}+4\,A\,C\,b^{18}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}+\frac{a\,\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+52\,C\,a^2\,b^{25}-160\,C\,a^3\,b^{24}-316\,C\,a^4\,b^{23}+816\,C\,a^5\,b^{22}+724\,C\,a^6\,b^{21}-1764\,C\,a^7\,b^{20}-896\,C\,a^8\,b^{19}+2076\,C\,a^9\,b^{18}+640\,C\,a^{10}\,b^{17}-1404\,C\,a^{11}\,b^{16}-248\,C\,a^{12}\,b^{15}+516\,C\,a^{13}\,b^{14}+40\,C\,a^{14}\,b^{13}-80\,C\,a^{15}\,b^{12}-32\,A\,a\,b^{26}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}+48\,a^{12}\,b^{14}-48\,a^{11}\,b^{15}-120\,a^{10}\,b^{16}+120\,a^9\,b^{17}+160\,a^8\,b^{18}-160\,a^7\,b^{19}-120\,a^6\,b^{20}+120\,a^5\,b^{21}+48\,a^4\,b^{22}-48\,a^3\,b^{23}-8\,a^2\,b^{24}+8\,a\,b^{25}\right)}{\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)\,\left(-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^4-8\,A^2\,a^{13}\,b^5-48\,A^2\,a^{12}\,b^6+48\,A^2\,a^{11}\,b^7+117\,A^2\,a^{10}\,b^8-120\,A^2\,a^9\,b^9-164\,A^2\,a^8\,b^{10}+160\,A^2\,a^7\,b^{11}+156\,A^2\,a^6\,b^{12}-120\,A^2\,a^5\,b^{13}-92\,A^2\,a^4\,b^{14}+48\,A^2\,a^3\,b^{15}+44\,A^2\,a^2\,b^{16}-8\,A^2\,a\,b^{17}+4\,A^2\,b^{18}+160\,A\,C\,a^{16}\,b^2-160\,A\,C\,a^{15}\,b^3-952\,A\,C\,a^{14}\,b^4+952\,A\,C\,a^{13}\,b^5+2322\,A\,C\,a^{12}\,b^6-2352\,A\,C\,a^{11}\,b^7-3124\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9+2588\,A\,C\,a^8\,b^{10}-2240\,A\,C\,a^7\,b^{11}-1284\,A\,C\,a^6\,b^{12}+840\,A\,C\,a^5\,b^{13}+276\,A\,C\,a^4\,b^{14}-112\,A\,C\,a^3\,b^{15}+60\,A\,C\,a^2\,b^{16}-8\,A\,C\,a\,b^{17}+4\,A\,C\,b^{18}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}-\frac{a\,\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+52\,C\,a^2\,b^{25}-160\,C\,a^3\,b^{24}-316\,C\,a^4\,b^{23}+816\,C\,a^5\,b^{22}+724\,C\,a^6\,b^{21}-1764\,C\,a^7\,b^{20}-896\,C\,a^8\,b^{19}+2076\,C\,a^9\,b^{18}+640\,C\,a^{10}\,b^{17}-1404\,C\,a^{11}\,b^{16}-248\,C\,a^{12}\,b^{15}+516\,C\,a^{13}\,b^{14}+40\,C\,a^{14}\,b^{13}-80\,C\,a^{15}\,b^{12}-32\,A\,a\,b^{26}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}+48\,a^{12}\,b^{14}-48\,a^{11}\,b^{15}-120\,a^{10}\,b^{16}+120\,a^9\,b^{17}+160\,a^8\,b^{18}-160\,a^7\,b^{19}-120\,a^6\,b^{20}+120\,a^5\,b^{21}+48\,a^4\,b^{22}-48\,a^3\,b^{23}-8\,a^2\,b^{24}+8\,a\,b^{25}\right)}{\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)\,\left(-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}","Not used",1,"(a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) + (a*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2)*1i)/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) - (a*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2)*1i)/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))/((8*(8000*C^3*a^19 + 32*A^3*a*b^18 - 4000*C^3*a^18*b + 96*A^3*a^2*b^17 - 128*A^3*a^3*b^16 - 128*A^3*a^4*b^15 + 220*A^3*a^5*b^14 + 132*A^3*a^6*b^13 - 220*A^3*a^7*b^12 - 68*A^3*a^8*b^11 + 140*A^3*a^9*b^10 + 22*A^3*a^10*b^9 - 52*A^3*a^11*b^8 - 4*A^3*a^12*b^7 + 8*A^3*a^13*b^6 + 40*C^3*a^3*b^16 - 40*C^3*a^4*b^15 + 1396*C^3*a^5*b^14 + 204*C^3*a^6*b^13 + 8281*C^3*a^7*b^12 + 16999*C^3*a^8*b^11 - 64479*C^3*a^9*b^10 - 57345*C^3*a^10*b^9 + 155991*C^3*a^11*b^8 + 82337*C^3*a^12*b^7 - 193689*C^3*a^13*b^6 - 62030*C^3*a^14*b^5 + 135260*C^3*a^15*b^4 + 24400*C^3*a^16*b^3 - 50800*C^3*a^17*b^2 + 8*A*C^2*a*b^18 + 32*A^2*C*a*b^18 - 8*A*C^2*a^2*b^17 + 448*A*C^2*a^3*b^16 + 192*A*C^2*a^4*b^15 + 4359*A*C^2*a^5*b^14 + 9657*A*C^2*a^6*b^13 - 25211*A*C^2*a^7*b^12 - 24901*A*C^2*a^8*b^11 + 53039*A*C^2*a^9*b^10 + 29513*A*C^2*a^10*b^9 - 60729*A*C^2*a^11*b^8 - 19233*A*C^2*a^12*b^7 + 41046*A*C^2*a^13*b^6 + 7080*A*C^2*a^14*b^5 - 15360*A*C^2*a^15*b^4 - 1200*A*C^2*a^16*b^3 + 2400*A*C^2*a^17*b^2 + 32*A^2*C*a^2*b^17 + 672*A^2*C*a^3*b^16 + 1760*A^2*C*a^4*b^15 - 3156*A^2*C*a^5*b^14 - 3196*A^2*C*a^6*b^13 + 5944*A^2*C*a^7*b^12 + 3448*A^2*C*a^8*b^11 - 6336*A^2*C*a^9*b^10 - 1983*A^2*C*a^10*b^9 + 4152*A^2*C*a^11*b^8 + 684*A^2*C*a^12*b^7 - 1548*A^2*C*a^13*b^6 - 120*A^2*C*a^14*b^5 + 240*A^2*C*a^15*b^4))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) + (a*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) - (a*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6))))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2)*1i)/(d*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)) - (atan((((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10))))/b^6 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10))*1i)/b^6 - ((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10))))/b^6 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10))*1i)/b^6)/(((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10))))/b^6 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))/b^6 - (8*(8000*C^3*a^19 + 32*A^3*a*b^18 - 4000*C^3*a^18*b + 96*A^3*a^2*b^17 - 128*A^3*a^3*b^16 - 128*A^3*a^4*b^15 + 220*A^3*a^5*b^14 + 132*A^3*a^6*b^13 - 220*A^3*a^7*b^12 - 68*A^3*a^8*b^11 + 140*A^3*a^9*b^10 + 22*A^3*a^10*b^9 - 52*A^3*a^11*b^8 - 4*A^3*a^12*b^7 + 8*A^3*a^13*b^6 + 40*C^3*a^3*b^16 - 40*C^3*a^4*b^15 + 1396*C^3*a^5*b^14 + 204*C^3*a^6*b^13 + 8281*C^3*a^7*b^12 + 16999*C^3*a^8*b^11 - 64479*C^3*a^9*b^10 - 57345*C^3*a^10*b^9 + 155991*C^3*a^11*b^8 + 82337*C^3*a^12*b^7 - 193689*C^3*a^13*b^6 - 62030*C^3*a^14*b^5 + 135260*C^3*a^15*b^4 + 24400*C^3*a^16*b^3 - 50800*C^3*a^17*b^2 + 8*A*C^2*a*b^18 + 32*A^2*C*a*b^18 - 8*A*C^2*a^2*b^17 + 448*A*C^2*a^3*b^16 + 192*A*C^2*a^4*b^15 + 4359*A*C^2*a^5*b^14 + 9657*A*C^2*a^6*b^13 - 25211*A*C^2*a^7*b^12 - 24901*A*C^2*a^8*b^11 + 53039*A*C^2*a^9*b^10 + 29513*A*C^2*a^10*b^9 - 60729*A*C^2*a^11*b^8 - 19233*A*C^2*a^12*b^7 + 41046*A*C^2*a^13*b^6 + 7080*A*C^2*a^14*b^5 - 15360*A*C^2*a^15*b^4 - 1200*A*C^2*a^16*b^3 + 2400*A*C^2*a^17*b^2 + 32*A^2*C*a^2*b^17 + 672*A^2*C*a^3*b^16 + 1760*A^2*C*a^4*b^15 - 3156*A^2*C*a^5*b^14 - 3196*A^2*C*a^6*b^13 + 5944*A^2*C*a^7*b^12 + 3448*A^2*C*a^8*b^11 - 6336*A^2*C*a^9*b^10 - 1983*A^2*C*a^10*b^9 + 4152*A^2*C*a^11*b^8 + 684*A^2*C*a^12*b^7 - 1548*A^2*C*a^13*b^6 - 120*A^2*C*a^14*b^5 + 240*A^2*C*a^15*b^4))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + ((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(((C*a^2*10i + b^2*(A*1i + (C*1i)/2))*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2))*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10))))/b^6 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 8*A*C*a*b^17 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))/b^6))*(C*a^2*10i + b^2*(A*1i + (C*1i)/2))*2i)/(b^6*d) - ((tan(c/2 + (d*x)/2)*(20*C*a^8 + C*b^8 + 12*A*a^2*b^6 - 4*A*a^3*b^5 - 6*A*a^4*b^4 + A*a^5*b^3 + 2*A*a^6*b^2 - 11*C*a^2*b^6 + 21*C*a^3*b^5 + 57*C*a^4*b^4 - 27*C*a^5*b^3 - 59*C*a^6*b^2 - 7*C*a*b^7 + 10*C*a^7*b))/(b^5*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^9*(20*C*a^8 + C*b^8 + 12*A*a^2*b^6 + 4*A*a^3*b^5 - 6*A*a^4*b^4 - A*a^5*b^3 + 2*A*a^6*b^2 - 11*C*a^2*b^6 - 21*C*a^3*b^5 + 57*C*a^4*b^4 + 27*C*a^5*b^3 - 59*C*a^6*b^2 + 7*C*a*b^7 - 10*C*a^7*b))/(b^5*(a + b)^3*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(120*C*a^9 - 6*C*b^9 + 60*A*a^3*b^6 - 8*A*a^4*b^5 - 37*A*a^5*b^4 + 3*A*a^6*b^3 + 12*A*a^7*b^2 - 3*C*a^2*b^7 - 111*C*a^3*b^6 + 45*C*a^4*b^5 + 369*C*a^5*b^4 - 71*C*a^6*b^3 - 364*C*a^7*b^2 + 21*C*a*b^8 + 30*C*a^8*b))/(3*b^5*(a + b)^2*(a - b)^3) + (2*tan(c/2 + (d*x)/2)^7*(120*C*a^9 + 6*C*b^9 + 60*A*a^3*b^6 + 8*A*a^4*b^5 - 37*A*a^5*b^4 - 3*A*a^6*b^3 + 12*A*a^7*b^2 + 3*C*a^2*b^7 - 111*C*a^3*b^6 - 45*C*a^4*b^5 + 369*C*a^5*b^4 + 71*C*a^6*b^3 - 364*C*a^7*b^2 + 21*C*a*b^8 - 30*C*a^8*b))/(3*b^5*(a + b)^3*(a - b)^2) + (2*tan(c/2 + (d*x)/2)^5*(180*C*a^10 + 9*C*b^10 - 36*A*a^2*b^8 + 110*A*a^4*b^6 - 62*A*a^6*b^4 + 18*A*a^8*b^2 + 36*C*a^2*b^8 - 324*C*a^4*b^6 + 740*C*a^6*b^4 - 611*C*a^8*b^2))/(3*b^5*(a + b)^3*(a - b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 + 9*a^2*b + 5*a^3 - b^3) - tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^2*b - 10*a^3 + 2*b^3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 6*a^2*b - 10*a^3 - 2*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^10*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 9*a^2*b + 5*a^3 + b^3)))","B"
586,1,10081,369,13.156676,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6-7\,A\,a^3\,b^5+10\,A\,a^4\,b^4-72\,C\,a^2\,b^6-60\,C\,a^3\,b^5+273\,C\,a^4\,b^4+47\,C\,a^5\,b^3-236\,C\,a^6\,b^2-18\,A\,a\,b^7-12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6+7\,A\,a^3\,b^5+10\,A\,a^4\,b^4-72\,C\,a^2\,b^6+60\,C\,a^3\,b^5+273\,C\,a^4\,b^4-47\,C\,a^5\,b^3-236\,C\,a^6\,b^2+18\,A\,a\,b^7+12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,C\,a^7-2\,C\,b^7-3\,A\,a^2\,b^5+2\,A\,a^3\,b^4+6\,C\,a^2\,b^5+26\,C\,a^3\,b^4-11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,C\,a\,b^6+4\,C\,a^6\,b\right)}{b^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(8\,C\,a^7+2\,C\,b^7+3\,A\,a^2\,b^5+2\,A\,a^3\,b^4-6\,C\,a^2\,b^5+26\,C\,a^3\,b^4+11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,C\,a\,b^6-4\,C\,a^6\,b\right)}{b^4\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a\,b^2-6\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3+6\,a^2\,b-2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3-6\,a^2\,b+2\,b^3\right)+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{8\,C\,a\,\mathrm{atan}\left(\frac{\frac{4\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)}{b^5}+\frac{4\,C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)}{b^5}}{\frac{32\,\left(18\,A^2\,C\,a^5\,b^{11}+24\,A^2\,C\,a^3\,b^{13}+8\,A^2\,C\,a\,b^{15}-48\,A\,C^2\,a^{11}\,b^5-48\,A\,C^2\,a^{10}\,b^6+160\,A\,C^2\,a^9\,b^7+112\,A\,C^2\,a^8\,b^8-148\,A\,C^2\,a^7\,b^9-48\,A\,C^2\,a^6\,b^{10}+8\,A\,C^2\,a^5\,b^{11}-48\,A\,C^2\,a^4\,b^{12}+128\,A\,C^2\,a^3\,b^{13}+32\,A\,C^2\,a^2\,b^{14}+128\,C^3\,a^{16}-64\,C^3\,a^{15}\,b-832\,C^3\,a^{14}\,b^2+400\,C^3\,a^{13}\,b^3+2288\,C^3\,a^{12}\,b^4-1088\,C^3\,a^{11}\,b^5-3472\,C^3\,a^{10}\,b^6+1602\,C^3\,a^9\,b^7+3088\,C^3\,a^8\,b^8-1280\,C^3\,a^7\,b^9-1520\,C^3\,a^6\,b^{10}+480\,C^3\,a^5\,b^{11}+320\,C^3\,a^4\,b^{12}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)\,4{}\mathrm{i}}{b^5}-\frac{C\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{C\,a\,\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{C\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)\,4{}\mathrm{i}}{b^5}}\right)}{b^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}{\frac{32\,\left(18\,A^2\,C\,a^5\,b^{11}+24\,A^2\,C\,a^3\,b^{13}+8\,A^2\,C\,a\,b^{15}-48\,A\,C^2\,a^{11}\,b^5-48\,A\,C^2\,a^{10}\,b^6+160\,A\,C^2\,a^9\,b^7+112\,A\,C^2\,a^8\,b^8-148\,A\,C^2\,a^7\,b^9-48\,A\,C^2\,a^6\,b^{10}+8\,A\,C^2\,a^5\,b^{11}-48\,A\,C^2\,a^4\,b^{12}+128\,A\,C^2\,a^3\,b^{13}+32\,A\,C^2\,a^2\,b^{14}+128\,C^3\,a^{16}-64\,C^3\,a^{15}\,b-832\,C^3\,a^{14}\,b^2+400\,C^3\,a^{13}\,b^3+2288\,C^3\,a^{12}\,b^4-1088\,C^3\,a^{11}\,b^5-3472\,C^3\,a^{10}\,b^6+1602\,C^3\,a^9\,b^7+3088\,C^3\,a^8\,b^8-1280\,C^3\,a^7\,b^9-1520\,C^3\,a^6\,b^{10}+480\,C^3\,a^5\,b^{11}+320\,C^3\,a^4\,b^{12}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{16\,\left(2\,A\,b^{24}-3\,A\,a^2\,b^{22}+3\,A\,a^3\,b^{21}-3\,A\,a^4\,b^{20}+3\,A\,a^5\,b^{19}+7\,A\,a^6\,b^{18}-7\,A\,a^7\,b^{17}-3\,A\,a^8\,b^{16}+3\,A\,a^9\,b^{15}+20\,C\,a^2\,b^{22}+36\,C\,a^3\,b^{21}-95\,C\,a^4\,b^{20}-73\,C\,a^5\,b^{19}+193\,C\,a^6\,b^{18}+87\,C\,a^7\,b^{17}-217\,C\,a^8\,b^{16}-63\,C\,a^9\,b^{15}+143\,C\,a^{10}\,b^{14}+25\,C\,a^{11}\,b^{13}-52\,C\,a^{12}\,b^{12}-4\,C\,a^{13}\,b^{11}+8\,C\,a^{14}\,b^{10}-2\,A\,a\,b^{23}-8\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 - 7*A*a^3*b^5 + 10*A*a^4*b^4 - 72*C*a^2*b^6 - 60*C*a^3*b^5 + 273*C*a^4*b^4 + 47*C*a^5*b^3 - 236*C*a^6*b^2 - 18*A*a*b^7 - 12*C*a^7*b))/(3*b^4*(a + b)^2*(a - b)^3) + (tan(c/2 + (d*x)/2)^5*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 + 7*A*a^3*b^5 + 10*A*a^4*b^4 - 72*C*a^2*b^6 + 60*C*a^3*b^5 + 273*C*a^4*b^4 - 47*C*a^5*b^3 - 236*C*a^6*b^2 + 18*A*a*b^7 + 12*C*a^7*b))/(3*b^4*(a + b)^3*(a - b)^2) + (tan(c/2 + (d*x)/2)*(8*C*a^7 - 2*C*b^7 - 3*A*a^2*b^5 + 2*A*a^3*b^4 + 6*C*a^2*b^5 + 26*C*a^3*b^4 - 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*C*a*b^6 + 4*C*a^6*b))/(b^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^7*(8*C*a^7 + 2*C*b^7 + 3*A*a^2*b^5 + 2*A*a^3*b^4 - 6*C*a^2*b^5 + 26*C*a^3*b^4 + 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*C*a*b^6 - 4*C*a^6*b))/(b^4*(a + b)^3*(a - b)))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^3) + tan(c/2 + (d*x)/2)^2*(6*a^2*b + 4*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)^6*(4*a^3 - 6*a^2*b + 2*b^3) + a^3 + b^3 + tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (8*C*a*atan(((4*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5))/b^5 + (4*C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5))/b^5)/((32*(128*C^3*a^16 - 64*C^3*a^15*b + 320*C^3*a^4*b^12 + 480*C^3*a^5*b^11 - 1520*C^3*a^6*b^10 - 1280*C^3*a^7*b^9 + 3088*C^3*a^8*b^8 + 1602*C^3*a^9*b^7 - 3472*C^3*a^10*b^6 - 1088*C^3*a^11*b^5 + 2288*C^3*a^12*b^4 + 400*C^3*a^13*b^3 - 832*C^3*a^14*b^2 + 8*A^2*C*a*b^15 + 32*A*C^2*a^2*b^14 + 128*A*C^2*a^3*b^13 - 48*A*C^2*a^4*b^12 + 8*A*C^2*a^5*b^11 - 48*A*C^2*a^6*b^10 - 148*A*C^2*a^7*b^9 + 112*A*C^2*a^8*b^8 + 160*A*C^2*a^9*b^7 - 48*A*C^2*a^10*b^6 - 48*A*C^2*a^11*b^5 + 24*A^2*C*a^3*b^13 + 18*A^2*C*a^5*b^11))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5)*4i)/b^5 - (C*a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (C*a*((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (C*a*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5)*4i)/b^5)))/(b^5*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))/((32*(128*C^3*a^16 - 64*C^3*a^15*b + 320*C^3*a^4*b^12 + 480*C^3*a^5*b^11 - 1520*C^3*a^6*b^10 - 1280*C^3*a^7*b^9 + 3088*C^3*a^8*b^8 + 1602*C^3*a^9*b^7 - 3472*C^3*a^10*b^6 - 1088*C^3*a^11*b^5 + 2288*C^3*a^12*b^4 + 400*C^3*a^13*b^3 - 832*C^3*a^14*b^2 + 8*A^2*C*a*b^15 + 32*A*C^2*a^2*b^14 + 128*A*C^2*a^3*b^13 - 48*A*C^2*a^4*b^12 + 8*A*C^2*a^5*b^11 - 48*A*C^2*a^6*b^10 - 148*A*C^2*a^7*b^9 + 112*A*C^2*a^8*b^8 + 160*A*C^2*a^9*b^7 - 48*A*C^2*a^10*b^6 - 48*A*C^2*a^11*b^5 + 24*A^2*C*a^3*b^13 + 18*A^2*C*a^5*b^11))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*C^2*a^16 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((16*(2*A*b^24 - 3*A*a^2*b^22 + 3*A*a^3*b^21 - 3*A*a^4*b^20 + 3*A*a^5*b^19 + 7*A*a^6*b^18 - 7*A*a^7*b^17 - 3*A*a^8*b^16 + 3*A*a^9*b^15 + 20*C*a^2*b^22 + 36*C*a^3*b^21 - 95*C*a^4*b^20 - 73*C*a^5*b^19 + 193*C*a^6*b^18 + 87*C*a^7*b^17 - 217*C*a^8*b^16 - 63*C*a^9*b^15 + 143*C*a^10*b^14 + 25*C*a^11*b^13 - 52*C*a^12*b^12 - 4*C*a^13*b^11 + 8*C*a^14*b^10 - 2*A*a*b^23 - 8*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2)*1i)/(d*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))","B"
587,1,9774,304,16.494865,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4-A\,a^3\,b^3+12\,C\,a^2\,b^4-4\,C\,a^3\,b^3-6\,C\,a^4\,b^2-2\,A\,a\,b^5+C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6+7\,A\,a^2\,b^4+18\,C\,a^2\,b^4-11\,C\,a^4\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4+A\,a^3\,b^3+12\,C\,a^2\,b^4+4\,C\,a^3\,b^3-6\,C\,a^4\,b^2+2\,A\,a\,b^5-C\,a^5\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^3}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{2\,C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{C\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}}\right)}{b^4\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(4\,A\,b^6-2\,C\,a^6+8\,C\,b^6+A\,a^2\,b^4-8\,C\,a^2\,b^4+7\,C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}","Not used",1,"(2*C*atan(((C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4))/b^4 + (C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4))/b^4)/((16*(4*C^3*a^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4)*1i)/b^4 + (C*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4)*1i)/b^4)))/(b^4*d) - ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 - A*a^3*b^3 + 12*C*a^2*b^4 - 4*C*a^3*b^3 - 6*C*a^4*b^2 - 2*A*a*b^5 + C*a^5*b))/((a + b)*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 + 7*A*a^2*b^4 + 18*C*a^2*b^4 - 11*C*a^4*b^2))/(3*(a + b)^2*(b^5 - 2*a*b^4 + a^2*b^3)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 + A*a^3*b^3 + 12*C*a^2*b^4 + 4*C*a^3*b^3 - 6*C*a^4*b^2 + 2*A*a*b^5 - C*a^5*b))/((a*b^3 - b^4)*(a + b)^3))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))/((16*(4*C^3*a^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (a*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (a*((8*(4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))))*(-(a + b)^7*(a - b)^7)^(1/2)*(4*A*b^6 - 2*C*a^6 + 8*C*b^6 + A*a^2*b^4 - 8*C*a^2*b^4 + 7*C*a^4*b^2)*1i)/(d*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))","B"
588,1,491,261,4.346518,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^3+C\,a^3+7\,A\,a\,b^2+9\,C\,a\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^3+A\,b^3+2\,C\,a^3+6\,A\,a\,b^2+2\,A\,a^2\,b+6\,C\,a\,b^2+3\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^3-A\,b^3+2\,C\,a^3+6\,A\,a\,b^2-2\,A\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\,\left(4\,A\,a^2+A\,b^2+3\,C\,a^2+2\,C\,b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}\,\left(A\,b^3+2\,C\,b^3+4\,A\,a^2\,b+3\,C\,a^2\,b\right)}\right)\,\left(4\,A\,a^2+A\,b^2+3\,C\,a^2+2\,C\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((4*tan(c/2 + (d*x)/2)^3*(3*A*a^3 + C*a^3 + 7*A*a*b^2 + 9*C*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*a^3 + A*b^3 + 2*C*a^3 + 6*A*a*b^2 + 2*A*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/((a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(2*A*a^3 - A*b^3 + 2*C*a^3 + 6*A*a*b^2 - 2*A*a^2*b + 6*C*a*b^2 - 3*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (b*atan((b*tan(c/2 + (d*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)*(4*A*a^2 + A*b^2 + 3*C*a^2 + 2*C*b^2))/(2*(a + b)^(1/2)*(a - b)^(7/2)*(A*b^3 + 2*C*b^3 + 4*A*a^2*b + 3*C*a^2*b)))*(4*A*a^2 + A*b^2 + 3*C*a^2 + 2*C*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
589,1,491,252,4.304037,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^4,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\,\left(2\,A\,a^2+3\,A\,b^2+C\,a^2+4\,C\,b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}\,\left(2\,A\,a^3+C\,a^3+3\,A\,a\,b^2+4\,C\,a\,b^2\right)}\right)\,\left(2\,A\,a^2+3\,A\,b^2+C\,a^2+4\,C\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^3+3\,C\,b^3+9\,A\,a^2\,b+7\,C\,a^2\,b\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^3+C\,a^3+2\,C\,b^3+3\,A\,a\,b^2+6\,A\,a^2\,b+2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^3-C\,a^3+2\,C\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)*(2*A*a^2 + 3*A*b^2 + C*a^2 + 4*C*b^2))/(2*(a + b)^(1/2)*(a - b)^(7/2)*(2*A*a^3 + C*a^3 + 3*A*a*b^2 + 4*C*a*b^2)))*(2*A*a^2 + 3*A*b^2 + C*a^2 + 4*C*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((4*tan(c/2 + (d*x)/2)^3*(A*b^3 + 3*C*b^3 + 9*A*a^2*b + 7*C*a^2*b))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^3 + C*a^3 + 2*C*b^3 + 3*A*a*b^2 + 6*A*a^2*b + 2*C*a*b^2 + 6*C*a^2*b))/((a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(2*A*b^3 - C*a^3 + 2*C*b^3 - 3*A*a*b^2 + 6*A*a^2*b - 2*C*a*b^2 + 6*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))","B"
590,1,9766,301,16.831606,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^4),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4-4\,A\,a^3\,b^3+12\,A\,a^4\,b^2-C\,a^3\,b^3+6\,C\,a^4\,b^2+A\,a\,b^5-2\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6-11\,A\,a^2\,b^4+18\,A\,a^4\,b^2+7\,C\,a^4\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4+4\,A\,a^3\,b^3+12\,A\,a^4\,b^2+C\,a^3\,b^3+6\,C\,a^4\,b^2-A\,a\,b^5+2\,C\,a^5\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^3}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)}{a^4}-\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)}{a^4}}\right)\,2{}\mathrm{i}}{a^4\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\left(\frac{8\,\left(4\,A\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,a^6-2\,A\,b^6+4\,C\,a^6+7\,A\,a^2\,b^4-8\,A\,a^4\,b^2+C\,a^4\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 - 4*A*a^3*b^3 + 12*A*a^4*b^2 - C*a^3*b^3 + 6*C*a^4*b^2 + A*a*b^5 - 2*C*a^5*b))/((a + b)*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) - (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 - 11*A*a^2*b^4 + 18*A*a^4*b^2 + 7*C*a^4*b^2))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 + 4*A*a^3*b^3 + 12*A*a^4*b^2 + C*a^3*b^3 + 6*C*a^4*b^2 - A*a*b^5 + 2*C*a^5*b))/((a^3*b - a^4)*(a + b)^3))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (A*atan(((A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4)*1i)/a^4 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4)*1i)/a^4)/((16*(4*A^3*b^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 + 8*A^2*C*a^12*b + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4))/a^4 - (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4))/a^4))*2i)/(a^4*d) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))/((16*(4*A^3*b^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 + 8*A^2*C*a^12*b + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*((8*(4*A*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*a^6 - 2*A*b^6 + 4*C*a^6 + 7*A*a^2*b^4 - 8*A*a^4*b^2 + C*a^4*b^2)*1i)/(d*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))","B"
591,1,10078,376,13.821908,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^4),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6+47\,A\,a^3\,b^5+273\,A\,a^4\,b^4-60\,A\,a^5\,b^3-72\,A\,a^6\,b^2+10\,C\,a^4\,b^4-7\,C\,a^5\,b^3+45\,C\,a^6\,b^2-12\,A\,a\,b^7-18\,C\,a^7\,b\right)}{3\,a^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6-47\,A\,a^3\,b^5+273\,A\,a^4\,b^4+60\,A\,a^5\,b^3-72\,A\,a^6\,b^2+10\,C\,a^4\,b^4+7\,C\,a^5\,b^3+45\,C\,a^6\,b^2+12\,A\,a\,b^7+18\,C\,a^7\,b\right)}{3\,a^4\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A\,b^7-2\,A\,a^7-24\,A\,a^2\,b^5-11\,A\,a^3\,b^4+26\,A\,a^4\,b^3+6\,A\,a^5\,b^2+2\,C\,a^4\,b^3-3\,C\,a^5\,b^2+4\,A\,a\,b^6-2\,A\,a^6\,b+6\,C\,a^6\,b\right)}{a^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,a^7+8\,A\,b^7-24\,A\,a^2\,b^5+11\,A\,a^3\,b^4+26\,A\,a^4\,b^3-6\,A\,a^5\,b^2+2\,C\,a^4\,b^3+3\,C\,a^5\,b^2-4\,A\,a\,b^6-2\,A\,a^6\,b+6\,C\,a^6\,b\right)}{a^4\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2\,b-6\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^3+6\,a\,b^2+4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^3-6\,a\,b^2+4\,b^3\right)+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{A\,b\,\mathrm{atan}\left(\frac{\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{4\,A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{32\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)\,4{}\mathrm{i}}{a^5}+\frac{A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{4\,A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{32\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)\,4{}\mathrm{i}}{a^5}}{\frac{32\,\left(320\,A^3\,a^{12}\,b^4+480\,A^3\,a^{11}\,b^5-1520\,A^3\,a^{10}\,b^6-1280\,A^3\,a^9\,b^7+3088\,A^3\,a^8\,b^8+1602\,A^3\,a^7\,b^9-3472\,A^3\,a^6\,b^{10}-1088\,A^3\,a^5\,b^{11}+2288\,A^3\,a^4\,b^{12}+400\,A^3\,a^3\,b^{13}-832\,A^3\,a^2\,b^{14}-64\,A^3\,a\,b^{15}+128\,A^3\,b^{16}+32\,A^2\,C\,a^{14}\,b^2+128\,A^2\,C\,a^{13}\,b^3-48\,A^2\,C\,a^{12}\,b^4+8\,A^2\,C\,a^{11}\,b^5-48\,A^2\,C\,a^{10}\,b^6-148\,A^2\,C\,a^9\,b^7+112\,A^2\,C\,a^8\,b^8+160\,A^2\,C\,a^7\,b^9-48\,A^2\,C\,a^6\,b^{10}-48\,A^2\,C\,a^5\,b^{11}+8\,A\,C^2\,a^{15}\,b+24\,A\,C^2\,a^{13}\,b^3+18\,A\,C^2\,a^{11}\,b^5\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{4\,A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{32\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)}{a^5}-\frac{4\,A\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{4\,A\,b\,\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{32\,A\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)}{a^5}}\right)\,8{}\mathrm{i}}{a^5\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}{\frac{32\,\left(320\,A^3\,a^{12}\,b^4+480\,A^3\,a^{11}\,b^5-1520\,A^3\,a^{10}\,b^6-1280\,A^3\,a^9\,b^7+3088\,A^3\,a^8\,b^8+1602\,A^3\,a^7\,b^9-3472\,A^3\,a^6\,b^{10}-1088\,A^3\,a^5\,b^{11}+2288\,A^3\,a^4\,b^{12}+400\,A^3\,a^3\,b^{13}-832\,A^3\,a^2\,b^{14}-64\,A^3\,a\,b^{15}+128\,A^3\,b^{16}+32\,A^2\,C\,a^{14}\,b^2+128\,A^2\,C\,a^{13}\,b^3-48\,A^2\,C\,a^{12}\,b^4+8\,A^2\,C\,a^{11}\,b^5-48\,A^2\,C\,a^{10}\,b^6-148\,A^2\,C\,a^9\,b^7+112\,A^2\,C\,a^8\,b^8+160\,A^2\,C\,a^7\,b^9-48\,A^2\,C\,a^6\,b^{10}-48\,A^2\,C\,a^5\,b^{11}+8\,A\,C^2\,a^{15}\,b+24\,A\,C^2\,a^{13}\,b^3+18\,A\,C^2\,a^{11}\,b^5\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{\left(\frac{16\,\left(2\,C\,a^{24}+8\,A\,a^{10}\,b^{14}-4\,A\,a^{11}\,b^{13}-52\,A\,a^{12}\,b^{12}+25\,A\,a^{13}\,b^{11}+143\,A\,a^{14}\,b^{10}-63\,A\,a^{15}\,b^9-217\,A\,a^{16}\,b^8+87\,A\,a^{17}\,b^7+193\,A\,a^{18}\,b^6-73\,A\,a^{19}\,b^5-95\,A\,a^{20}\,b^4+36\,A\,a^{21}\,b^3+20\,A\,a^{22}\,b^2+3\,C\,a^{15}\,b^9-3\,C\,a^{16}\,b^8-7\,C\,a^{17}\,b^7+7\,C\,a^{18}\,b^6+3\,C\,a^{19}\,b^5-3\,C\,a^{20}\,b^4+3\,C\,a^{21}\,b^3-3\,C\,a^{22}\,b^2-8\,A\,a^{23}\,b-2\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2+3\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 + 47*A*a^3*b^5 + 273*A*a^4*b^4 - 60*A*a^5*b^3 - 72*A*a^6*b^2 + 10*C*a^4*b^4 - 7*C*a^5*b^3 + 45*C*a^6*b^2 - 12*A*a*b^7 - 18*C*a^7*b))/(3*a^4*(a + b)^2*(a - b)^3) + (tan(c/2 + (d*x)/2)^5*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 - 47*A*a^3*b^5 + 273*A*a^4*b^4 + 60*A*a^5*b^3 - 72*A*a^6*b^2 + 10*C*a^4*b^4 + 7*C*a^5*b^3 + 45*C*a^6*b^2 + 12*A*a*b^7 + 18*C*a^7*b))/(3*a^4*(a + b)^3*(a - b)^2) - (tan(c/2 + (d*x)/2)*(8*A*b^7 - 2*A*a^7 - 24*A*a^2*b^5 - 11*A*a^3*b^4 + 26*A*a^4*b^3 + 6*A*a^5*b^2 + 2*C*a^4*b^3 - 3*C*a^5*b^2 + 4*A*a*b^6 - 2*A*a^6*b + 6*C*a^6*b))/(a^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^7*(2*A*a^7 + 8*A*b^7 - 24*A*a^2*b^5 + 11*A*a^3*b^4 + 26*A*a^4*b^3 - 6*A*a^5*b^2 + 2*C*a^4*b^3 + 3*C*a^5*b^2 - 4*A*a*b^6 - 2*A*a^6*b + 6*C*a^6*b))/(a^4*(a + b)^3*(a - b)))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a^2*b - 6*b^3) - tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 2*a^3 + 4*b^3) - tan(c/2 + (d*x)/2)^6*(2*a^3 - 6*a*b^2 + 4*b^3) + a^3 + b^3 - tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (A*b*atan(((A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (4*A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (32*A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5)*4i)/a^5 + (A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (4*A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (32*A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5)*4i)/a^5)/((32*(128*A^3*b^16 - 64*A^3*a*b^15 - 832*A^3*a^2*b^14 + 400*A^3*a^3*b^13 + 2288*A^3*a^4*b^12 - 1088*A^3*a^5*b^11 - 3472*A^3*a^6*b^10 + 1602*A^3*a^7*b^9 + 3088*A^3*a^8*b^8 - 1280*A^3*a^9*b^7 - 1520*A^3*a^10*b^6 + 480*A^3*a^11*b^5 + 320*A^3*a^12*b^4 + 8*A*C^2*a^15*b + 18*A*C^2*a^11*b^5 + 24*A*C^2*a^13*b^3 - 48*A^2*C*a^5*b^11 - 48*A^2*C*a^6*b^10 + 160*A^2*C*a^7*b^9 + 112*A^2*C*a^8*b^8 - 148*A^2*C*a^9*b^7 - 48*A^2*C*a^10*b^6 + 8*A^2*C*a^11*b^5 - 48*A^2*C*a^12*b^4 + 128*A^2*C*a^13*b^3 + 32*A^2*C*a^14*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (4*A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (32*A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5))/a^5 - (4*A*b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (4*A*b*((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (32*A*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5))/a^5))*8i)/(a^5*d) + (atan(((((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))/((32*(128*A^3*b^16 - 64*A^3*a*b^15 - 832*A^3*a^2*b^14 + 400*A^3*a^3*b^13 + 2288*A^3*a^4*b^12 - 1088*A^3*a^5*b^11 - 3472*A^3*a^6*b^10 + 1602*A^3*a^7*b^9 + 3088*A^3*a^8*b^8 - 1280*A^3*a^9*b^7 - 1520*A^3*a^10*b^6 + 480*A^3*a^11*b^5 + 320*A^3*a^12*b^4 + 8*A*C^2*a^15*b + 18*A*C^2*a^11*b^5 + 24*A*C^2*a^13*b^3 - 48*A^2*C*a^5*b^11 - 48*A^2*C*a^6*b^10 + 160*A^2*C*a^7*b^9 + 112*A^2*C*a^8*b^8 - 148*A^2*C*a^9*b^7 - 48*A^2*C*a^10*b^6 + 8*A^2*C*a^11*b^5 - 48*A^2*C*a^12*b^4 + 128*A^2*C*a^13*b^3 + 32*A^2*C*a^14*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) - (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((16*(2*C*a^24 + 8*A*a^10*b^14 - 4*A*a^11*b^13 - 52*A*a^12*b^12 + 25*A*a^13*b^11 + 143*A*a^14*b^10 - 63*A*a^15*b^9 - 217*A*a^16*b^8 + 87*A*a^17*b^7 + 193*A*a^18*b^6 - 73*A*a^19*b^5 - 95*A*a^20*b^4 + 36*A*a^21*b^3 + 20*A*a^22*b^2 + 3*C*a^15*b^9 - 3*C*a^16*b^8 - 7*C*a^17*b^7 + 7*C*a^18*b^6 + 3*C*a^19*b^5 - 3*C*a^20*b^4 + 3*C*a^21*b^3 - 3*C*a^22*b^2 - 8*A*a^23*b - 2*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 + 3*C*a^6*b^2)*1i)/(d*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))","B"
592,1,14213,522,18.942274,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^4),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^8+20\,A\,b^8-59\,A\,a^2\,b^6-27\,A\,a^3\,b^5+57\,A\,a^4\,b^4+21\,A\,a^5\,b^3-11\,A\,a^6\,b^2+2\,C\,a^2\,b^6+C\,a^3\,b^5-6\,C\,a^4\,b^4-4\,C\,a^5\,b^3+12\,C\,a^6\,b^2+10\,A\,a\,b^7-7\,A\,a^7\,b\right)}{a^5\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(A\,a^8+20\,A\,b^8-59\,A\,a^2\,b^6+27\,A\,a^3\,b^5+57\,A\,a^4\,b^4-21\,A\,a^5\,b^3-11\,A\,a^6\,b^2+2\,C\,a^2\,b^6-C\,a^3\,b^5-6\,C\,a^4\,b^4+4\,C\,a^5\,b^3+12\,C\,a^6\,b^2-10\,A\,a\,b^7+7\,A\,a^7\,b\right)}{a^5\,{\left(a+b\right)}^3\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(120\,A\,b^9-6\,A\,a^9-364\,A\,a^2\,b^7-71\,A\,a^3\,b^6+369\,A\,a^4\,b^5+45\,A\,a^5\,b^4-111\,A\,a^6\,b^3-3\,A\,a^7\,b^2+12\,C\,a^2\,b^7+3\,C\,a^3\,b^6-37\,C\,a^4\,b^5-8\,C\,a^5\,b^4+60\,C\,a^6\,b^3+30\,A\,a\,b^8+21\,A\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,A\,a^9+120\,A\,b^9-364\,A\,a^2\,b^7+71\,A\,a^3\,b^6+369\,A\,a^4\,b^5-45\,A\,a^5\,b^4-111\,A\,a^6\,b^3+3\,A\,a^7\,b^2+12\,C\,a^2\,b^7-3\,C\,a^3\,b^6-37\,C\,a^4\,b^5+8\,C\,a^5\,b^4+60\,C\,a^6\,b^3-30\,A\,a\,b^8+21\,A\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,A\,a^{10}+180\,A\,b^{10}-611\,A\,a^2\,b^8+740\,A\,a^4\,b^6-324\,A\,a^6\,b^4+36\,A\,a^8\,b^2+18\,C\,a^2\,b^8-62\,C\,a^4\,b^6+110\,C\,a^6\,b^4-36\,C\,a^8\,b^2\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^3-6\,a^2\,b+6\,a\,b^2+10\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^3+3\,a^2\,b+9\,a\,b^2+5\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-2\,a^3+6\,a^2\,b+6\,a\,b^2-10\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3+3\,a^2\,b-9\,a\,b^2+5\,b^3\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,1{}\mathrm{i}}{a^6}-\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,1{}\mathrm{i}}{a^6}}{\frac{8\,\left(40\,A^3\,a^{16}\,b^3-40\,A^3\,a^{15}\,b^4+1396\,A^3\,a^{14}\,b^5+204\,A^3\,a^{13}\,b^6+8281\,A^3\,a^{12}\,b^7+16999\,A^3\,a^{11}\,b^8-64479\,A^3\,a^{10}\,b^9-57345\,A^3\,a^9\,b^{10}+155991\,A^3\,a^8\,b^{11}+82337\,A^3\,a^7\,b^{12}-193689\,A^3\,a^6\,b^{13}-62030\,A^3\,a^5\,b^{14}+135260\,A^3\,a^4\,b^{15}+24400\,A^3\,a^3\,b^{16}-50800\,A^3\,a^2\,b^{17}-4000\,A^3\,a\,b^{18}+8000\,A^3\,b^{19}+8\,A^2\,C\,a^{18}\,b-8\,A^2\,C\,a^{17}\,b^2+448\,A^2\,C\,a^{16}\,b^3+192\,A^2\,C\,a^{15}\,b^4+4359\,A^2\,C\,a^{14}\,b^5+9657\,A^2\,C\,a^{13}\,b^6-25211\,A^2\,C\,a^{12}\,b^7-24901\,A^2\,C\,a^{11}\,b^8+53039\,A^2\,C\,a^{10}\,b^9+29513\,A^2\,C\,a^9\,b^{10}-60729\,A^2\,C\,a^8\,b^{11}-19233\,A^2\,C\,a^7\,b^{12}+41046\,A^2\,C\,a^6\,b^{13}+7080\,A^2\,C\,a^5\,b^{14}-15360\,A^2\,C\,a^4\,b^{15}-1200\,A^2\,C\,a^3\,b^{16}+2400\,A^2\,C\,a^2\,b^{17}+32\,A\,C^2\,a^{18}\,b+32\,A\,C^2\,a^{17}\,b^2+672\,A\,C^2\,a^{16}\,b^3+1760\,A\,C^2\,a^{15}\,b^4-3156\,A\,C^2\,a^{14}\,b^5-3196\,A\,C^2\,a^{13}\,b^6+5944\,A\,C^2\,a^{12}\,b^7+3448\,A\,C^2\,a^{11}\,b^8-6336\,A\,C^2\,a^{10}\,b^9-1983\,A\,C^2\,a^9\,b^{10}+4152\,A\,C^2\,a^8\,b^{11}+684\,A\,C^2\,a^7\,b^{12}-1548\,A\,C^2\,a^6\,b^{13}-120\,A\,C^2\,a^5\,b^{14}+240\,A\,C^2\,a^4\,b^{15}+32\,C^3\,a^{18}\,b+96\,C^3\,a^{17}\,b^2-128\,C^3\,a^{16}\,b^3-128\,C^3\,a^{15}\,b^4+220\,C^3\,a^{14}\,b^5+132\,C^3\,a^{13}\,b^6-220\,C^3\,a^{12}\,b^7-68\,C^3\,a^{11}\,b^8+140\,C^3\,a^{10}\,b^9+22\,C^3\,a^9\,b^{10}-52\,C^3\,a^8\,b^{11}-4\,C^3\,a^7\,b^{12}+8\,C^3\,a^6\,b^{13}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(\frac{\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\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\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)}{a^6}}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2+10\,A\,b^2\right)\,2{}\mathrm{i}}{a^6\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{b\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}}{\frac{8\,\left(40\,A^3\,a^{16}\,b^3-40\,A^3\,a^{15}\,b^4+1396\,A^3\,a^{14}\,b^5+204\,A^3\,a^{13}\,b^6+8281\,A^3\,a^{12}\,b^7+16999\,A^3\,a^{11}\,b^8-64479\,A^3\,a^{10}\,b^9-57345\,A^3\,a^9\,b^{10}+155991\,A^3\,a^8\,b^{11}+82337\,A^3\,a^7\,b^{12}-193689\,A^3\,a^6\,b^{13}-62030\,A^3\,a^5\,b^{14}+135260\,A^3\,a^4\,b^{15}+24400\,A^3\,a^3\,b^{16}-50800\,A^3\,a^2\,b^{17}-4000\,A^3\,a\,b^{18}+8000\,A^3\,b^{19}+8\,A^2\,C\,a^{18}\,b-8\,A^2\,C\,a^{17}\,b^2+448\,A^2\,C\,a^{16}\,b^3+192\,A^2\,C\,a^{15}\,b^4+4359\,A^2\,C\,a^{14}\,b^5+9657\,A^2\,C\,a^{13}\,b^6-25211\,A^2\,C\,a^{12}\,b^7-24901\,A^2\,C\,a^{11}\,b^8+53039\,A^2\,C\,a^{10}\,b^9+29513\,A^2\,C\,a^9\,b^{10}-60729\,A^2\,C\,a^8\,b^{11}-19233\,A^2\,C\,a^7\,b^{12}+41046\,A^2\,C\,a^6\,b^{13}+7080\,A^2\,C\,a^5\,b^{14}-15360\,A^2\,C\,a^4\,b^{15}-1200\,A^2\,C\,a^3\,b^{16}+2400\,A^2\,C\,a^2\,b^{17}+32\,A\,C^2\,a^{18}\,b+32\,A\,C^2\,a^{17}\,b^2+672\,A\,C^2\,a^{16}\,b^3+1760\,A\,C^2\,a^{15}\,b^4-3156\,A\,C^2\,a^{14}\,b^5-3196\,A\,C^2\,a^{13}\,b^6+5944\,A\,C^2\,a^{12}\,b^7+3448\,A\,C^2\,a^{11}\,b^8-6336\,A\,C^2\,a^{10}\,b^9-1983\,A\,C^2\,a^9\,b^{10}+4152\,A\,C^2\,a^8\,b^{11}+684\,A\,C^2\,a^7\,b^{12}-1548\,A\,C^2\,a^6\,b^{13}-120\,A\,C^2\,a^5\,b^{14}+240\,A\,C^2\,a^4\,b^{15}+32\,C^3\,a^{18}\,b+96\,C^3\,a^{17}\,b^2-128\,C^3\,a^{16}\,b^3-128\,C^3\,a^{15}\,b^4+220\,C^3\,a^{14}\,b^5+132\,C^3\,a^{13}\,b^6-220\,C^3\,a^{12}\,b^7-68\,C^3\,a^{11}\,b^8+140\,C^3\,a^{10}\,b^9+22\,C^3\,a^9\,b^{10}-52\,C^3\,a^8\,b^{11}-4\,C^3\,a^7\,b^{12}+8\,C^3\,a^6\,b^{13}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{b\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2\right)\,1{}\mathrm{i}}{d\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(A*a^8 + 20*A*b^8 - 59*A*a^2*b^6 - 27*A*a^3*b^5 + 57*A*a^4*b^4 + 21*A*a^5*b^3 - 11*A*a^6*b^2 + 2*C*a^2*b^6 + C*a^3*b^5 - 6*C*a^4*b^4 - 4*C*a^5*b^3 + 12*C*a^6*b^2 + 10*A*a*b^7 - 7*A*a^7*b))/(a^5*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^9*(A*a^8 + 20*A*b^8 - 59*A*a^2*b^6 + 27*A*a^3*b^5 + 57*A*a^4*b^4 - 21*A*a^5*b^3 - 11*A*a^6*b^2 + 2*C*a^2*b^6 - C*a^3*b^5 - 6*C*a^4*b^4 + 4*C*a^5*b^3 + 12*C*a^6*b^2 - 10*A*a*b^7 + 7*A*a^7*b))/(a^5*(a + b)^3*(a - b)) - (2*tan(c/2 + (d*x)/2)^3*(120*A*b^9 - 6*A*a^9 - 364*A*a^2*b^7 - 71*A*a^3*b^6 + 369*A*a^4*b^5 + 45*A*a^5*b^4 - 111*A*a^6*b^3 - 3*A*a^7*b^2 + 12*C*a^2*b^7 + 3*C*a^3*b^6 - 37*C*a^4*b^5 - 8*C*a^5*b^4 + 60*C*a^6*b^3 + 30*A*a*b^8 + 21*A*a^8*b))/(3*a^5*(a + b)^2*(a - b)^3) + (2*tan(c/2 + (d*x)/2)^7*(6*A*a^9 + 120*A*b^9 - 364*A*a^2*b^7 + 71*A*a^3*b^6 + 369*A*a^4*b^5 - 45*A*a^5*b^4 - 111*A*a^6*b^3 + 3*A*a^7*b^2 + 12*C*a^2*b^7 - 3*C*a^3*b^6 - 37*C*a^4*b^5 + 8*C*a^5*b^4 + 60*C*a^6*b^3 - 30*A*a*b^8 + 21*A*a^8*b))/(3*a^5*(a + b)^3*(a - b)^2) + (2*tan(c/2 + (d*x)/2)^5*(9*A*a^10 + 180*A*b^10 - 611*A*a^2*b^8 + 740*A*a^4*b^6 - 324*A*a^6*b^4 + 36*A*a^8*b^2 + 18*C*a^2*b^8 - 62*C*a^4*b^6 + 110*C*a^6*b^4 - 36*C*a^8*b^2))/(3*a^5*(a + b)^3*(a - b)^3))/(d*(tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^2*b - 2*a^3 + 10*b^3) - tan(c/2 + (d*x)/2)^2*(9*a*b^2 + 3*a^2*b - a^3 + 5*b^3) + tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 6*a^2*b - 2*a^3 - 10*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^10*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + tan(c/2 + (d*x)/2)^8*(3*a^2*b - 9*a*b^2 + a^3 + 5*b^3))) + (atan((((10*A*b^2 + a^2*(A/2 + C))*(((10*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 - (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*1i)/a^6 - ((10*A*b^2 + a^2*(A/2 + C))*(((10*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 + (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*1i)/a^6)/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + ((10*A*b^2 + a^2*(A/2 + C))*(((10*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 - (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))/a^6 + ((10*A*b^2 + a^2*(A/2 + C))*(((10*A*b^2 + a^2*(A/2 + C))*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C))*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))))/a^6 + (8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))/a^6))*(10*A*b^2 + a^2*(A/2 + C))*2i)/(a^6*d) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 8*A*C*a^17*b + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2)*1i)/(d*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))","B"
593,1,240,193,2.591818,"\text{Not used}","int(-(cos(c + d*x)^3*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x)),x)","\frac{a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4}}{b^3\,d}-\frac{\frac{a\,\sin\left(c+d\,x\right)}{4}-\frac{a\,\sin\left(3\,c+3\,d\,x\right)}{12}}{b^2\,d}+\frac{\frac{\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}-\frac{\sin\left(4\,c+4\,d\,x\right)}{32}}{b\,d}+\frac{a^3\,\sin\left(c+d\,x\right)}{b^4\,d}-\frac{2\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^5\,d}-\frac{2\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{b^5\,d}","Not used",1,"(a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (a^2*sin(2*c + 2*d*x))/4)/(b^3*d) - ((a*sin(c + d*x))/4 - (a*sin(3*c + 3*d*x))/12)/(b^2*d) + (atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/4 - sin(4*c + 4*d*x)/32)/(b*d) + (a^3*sin(c + d*x))/(b^4*d) - (2*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^5*d) - (2*a^3*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(b^5*d)","B"
594,1,183,150,1.950746,"\text{Not used}","int(-(cos(c + d*x)^2*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x)),x)","\frac{\frac{\sin\left(c+d\,x\right)}{4}-\frac{\sin\left(3\,c+3\,d\,x\right)}{12}}{b\,d}-\frac{a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4}}{b^2\,d}-\frac{a^2\,\sin\left(c+d\,x\right)}{b^3\,d}+\frac{2\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^4\,d}+\frac{2\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)}\right)\,\sqrt{b^2-a^2}}{b^4\,d}","Not used",1,"(sin(c + d*x)/4 - sin(3*c + 3*d*x)/12)/(b*d) - (a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (a*sin(2*c + 2*d*x))/4)/(b^2*d) - (a^2*sin(c + d*x))/(b^3*d) + (2*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^4*d) + (2*a^2*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a + b)))*(b^2 - a^2)^(1/2))/(b^4*d)","B"
595,1,147,109,1.774426,"\text{Not used}","int(-(cos(c + d*x)*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x)),x)","\frac{\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{\sin\left(2\,c+2\,d\,x\right)}{4}}{b\,d}-\frac{2\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^3\,d}+\frac{a\,\sin\left(c+d\,x\right)}{b^2\,d}-\frac{2\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)}\right)\,\sqrt{b^2-a^2}}{b^3\,d}","Not used",1,"(atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - sin(2*c + 2*d*x)/4)/(b*d) - (2*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^3*d) + (a*sin(c + d*x))/(b^2*d) - (2*a*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a + b)))*(b^2 - a^2)^(1/2))/(b^3*d)","B"
596,1,112,73,1.561603,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(a + b*cos(c + d*x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{b^2\,d}-\frac{\sin\left(c+d\,x\right)}{b\,d}+\frac{2\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d}","Not used",1,"(2*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(b^2*d) - sin(c + d*x)/(b*d) + (2*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d)","B"
597,1,121,76,1.669211,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)*(a + b*cos(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}-\frac{2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d}-\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)}\right)\,\sqrt{b^2-a^2}}{a\,b\,d}","Not used",1,"(2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) - (2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d) - (2*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a + b)))*(b^2 - a^2)^(1/2))/(a*b*d)","B"
598,1,436,82,1.624176,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^2*(a + b*cos(c + d*x))),x)","\frac{2\,b\,\mathrm{atanh}\left(\frac{64\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b-64\,b^2-\frac{64\,b^3}{a}+\frac{64\,b^4}{a^2}}-\frac{64\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b^2-64\,a^2\,b+64\,b^3-\frac{64\,b^4}{a}}+\frac{64\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-64\,a^3\,b+64\,a^2\,b^2+64\,a\,b^3-64\,b^4}-\frac{64\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b-64\,b^2-\frac{64\,b^3}{a}+\frac{64\,b^4}{a^2}}\right)}{a^2\,d}-\frac{2\,\mathrm{atanh}\left(\frac{64\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{64\,a^4-128\,a^3\,b+128\,a\,b^3-64\,b^4}+\frac{192\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a^2\,b-64\,a^3-128\,b^3+\frac{64\,b^4}{a}}+\frac{64\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b-64\,a^2-\frac{128\,b^3}{a}+\frac{64\,b^4}{a^2}}-\frac{192\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{128\,a\,b-64\,a^2-\frac{128\,b^3}{a}+\frac{64\,b^4}{a^2}}\right)\,\sqrt{b^2-a^2}}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*b*atanh((64*b^2*tan(c/2 + (d*x)/2))/(64*a*b - 64*b^2 - (64*b^3)/a + (64*b^4)/a^2) - (64*b^3*tan(c/2 + (d*x)/2))/(64*a*b^2 - 64*a^2*b + 64*b^3 - (64*b^4)/a) + (64*b^4*tan(c/2 + (d*x)/2))/(64*a*b^3 - 64*a^3*b - 64*b^4 + 64*a^2*b^2) - (64*a*b*tan(c/2 + (d*x)/2))/(64*a*b - 64*b^2 - (64*b^3)/a + (64*b^4)/a^2)))/(a^2*d) - (2*atanh((64*b^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b^3 - 128*a^3*b + 64*a^4 - 64*b^4) + (192*b^2*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a^2*b - 64*a^3 - 128*b^3 + (64*b^4)/a) + (64*a*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b - 64*a^2 - (128*b^3)/a + (64*b^4)/a^2) - (192*b*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(128*a*b - 64*a^2 - (128*b^3)/a + (64*b^4)/a^2))*(b^2 - a^2)^(1/2))/(a^2*d) - (2*tan(c/2 + (d*x)/2))/(a*d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
599,1,176,117,1.743209,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^3*(a + b*cos(c + d*x))),x)","\frac{\sin\left(c+d\,x\right)}{2\,a\,d\,{\cos\left(c+d\,x\right)}^2}-\frac{\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}+\frac{2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^3\,d}-\frac{b\,\sin\left(c+d\,x\right)}{a^2\,d\,\cos\left(c+d\,x\right)}-\frac{2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{a^3\,d}","Not used",1,"sin(c + d*x)/(2*a*d*cos(c + d*x)^2) - atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(a*d) + (2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^3*d) - (b*sin(c + d*x))/(a^2*d*cos(c + d*x)) - (2*b*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(a^3*d)","B"
600,1,224,155,1.822690,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^4*(a + b*cos(c + d*x))),x)","\frac{\sin\left(c+d\,x\right)}{3\,a\,d\,{\cos\left(c+d\,x\right)}^3}-\frac{\sin\left(c+d\,x\right)}{3\,a\,d\,\cos\left(c+d\,x\right)}-\frac{2\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^4\,d}+\frac{b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^2\,d}+\frac{2\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{a^4\,d}-\frac{b\,\sin\left(c+d\,x\right)}{2\,a^2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{b^2\,\sin\left(c+d\,x\right)}{a^3\,d\,\cos\left(c+d\,x\right)}","Not used",1,"sin(c + d*x)/(3*a*d*cos(c + d*x)^3) - sin(c + d*x)/(3*a*d*cos(c + d*x)) - (2*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^4*d) + (b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d) + (2*b^2*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2))/(a^4*d) - (b*sin(c + d*x))/(2*a^2*d*cos(c + d*x)^2) + (b^2*sin(c + d*x))/(a^3*d*cos(c + d*x))","B"
601,1,2971,237,4.778826,"\text{Not used}","int(-(cos(c + d*x)^4*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-40\,a^4-20\,a^3\,b+12\,a^2\,b^2+a\,b^3+b^4\right)}{4\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(-40\,a^4+20\,a^3\,b+12\,a^2\,b^2-a\,b^3+b^4\right)}{4\,b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-360\,a^4+28\,a^2\,b^2+21\,b^4\right)}{6\,b^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(240\,a^4+60\,a^3\,b-32\,a^2\,b^2-23\,a\,b^3+12\,b^4\right)}{6\,b^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(240\,a^4-60\,a^3\,b-32\,a^2\,b^2+23\,a\,b^3+12\,b^4\right)}{6\,b^5}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(5\,a-3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(10\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(10\,a+2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(5\,a+3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}-\frac{\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{16\,b^{16}}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^6}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^6}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}+\frac{\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{16\,b^{16}}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^6}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^6}}{\frac{-8000\,a^{14}+12000\,a^{13}\,b+7200\,a^{12}\,b^2-15800\,a^{11}\,b^3+440\,a^{10}\,b^4+5240\,a^9\,b^5-944\,a^8\,b^6-99\,a^7\,b^7+54\,a^6\,b^8-95\,a^5\,b^9+8\,a^4\,b^{10}-4\,a^3\,b^{11}}{b^{15}}-\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}-\frac{\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{16\,b^{16}}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^6}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^6}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}+\frac{\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{16\,b^{16}}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^6}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)}{8\,b^6}}\right)\,\left(-a^4\,40{}\mathrm{i}+a^2\,b^2\,12{}\mathrm{i}+b^4\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,b^6\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{2\,b^{10}\,\left(b^8-a^2\,b^6\right)}\right)}{b^8-a^2\,b^6}\right)\,\left(5\,a^2-4\,b^2\right)\,1{}\mathrm{i}}{b^8-a^2\,b^6}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{2\,b^{10}\,\left(b^8-a^2\,b^6\right)}\right)}{b^8-a^2\,b^6}\right)\,\left(5\,a^2-4\,b^2\right)\,1{}\mathrm{i}}{b^8-a^2\,b^6}}{\frac{-8000\,a^{14}+12000\,a^{13}\,b+7200\,a^{12}\,b^2-15800\,a^{11}\,b^3+440\,a^{10}\,b^4+5240\,a^9\,b^5-944\,a^8\,b^6-99\,a^7\,b^7+54\,a^6\,b^8-95\,a^5\,b^9+8\,a^4\,b^{10}-4\,a^3\,b^{11}}{b^{15}}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{2\,b^{10}\,\left(b^8-a^2\,b^6\right)}\right)}{b^8-a^2\,b^6}\right)\,\left(5\,a^2-4\,b^2\right)}{b^8-a^2\,b^6}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3200\,a^{11}-6400\,a^{10}\,b+1280\,a^9\,b^2+3840\,a^8\,b^3-1792\,a^7\,b^4-256\,a^6\,b^5+216\,a^5\,b^6-136\,a^4\,b^7+73\,a^3\,b^8-27\,a^2\,b^9+3\,a\,b^{10}-b^{11}\right)}{2\,b^{10}}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(\frac{-160\,a^6\,b^{12}+240\,a^5\,b^{13}+48\,a^4\,b^{14}-172\,a^3\,b^{15}+44\,a^2\,b^{16}-4\,a\,b^{17}+4\,b^{18}}{b^{15}}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,\left(128\,a^3\,b^{12}-256\,a^2\,b^{13}+128\,a\,b^{14}\right)}{2\,b^{10}\,\left(b^8-a^2\,b^6\right)}\right)}{b^8-a^2\,b^6}\right)\,\left(5\,a^2-4\,b^2\right)}{b^8-a^2\,b^6}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(5\,a^2-4\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^8-a^2\,b^6\right)}","Not used",1,"(atan(((((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) - (((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 - (tan(c/2 + (d*x)/2)*(b^4*1i - a^4*40i + a^2*b^2*12i)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(16*b^16))*(b^4*1i - a^4*40i + a^2*b^2*12i))/(8*b^6))*(b^4*1i - a^4*40i + a^2*b^2*12i)*1i)/(8*b^6) + (((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) + (((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 + (tan(c/2 + (d*x)/2)*(b^4*1i - a^4*40i + a^2*b^2*12i)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(16*b^16))*(b^4*1i - a^4*40i + a^2*b^2*12i))/(8*b^6))*(b^4*1i - a^4*40i + a^2*b^2*12i)*1i)/(8*b^6))/((12000*a^13*b - 8000*a^14 - 4*a^3*b^11 + 8*a^4*b^10 - 95*a^5*b^9 + 54*a^6*b^8 - 99*a^7*b^7 - 944*a^8*b^6 + 5240*a^9*b^5 + 440*a^10*b^4 - 15800*a^11*b^3 + 7200*a^12*b^2)/b^15 - (((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) - (((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 - (tan(c/2 + (d*x)/2)*(b^4*1i - a^4*40i + a^2*b^2*12i)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(16*b^16))*(b^4*1i - a^4*40i + a^2*b^2*12i))/(8*b^6))*(b^4*1i - a^4*40i + a^2*b^2*12i))/(8*b^6) + (((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) + (((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 + (tan(c/2 + (d*x)/2)*(b^4*1i - a^4*40i + a^2*b^2*12i)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(16*b^16))*(b^4*1i - a^4*40i + a^2*b^2*12i))/(8*b^6))*(b^4*1i - a^4*40i + a^2*b^2*12i))/(8*b^6)))*(b^4*1i - a^4*40i + a^2*b^2*12i)*1i)/(4*b^6*d) - ((tan(c/2 + (d*x)/2)*(a*b^3 - 20*a^3*b - 40*a^4 + b^4 + 12*a^2*b^2))/(4*b^5) + (tan(c/2 + (d*x)/2)^9*(20*a^3*b - a*b^3 - 40*a^4 + b^4 + 12*a^2*b^2))/(4*b^5) + (tan(c/2 + (d*x)/2)^5*(21*b^4 - 360*a^4 + 28*a^2*b^2))/(6*b^5) - (tan(c/2 + (d*x)/2)^3*(60*a^3*b - 23*a*b^3 + 240*a^4 + 12*b^4 - 32*a^2*b^2))/(6*b^5) - (tan(c/2 + (d*x)/2)^7*(23*a*b^3 - 60*a^3*b + 240*a^4 + 12*b^4 - 32*a^2*b^2))/(6*b^5))/(d*(a + b + tan(c/2 + (d*x)/2)^10*(a - b) + tan(c/2 + (d*x)/2)^2*(5*a + 3*b) + tan(c/2 + (d*x)/2)^4*(10*a + 2*b) + tan(c/2 + (d*x)/2)^8*(5*a - 3*b) + tan(c/2 + (d*x)/2)^6*(10*a - 2*b))) + (a^3*atan(((a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) + (a^3*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 + (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(2*b^10*(b^8 - a^2*b^6))))/(b^8 - a^2*b^6))*(5*a^2 - 4*b^2)*1i)/(b^8 - a^2*b^6) + (a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) - (a^3*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 - (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(2*b^10*(b^8 - a^2*b^6))))/(b^8 - a^2*b^6))*(5*a^2 - 4*b^2)*1i)/(b^8 - a^2*b^6))/((12000*a^13*b - 8000*a^14 - 4*a^3*b^11 + 8*a^4*b^10 - 95*a^5*b^9 + 54*a^6*b^8 - 99*a^7*b^7 - 944*a^8*b^6 + 5240*a^9*b^5 + 440*a^10*b^4 - 15800*a^11*b^3 + 7200*a^12*b^2)/b^15 + (a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) + (a^3*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 + (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(2*b^10*(b^8 - a^2*b^6))))/(b^8 - a^2*b^6))*(5*a^2 - 4*b^2))/(b^8 - a^2*b^6) - (a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(3*a*b^10 - 6400*a^10*b + 3200*a^11 - b^11 - 27*a^2*b^9 + 73*a^3*b^8 - 136*a^4*b^7 + 216*a^5*b^6 - 256*a^6*b^5 - 1792*a^7*b^4 + 3840*a^8*b^3 + 1280*a^9*b^2))/(2*b^10) - (a^3*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*((4*b^18 - 4*a*b^17 + 44*a^2*b^16 - 172*a^3*b^15 + 48*a^4*b^14 + 240*a^5*b^13 - 160*a^6*b^12)/b^15 - (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*(128*a*b^14 - 256*a^2*b^13 + 128*a^3*b^12))/(2*b^10*(b^8 - a^2*b^6))))/(b^8 - a^2*b^6))*(5*a^2 - 4*b^2))/(b^8 - a^2*b^6)))*(-(a + b)*(a - b))^(1/2)*(5*a^2 - 4*b^2)*2i)/(d*(b^8 - a^2*b^6))","B"
602,1,1652,189,3.732112,"\text{Not used}","int(-(cos(c + d*x)^3*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-4\,a^3+2\,a^2\,b+a\,b^2\right)}{b^4}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^3+2\,a^2\,b-a\,b^2\right)}{b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-36\,a^3-6\,a^2\,b+a\,b^2+4\,b^3\right)}{3\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-36\,a^3+6\,a^2\,b+a\,b^2-4\,b^3\right)}{3\,b^4}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(4\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a+2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{256\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^4\,b+256\,a^5-64\,a^3\,b^2-\frac{256\,a^6}{b}}-\frac{64\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^3\,b-64\,a^4-\frac{256\,a^5}{b}+\frac{256\,a^6}{b^2}}-\frac{256\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-256\,a^6+256\,a^5\,b+64\,a^4\,b^2-64\,a^3\,b^3}+\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^3-\frac{64\,a^4}{b}-\frac{256\,a^5}{b^2}+\frac{256\,a^6}{b^3}}\right)\,\left(a\,b^2\,1{}\mathrm{i}-a^3\,4{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^5\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9+64\,a^8\,b-16\,a^7\,b^2-32\,a^6\,b^3+14\,a^5\,b^4+4\,a^4\,b^5-3\,a^3\,b^6+a^2\,b^7\right)}{b^8}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-4\,a^5\,b^{10}+6\,a^4\,b^{11}+a^3\,b^{12}-4\,a^2\,b^{13}+a\,b^{14}\right)}{b^{12}}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(2\,a^3\,b^{10}-4\,a^2\,b^{11}+2\,a\,b^{12}\right)}{b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9+64\,a^8\,b-16\,a^7\,b^2-32\,a^6\,b^3+14\,a^5\,b^4+4\,a^4\,b^5-3\,a^3\,b^6+a^2\,b^7\right)}{b^8}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-4\,a^5\,b^{10}+6\,a^4\,b^{11}+a^3\,b^{12}-4\,a^2\,b^{13}+a\,b^{14}\right)}{b^{12}}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(2\,a^3\,b^{10}-4\,a^2\,b^{11}+2\,a\,b^{12}\right)}{b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}}{\frac{64\,\left(-64\,a^{11}+96\,a^{10}\,b+48\,a^9\,b^2-112\,a^8\,b^3+4\,a^7\,b^4+34\,a^6\,b^5-3\,a^5\,b^6-3\,a^4\,b^7\right)}{b^{12}}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9+64\,a^8\,b-16\,a^7\,b^2-32\,a^6\,b^3+14\,a^5\,b^4+4\,a^4\,b^5-3\,a^3\,b^6+a^2\,b^7\right)}{b^8}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-4\,a^5\,b^{10}+6\,a^4\,b^{11}+a^3\,b^{12}-4\,a^2\,b^{13}+a\,b^{14}\right)}{b^{12}}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(2\,a^3\,b^{10}-4\,a^2\,b^{11}+2\,a\,b^{12}\right)}{b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-32\,a^9+64\,a^8\,b-16\,a^7\,b^2-32\,a^6\,b^3+14\,a^5\,b^4+4\,a^4\,b^5-3\,a^3\,b^6+a^2\,b^7\right)}{b^8}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-4\,a^5\,b^{10}+6\,a^4\,b^{11}+a^3\,b^{12}-4\,a^2\,b^{13}+a\,b^{14}\right)}{b^{12}}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,\left(2\,a^3\,b^{10}-4\,a^2\,b^{11}+2\,a\,b^{12}\right)}{b^8\,\left(b^7-a^2\,b^5\right)}\right)}{b^7-a^2\,b^5}\right)}{b^7-a^2\,b^5}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(4\,a^2-3\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^7-a^2\,b^5\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^7*(a*b^2 + 2*a^2*b - 4*a^3))/b^4 - (2*tan(c/2 + (d*x)/2)*(2*a^2*b - a*b^2 + 4*a^3))/b^4 + (2*tan(c/2 + (d*x)/2)^3*(a*b^2 - 6*a^2*b - 36*a^3 + 4*b^3))/(3*b^4) + (2*tan(c/2 + (d*x)/2)^5*(a*b^2 + 6*a^2*b - 36*a^3 - 4*b^3))/(3*b^4))/(d*(a + b + tan(c/2 + (d*x)/2)^8*(a - b) + tan(c/2 + (d*x)/2)^2*(4*a + 2*b) + tan(c/2 + (d*x)/2)^6*(4*a - 2*b) + 6*a*tan(c/2 + (d*x)/2)^4)) + (atan((256*a^5*tan(c/2 + (d*x)/2))/(64*a^4*b + 256*a^5 - 64*a^3*b^2 - (256*a^6)/b) - (64*a^4*tan(c/2 + (d*x)/2))/(64*a^3*b - 64*a^4 - (256*a^5)/b + (256*a^6)/b^2) - (256*a^6*tan(c/2 + (d*x)/2))/(256*a^5*b - 256*a^6 - 64*a^3*b^3 + 64*a^4*b^2) + (64*a^3*tan(c/2 + (d*x)/2))/(64*a^3 - (64*a^4)/b - (256*a^5)/b^2 + (256*a^6)/b^3))*(a*b^2*1i - a^3*4i)*2i)/(b^5*d) + (a^2*atan(((a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a^8*b - 32*a^9 + a^2*b^7 - 3*a^3*b^6 + 4*a^4*b^5 + 14*a^5*b^4 - 32*a^6*b^3 - 16*a^7*b^2))/b^8 + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a*b^14 - 4*a^2*b^13 + a^3*b^12 + 6*a^4*b^11 - 4*a^5*b^10))/b^12 - (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(2*a*b^12 - 4*a^2*b^11 + 2*a^3*b^10))/(b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5))*1i)/(b^7 - a^2*b^5) + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a^8*b - 32*a^9 + a^2*b^7 - 3*a^3*b^6 + 4*a^4*b^5 + 14*a^5*b^4 - 32*a^6*b^3 - 16*a^7*b^2))/b^8 - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a*b^14 - 4*a^2*b^13 + a^3*b^12 + 6*a^4*b^11 - 4*a^5*b^10))/b^12 + (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(2*a*b^12 - 4*a^2*b^11 + 2*a^3*b^10))/(b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5))*1i)/(b^7 - a^2*b^5))/((64*(96*a^10*b - 64*a^11 - 3*a^4*b^7 - 3*a^5*b^6 + 34*a^6*b^5 + 4*a^7*b^4 - 112*a^8*b^3 + 48*a^9*b^2))/b^12 + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a^8*b - 32*a^9 + a^2*b^7 - 3*a^3*b^6 + 4*a^4*b^5 + 14*a^5*b^4 - 32*a^6*b^3 - 16*a^7*b^2))/b^8 + (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a*b^14 - 4*a^2*b^13 + a^3*b^12 + 6*a^4*b^11 - 4*a^5*b^10))/b^12 - (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(2*a*b^12 - 4*a^2*b^11 + 2*a^3*b^10))/(b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5) - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a^8*b - 32*a^9 + a^2*b^7 - 3*a^3*b^6 + 4*a^4*b^5 + 14*a^5*b^4 - 32*a^6*b^3 - 16*a^7*b^2))/b^8 - (a^2*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*((32*(a*b^14 - 4*a^2*b^13 + a^3*b^12 + 6*a^4*b^11 - 4*a^5*b^10))/b^12 + (32*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*(2*a*b^12 - 4*a^2*b^11 + 2*a^3*b^10))/(b^8*(b^7 - a^2*b^5))))/(b^7 - a^2*b^5)))/(b^7 - a^2*b^5)))*(-(a + b)*(a - b))^(1/2)*(4*a^2 - 3*b^2)*2i)/(d*(b^7 - a^2*b^5))","B"
603,1,664,154,2.012676,"\text{Not used}","int(-(cos(c + d*x)^2*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^2+b^2\right)}{b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2+3\,a\,b-b^2\right)}{b^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-6\,a^2+3\,a\,b+b^2\right)}{b^3}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(3\,a+b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\ln\left(b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\left(3\,a^3\,\sqrt{b^2-a^2}-2\,a\,b^2\,\sqrt{b^2-a^2}\right)}{b^4\,d\,\left(a^2-b^2\right)}-\frac{a\,\ln\left(a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-2\,b^2\right)}{d\,\left(b^6-a^2\,b^4\right)}-\frac{\mathrm{atan}\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{8\,a}{b}+\frac{24\,a^2}{b^2}-\frac{24\,a^3}{b^3}+\frac{144\,a^4}{b^4}-\frac{144\,a^5}{b^5}-8}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a-8\,b+\frac{24\,a^2}{b}-\frac{24\,a^3}{b^2}+\frac{144\,a^4}{b^3}-\frac{144\,a^5}{b^4}}-\frac{24\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,b+24\,a^2-8\,b^2-\frac{24\,a^3}{b}+\frac{144\,a^4}{b^2}-\frac{144\,a^5}{b^3}}+\frac{24\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,b^2+24\,a^2\,b-24\,a^3-8\,b^3+\frac{144\,a^4}{b}-\frac{144\,a^5}{b^2}}-\frac{144\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,b^3-24\,a^3\,b+144\,a^4-8\,b^4+24\,a^2\,b^2-\frac{144\,a^5}{b}}+\frac{144\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-144\,a^5+144\,a^4\,b-24\,a^3\,b^2+24\,a^2\,b^3+8\,a\,b^4-8\,b^5}\right)\,\left(a^2\,6{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4\,d}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(6*a^2 + b^2))/b^3 + (tan(c/2 + (d*x)/2)*(3*a*b + 6*a^2 - b^2))/b^3 - (tan(c/2 + (d*x)/2)^5*(3*a*b - 6*a^2 + b^2))/b^3)/(d*(a + b + tan(c/2 + (d*x)/2)^2*(3*a + b) + tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) - (atan((8*tan(c/2 + (d*x)/2))/((8*a)/b + (24*a^2)/b^2 - (24*a^3)/b^3 + (144*a^4)/b^4 - (144*a^5)/b^5 - 8) - (8*a*tan(c/2 + (d*x)/2))/(8*a - 8*b + (24*a^2)/b - (24*a^3)/b^2 + (144*a^4)/b^3 - (144*a^5)/b^4) - (24*a^2*tan(c/2 + (d*x)/2))/(8*a*b + 24*a^2 - 8*b^2 - (24*a^3)/b + (144*a^4)/b^2 - (144*a^5)/b^3) + (24*a^3*tan(c/2 + (d*x)/2))/(8*a*b^2 + 24*a^2*b - 24*a^3 - 8*b^3 + (144*a^4)/b - (144*a^5)/b^2) - (144*a^4*tan(c/2 + (d*x)/2))/(8*a*b^3 - 24*a^3*b + 144*a^4 - 8*b^4 + 24*a^2*b^2 - (144*a^5)/b) + (144*a^5*tan(c/2 + (d*x)/2))/(8*a*b^4 + 144*a^4*b - 144*a^5 - 8*b^5 + 24*a^2*b^3 - 24*a^3*b^2))*(a^2*6i - b^2*1i)*1i)/(b^4*d) - (log(b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(3*a^3*(b^2 - a^2)^(1/2) - 2*a*b^2*(b^2 - a^2)^(1/2)))/(b^4*d*(a^2 - b^2)) - (a*log(a*tan(c/2 + (d*x)/2) - b*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 2*b^2))/(d*(b^6 - a^2*b^4))","B"
604,1,314,112,1.758970,"\text{Not used}","int(-(cos(c + d*x)*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^2,x)","\frac{4\,a\,\mathrm{atan}\left(\frac{128\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,a-\frac{128\,a^2}{b}}-\frac{128\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,a\,b-128\,a^2}\right)}{b^3\,d}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a-b\right)}{b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)}{b^2}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\ln\left(b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-b^2\right)}{d\,\left(b^5-a^2\,b^3\right)}-\frac{\ln\left(a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sqrt{b^2-a^2}\right)\,\left(2\,a^2\,\sqrt{b^2-a^2}-b^2\,\sqrt{b^2-a^2}\right)}{b^3\,d\,\left(a^2-b^2\right)}","Not used",1,"(4*a*atan((128*a*tan(c/2 + (d*x)/2))/(128*a - (128*a^2)/b) - (128*a^2*tan(c/2 + (d*x)/2))/(128*a*b - 128*a^2)))/(b^3*d) - ((2*tan(c/2 + (d*x)/2)^3*(2*a - b))/b^2 + (2*tan(c/2 + (d*x)/2)*(2*a + b))/b^2)/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) + 2*a*tan(c/2 + (d*x)/2)^2)) - (log(b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(-(a + b)*(a - b))^(1/2)*(2*a^2 - b^2))/(d*(b^5 - a^2*b^3)) - (log(a*tan(c/2 + (d*x)/2) - b*tan(c/2 + (d*x)/2) + (b^2 - a^2)^(1/2))*(2*a^2*(b^2 - a^2)^(1/2) - b^2*(b^2 - a^2)^(1/2)))/(b^3*d*(a^2 - b^2))","B"
605,1,277,85,1.873111,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(a + b*cos(c + d*x))^2,x)","\frac{2\,\left(-a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}+a^2\,\mathrm{atan}\left(\frac{\left(a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}\right)\,1{}\mathrm{i}\right)}{b^2\,d\,\sqrt{b^2-a^2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)}+\frac{2\,\left(\frac{\sin\left(c+d\,x\right)\,\sqrt{b^2-a^2}}{2}-\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}+a\,\mathrm{atan}\left(\frac{\left(a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}\right)\,\cos\left(c+d\,x\right)\,1{}\mathrm{i}\right)}{b\,d\,\sqrt{b^2-a^2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)}","Not used",1,"(2*(a^2*atan(((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2))*1i)/(cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)))*1i - a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*(b^2 - a^2)^(1/2)))/(b^2*d*(b^2 - a^2)^(1/2)*(a + b*cos(c + d*x))) + (2*((sin(c + d*x)*(b^2 - a^2)^(1/2))/2 - cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*(b^2 - a^2)^(1/2) + a*atan(((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2))*1i)/(cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)))*cos(c + d*x)*1i))/(b*d*(b^2 - a^2)^(1/2)*(a + b*cos(c + d*x)))","B"
606,1,486,94,1.939989,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)*(a + b*cos(c + d*x))^2),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^2\,d}+\frac{b^2\,\left(a\,\sin\left(c+d\,x\right)+2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a\,b^2-a^3\right)}^2}\right)\,\sqrt{b^2-a^2}\right)-a^3\,\sin\left(c+d\,x\right)+2\,a\,b\,\mathrm{atanh}\left(\frac{a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a\,b^2-a^3\right)}^2}\right)\,\sqrt{b^2-a^2}}{a^2\,d\,\left(a^2-b^2\right)\,\left(a+b\,\cos\left(c+d\,x\right)\right)}","Not used",1,"(2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d) + (b^2*(a*sin(c + d*x) + 2*cos(c + d*x)*atanh((a^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)^2))*(b^2 - a^2)^(1/2)) - a^3*sin(c + d*x) + 2*a*b*atanh((a^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)^2))*(b^2 - a^2)^(1/2))/(a^2*d*(a^2 - b^2)*(a + b*cos(c + d*x)))","B"
607,1,1091,118,2.487331,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^2),x)","\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+2\,b\right)}{a^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a-2\,b\right)}{a^2}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{4\,b\,\mathrm{atanh}\left(\frac{128\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,b-\frac{128\,b^2}{a}}-\frac{128\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,a\,b-128\,b^2}\right)}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^5+a^4\,b+8\,a^2\,b^3-16\,a\,b^4+8\,b^5\right)}{a^4}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^9-3\,a^7\,b^2+2\,a^6\,b^3\right)}{a^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(2\,a^8\,b-4\,a^7\,b^2+2\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,\left(a^2-2\,b^2\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^5+a^4\,b+8\,a^2\,b^3-16\,a\,b^4+8\,b^5\right)}{a^4}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^9-3\,a^7\,b^2+2\,a^6\,b^3\right)}{a^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(2\,a^8\,b-4\,a^7\,b^2+2\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,\left(a^2-2\,b^2\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}}{\frac{64\,\left(2\,a^4\,b-6\,a^3\,b^2+12\,a\,b^4-8\,b^5\right)}{a^6}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^5+a^4\,b+8\,a^2\,b^3-16\,a\,b^4+8\,b^5\right)}{a^4}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^9-3\,a^7\,b^2+2\,a^6\,b^3\right)}{a^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(2\,a^8\,b-4\,a^7\,b^2+2\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,\left(a^2-2\,b^2\right)}{a^5-a^3\,b^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^5+a^4\,b+8\,a^2\,b^3-16\,a\,b^4+8\,b^5\right)}{a^4}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^9-3\,a^7\,b^2+2\,a^6\,b^3\right)}{a^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,\left(2\,a^8\,b-4\,a^7\,b^2+2\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)}{a^5-a^3\,b^2}\right)\,\left(a^2-2\,b^2\right)}{a^5-a^3\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^2-2\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^5-a^3\,b^2\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)*(a + 2*b))/a^2 + (2*tan(c/2 + (d*x)/2)^3*(a - 2*b))/a^2)/(d*(a + b - tan(c/2 + (d*x)/2)^4*(a - b) - 2*b*tan(c/2 + (d*x)/2)^2)) - (4*b*atanh((128*b*tan(c/2 + (d*x)/2))/(128*b - (128*b^2)/a) - (128*b^2*tan(c/2 + (d*x)/2))/(128*a*b - 128*b^2)))/(a^3*d) - (atan((((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(a^4*b - 16*a*b^4 - a^5 + 8*b^5 + 8*a^2*b^3))/a^4 + ((-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((32*(a^9 + 2*a^6*b^3 - 3*a^7*b^2))/a^6 - (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*(2*a^8*b + 2*a^6*b^3 - 4*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*(a^2 - 2*b^2)*1i)/(a^5 - a^3*b^2) + ((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(a^4*b - 16*a*b^4 - a^5 + 8*b^5 + 8*a^2*b^3))/a^4 - ((-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((32*(a^9 + 2*a^6*b^3 - 3*a^7*b^2))/a^6 + (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*(2*a^8*b + 2*a^6*b^3 - 4*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*(a^2 - 2*b^2)*1i)/(a^5 - a^3*b^2))/((64*(12*a*b^4 + 2*a^4*b - 8*b^5 - 6*a^3*b^2))/a^6 + ((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(a^4*b - 16*a*b^4 - a^5 + 8*b^5 + 8*a^2*b^3))/a^4 + ((-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((32*(a^9 + 2*a^6*b^3 - 3*a^7*b^2))/a^6 - (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*(2*a^8*b + 2*a^6*b^3 - 4*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*(a^2 - 2*b^2))/(a^5 - a^3*b^2) - ((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(a^4*b - 16*a*b^4 - a^5 + 8*b^5 + 8*a^2*b^3))/a^4 - ((-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*((32*(a^9 + 2*a^6*b^3 - 3*a^7*b^2))/a^6 + (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*(2*a^8*b + 2*a^6*b^3 - 4*a^7*b^2))/(a^4*(a^5 - a^3*b^2))))/(a^5 - a^3*b^2))*(a^2 - 2*b^2))/(a^5 - a^3*b^2)))*(-(a + b)*(a - b))^(1/2)*(a^2 - 2*b^2)*2i)/(d*(a^5 - a^3*b^2))","B"
608,1,1662,160,3.320361,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^2),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+6\,b^2\right)}{a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^2+3\,a\,b+6\,b^2\right)}{a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^2+3\,a\,b-6\,b^2\right)}{a^3}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-a-3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atanh}\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{8\,b}{a}+\frac{24\,b^2}{a^2}-\frac{24\,b^3}{a^3}+\frac{144\,b^4}{a^4}-\frac{144\,b^5}{a^5}-8}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a-8\,b-\frac{24\,b^2}{a}+\frac{24\,b^3}{a^2}-\frac{144\,b^4}{a^3}+\frac{144\,b^5}{a^4}}-\frac{24\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,b-8\,a^2+24\,b^2-\frac{24\,b^3}{a}+\frac{144\,b^4}{a^2}-\frac{144\,b^5}{a^3}}+\frac{24\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24\,a\,b^2+8\,a^2\,b-8\,a^3-24\,b^3+\frac{144\,b^4}{a}-\frac{144\,b^5}{a^2}}+\frac{144\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24\,a\,b^3-8\,a^3\,b+8\,a^4-144\,b^4-24\,a^2\,b^2+\frac{144\,b^5}{a}}+\frac{144\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-8\,a^5+8\,a^4\,b+24\,a^3\,b^2-24\,a^2\,b^3+144\,a\,b^4-144\,b^5}\right)\,\left(a^2-6\,b^2\right)}{a^4\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(-2\,a^7\,b-4\,a^6\,b^2+33\,a^5\,b^3+18\,a^4\,b^4-153\,a^3\,b^5+54\,a^2\,b^6+162\,a\,b^7-108\,b^8\right)}{a^9}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(a^2 + 6*b^2))/a^3 - (tan(c/2 + (d*x)/2)*(3*a*b - a^2 + 6*b^2))/a^3 + (tan(c/2 + (d*x)/2)^5*(3*a*b + a^2 - 6*b^2))/a^3)/(d*(a + b - tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) + tan(c/2 + (d*x)/2)^6*(a - b))) + (atanh((8*tan(c/2 + (d*x)/2))/((8*b)/a + (24*b^2)/a^2 - (24*b^3)/a^3 + (144*b^4)/a^4 - (144*b^5)/a^5 - 8) + (8*b*tan(c/2 + (d*x)/2))/(8*a - 8*b - (24*b^2)/a + (24*b^3)/a^2 - (144*b^4)/a^3 + (144*b^5)/a^4) - (24*b^2*tan(c/2 + (d*x)/2))/(8*a*b - 8*a^2 + 24*b^2 - (24*b^3)/a + (144*b^4)/a^2 - (144*b^5)/a^3) + (24*b^3*tan(c/2 + (d*x)/2))/(24*a*b^2 + 8*a^2*b - 8*a^3 - 24*b^3 + (144*b^4)/a - (144*b^5)/a^2) + (144*b^4*tan(c/2 + (d*x)/2))/(24*a*b^3 - 8*a^3*b + 8*a^4 - 144*b^4 - 24*a^2*b^2 + (144*b^5)/a) + (144*b^5*tan(c/2 + (d*x)/2))/(144*a*b^4 + 8*a^4*b - 8*a^5 - 144*b^5 - 24*a^2*b^3 + 24*a^3*b^2))*(a^2 - 6*b^2))/(a^4*d) - (b*atan(((b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 + (b*(-(a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 - (b*(-(a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2))/((16*(162*a*b^7 - 2*a^7*b - 108*b^8 + 54*a^2*b^6 - 153*a^3*b^5 + 18*a^4*b^4 + 33*a^5*b^3 - 4*a^6*b^2))/a^9 - (b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 + (b*(-(a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) + (b*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 - (b*(-(a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*(-(a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*2i)/(d*(a^6 - a^4*b^2))","B"
609,1,1650,195,3.628793,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^2),x)","\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^2\,b+2\,a\,b^2+4\,b^3\right)}{a^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^2\,b+2\,a\,b^2-4\,b^3\right)}{a^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-4\,a^3-a^2\,b+6\,a\,b^2+36\,b^3\right)}{3\,a^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-4\,a^3+a^2\,b+6\,a\,b^2-36\,b^3\right)}{3\,a^4}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{2\,b\,\mathrm{atanh}\left(\frac{256\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b^4+256\,b^5-64\,a^2\,b^3-\frac{256\,b^6}{a}}-\frac{64\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a\,b^3-64\,b^4-\frac{256\,b^5}{a}+\frac{256\,b^6}{a^2}}-\frac{256\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-64\,a^3\,b^3+64\,a^2\,b^4+256\,a\,b^5-256\,b^6}+\frac{64\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,b^3-\frac{64\,b^4}{a}-\frac{256\,b^5}{a^2}+\frac{256\,b^6}{a^3}}\right)\,\left(a^2-4\,b^2\right)}{a^5\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b^2-3\,a^6\,b^3+4\,a^5\,b^4+14\,a^4\,b^5-32\,a^3\,b^6-16\,a^2\,b^7+64\,a\,b^8-32\,b^9\right)}{a^8}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\left(a^{14}\,b-4\,a^{13}\,b^2+a^{12}\,b^3+6\,a^{11}\,b^4-4\,a^{10}\,b^5\right)}{a^{12}}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(2\,a^{12}\,b-4\,a^{11}\,b^2+2\,a^{10}\,b^3\right)}{a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b^2-3\,a^6\,b^3+4\,a^5\,b^4+14\,a^4\,b^5-32\,a^3\,b^6-16\,a^2\,b^7+64\,a\,b^8-32\,b^9\right)}{a^8}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\left(a^{14}\,b-4\,a^{13}\,b^2+a^{12}\,b^3+6\,a^{11}\,b^4-4\,a^{10}\,b^5\right)}{a^{12}}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(2\,a^{12}\,b-4\,a^{11}\,b^2+2\,a^{10}\,b^3\right)}{a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}}{\frac{64\,\left(-3\,a^7\,b^4-3\,a^6\,b^5+34\,a^5\,b^6+4\,a^4\,b^7-112\,a^3\,b^8+48\,a^2\,b^9+96\,a\,b^{10}-64\,b^{11}\right)}{a^{12}}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b^2-3\,a^6\,b^3+4\,a^5\,b^4+14\,a^4\,b^5-32\,a^3\,b^6-16\,a^2\,b^7+64\,a\,b^8-32\,b^9\right)}{a^8}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\left(a^{14}\,b-4\,a^{13}\,b^2+a^{12}\,b^3+6\,a^{11}\,b^4-4\,a^{10}\,b^5\right)}{a^{12}}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(2\,a^{12}\,b-4\,a^{11}\,b^2+2\,a^{10}\,b^3\right)}{a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7\,b^2-3\,a^6\,b^3+4\,a^5\,b^4+14\,a^4\,b^5-32\,a^3\,b^6-16\,a^2\,b^7+64\,a\,b^8-32\,b^9\right)}{a^8}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(\frac{32\,\left(a^{14}\,b-4\,a^{13}\,b^2+a^{12}\,b^3+6\,a^{11}\,b^4-4\,a^{10}\,b^5\right)}{a^{12}}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,\left(2\,a^{12}\,b-4\,a^{11}\,b^2+2\,a^{10}\,b^3\right)}{a^8\,\left(a^7-a^5\,b^2\right)}\right)}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(3\,a^2-4\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)*(2*a*b^2 - a^2*b + 4*b^3))/a^4 + (2*tan(c/2 + (d*x)/2)^7*(2*a*b^2 + a^2*b - 4*b^3))/a^4 - (2*tan(c/2 + (d*x)/2)^3*(6*a*b^2 - a^2*b - 4*a^3 + 36*b^3))/(3*a^4) - (2*tan(c/2 + (d*x)/2)^5*(6*a*b^2 + a^2*b - 4*a^3 - 36*b^3))/(3*a^4))/(d*(a + b - tan(c/2 + (d*x)/2)^8*(a - b) - tan(c/2 + (d*x)/2)^2*(2*a + 4*b) + tan(c/2 + (d*x)/2)^6*(2*a - 4*b) + 6*b*tan(c/2 + (d*x)/2)^4)) + (2*b*atanh((256*b^5*tan(c/2 + (d*x)/2))/(64*a*b^4 + 256*b^5 - 64*a^2*b^3 - (256*b^6)/a) - (64*b^4*tan(c/2 + (d*x)/2))/(64*a*b^3 - 64*b^4 - (256*b^5)/a + (256*b^6)/a^2) - (256*b^6*tan(c/2 + (d*x)/2))/(256*a*b^5 - 256*b^6 + 64*a^2*b^4 - 64*a^3*b^3) + (64*b^3*tan(c/2 + (d*x)/2))/(64*b^3 - (64*b^4)/a - (256*b^5)/a^2 + (256*b^6)/a^3))*(a^2 - 4*b^2))/(a^5*d) + (b^2*atan(((b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a*b^8 - 32*b^9 - 16*a^2*b^7 - 32*a^3*b^6 + 14*a^4*b^5 + 4*a^5*b^4 - 3*a^6*b^3 + a^7*b^2))/a^8 + (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*(a^14*b - 4*a^10*b^5 + 6*a^11*b^4 + a^12*b^3 - 4*a^13*b^2))/a^12 + (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*(2*a^12*b + 2*a^10*b^3 - 4*a^11*b^2))/(a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2) + (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a*b^8 - 32*b^9 - 16*a^2*b^7 - 32*a^3*b^6 + 14*a^4*b^5 + 4*a^5*b^4 - 3*a^6*b^3 + a^7*b^2))/a^8 - (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*(a^14*b - 4*a^10*b^5 + 6*a^11*b^4 + a^12*b^3 - 4*a^13*b^2))/a^12 - (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*(2*a^12*b + 2*a^10*b^3 - 4*a^11*b^2))/(a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2))/((64*(96*a*b^10 - 64*b^11 + 48*a^2*b^9 - 112*a^3*b^8 + 4*a^4*b^7 + 34*a^5*b^6 - 3*a^6*b^5 - 3*a^7*b^4))/a^12 - (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a*b^8 - 32*b^9 - 16*a^2*b^7 - 32*a^3*b^6 + 14*a^4*b^5 + 4*a^5*b^4 - 3*a^6*b^3 + a^7*b^2))/a^8 + (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*(a^14*b - 4*a^10*b^5 + 6*a^11*b^4 + a^12*b^3 - 4*a^13*b^2))/a^12 + (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*(2*a^12*b + 2*a^10*b^3 - 4*a^11*b^2))/(a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2) + (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*tan(c/2 + (d*x)/2)*(64*a*b^8 - 32*b^9 - 16*a^2*b^7 - 32*a^3*b^6 + 14*a^4*b^5 + 4*a^5*b^4 - 3*a^6*b^3 + a^7*b^2))/a^8 - (b^2*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*((32*(a^14*b - 4*a^10*b^5 + 6*a^11*b^4 + a^12*b^3 - 4*a^13*b^2))/a^12 - (32*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*(2*a^12*b + 2*a^10*b^3 - 4*a^11*b^2))/(a^8*(a^7 - a^5*b^2))))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2)))*(-(a + b)*(a - b))^(1/2)*(3*a^2 - 4*b^2)*2i)/(d*(a^7 - a^5*b^2))","B"
610,1,4245,326,8.962913,"\text{Not used}","int(-(cos(c + d*x)^4*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^3,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^5+10\,a^4\,b-23\,a^3\,b^2-9\,a^2\,b^3+3\,a\,b^4\right)}{a\,b^5-b^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(20\,a^5-10\,a^4\,b-23\,a^3\,b^2+9\,a^2\,b^3+3\,a\,b^4\right)}{b^5\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(180\,a^6-197\,a^4\,b^2+34\,a^2\,b^4-8\,b^6\right)}{3\,\left(a\,b^5-b^6\right)\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-120\,a^6-90\,a^5\,b+118\,a^4\,b^2+86\,a^3\,b^3+a\,b^5-4\,b^6\right)}{3\,\left(a\,b^5-b^6\right)\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(120\,a^6-90\,a^5\,b-118\,a^4\,b^2+86\,a^3\,b^3+a\,b^5+4\,b^6\right)}{3\,b^5\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(10\,a^2+4\,a\,b-2\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-10\,a^2+4\,a\,b+2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^2+6\,a\,b+b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^2-6\,a\,b+b^2\right)\right)}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(20\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^2-3\,b^2\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,4{}\mathrm{i}}{b^6\,\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(20\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^6}\right)}{2\,b^6}+\frac{a\,\left(20\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^2-3\,b^2\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,4{}\mathrm{i}}{b^6\,\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(20\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^6}\right)}{2\,b^6}}{\frac{8\,\left(-8000\,a^{14}+4000\,a^{13}\,b+23600\,a^{12}\,b^2-10800\,a^{11}\,b^3-24540\,a^{10}\,b^4+9870\,a^9\,b^5+10677\,a^8\,b^6-3411\,a^7\,b^7-1845\,a^6\,b^8+324\,a^5\,b^9+108\,a^4\,b^{10}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}-\frac{a\,\left(20\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^2-3\,b^2\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,4{}\mathrm{i}}{b^6\,\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(20\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^6}\right)\,1{}\mathrm{i}}{2\,b^6}+\frac{a\,\left(20\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(20\,a^2-3\,b^2\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,4{}\mathrm{i}}{b^6\,\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(20\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,b^6}\right)\,1{}\mathrm{i}}{2\,b^6}}\right)\,\left(20\,a^2-3\,b^2\right)}{b^6\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a^2\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}-\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a^2\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}+\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}}{\frac{8\,\left(-8000\,a^{14}+4000\,a^{13}\,b+23600\,a^{12}\,b^2-10800\,a^{11}\,b^3-24540\,a^{10}\,b^4+9870\,a^9\,b^5+10677\,a^8\,b^6-3411\,a^7\,b^7-1845\,a^6\,b^8+324\,a^5\,b^9+108\,a^4\,b^{10}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}-\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a^2\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}-\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(800\,a^{12}-800\,a^{11}\,b-1840\,a^{10}\,b^2+1840\,a^9\,b^3+1298\,a^8\,b^4-1298\,a^7\,b^5-281\,a^6\,b^6+276\,a^5\,b^7+15\,a^4\,b^8-18\,a^3\,b^9+9\,a^2\,b^{10}\right)}{-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a^2\,\left(\frac{4\,\left(80\,a^8\,b^{12}-40\,a^7\,b^{13}-212\,a^6\,b^{14}+96\,a^5\,b^{15}+180\,a^4\,b^{16}-68\,a^3\,b^{17}-48\,a^2\,b^{18}+12\,a\,b^{19}\right)}{-a^3\,b^{15}-a^2\,b^{16}+a\,b^{17}+b^{18}}+\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)\,\left(-8\,a^6\,b^{12}+8\,a^5\,b^{13}+16\,a^4\,b^{14}-16\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^3\,b^{10}-a^2\,b^{11}+a\,b^{12}+b^{13}\right)\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)}{2\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(20\,a^4-33\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{d\,\left(-a^6\,b^6+3\,a^4\,b^8-3\,a^2\,b^{10}+b^{12}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(3*a*b^4 + 10*a^4*b + 20*a^5 - 9*a^2*b^3 - 23*a^3*b^2))/(a*b^5 - b^6) + (tan(c/2 + (d*x)/2)^9*(3*a*b^4 - 10*a^4*b + 20*a^5 + 9*a^2*b^3 - 23*a^3*b^2))/(b^5*(a + b)) + (2*tan(c/2 + (d*x)/2)^5*(180*a^6 - 8*b^6 + 34*a^2*b^4 - 197*a^4*b^2))/(3*(a*b^5 - b^6)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(a*b^5 - 90*a^5*b - 120*a^6 - 4*b^6 + 86*a^3*b^3 + 118*a^4*b^2))/(3*(a*b^5 - b^6)*(a + b)) + (2*tan(c/2 + (d*x)/2)^7*(a*b^5 - 90*a^5*b + 120*a^6 + 4*b^6 + 86*a^3*b^3 - 118*a^4*b^2))/(3*b^5*(a + b)*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(4*a*b + 10*a^2 - 2*b^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 10*a^2 + 2*b^2) + tan(c/2 + (d*x)/2)^10*(a^2 - 2*a*b + b^2) + a^2 + b^2 + tan(c/2 + (d*x)/2)^2*(6*a*b + 5*a^2 + b^2) + tan(c/2 + (d*x)/2)^8*(5*a^2 - 6*a*b + b^2))) - (a*atan(((a*(20*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) + (a*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) - (a*tan(c/2 + (d*x)/2)*(20*a^2 - 3*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12)*4i)/(b^6*(a*b^12 + b^13 - a^2*b^11 - a^3*b^10)))*(20*a^2 - 3*b^2)*1i)/(2*b^6)))/(2*b^6) + (a*(20*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) - (a*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) + (a*tan(c/2 + (d*x)/2)*(20*a^2 - 3*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12)*4i)/(b^6*(a*b^12 + b^13 - a^2*b^11 - a^3*b^10)))*(20*a^2 - 3*b^2)*1i)/(2*b^6)))/(2*b^6))/((8*(4000*a^13*b - 8000*a^14 + 108*a^4*b^10 + 324*a^5*b^9 - 1845*a^6*b^8 - 3411*a^7*b^7 + 10677*a^8*b^6 + 9870*a^9*b^5 - 24540*a^10*b^4 - 10800*a^11*b^3 + 23600*a^12*b^2))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) - (a*(20*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) + (a*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) - (a*tan(c/2 + (d*x)/2)*(20*a^2 - 3*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12)*4i)/(b^6*(a*b^12 + b^13 - a^2*b^11 - a^3*b^10)))*(20*a^2 - 3*b^2)*1i)/(2*b^6))*1i)/(2*b^6) + (a*(20*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) - (a*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) + (a*tan(c/2 + (d*x)/2)*(20*a^2 - 3*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12)*4i)/(b^6*(a*b^12 + b^13 - a^2*b^11 - a^3*b^10)))*(20*a^2 - 3*b^2)*1i)/(2*b^6))*1i)/(2*b^6)))*(20*a^2 - 3*b^2))/(b^6*d) - (a^2*atan(((a^2*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) + (a^2*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) - (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12))/((a*b^12 + b^13 - a^2*b^11 - a^3*b^10)*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2))/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2)*1i)/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)) + (a^2*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) - (a^2*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) + (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12))/((a*b^12 + b^13 - a^2*b^11 - a^3*b^10)*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2))/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2)*1i)/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))/((8*(4000*a^13*b - 8000*a^14 + 108*a^4*b^10 + 324*a^5*b^9 - 1845*a^6*b^8 - 3411*a^7*b^7 + 10677*a^8*b^6 + 9870*a^9*b^5 - 24540*a^10*b^4 - 10800*a^11*b^3 + 23600*a^12*b^2))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) - (a^2*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) + (a^2*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) - (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12))/((a*b^12 + b^13 - a^2*b^11 - a^3*b^10)*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2))/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2))/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)) + (a^2*((8*tan(c/2 + (d*x)/2)*(800*a^12 - 800*a^11*b + 9*a^2*b^10 - 18*a^3*b^9 + 15*a^4*b^8 + 276*a^5*b^7 - 281*a^6*b^6 - 1298*a^7*b^5 + 1298*a^8*b^4 + 1840*a^9*b^3 - 1840*a^10*b^2))/(a*b^12 + b^13 - a^2*b^11 - a^3*b^10) - (a^2*((4*(12*a*b^19 - 48*a^2*b^18 - 68*a^3*b^17 + 180*a^4*b^16 + 96*a^5*b^15 - 212*a^6*b^14 - 40*a^7*b^13 + 80*a^8*b^12))/(a*b^17 + b^18 - a^2*b^16 - a^3*b^15) + (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 16*a^3*b^15 + 16*a^4*b^14 + 8*a^5*b^13 - 8*a^6*b^12))/((a*b^12 + b^13 - a^2*b^11 - a^3*b^10)*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2))/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6)))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2))/(2*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6))))*(-(a + b)^3*(a - b)^3)^(1/2)*(20*a^4 + 12*b^4 - 33*a^2*b^2)*1i)/(d*(b^12 - 3*a^2*b^10 + 3*a^4*b^8 - a^6*b^6))","B"
611,1,4038,268,8.843201,"\text{Not used}","int(-(cos(c + d*x)^3*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^4+6\,a^3\,b-13\,a^2\,b^2-5\,a\,b^3+b^4\right)}{a\,b^4-b^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^5+18\,a^4\,b-37\,a^3\,b^2-14\,a^2\,b^3+4\,a\,b^4-3\,b^5\right)}{\left(a\,b^4-b^5\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(36\,a^5-18\,a^4\,b-37\,a^3\,b^2+14\,a^2\,b^3+4\,a\,b^4+3\,b^5\right)}{\left(a\,b^4-b^5\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(12\,a^4-6\,a^3\,b-13\,a^2\,b^2+5\,a\,b^3+b^4\right)}{b^4\,\left(a+b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,1{}\mathrm{i}}{2\,b^5}-\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)}{2\,b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{8\,\left(-1728\,a^{11}+864\,a^{10}\,b+4752\,a^9\,b^2-2160\,a^8\,b^3-4356\,a^7\,b^4+1746\,a^6\,b^5+1495\,a^5\,b^6-491\,a^4\,b^7-169\,a^3\,b^8+30\,a^2\,b^9+6\,a\,b^{10}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)}{2\,b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)}{2\,b^5}+\frac{\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)}{2\,b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)}{2\,b^5}}\right)\,\left(a^2\,12{}\mathrm{i}-b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}}{\frac{8\,\left(-1728\,a^{11}+864\,a^{10}\,b+4752\,a^9\,b^2-2160\,a^8\,b^3-4356\,a^7\,b^4+1746\,a^6\,b^5+1495\,a^5\,b^6-491\,a^4\,b^7-169\,a^3\,b^8+30\,a^2\,b^9+6\,a\,b^{10}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{10}-288\,a^9\,b-624\,a^8\,b^2+624\,a^7\,b^3+386\,a^6\,b^4-386\,a^5\,b^5-61\,a^4\,b^6+52\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{4\,\left(-48\,a^7\,b^{10}+24\,a^6\,b^{11}+124\,a^5\,b^{12}-56\,a^4\,b^{13}-100\,a^3\,b^{14}+36\,a^2\,b^{15}+24\,a\,b^{16}-4\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-19\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{d\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(6*a^3*b - 5*a*b^3 + 12*a^4 + b^4 - 13*a^2*b^2))/(a*b^4 - b^5) + (tan(c/2 + (d*x)/2)^3*(4*a*b^4 + 18*a^4*b + 36*a^5 - 3*b^5 - 14*a^2*b^3 - 37*a^3*b^2))/((a*b^4 - b^5)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(4*a*b^4 - 18*a^4*b + 36*a^5 + 3*b^5 + 14*a^2*b^3 - 37*a^3*b^2))/((a*b^4 - b^5)*(a + b)) + (tan(c/2 + (d*x)/2)^7*(5*a*b^3 - 6*a^3*b + 12*a^4 + b^4 - 13*a^2*b^2))/(b^4*(a + b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(6*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^2*(4*a*b + 4*a^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 4*a^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan((((a^2*12i - b^2*1i)*((((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (4*tan(c/2 + (d*x)/2)*(a^2*12i - b^2*1i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(a^2*12i - b^2*1i))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*1i)/(2*b^5) - ((a^2*12i - b^2*1i)*((((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (4*tan(c/2 + (d*x)/2)*(a^2*12i - b^2*1i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(a^2*12i - b^2*1i))/(2*b^5) - (8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*1i)/(2*b^5))/((8*(6*a*b^10 + 864*a^10*b - 1728*a^11 + 30*a^2*b^9 - 169*a^3*b^8 - 491*a^4*b^7 + 1495*a^5*b^6 + 1746*a^6*b^5 - 4356*a^7*b^4 - 2160*a^8*b^3 + 4752*a^9*b^2))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + ((a^2*12i - b^2*1i)*((((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (4*tan(c/2 + (d*x)/2)*(a^2*12i - b^2*1i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(a^2*12i - b^2*1i))/(2*b^5) + (8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))/(2*b^5) + ((a^2*12i - b^2*1i)*((((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (4*tan(c/2 + (d*x)/2)*(a^2*12i - b^2*1i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*(a^2*12i - b^2*1i))/(2*b^5) - (8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))/(2*b^5)))*(a^2*12i - b^2*1i)*1i)/(b^5*d) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a*((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*1i)/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)) + (a*((8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a*((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*1i)/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))/((8*(6*a*b^10 + 864*a^10*b - 1728*a^11 + 30*a^2*b^9 - 169*a^3*b^8 - 491*a^4*b^7 + 1495*a^5*b^6 + 1746*a^6*b^5 - 4356*a^7*b^4 - 2160*a^8*b^3 + 4752*a^9*b^2))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (a*((8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a*((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)) - (a*((8*tan(c/2 + (d*x)/2)*(288*a^10 - 288*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 + 52*a^3*b^7 - 61*a^4*b^6 - 386*a^5*b^5 + 386*a^6*b^4 + 624*a^7*b^3 - 624*a^8*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a*((4*(24*a*b^16 - 4*b^17 + 36*a^2*b^15 - 100*a^3*b^14 - 56*a^4*b^13 + 124*a^5*b^12 + 24*a^6*b^11 - 48*a^7*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2))/(2*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 6*b^4 - 19*a^2*b^2)*1i)/(d*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))","B"
612,1,3380,182,8.228519,"\text{Not used}","int(-(cos(c + d*x)^2*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-6\,a^3-3\,a^2\,b+6\,a\,b^2+2\,b^3\right)}{a\,b^3-b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-6\,a^3+3\,a^2\,b+6\,a\,b^2-2\,b^3\right)}{b^3\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^4-7\,a^2\,b^2+2\,b^4\right)}{b^3\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+2\,a\,b-b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^2+2\,a\,b+b^2\right)\right)}+\frac{6\,a\,\mathrm{atan}\left(\frac{\frac{3\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}+\frac{3\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}}{\frac{16\,\left(108\,a^8-54\,a^7\,b-270\,a^6\,b^2+117\,a^5\,b^3+198\,a^4\,b^4-72\,a^3\,b^5-36\,a^2\,b^6+12\,a\,b^7\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}}\right)}{b^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(108\,a^8-54\,a^7\,b-270\,a^6\,b^2+117\,a^5\,b^3+198\,a^4\,b^4-72\,a^3\,b^5-36\,a^2\,b^6+12\,a\,b^7\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^8-72\,a^7\,b-144\,a^6\,b^2+144\,a^5\,b^3+69\,a^4\,b^4-72\,a^3\,b^5+4\,b^8\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(-12\,a^6\,b^8+6\,a^5\,b^9+30\,a^4\,b^{10}-14\,a^3\,b^{11}-22\,a^2\,b^{12}+8\,a\,b^{13}+4\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,a^4-\frac{9\,a^2\,b^2}{2}+b^4\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(6*a*b^2 - 3*a^2*b - 6*a^3 + 2*b^3))/(a*b^3 - b^4) + (tan(c/2 + (d*x)/2)^5*(6*a*b^2 + 3*a^2*b - 6*a^3 - 2*b^3))/(b^3*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(6*a^4 + 2*b^4 - 7*a^2*b^2))/(b^3*(a + b)*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) + (6*a*atan(((3*a*((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a*tan(c/2 + (d*x)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*24i)/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*3i)/b^4))/b^4 + (3*a*((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (a*tan(c/2 + (d*x)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*24i)/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*3i)/b^4))/b^4)/((16*(12*a*b^7 - 54*a^7*b + 108*a^8 - 36*a^2*b^6 - 72*a^3*b^5 + 198*a^4*b^4 + 117*a^5*b^3 - 270*a^6*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a*((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a*tan(c/2 + (d*x)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*24i)/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*3i)/b^4)*3i)/b^4 + (a*((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (a*tan(c/2 + (d*x)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*24i)/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*3i)/b^4)*3i)/b^4)))/(b^4*d) + (atan(((((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(12*a*b^7 - 54*a^7*b + 108*a^8 - 36*a^2*b^6 - 72*a^3*b^5 + 198*a^4*b^4 + 117*a^5*b^3 - 270*a^6*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*a^8 - 72*a^7*b + 4*b^8 - 72*a^3*b^5 + 69*a^4*b^4 + 144*a^5*b^3 - 144*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(8*a*b^13 + 4*b^14 - 22*a^2*b^12 - 14*a^3*b^11 + 30*a^4*b^10 + 6*a^5*b^9 - 12*a^6*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*a^4 + b^4 - (9*a^2*b^2)/2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
613,1,3095,149,7.030829,"\text{Not used}","int(-(cos(c + d*x)*(cos(c + d*x)^2 - 1))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+a\,b-2\,b^2\right)}{a\,b^2-b^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-2\,a^2+a\,b+2\,b^2\right)}{b^2\,\left(a+b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,1{}\mathrm{i}}{b^3}}{b^3}-\frac{-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,1{}\mathrm{i}}{b^3}}{b^3}}{\frac{16\,\left(4\,a^5-2\,a^4\,b-10\,a^3\,b^2+3\,a^2\,b^3+6\,a\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}\right)}{b^3\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}}{\frac{16\,\left(4\,a^5-2\,a^4\,b-10\,a^3\,b^2+3\,a^2\,b^3+6\,a\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}-\frac{a\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^6-8\,a^5\,b-16\,a^4\,b^2+16\,a^3\,b^3+5\,a^2\,b^4-8\,a\,b^5+4\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{8\,\left(4\,a^5\,b^6-2\,a^4\,b^7-10\,a^3\,b^8+6\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^6+8\,a^5\,b^7+16\,a^4\,b^8-16\,a^3\,b^9-8\,a^2\,b^{10}+8\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)}{2\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(a*b + 2*a^2 - 2*b^2))/(a*b^2 - b^3) - (tan(c/2 + (d*x)/2)^3*(a*b - 2*a^2 + 2*b^2))/(b^2*(a + b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (2*atan((((((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (tan(c/2 + (d*x)/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6)*8i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))/b^3 - ((((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (tan(c/2 + (d*x)/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6)*8i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))/b^3)/((16*(6*a*b^4 - 2*a^4*b + 4*a^5 + 3*a^2*b^3 - 10*a^3*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (tan(c/2 + (d*x)/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6)*8i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))*1i)/b^3 + (((((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (tan(c/2 + (d*x)/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6)*8i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))*1i)/b^3)))/(b^3*d) - (a*atan(((a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (4*a*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*1i)/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (4*a*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*1i)/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))/((16*(6*a*b^4 - 2*a^4*b + 4*a^5 + 3*a^2*b^3 - 10*a^3*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (4*a*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)) - (a*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*a^6 - 8*a^5*b - 8*a*b^5 + 4*b^6 + 5*a^2*b^4 + 16*a^3*b^3 - 16*a^4*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((8*(6*a*b^10 - 4*b^11 + 6*a^2*b^9 - 10*a^3*b^8 - 2*a^4*b^7 + 4*a^5*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (4*a*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^11 - 8*a^2*b^10 - 16*a^3*b^9 + 16*a^4*b^8 + 8*a^5*b^7 - 8*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))/(2*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
614,1,148,117,2.829043,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(a + b*cos(c + d*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a+b}\,\sqrt{a-b}}\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a-b}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a+b}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"atan((tan(c/2 + (d*x)/2)*(2*a - 2*b))/(2*(a + b)^(1/2)*(a - b)^(1/2)))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (tan(c/2 + (d*x)/2)/(a - b) - tan(c/2 + (d*x)/2)^3/(a + b))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
615,1,3083,155,6.990287,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^2+a\,b+2\,b^2\right)}{a^2\,b-a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^2+a\,b-2\,b^2\right)}{a^2\,\left(a+b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}\right)\,1{}\mathrm{i}}{a^3}-\frac{\left(\frac{\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}\right)\,1{}\mathrm{i}}{a^3}}{\frac{\frac{\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}}{a^3}-\frac{16\,\left(6\,a^4\,b+3\,a^3\,b^2-10\,a^2\,b^3-2\,a\,b^4+4\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\frac{\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}}{a^3}}\right)\,2{}\mathrm{i}}{a^3\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}+\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}}{\frac{16\,\left(6\,a^4\,b+3\,a^3\,b^2-10\,a^2\,b^3-2\,a\,b^4+4\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}-\frac{b\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-8\,a^5\,b+5\,a^4\,b^2+16\,a^3\,b^3-16\,a^2\,b^4-8\,a\,b^5+8\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{8\,\left(-4\,a^{11}+6\,a^{10}\,b+6\,a^9\,b^2-10\,a^8\,b^3-2\,a^7\,b^4+4\,a^6\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{11}\,b-8\,a^{10}\,b^2-16\,a^9\,b^3+16\,a^8\,b^4+8\,a^7\,b^5-8\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)}{2\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(a*b - 2*a^2 + 2*b^2))/(a^2*b - a^3) + (tan(c/2 + (d*x)/2)^3*(a*b + 2*a^2 - 2*b^2))/(a^2*(a + b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (atan((((((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (8*tan(c/2 + (d*x)/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2))*1i)/a^3 - ((((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2))*1i)/a^3)/((((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (8*tan(c/2 + (d*x)/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2))/a^3 - (16*(6*a^4*b - 2*a*b^4 + 4*b^5 - 10*a^2*b^3 + 3*a^3*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2))/a^3))*2i)/(a^3*d) - (b*atan(((b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (4*b*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*1i)/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)) + (b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (4*b*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*1i)/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))/((16*(6*a^4*b - 2*a*b^4 + 4*b^5 - 10*a^2*b^3 + 3*a^3*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (4*b*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)) - (b*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*a^6 - 8*a^5*b - 8*a*b^5 + 8*b^6 - 16*a^2*b^4 + 16*a^3*b^3 + 5*a^4*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((8*(6*a^10*b - 4*a^11 + 4*a^6*b^5 - 2*a^7*b^4 - 10*a^8*b^3 + 6*a^9*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (4*b*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^11*b - 8*a^6*b^6 + 8*a^7*b^5 + 16*a^8*b^4 - 16*a^9*b^3 - 8*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))))/(2*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
616,1,3376,204,8.284543,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^3),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^3-6\,a^2\,b+3\,a\,b^2+6\,b^3\right)}{a^3\,b-a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-2\,a^3+6\,a^2\,b+3\,a\,b^2-6\,b^3\right)}{a^3\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^4-7\,a^2\,b^2+6\,b^4\right)}{a^3\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^2+2\,a\,b+3\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,a\,b-3\,b^2\right)\right)}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{3\,b\,\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}\right)\,3{}\mathrm{i}}{a^4}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{3\,b\,\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}\right)\,3{}\mathrm{i}}{a^4}}{\frac{16\,\left(-12\,a^7\,b+36\,a^6\,b^2+72\,a^5\,b^3-198\,a^4\,b^4-117\,a^3\,b^5+270\,a^2\,b^6+54\,a\,b^7-108\,b^8\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{3\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{3\,b\,\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}\right)}{a^4}-\frac{3\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{3\,b\,\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)}{a^4}\right)}{a^4}}\right)\,6{}\mathrm{i}}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{16\,\left(-12\,a^7\,b+36\,a^6\,b^2+72\,a^5\,b^3-198\,a^4\,b^4-117\,a^3\,b^5+270\,a^2\,b^6+54\,a\,b^7-108\,b^8\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^8-72\,a^5\,b^3+69\,a^4\,b^4+144\,a^3\,b^5-144\,a^2\,b^6-72\,a\,b^7+72\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(4\,a^{14}+8\,a^{13}\,b-22\,a^{12}\,b^2-14\,a^{11}\,b^3+30\,a^{10}\,b^4+6\,a^9\,b^5-12\,a^8\,b^6\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(3*a*b^2 - 6*a^2*b - 2*a^3 + 6*b^3))/(a^3*b - a^4) - (tan(c/2 + (d*x)/2)^5*(3*a*b^2 + 6*a^2*b - 2*a^3 - 6*b^3))/(a^3*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(2*a^4 + 6*b^4 - 7*a^2*b^2))/(a^3*(a + b)*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (3*b*((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (24*b*tan(c/2 + (d*x)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4)*3i)/a^4 + (b*((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (3*b*((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (24*b*tan(c/2 + (d*x)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4)*3i)/a^4)/((16*(54*a*b^7 - 12*a^7*b - 108*b^8 + 270*a^2*b^6 - 117*a^3*b^5 - 198*a^4*b^4 + 72*a^5*b^3 + 36*a^6*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (3*b*((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (3*b*((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (24*b*tan(c/2 + (d*x)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4))/a^4 - (3*b*((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (3*b*((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (24*b*tan(c/2 + (d*x)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/a^4))/a^4))*6i)/(a^4*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((16*(54*a*b^7 - 12*a^7*b - 108*b^8 + 270*a^2*b^6 - 117*a^3*b^5 - 198*a^4*b^4 + 72*a^5*b^3 + 36*a^6*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (((8*tan(c/2 + (d*x)/2)*(4*a^8 - 72*a*b^7 + 72*b^8 - 144*a^2*b^6 + 144*a^3*b^5 + 69*a^4*b^4 - 72*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(8*a^13*b + 4*a^14 - 12*a^8*b^6 + 6*a^9*b^5 + 30*a^10*b^4 - 14*a^11*b^3 - 22*a^12*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
617,1,3990,271,9.105052,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-5\,a^3\,b-13\,a^2\,b^2+6\,a\,b^3+12\,b^4\right)}{a^4\,b-a^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-3\,a^5+4\,a^4\,b-14\,a^3\,b^2-37\,a^2\,b^3+18\,a\,b^4+36\,b^5\right)}{\left(a^4\,b-a^5\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^5+4\,a^4\,b+14\,a^3\,b^2-37\,a^2\,b^3-18\,a\,b^4+36\,b^5\right)}{\left(a^4\,b-a^5\right)\,\left(a+b\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^4+5\,a^3\,b-13\,a^2\,b^2-6\,a\,b^3+12\,b^4\right)}{a^4\,\left(a+b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-6\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,b^2+4\,a\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-12\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2-12\,b^2\right)}{2\,a^5}\right)\,\left(a^2-12\,b^2\right)\,1{}\mathrm{i}}{2\,a^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-12\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2-12\,b^2\right)}{2\,a^5}\right)\,\left(a^2-12\,b^2\right)\,1{}\mathrm{i}}{2\,a^5}}{\frac{8\,\left(6\,a^{10}\,b+30\,a^9\,b^2-169\,a^8\,b^3-491\,a^7\,b^4+1495\,a^6\,b^5+1746\,a^5\,b^6-4356\,a^4\,b^7-2160\,a^3\,b^8+4752\,a^2\,b^9+864\,a\,b^{10}-1728\,b^{11}\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-12\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2-12\,b^2\right)}{2\,a^5}\right)\,\left(a^2-12\,b^2\right)}{2\,a^5}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-12\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2-12\,b^2\right)}{2\,a^5}\right)\,\left(a^2-12\,b^2\right)}{2\,a^5}}\right)\,\left(a^2-12\,b^2\right)\,1{}\mathrm{i}}{a^5\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}}{\frac{8\,\left(6\,a^{10}\,b+30\,a^9\,b^2-169\,a^8\,b^3-491\,a^7\,b^4+1495\,a^6\,b^5+1746\,a^5\,b^6-4356\,a^4\,b^7-2160\,a^3\,b^8+4752\,a^2\,b^9+864\,a\,b^{10}-1728\,b^{11}\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"(atan(((((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2 - 12*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2 - 12*b^2))/(2*a^5))*(a^2 - 12*b^2)*1i)/(2*a^5) + (((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2 - 12*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2 - 12*b^2))/(2*a^5))*(a^2 - 12*b^2)*1i)/(2*a^5))/((8*(864*a*b^10 + 6*a^10*b - 1728*b^11 + 4752*a^2*b^9 - 2160*a^3*b^8 - 4356*a^4*b^7 + 1746*a^5*b^6 + 1495*a^6*b^5 - 491*a^7*b^4 - 169*a^8*b^3 + 30*a^9*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2 - 12*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2 - 12*b^2))/(2*a^5))*(a^2 - 12*b^2))/(2*a^5) - (((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2 - 12*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2 - 12*b^2))/(2*a^5))*(a^2 - 12*b^2))/(2*a^5)))*(a^2 - 12*b^2)*1i)/(a^5*d) - ((tan(c/2 + (d*x)/2)*(6*a*b^3 - 5*a^3*b + a^4 + 12*b^4 - 13*a^2*b^2))/(a^4*b - a^5) - (tan(c/2 + (d*x)/2)^3*(18*a*b^4 + 4*a^4*b - 3*a^5 + 36*b^5 - 37*a^2*b^3 - 14*a^3*b^2))/((a^4*b - a^5)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(4*a^4*b - 18*a*b^4 + 3*a^5 + 36*b^5 - 37*a^2*b^3 + 14*a^3*b^2))/((a^4*b - a^5)*(a + b)) - (tan(c/2 + (d*x)/2)^7*(5*a^3*b - 6*a*b^3 + a^4 + 12*b^4 - 13*a^2*b^2))/(a^4*(a + b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^4*(2*a^2 - 6*b^2) - tan(c/2 + (d*x)/2)^2*(4*a*b + 4*b^2) + tan(c/2 + (d*x)/2)^6*(4*a*b - 4*b^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*1i)/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*1i)/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))/((8*(864*a*b^10 + 6*a^10*b - 1728*b^11 + 4752*a^2*b^9 - 2160*a^3*b^8 - 4356*a^4*b^7 + 1746*a^5*b^6 + 1495*a^6*b^5 - 491*a^7*b^4 - 169*a^8*b^3 + 30*a^9*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)) - (b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))))*(-(a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*1i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
618,1,4231,335,9.192109,"\text{Not used}","int(-(cos(c + d*x)^2 - 1)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(3\,a^4\,b+9\,a^3\,b^2-23\,a^2\,b^3-10\,a\,b^4+20\,b^5\right)}{a^5\,\left(a+b\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^4\,b-9\,a^3\,b^2-23\,a^2\,b^3+10\,a\,b^4+20\,b^5\right)}{a^5\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(8\,a^6-34\,a^4\,b^2+197\,a^2\,b^4-180\,b^6\right)}{3\,a^5\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^6-a^5\,b-86\,a^3\,b^3-118\,a^2\,b^4+90\,a\,b^5+120\,b^6\right)}{3\,a^5\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,a^6+a^5\,b+86\,a^3\,b^3-118\,a^2\,b^4-90\,a\,b^5+120\,b^6\right)}{3\,a^5\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^2+4\,a\,b+10\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2+4\,a\,b-10\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+6\,a\,b+5\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-6\,a\,b+5\,b^2\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,b-20\,b^3\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{a^6\,\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)}\right)}{2\,a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}\right)\,1{}\mathrm{i}}{2\,a^6}-\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,b-20\,b^3\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{a^6\,\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)}\right)}{2\,a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}\right)\,1{}\mathrm{i}}{2\,a^6}}{\frac{8\,\left(108\,a^{10}\,b^4+324\,a^9\,b^5-1845\,a^8\,b^6-3411\,a^7\,b^7+10677\,a^6\,b^8+9870\,a^5\,b^9-24540\,a^4\,b^{10}-10800\,a^3\,b^{11}+23600\,a^2\,b^{12}+4000\,a\,b^{13}-8000\,b^{14}\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}+\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,b-20\,b^3\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{a^6\,\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)}\right)}{2\,a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}\right)}{2\,a^6}+\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{\left(3\,a^2\,b-20\,b^3\right)\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,b-20\,b^3\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{a^6\,\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)}\right)}{2\,a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}\right)}{2\,a^6}}\right)\,\left(3\,a^2\,b-20\,b^3\right)\,1{}\mathrm{i}}{a^6\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}-\frac{b^2\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}-\frac{4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}+\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}+\frac{b^2\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}+\frac{4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}}{\frac{8\,\left(108\,a^{10}\,b^4+324\,a^9\,b^5-1845\,a^8\,b^6-3411\,a^7\,b^7+10677\,a^6\,b^8+9870\,a^5\,b^9-24540\,a^4\,b^{10}-10800\,a^3\,b^{11}+23600\,a^2\,b^{12}+4000\,a\,b^{13}-8000\,b^{14}\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}-\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}-\frac{b^2\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}-\frac{4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}+\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{10}\,b^2-18\,a^9\,b^3+15\,a^8\,b^4+276\,a^7\,b^5-281\,a^6\,b^6-1298\,a^5\,b^7+1298\,a^4\,b^8+1840\,a^3\,b^9-1840\,a^2\,b^{10}-800\,a\,b^{11}+800\,b^{12}\right)}{a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3}+\frac{b^2\,\left(\frac{4\,\left(12\,a^{19}\,b-48\,a^{18}\,b^2-68\,a^{17}\,b^3+180\,a^{16}\,b^4+96\,a^{15}\,b^5-212\,a^{14}\,b^6-40\,a^{13}\,b^7+80\,a^{12}\,b^8\right)}{a^{18}+a^{17}\,b-a^{16}\,b^2-a^{15}\,b^3}+\frac{4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-16\,a^{15}\,b^3+16\,a^{14}\,b^4+8\,a^{13}\,b^5-8\,a^{12}\,b^6\right)}{\left(a^{13}+a^{12}\,b-a^{11}\,b^2-a^{10}\,b^3\right)\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)}{2\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(12\,a^4-33\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{d\,\left(a^{12}-3\,a^{10}\,b^2+3\,a^8\,b^4-a^6\,b^6\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^9*(3*a^4*b - 10*a*b^4 + 20*b^5 - 23*a^2*b^3 + 9*a^3*b^2))/(a^5*(a + b)) - (tan(c/2 + (d*x)/2)*(10*a*b^4 + 3*a^4*b + 20*b^5 - 23*a^2*b^3 - 9*a^3*b^2))/(a^5*(a - b)) + (2*tan(c/2 + (d*x)/2)^5*(8*a^6 - 180*b^6 + 197*a^2*b^4 - 34*a^4*b^2))/(3*a^5*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(90*a*b^5 - a^5*b + 4*a^6 + 120*b^6 - 118*a^2*b^4 - 86*a^3*b^3))/(3*a^5*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^7*(a^5*b - 90*a*b^5 + 4*a^6 + 120*b^6 - 118*a^2*b^4 + 86*a^3*b^3))/(3*a^5*(a + b)*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(4*a*b - 2*a^2 + 10*b^2) + tan(c/2 + (d*x)/2)^6*(4*a*b + 2*a^2 - 10*b^2) - tan(c/2 + (d*x)/2)^10*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^2*(6*a*b + a^2 + 5*b^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 6*a*b + 5*b^2))) + (atan((((3*a^2*b - 20*b^3)*(((3*a^2*b - 20*b^3)*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) - (4*tan(c/2 + (d*x)/2)*(3*a^2*b - 20*b^3)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/(a^6*(a^12*b + a^13 - a^10*b^3 - a^11*b^2))))/(2*a^6) - (8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2))*1i)/(2*a^6) - ((3*a^2*b - 20*b^3)*(((3*a^2*b - 20*b^3)*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) + (4*tan(c/2 + (d*x)/2)*(3*a^2*b - 20*b^3)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/(a^6*(a^12*b + a^13 - a^10*b^3 - a^11*b^2))))/(2*a^6) + (8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2))*1i)/(2*a^6))/((8*(4000*a*b^13 - 8000*b^14 + 23600*a^2*b^12 - 10800*a^3*b^11 - 24540*a^4*b^10 + 9870*a^5*b^9 + 10677*a^6*b^8 - 3411*a^7*b^7 - 1845*a^8*b^6 + 324*a^9*b^5 + 108*a^10*b^4))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) + ((3*a^2*b - 20*b^3)*(((3*a^2*b - 20*b^3)*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) - (4*tan(c/2 + (d*x)/2)*(3*a^2*b - 20*b^3)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/(a^6*(a^12*b + a^13 - a^10*b^3 - a^11*b^2))))/(2*a^6) - (8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2)))/(2*a^6) + ((3*a^2*b - 20*b^3)*(((3*a^2*b - 20*b^3)*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) + (4*tan(c/2 + (d*x)/2)*(3*a^2*b - 20*b^3)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/(a^6*(a^12*b + a^13 - a^10*b^3 - a^11*b^2))))/(2*a^6) + (8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2)))/(2*a^6)))*(3*a^2*b - 20*b^3)*1i)/(a^6*d) - (b^2*atan(((b^2*((8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2) - (b^2*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) - (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/((a^12*b + a^13 - a^10*b^3 - a^11*b^2)*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2))/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2)*1i)/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)) + (b^2*((8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2) + (b^2*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) + (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/((a^12*b + a^13 - a^10*b^3 - a^11*b^2)*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2))/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2)*1i)/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))/((8*(4000*a*b^13 - 8000*b^14 + 23600*a^2*b^12 - 10800*a^3*b^11 - 24540*a^4*b^10 + 9870*a^5*b^9 + 10677*a^6*b^8 - 3411*a^7*b^7 - 1845*a^8*b^6 + 324*a^9*b^5 + 108*a^10*b^4))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) - (b^2*((8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2) - (b^2*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) - (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/((a^12*b + a^13 - a^10*b^3 - a^11*b^2)*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2))/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2))/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)) + (b^2*((8*tan(c/2 + (d*x)/2)*(800*b^12 - 800*a*b^11 - 1840*a^2*b^10 + 1840*a^3*b^9 + 1298*a^4*b^8 - 1298*a^5*b^7 - 281*a^6*b^6 + 276*a^7*b^5 + 15*a^8*b^4 - 18*a^9*b^3 + 9*a^10*b^2))/(a^12*b + a^13 - a^10*b^3 - a^11*b^2) + (b^2*((4*(12*a^19*b + 80*a^12*b^8 - 40*a^13*b^7 - 212*a^14*b^6 + 96*a^15*b^5 + 180*a^16*b^4 - 68*a^17*b^3 - 48*a^18*b^2))/(a^17*b + a^18 - a^15*b^3 - a^16*b^2) + (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2)*(8*a^17*b - 8*a^12*b^6 + 8*a^13*b^5 + 16*a^14*b^4 - 16*a^15*b^3 - 8*a^16*b^2))/((a^12*b + a^13 - a^10*b^3 - a^11*b^2)*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2))/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2))/(2*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2))))*(-(a + b)^3*(a - b)^3)^(1/2)*(12*a^4 + 20*b^4 - 33*a^2*b^2)*1i)/(d*(a^12 - a^6*b^6 + 3*a^8*b^4 - 3*a^10*b^2))","B"
619,1,19,16,1.457655,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x)),x)","-\frac{b\,\sin\left(c+d\,x\right)-a\,d\,x}{d}","Not used",1,"-(b*sin(c + d*x) - a*d*x)/d","B"
620,1,69,54,1.650400,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^2,x)","-x-\frac{4\,a\,\mathrm{atanh}\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}\right)}{d\,\sqrt{b^2-a^2}}","Not used",1,"- x - (4*a*atanh((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))))/(d*(b^2 - a^2)^(1/2))","B"
621,1,106,93,1.624309,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^3,x)","\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a+b}\,\sqrt{a-b}}\right)\,\left(a^2+b^2\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a+b\right)\,\left(a-b\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*atan((tan(c/2 + (d*x)/2)*(2*a - 2*b))/(2*(a + b)^(1/2)*(a - b)^(1/2)))*(a^2 + b^2))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (4*a*b*tan(c/2 + (d*x)/2))/(d*(a + b)*(a - b)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
622,1,242,140,4.135587,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^4,x)","\frac{2\,a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}\,\left(a^3+2\,a\,b^2\right)}\right)\,\left(a^2+2\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2\,b+a\,b^2+b^3\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2\,b-a\,b^2+b^3\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"(2*a*atan((a*tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)*(2*a*b^2 + a^3)))*(a^2 + 2*b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((2*tan(c/2 + (d*x)/2)^3*(a*b^2 + 3*a^2*b + b^3))/((a + b)^2*(a - b)) + (2*tan(c/2 + (d*x)/2)*(3*a^2*b - a*b^2 + b^3))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
623,0,-1,364,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
624,0,-1,291,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
625,0,-1,218,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
626,0,-1,231,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
627,0,-1,205,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
628,0,-1,277,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
629,0,-1,365,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^4, x)","F"
630,0,-1,443,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
631,0,-1,356,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
632,0,-1,285,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
633,0,-1,281,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
634,0,-1,270,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
635,0,-1,276,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
636,0,-1,365,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^4, x)","F"
637,0,-1,436,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^5,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^5, x)","F"
638,0,-1,523,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2), x)","F"
639,0,-1,435,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2), x)","F"
640,0,-1,350,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2), x)","F"
641,0,-1,342,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
642,0,-1,327,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
643,0,-1,329,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^3, x)","F"
644,0,-1,363,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^4, x)","F"
645,0,-1,437,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^5,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^5, x)","F"
646,0,-1,246,0.000000,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(a^2-b^2\,{\cos\left(c+d\,x\right)}^2\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a^2 - b^2*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
647,0,-1,197,0.000000,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(a^2-b^2\,{\cos\left(c+d\,x\right)}^2\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a^2 - b^2*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
648,0,-1,378,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
649,0,-1,305,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
650,0,-1,233,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
651,1,171,174,1.671434,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{3\,b\,d}+\frac{2\,C\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}\,\left(\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(2\,a^2+b^2\right)-2\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)\right)}{3\,b^2\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2)) + (2*C*sin(c + d*x)*(a + b*cos(c + d*x))^(1/2))/(3*b*d) + (2*C*((a + b*cos(c + d*x))/(a + b))^(1/2)*(ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*(2*a^2 + b^2) - 2*a*ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b)))/(3*b^2*d*(a + b*cos(c + d*x))^(1/2))","B"
652,0,-1,183,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\cos\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)), x)","F"
653,0,-1,214,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)), x)","F"
654,0,-1,278,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)), x)","F"
655,0,-1,370,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^(1/2)), x)","F"
656,0,-1,473,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
657,0,-1,375,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
658,0,-1,256,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
659,0,-1,202,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2), x)","F"
660,0,-1,259,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)), x)","F"
661,0,-1,296,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)), x)","F"
662,0,-1,370,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)), x)","F"
663,0,-1,521,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
664,0,-1,392,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
665,0,-1,314,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
666,0,-1,298,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2), x)","F"
667,0,-1,375,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)), x)","F"
668,0,-1,416,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)), x)","F"
669,0,-1,389,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(7/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(7/2), x)","F"
670,1,166,157,1.811372,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}-\frac{2\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}\,\left(\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(2\,a^2+b^2\right)-2\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)\right)}{3\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}-\frac{2\,b\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{3\,d}","Not used",1,"(2*a^2*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2)) - (2*((a + b*cos(c + d*x))/(a + b))^(1/2)*(ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*(2*a^2 + b^2) - 2*a*ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b)))/(3*d*(a + b*cos(c + d*x))^(1/2)) - (2*b*sin(c + d*x)*(a + b*cos(c + d*x))^(1/2))/(3*d)","B"
671,0,-1,116,0.000000,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{a^2-b^2\,{\cos\left(c+d\,x\right)}^2}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2), x)","F"
672,0,-1,165,0.000000,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{a^2-b^2\,{\cos\left(c+d\,x\right)}^2}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2), x)","F"
673,0,-1,243,0.000000,"\text{Not used}","int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(7/2),x)","\int \frac{a^2-b^2\,{\cos\left(c+d\,x\right)}^2}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a^2 - b^2*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(7/2), x)","F"
674,1,177,196,2.673844,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","-\frac{2\,A\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*A*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
675,1,166,165,2.357621,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
676,1,139,134,2.306394,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\frac{2\,A\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
677,1,112,101,0.747771,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
678,1,112,95,2.575527,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\frac{2\,C\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
679,1,123,95,3.286831,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(5/2),x)","\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
680,1,150,132,3.738631,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\frac{2\,C\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
681,1,177,165,4.356214,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(9/2),x)","\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
682,1,264,254,2.727346,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
683,1,240,205,2.643684,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
684,1,201,171,2.433223,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(1/2),x)","\frac{A\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(A*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a*b*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
685,1,186,166,2.981111,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(3/2),x)","\frac{2\,A\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,A\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*A*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
686,1,185,154,3.190493,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(5/2),x)","\frac{C\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
687,1,200,169,4.118879,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(7/2),x)","\frac{6\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,A\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*A*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*A*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
688,1,227,203,4.436053,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(9/2),x)","\frac{30\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,A\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,A\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(30*A*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*A*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 84*A*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
689,1,337,295,2.994881,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3,x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{2\,A\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + A*a^2*b*ellipticF(c/2 + (d*x)/2, 2) + A*a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (2*A*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
690,1,302,245,2.830515,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(1/2),x)","\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,A\,a\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*A*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (3*A*a*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2))","B"
691,1,274,244,2.817160,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(3/2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{A\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,A\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + C*a^2*b*ellipticF(c/2 + (d*x)/2, 2) + C*a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (A*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*A*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*A*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
692,1,256,218,3.570707,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(5/2),x)","\frac{2\,\left(A\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,C\,a\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*b^3*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (3*C*a*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (6*A*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
693,1,283,229,4.055262,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(7/2),x)","\frac{C\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,A\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*A*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
694,1,283,243,6.109942,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(9/2),x)","\frac{2\,\left(C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,A\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+\frac{6\,A\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*b^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + ((2*A*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*A*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 2*A*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + (6*A*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5)/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
695,1,312,293,6.225710,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(11/2),x)","\frac{70\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,A\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,A\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(70*A*a^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 210*A*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*A*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 270*A*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
696,1,677,382,3.565954,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4,x)","\frac{2\,A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{136\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{23}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{11\,C\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{42\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{21945\,d}-\frac{2\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{165\,C\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{52\,C\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{36\,C\,a^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{77\,C\,b^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{630\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{168\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{1155\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{13\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{9\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{117\,d}+\frac{4\,A\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{160\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{21}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{663\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{12\,A\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^4*ellipticE(c/2 + (d*x)/2, 2))/d - (136*hypergeom([1/2, 15/4], 23/4, cos(c + d*x)^2)*((11*C*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (9*C*a^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (42*C*a^2*b^2*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2)))/(21945*d) - (2*hypergeom([1/2, 15/4], 19/4, cos(c + d*x)^2)*((165*C*a^4*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (52*C*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (36*C*a^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (77*C*b^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (630*C*a^2*b^2*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (168*C*a^2*b^2*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2)))/(1155*d) - (8*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2)*((13*C*a^3*b*cos(c + d*x)^(9/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (9*C*a*b^3*cos(c + d*x)^(13/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (4*C*a^3*b*cos(c + d*x)^(13/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2)))/(117*d) + (4*A*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (8*A*a*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (160*C*a^3*b*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 21/4, cos(c + d*x)^2))/(663*d*(sin(c + d*x)^2)^(1/2)) - (12*A*a^2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
697,1,400,329,3.190636,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^(1/2),x)","\frac{2\,\left(A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,A\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,A\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,A\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*A*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + 2*A*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*A*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (8*A*a*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a^3*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2))","B"
698,1,374,320,3.300725,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^(3/2),x)","\frac{2\,C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,C\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,A\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{12\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*A*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*C*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*A*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*A*b^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (12*C*a^2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
699,1,343,300,3.495139,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^(5/2),x)","\frac{2\,\left(C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,C\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,C\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,C\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{2\,\left(A\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,A\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,b^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,A\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*C*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + 2*C*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*C*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (2*(A*b^4*ellipticF(c/2 + (d*x)/2, 2) + 12*A*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + A*b^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*A*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) + (8*A*a^3*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (8*C*a*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
700,1,355,321,4.986433,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^(7/2),x)","\frac{2\,A\,b^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,C\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,C\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*b^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*A*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (8*C*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*C*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (8*A*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (12*A*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
701,1,378,316,5.525520,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^(9/2),x)","\frac{2\,\left(C\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,C\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,b^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,C\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*b^4*ellipticF(c/2 + (d*x)/2, 2) + 12*C*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + C*b^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*C*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*b^4*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*A*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*A*a^3*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^3*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a^2*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
702,1,658,325,7.388439,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^(11/2),x)","\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{3\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,A\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{28\,A\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{45\,A\,b^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{216\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,C\,b^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,C\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{32\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(8*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((7*A*a*b^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (3*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((7*A*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (5*A*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (54*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((28*A*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (12*A*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*A*a^4*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2)) + (45*A*b^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (216*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (54*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (2*C*b^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*C*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (32*A*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (12*C*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
703,1,685,377,7.729922,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/cos(c + d*x)^(13/2),x)","\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{9\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{9\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{7\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{66\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{231\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{36\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{21\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{11/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{77\,A\,b^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{264\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{198\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{231\,d}+\frac{2\,C\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{32\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(8*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2)*((9*A*a*b^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (8*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2)*((9*A*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (7*A*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (66*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))))/(231*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((36*A*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (20*A*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (21*A*a^4*sin(c + d*x))/(cos(c + d*x)^(11/2)*(sin(c + d*x)^2)^(1/2)) + (77*A*b^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (264*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (198*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))))/(231*d) + (2*C*b^4*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) - (32*A*a^3*b*sin(c + d*x)*hypergeom([-5/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^3*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a^2*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
704,0,-1,299,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
705,0,-1,239,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
706,0,-1,181,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
707,0,-1,130,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
708,0,-1,85,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))), x)","F"
709,0,-1,112,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))), x)","F"
710,0,-1,140,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))), x)","F"
711,0,-1,206,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))), x)","F"
712,0,-1,270,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{9/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))), x)","F"
713,0,-1,344,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(11/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{11/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(11/2)*(a + b*cos(c + d*x))), x)","F"
714,0,-1,370,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
715,0,-1,292,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
716,0,-1,217,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
717,0,-1,214,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
718,0,-1,270,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
719,0,-1,336,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
720,0,-1,427,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^2), x)","F"
721,0,-1,433,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
722,0,-1,345,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
723,0,-1,348,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
724,0,-1,345,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
725,0,-1,417,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
726,0,-1,494,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
727,0,-1,553,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
728,0,-1,455,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
729,0,-1,439,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
730,0,-1,394,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2), x)","F"
731,0,-1,345,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2), x)","F"
732,0,-1,415,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(9/2), x)","F"
733,0,-1,638,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
734,0,-1,553,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
735,0,-1,509,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
736,0,-1,500,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2), x)","F"
737,0,-1,465,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2), x)","F"
738,0,-1,418,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(9/2), x)","F"
739,0,-1,502,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(11/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(11/2), x)","F"
740,0,-1,746,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2), x)","F"
741,0,-1,635,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
742,0,-1,609,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
743,0,-1,567,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
744,0,-1,606,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2), x)","F"
745,0,-1,540,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2), x)","F"
746,0,-1,504,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(11/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(11/2), x)","F"
747,0,-1,587,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(13/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{13/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(13/2), x)","F"
748,0,-1,554,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
749,0,-1,455,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
750,0,-1,393,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
751,0,-1,343,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
752,0,-1,283,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
753,0,-1,354,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
754,0,-1,429,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
755,0,-1,604,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
756,0,-1,503,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
757,0,-1,421,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
758,0,-1,308,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
759,0,-1,392,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
760,0,-1,494,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
761,0,-1,650,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
762,0,-1,563,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
763,0,-1,417,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
764,0,-1,449,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
765,0,-1,549,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
766,0,-1,318,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\int {\cos\left(c+d\,x\right)}^m\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(c + d*x)^m*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2, x)","F"
767,0,-1,217,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^m\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)), x)","F"
768,0,-1,353,0.000000,"\text{Not used}","int((cos(c + d*x)^m*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^m\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^m*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
769,0,-1,514,0.000000,"\text{Not used}","int((cos(c + d*x)^m*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^m\,\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^m*(A + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
770,1,117,105,1.957920,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\frac{B\,a\,x}{2}+\frac{3\,C\,b\,x}{8}+\frac{3\,B\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(B*a*x)/2 + (3*C*b*x)/8 + (3*B*b*sin(c + d*x))/(4*d) + (3*C*a*sin(c + d*x))/(4*d) + (B*a*sin(2*c + 2*d*x))/(4*d) + (B*b*sin(3*c + 3*d*x))/(12*d) + (C*a*sin(3*c + 3*d*x))/(12*d) + (C*b*sin(2*c + 2*d*x))/(4*d) + (C*b*sin(4*c + 4*d*x))/(32*d)","B"
771,1,84,84,1.762959,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\frac{B\,b\,x}{2}+\frac{C\,a\,x}{2}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(B*b*x)/2 + (C*a*x)/2 + (B*a*sin(c + d*x))/d + (3*C*b*sin(c + d*x))/(4*d) + (B*b*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d) + (C*b*sin(3*c + 3*d*x))/(12*d)","B"
772,1,50,52,1.659179,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x),x)","B\,a\,x+\frac{C\,b\,x}{2}+\frac{B\,b\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{C\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"B*a*x + (C*b*x)/2 + (B*b*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (C*b*sin(2*c + 2*d*x))/(4*d)","B"
773,1,100,35,1.786203,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^2,x)","\frac{C\,b\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(C*b*sin(c + d*x))/d + (2*B*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
774,1,114,35,1.831834,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{2\,C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(2*C*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (B*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (B*a*sin(c + d*x))/(d*cos(c + d*x))","B"
775,1,104,61,2.774317,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^4,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a+2\,B\,b+2\,C\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b-B\,a+2\,C\,a\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B\,a+2\,C\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(B*a + 2*B*b + 2*C*a) - tan(c/2 + (d*x)/2)^3*(2*B*b - B*a + 2*C*a))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (atanh(tan(c/2 + (d*x)/2))*(B*a + 2*C*b))/d","B"
776,1,145,93,4.011534,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^5,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(B\,b+C\,a\right)}{d}-\frac{\left(2\,B\,a-B\,b-C\,a+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,B\,a}{3}-4\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a+B\,b+C\,a+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(B*b + C*a))/d - (tan(c/2 + (d*x)/2)*(2*B*a + B*b + C*a + 2*C*b) - tan(c/2 + (d*x)/2)^3*((4*B*a)/3 + 4*C*b) + tan(c/2 + (d*x)/2)^5*(2*B*a - B*b - C*a + 2*C*b))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
777,1,194,114,5.330605,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^6,x)","\frac{\left(\frac{5\,B\,a}{4}-2\,B\,b-2\,C\,a+C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,B\,a}{4}+\frac{10\,B\,b}{3}+\frac{10\,C\,a}{3}-C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,B\,a}{4}-\frac{10\,B\,b}{3}-\frac{10\,C\,a}{3}-C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,B\,a}{4}+2\,B\,b+2\,C\,a+C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,B\,a}{4}+C\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*B*a)/4 + 2*B*b + 2*C*a + C*b) + tan(c/2 + (d*x)/2)^7*((5*B*a)/4 - 2*B*b - 2*C*a + C*b) - tan(c/2 + (d*x)/2)^3*((10*B*b)/3 - (3*B*a)/4 + (10*C*a)/3 + C*b) + tan(c/2 + (d*x)/2)^5*((3*B*a)/4 + (10*B*b)/3 + (10*C*a)/3 - C*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh(tan(c/2 + (d*x)/2))*((3*B*a)/4 + C*b))/d","B"
778,1,307,189,5.409491,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\frac{x\,\left(B\,a^2+\frac{3\,C\,a\,b}{2}+\frac{3\,B\,b^2}{4}\right)}{2}+\frac{\left(2\,C\,a^2-\frac{5\,B\,b^2}{4}-B\,a^2+2\,C\,b^2+4\,B\,a\,b-\frac{5\,C\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{16\,C\,a^2}{3}-\frac{B\,b^2}{2}-2\,B\,a^2+\frac{8\,C\,b^2}{3}+\frac{32\,B\,a\,b}{3}-C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,C\,a^2}{3}+\frac{40\,B\,a\,b}{3}+\frac{116\,C\,b^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,B\,a^2+\frac{B\,b^2}{2}+\frac{16\,C\,a^2}{3}+\frac{8\,C\,b^2}{3}+\frac{32\,B\,a\,b}{3}+C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B\,a^2+\frac{5\,B\,b^2}{4}+2\,C\,a^2+2\,C\,b^2+4\,B\,a\,b+\frac{5\,C\,a\,b}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*(B*a^2 + (3*B*b^2)/4 + (3*C*a*b)/2))/2 + (tan(c/2 + (d*x)/2)^5*((20*C*a^2)/3 + (116*C*b^2)/15 + (40*B*a*b)/3) - tan(c/2 + (d*x)/2)^9*(B*a^2 + (5*B*b^2)/4 - 2*C*a^2 - 2*C*b^2 - 4*B*a*b + (5*C*a*b)/2) + tan(c/2 + (d*x)/2)^3*(2*B*a^2 + (B*b^2)/2 + (16*C*a^2)/3 + (8*C*b^2)/3 + (32*B*a*b)/3 + C*a*b) - tan(c/2 + (d*x)/2)^7*(2*B*a^2 + (B*b^2)/2 - (16*C*a^2)/3 - (8*C*b^2)/3 - (32*B*a*b)/3 + C*a*b) + tan(c/2 + (d*x)/2)*(B*a^2 + (5*B*b^2)/4 + 2*C*a^2 + 2*C*b^2 + 4*B*a*b + (5*C*a*b)/2))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1))","B"
779,1,169,170,1.799157,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\frac{C\,a^2\,x}{2}+\frac{3\,C\,b^2\,x}{8}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+B\,a\,b\,x+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,C\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{B\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}","Not used",1,"(C*a^2*x)/2 + (3*C*b^2*x)/8 + (B*a^2*sin(c + d*x))/d + (3*B*b^2*sin(c + d*x))/(4*d) + B*a*b*x + (C*a^2*sin(2*c + 2*d*x))/(4*d) + (B*b^2*sin(3*c + 3*d*x))/(12*d) + (C*b^2*sin(2*c + 2*d*x))/(4*d) + (C*b^2*sin(4*c + 4*d*x))/(32*d) + (3*C*a*b*sin(c + d*x))/(2*d) + (B*a*b*sin(2*c + 2*d*x))/(2*d) + (C*a*b*sin(3*c + 3*d*x))/(6*d)","B"
780,1,115,107,1.651801,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x),x)","B\,a^2\,x+\frac{B\,b^2\,x}{2}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+C\,a\,b\,x+\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{2\,B\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"B*a^2*x + (B*b^2*x)/2 + (C*a^2*sin(c + d*x))/d + (3*C*b^2*sin(c + d*x))/(4*d) + C*a*b*x + (B*b^2*sin(2*c + 2*d*x))/(4*d) + (C*b^2*sin(3*c + 3*d*x))/(12*d) + (2*B*a*b*sin(c + d*x))/d + (C*a*b*sin(2*c + 2*d*x))/(2*d)","B"
781,1,169,86,1.963321,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{B\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{2\,C\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{4\,B\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(B*b^2*sin(c + d*x))/d + (2*B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b^2*sin(2*c + 2*d*x))/(4*d) + (2*C*a*b*sin(c + d*x))/d + (4*B*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
782,1,169,60,2.248032,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^3,x)","\frac{B\,a^2\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}+\frac{4\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{C\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{B\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}","Not used",1,"(B*a^2*tan(c + d*x))/d + (2*B*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (C*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (C*b^2*sin(2*c + 2*d*x))/(2*d*cos(c + d*x)) - (B*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (4*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
783,1,176,80,2.313414,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^4,x)","\frac{2\,\left(\frac{B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+B\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{2}+B\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + B*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((C*a^2*sin(2*c + 2*d*x))/2 + (B*a^2*sin(c + d*x))/2 + B*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
784,1,227,116,5.092101,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{C\,a^2}{2}+B\,a\,b+C\,b^2\right)}{2\,C\,a^2+4\,B\,a\,b+4\,C\,b^2}\right)\,\left(C\,a^2+2\,B\,a\,b+2\,C\,b^2\right)}{d}-\frac{\left(2\,B\,a^2+2\,B\,b^2-C\,a^2-2\,B\,a\,b+4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,B\,a^2}{3}-8\,C\,a\,b-4\,B\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a^2+2\,B\,b^2+C\,a^2+2\,B\,a\,b+4\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((C*a^2)/2 + C*b^2 + B*a*b))/(2*C*a^2 + 4*C*b^2 + 4*B*a*b))*(C*a^2 + 2*C*b^2 + 2*B*a*b))/d - (tan(c/2 + (d*x)/2)*(2*B*a^2 + 2*B*b^2 + C*a^2 + 2*B*a*b + 4*C*a*b) - tan(c/2 + (d*x)/2)^3*((4*B*a^2)/3 + 4*B*b^2 + 8*C*a*b) + tan(c/2 + (d*x)/2)^5*(2*B*a^2 + 2*B*b^2 - C*a^2 - 2*B*a*b + 4*C*a*b))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
785,1,314,156,5.282597,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,B\,a^2}{8}+C\,a\,b+\frac{B\,b^2}{2}\right)}{\frac{3\,B\,a^2}{2}+4\,C\,a\,b+2\,B\,b^2}\right)\,\left(\frac{3\,B\,a^2}{4}+2\,C\,a\,b+B\,b^2\right)}{d}+\frac{\left(\frac{5\,B\,a^2}{4}+B\,b^2-2\,C\,a^2-2\,C\,b^2-4\,B\,a\,b+2\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,B\,a^2}{4}-B\,b^2+\frac{10\,C\,a^2}{3}+6\,C\,b^2+\frac{20\,B\,a\,b}{3}-2\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,B\,a^2}{4}-B\,b^2-\frac{10\,C\,a^2}{3}-6\,C\,b^2-\frac{20\,B\,a\,b}{3}-2\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,B\,a^2}{4}+B\,b^2+2\,C\,a^2+2\,C\,b^2+4\,B\,a\,b+2\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((3*B*a^2)/8 + (B*b^2)/2 + C*a*b))/((3*B*a^2)/2 + 2*B*b^2 + 4*C*a*b))*((3*B*a^2)/4 + B*b^2 + 2*C*a*b))/d + (tan(c/2 + (d*x)/2)^7*((5*B*a^2)/4 + B*b^2 - 2*C*a^2 - 2*C*b^2 - 4*B*a*b + 2*C*a*b) - tan(c/2 + (d*x)/2)^3*(B*b^2 - (3*B*a^2)/4 + (10*C*a^2)/3 + 6*C*b^2 + (20*B*a*b)/3 + 2*C*a*b) + tan(c/2 + (d*x)/2)^5*((3*B*a^2)/4 - B*b^2 + (10*C*a^2)/3 + 6*C*b^2 + (20*B*a*b)/3 - 2*C*a*b) + tan(c/2 + (d*x)/2)*((5*B*a^2)/4 + B*b^2 + 2*C*a^2 + 2*C*b^2 + 4*B*a*b + 2*C*a*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
786,1,277,243,2.027766,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3,x)","\frac{3\,B\,b^3\,x}{8}+\frac{C\,a^3\,x}{2}+\frac{3\,B\,a^2\,b\,x}{2}+\frac{9\,C\,a\,b^2\,x}{8}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,C\,b^3\,\sin\left(c+d\,x\right)}{8\,d}+\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{5\,C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{C\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,C\,a\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{9\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{9\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(3*B*b^3*x)/8 + (C*a^3*x)/2 + (3*B*a^2*b*x)/2 + (9*C*a*b^2*x)/8 + (B*a^3*sin(c + d*x))/d + (5*C*b^3*sin(c + d*x))/(8*d) + (B*b^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(2*c + 2*d*x))/(4*d) + (B*b^3*sin(4*c + 4*d*x))/(32*d) + (5*C*b^3*sin(3*c + 3*d*x))/(48*d) + (C*b^3*sin(5*c + 5*d*x))/(80*d) + (3*B*a^2*b*sin(2*c + 2*d*x))/(4*d) + (B*a*b^2*sin(3*c + 3*d*x))/(4*d) + (3*C*a*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*b*sin(3*c + 3*d*x))/(4*d) + (3*C*a*b^2*sin(4*c + 4*d*x))/(32*d) + (9*B*a*b^2*sin(c + d*x))/(4*d) + (9*C*a^2*b*sin(c + d*x))/(4*d)","B"
787,1,202,171,1.844321,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x),x)","B\,a^3\,x+\frac{3\,C\,b^3\,x}{8}+\frac{3\,B\,a\,b^2\,x}{2}+\frac{3\,C\,a^2\,b\,x}{2}+\frac{3\,B\,b^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{B\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,C\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,B\,a^2\,b\,\sin\left(c+d\,x\right)}{d}+\frac{9\,C\,a\,b^2\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"B*a^3*x + (3*C*b^3*x)/8 + (3*B*a*b^2*x)/2 + (3*C*a^2*b*x)/2 + (3*B*b^3*sin(c + d*x))/(4*d) + (C*a^3*sin(c + d*x))/d + (B*b^3*sin(3*c + 3*d*x))/(12*d) + (C*b^3*sin(2*c + 2*d*x))/(4*d) + (C*b^3*sin(4*c + 4*d*x))/(32*d) + (3*B*a*b^2*sin(2*c + 2*d*x))/(4*d) + (3*C*a^2*b*sin(2*c + 2*d*x))/(4*d) + (C*a*b^2*sin(3*c + 3*d*x))/(4*d) + (3*B*a^2*b*sin(c + d*x))/d + (9*C*a*b^2*sin(c + d*x))/(4*d)","B"
788,1,1924,137,3.252621,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{\left(2\,C\,b^3-B\,b^3+6\,B\,a\,b^2-3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(12\,C\,a^2\,b+12\,B\,a\,b^2+\frac{4\,C\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(B\,b^3+2\,C\,b^3+6\,B\,a\,b^2+3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)\,1{}\mathrm{i}-\left(\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)\,1{}\mathrm{i}}{\left(\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)+\left(\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,C\,a^3+3{}\mathrm{i}\,B\,a^2\,b+\frac{3{}\mathrm{i}\,C\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,B\,b^3}{2}\right)+64\,B\,C^2\,a^9-64\,B^2\,C\,a^9-192\,B^3\,a^8\,b+16\,B^3\,a^3\,b^6+192\,B^3\,a^5\,b^4-32\,B^3\,a^6\,b^3+576\,B^3\,a^7\,b^2+384\,B^2\,C\,a^8\,b+144\,B\,C^2\,a^5\,b^4+192\,B\,C^2\,a^7\,b^2+96\,B^2\,C\,a^4\,b^5+640\,B^2\,C\,a^6\,b^3-96\,B^2\,C\,a^7\,b^2}\right)\,\left(2\,C\,a^3+6\,B\,a^2\,b+3\,C\,a\,b^2+B\,b^3\right)}{d}-\frac{B\,a^3\,\mathrm{atan}\left(\frac{B\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)+B\,a^3\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}+B\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)-B\,a^3\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\right)\,1{}\mathrm{i}}{64\,B\,C^2\,a^9-64\,B^2\,C\,a^9-192\,B^3\,a^8\,b+16\,B^3\,a^3\,b^6+192\,B^3\,a^5\,b^4-32\,B^3\,a^6\,b^3+576\,B^3\,a^7\,b^2+B\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)+B\,a^3\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\right)-B\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)-B\,a^3\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,B\,a^2\,b+48\,C\,a\,b^2\right)\right)+384\,B^2\,C\,a^8\,b+144\,B\,C^2\,a^5\,b^4+192\,B\,C^2\,a^7\,b^2+96\,B^2\,C\,a^4\,b^5+640\,B^2\,C\,a^6\,b^3-96\,B^2\,C\,a^7\,b^2}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(2*C*b^3 - B*b^3 + 6*B*a*b^2 - 3*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)*(B*b^3 + 2*C*b^3 + 6*B*a*b^2 + 3*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*((4*C*b^3)/3 + 12*B*a*b^2 + 12*C*a^2*b))/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) + (atan(((((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2) + tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3))*((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2)*1i - (((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2) - tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3))*((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2)*1i)/((((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2) + tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3))*((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2) + (((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2) - tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3))*((B*b^3*1i)/2 + C*a^3*1i + B*a^2*b*3i + (C*a*b^2*3i)/2) + 64*B*C^2*a^9 - 64*B^2*C*a^9 - 192*B^3*a^8*b + 16*B^3*a^3*b^6 + 192*B^3*a^5*b^4 - 32*B^3*a^6*b^3 + 576*B^3*a^7*b^2 + 384*B^2*C*a^8*b + 144*B*C^2*a^5*b^4 + 192*B*C^2*a^7*b^2 + 96*B^2*C*a^4*b^5 + 640*B^2*C*a^6*b^3 - 96*B^2*C*a^7*b^2))*(B*b^3 + 2*C*a^3 + 6*B*a^2*b + 3*C*a*b^2))/d - (B*a^3*atan((B*a^3*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3) + B*a^3*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2))*1i + B*a^3*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3) - B*a^3*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2))*1i)/(64*B*C^2*a^9 - 64*B^2*C*a^9 - 192*B^3*a^8*b + 16*B^3*a^3*b^6 + 192*B^3*a^5*b^4 - 32*B^3*a^6*b^3 + 576*B^3*a^7*b^2 + B*a^3*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3) + B*a^3*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2)) - B*a^3*(tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 48*B*C*a*b^5 + 192*B*C*a^5*b + 320*B*C*a^3*b^3) - B*a^3*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*B*a^2*b + 48*C*a*b^2)) + 384*B^2*C*a^8*b + 144*B*C^2*a^5*b^4 + 192*B*C^2*a^7*b^2 + 96*B^2*C*a^4*b^5 + 640*B^2*C*a^6*b^3 - 96*B^2*C*a^7*b^2))*2i)/d","B"
789,1,236,131,2.654801,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^3,x)","\frac{C\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+6\,B\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+6\,C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}-B\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}}{d}+\frac{\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+B\,a^3\,\sin\left(c+d\,x\right)+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{8}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(C*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i + 6*B*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - B*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i + 6*C*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + ((B*b^3*sin(2*c + 2*d*x))/2 + (C*b^3*sin(3*c + 3*d*x))/8 + B*a^3*sin(c + d*x) + (C*b^3*sin(c + d*x))/8 + (3*C*a*b^2*sin(2*c + 2*d*x))/2)/(d*cos(c + d*x))","B"
790,1,249,124,2.842520,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^4,x)","\frac{\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{4}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{2\,\left(\frac{B\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2}-B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+B\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}-3\,C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}\right)}{d}","Not used",1,"((C*a^3*sin(2*c + 2*d*x))/2 + (C*b^3*sin(3*c + 3*d*x))/4 + (B*a^3*sin(c + d*x))/2 + (C*b^3*sin(c + d*x))/4 + (3*B*a^2*b*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*((B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/2 - B*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i - 3*C*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i))/d","B"
791,1,526,145,3.299400,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{4}-\frac{B\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{2}-\frac{C\,a^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{4}+\frac{3\,C\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{3\,B\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4}-\frac{B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{2}-\frac{C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{4}+\frac{C\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{B\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{4}-\frac{C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,3{}\mathrm{i}}{2}-\frac{B\,a^2\,b\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{4}-\frac{C\,a\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,9{}\mathrm{i}}{2}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((B*a^3*sin(3*c + 3*d*x))/6 + (C*a^3*sin(2*c + 2*d*x))/4 + (B*a^3*sin(c + d*x))/2 + (3*B*a*b^2*sin(c + d*x))/4 + (3*C*a^2*b*sin(c + d*x))/4 - (B*b^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/2 - (C*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/4 + (3*C*b^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (3*B*a^2*b*sin(2*c + 2*d*x))/4 + (3*B*a*b^2*sin(3*c + 3*d*x))/4 + (3*C*a^2*b*sin(3*c + 3*d*x))/4 - (B*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/2 - (C*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/4 + (C*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (B*a^2*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/4 - (C*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i)/2 - (B*a^2*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/4 - (C*a*b^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/2)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
792,1,395,188,5.393285,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,B\,a^3}{8}+\frac{3\,C\,a^2\,b}{2}+\frac{3\,B\,a\,b^2}{2}+C\,b^3\right)}{\frac{3\,B\,a^3}{2}+6\,C\,a^2\,b+6\,B\,a\,b^2+4\,C\,b^3}\right)\,\left(\frac{3\,B\,a^3}{4}+3\,C\,a^2\,b+3\,B\,a\,b^2+2\,C\,b^3\right)}{d}-\frac{\left(2\,B\,b^3-\frac{5\,B\,a^3}{4}+2\,C\,a^3-3\,B\,a\,b^2+6\,B\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(3\,B\,a\,b^2-6\,B\,b^3-\frac{10\,C\,a^3}{3}-\frac{3\,B\,a^3}{4}-10\,B\,a^2\,b-18\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,B\,b^3-\frac{3\,B\,a^3}{4}+\frac{10\,C\,a^3}{3}+3\,B\,a\,b^2+10\,B\,a^2\,b+18\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{5\,B\,a^3}{4}-2\,B\,b^3-2\,C\,a^3-3\,B\,a\,b^2-6\,B\,a^2\,b-6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((3*B*a^3)/8 + C*b^3 + (3*B*a*b^2)/2 + (3*C*a^2*b)/2))/((3*B*a^3)/2 + 4*C*b^3 + 6*B*a*b^2 + 6*C*a^2*b))*((3*B*a^3)/4 + 2*C*b^3 + 3*B*a*b^2 + 3*C*a^2*b))/d - (tan(c/2 + (d*x)/2)^7*(2*B*b^3 - (5*B*a^3)/4 + 2*C*a^3 - 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 - 3*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(6*B*b^3 - (3*B*a^3)/4 + (10*C*a^3)/3 + 3*B*a*b^2 + 10*B*a^2*b + 18*C*a*b^2 + 3*C*a^2*b) - tan(c/2 + (d*x)/2)^5*((3*B*a^3)/4 + 6*B*b^3 + (10*C*a^3)/3 - 3*B*a*b^2 + 10*B*a^2*b + 18*C*a*b^2 - 3*C*a^2*b) - tan(c/2 + (d*x)/2)*((5*B*a^3)/4 + 2*B*b^3 + 2*C*a^3 + 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
793,1,470,236,5.378867,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^7,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,C\,a^3}{8}+\frac{9\,B\,a^2\,b}{8}+\frac{3\,C\,a\,b^2}{2}+\frac{B\,b^3}{2}\right)}{\frac{3\,C\,a^3}{2}+\frac{9\,B\,a^2\,b}{2}+6\,C\,a\,b^2+2\,B\,b^3}\right)\,\left(\frac{3\,C\,a^3}{4}+\frac{9\,B\,a^2\,b}{4}+3\,C\,a\,b^2+B\,b^3\right)}{d}-\frac{\left(2\,B\,a^3-B\,b^3-\frac{5\,C\,a^3}{4}+2\,C\,b^3+6\,B\,a\,b^2-\frac{15\,B\,a^2\,b}{4}-3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,B\,b^3-\frac{8\,B\,a^3}{3}+\frac{C\,a^3}{2}-8\,C\,b^3-16\,B\,a\,b^2+\frac{3\,B\,a^2\,b}{2}+6\,C\,a\,b^2-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,B\,a^3}{15}+20\,C\,a^2\,b+20\,B\,a\,b^2+12\,C\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,B\,a^3}{3}-2\,B\,b^3-\frac{C\,a^3}{2}-8\,C\,b^3-16\,B\,a\,b^2-\frac{3\,B\,a^2\,b}{2}-6\,C\,a\,b^2-16\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,B\,a^3+B\,b^3+\frac{5\,C\,a^3}{4}+2\,C\,b^3+6\,B\,a\,b^2+\frac{15\,B\,a^2\,b}{4}+3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((B*b^3)/2 + (3*C*a^3)/8 + (9*B*a^2*b)/8 + (3*C*a*b^2)/2))/(2*B*b^3 + (3*C*a^3)/2 + (9*B*a^2*b)/2 + 6*C*a*b^2))*(B*b^3 + (3*C*a^3)/4 + (9*B*a^2*b)/4 + 3*C*a*b^2))/d - (tan(c/2 + (d*x)/2)*(2*B*a^3 + B*b^3 + (5*C*a^3)/4 + 2*C*b^3 + 6*B*a*b^2 + (15*B*a^2*b)/4 + 3*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((116*B*a^3)/15 + 12*C*b^3 + 20*B*a*b^2 + 20*C*a^2*b) + tan(c/2 + (d*x)/2)^9*(2*B*a^3 - B*b^3 - (5*C*a^3)/4 + 2*C*b^3 + 6*B*a*b^2 - (15*B*a^2*b)/4 - 3*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^3*((8*B*a^3)/3 + 2*B*b^3 + (C*a^3)/2 + 8*C*b^3 + 16*B*a*b^2 + (3*B*a^2*b)/2 + 6*C*a*b^2 + 16*C*a^2*b) - tan(c/2 + (d*x)/2)^7*((8*B*a^3)/3 - 2*B*b^3 - (C*a^3)/2 + 8*C*b^3 + 16*B*a*b^2 - (3*B*a^2*b)/2 - 6*C*a*b^2 + 16*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
794,1,4568,178,6.429584,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^2+2\,C\,a^2+2\,C\,b^2-2\,B\,a\,b-C\,a\,b\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,a^2-B\,b^2+2\,C\,b^2-2\,B\,a\,b+C\,a\,b\right)}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,C\,a^2-3\,B\,a\,b+C\,b^2\right)}{3\,b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}+\frac{\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}}{\frac{16\,\left(-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}-\frac{\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}}\right)\,\left(2\,a^2+b^2\right)\,\left(B\,b-C\,a\right)}{b^4\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,b^{13}+2\,B\,a^2\,b^{11}-6\,B\,a^3\,b^{10}+4\,B\,a^4\,b^9+2\,C\,a^2\,b^{11}-2\,C\,a^3\,b^{10}+6\,C\,a^4\,b^9-4\,C\,a^5\,b^8-2\,B\,a\,b^{12}-2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(B\,b-C\,a\right)}{b^6-a^2\,b^4}\right)}{b^6-a^2\,b^4}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(B*b^2 + 2*C*a^2 + 2*C*b^2 - 2*B*a*b - C*a*b))/b^3 + (tan(c/2 + (d*x)/2)^5*(2*C*a^2 - B*b^2 + 2*C*b^2 - 2*B*a*b + C*a*b))/b^3 + (4*tan(c/2 + (d*x)/2)^3*(3*C*a^2 + C*b^2 - 3*B*a*b))/(3*b^3))/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) + (atan((((2*a^2 + b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 + b^2)*(B*b - C*a)*1i)/(2*b^4)))/(2*b^4) + ((2*a^2 + b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 + b^2)*(B*b - C*a)*1i)/(2*b^4)))/(2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2))/b^9 - ((2*a^2 + b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 + b^2)*(B*b - C*a)*1i)/(2*b^4))*1i)/(2*b^4) + ((2*a^2 + b^2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*(2*a^2 + b^2)*(B*b - C*a)*1i)/(2*b^4))*1i)/(2*b^4)))*(2*a^2 + b^2)*(B*b - C*a))/(b^4*d) + (a^3*atan(((a^3*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4) + (a^3*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2))/b^9 - (a^3*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4) + (a^3*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*b^13 + 2*B*a^2*b^11 - 6*B*a^3*b^10 + 4*B*a^4*b^9 + 2*C*a^2*b^11 - 2*C*a^3*b^10 + 6*C*a^4*b^9 - 4*C*a^5*b^8 - 2*B*a*b^12 - 2*C*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(B*b - C*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*2i)/(d*(b^6 - a^2*b^4))","B"
795,1,3761,134,5.433995,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b-2\,C\,a+C\,b\right)}{b^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a-2\,B\,b+C\,b\right)}{b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{2\,b^3}-\frac{\left(\frac{\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{2\,b^3}}{\frac{16\,\left(-4\,B^3\,a^5\,b^3+4\,B^3\,a^4\,b^4+12\,B^2\,C\,a^6\,b^2-14\,B^2\,C\,a^5\,b^3+6\,B^2\,C\,a^4\,b^4-4\,B^2\,C\,a^3\,b^5-12\,B\,C^2\,a^7\,b+16\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3+9\,B\,C^2\,a^4\,b^4-2\,B\,C^2\,a^3\,b^5+B\,C^2\,a^2\,b^6+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}+\frac{\left(\frac{\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^3}+\frac{\left(\frac{\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^7}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^3}}\right)\,\left(2{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{b^3\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}+\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)}{b^5-a^2\,b^3}\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}-\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)}{b^5-a^2\,b^3}\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}}{\frac{16\,\left(-4\,B^3\,a^5\,b^3+4\,B^3\,a^4\,b^4+12\,B^2\,C\,a^6\,b^2-14\,B^2\,C\,a^5\,b^3+6\,B^2\,C\,a^4\,b^4-4\,B^2\,C\,a^3\,b^5-12\,B\,C^2\,a^7\,b+16\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3+9\,B\,C^2\,a^4\,b^4-2\,B\,C^2\,a^3\,b^5+B\,C^2\,a^2\,b^6+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}+\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+12\,B^2\,a^3\,b^4-4\,B^2\,a^2\,b^5-16\,B\,C\,a^6\,b+32\,B\,C\,a^5\,b^2-28\,B\,C\,a^4\,b^3+20\,B\,C\,a^3\,b^4-12\,B\,C\,a^2\,b^5+4\,B\,C\,a\,b^6+8\,C^2\,a^7-16\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-16\,C^2\,a^4\,b^3+13\,C^2\,a^3\,b^4-7\,C^2\,a^2\,b^5+3\,C^2\,a\,b^6-C^2\,b^7\right)}{b^4}-\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{10}+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(B\,b-C\,a\right)\,2{}\mathrm{i}}{d\,\left(b^5-a^2\,b^3\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*B*b - 2*C*a + C*b))/b^2 - (tan(c/2 + (d*x)/2)^3*(2*C*a - 2*B*b + C*b))/b^2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (atan(((((((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (4*tan(c/2 + (d*x)/2)*(C*a^2*2i + C*b^2*1i - B*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2*2i + C*b^2*1i - B*a*b*2i))/(2*b^3) - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4)*(C*a^2*2i + C*b^2*1i - B*a*b*2i)*1i)/(2*b^3) - (((((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (4*tan(c/2 + (d*x)/2)*(C*a^2*2i + C*b^2*1i - B*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2*2i + C*b^2*1i - B*a*b*2i))/(2*b^3) + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4)*(C*a^2*2i + C*b^2*1i - B*a*b*2i)*1i)/(2*b^3))/((16*(4*C^3*a^8 - 6*C^3*a^7*b + 4*B^3*a^4*b^4 - 4*B^3*a^5*b^3 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - 12*B*C^2*a^7*b + B*C^2*a^2*b^6 - 2*B*C^2*a^3*b^5 + 9*B*C^2*a^4*b^4 - 12*B*C^2*a^5*b^3 + 16*B*C^2*a^6*b^2 - 4*B^2*C*a^3*b^5 + 6*B^2*C*a^4*b^4 - 14*B^2*C*a^5*b^3 + 12*B^2*C*a^6*b^2))/b^6 + (((((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (4*tan(c/2 + (d*x)/2)*(C*a^2*2i + C*b^2*1i - B*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2*2i + C*b^2*1i - B*a*b*2i))/(2*b^3) - (8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4)*(C*a^2*2i + C*b^2*1i - B*a*b*2i))/(2*b^3) + (((((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (4*tan(c/2 + (d*x)/2)*(C*a^2*2i + C*b^2*1i - B*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(C*a^2*2i + C*b^2*1i - B*a*b*2i))/(2*b^3) + (8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4)*(C*a^2*2i + C*b^2*1i - B*a*b*2i))/(2*b^3)))*(C*a^2*2i + C*b^2*1i - B*a*b*2i)*1i)/(b^3*d) + (a^2*atan(((a^2*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4 + (a^2*((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(-(a + b)*(a - b))^(1/2)*(B*b - C*a))/(b^5 - a^2*b^3))*1i)/(b^5 - a^2*b^3) + (a^2*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4 - (a^2*((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(-(a + b)*(a - b))^(1/2)*(B*b - C*a))/(b^5 - a^2*b^3))*1i)/(b^5 - a^2*b^3))/((16*(4*C^3*a^8 - 6*C^3*a^7*b + 4*B^3*a^4*b^4 - 4*B^3*a^5*b^3 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - 12*B*C^2*a^7*b + B*C^2*a^2*b^6 - 2*B*C^2*a^3*b^5 + 9*B*C^2*a^4*b^4 - 12*B*C^2*a^5*b^3 + 16*B*C^2*a^6*b^2 - 4*B^2*C*a^3*b^5 + 6*B^2*C*a^4*b^4 - 14*B^2*C*a^5*b^3 + 12*B^2*C*a^6*b^2))/b^6 + (a^2*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4 + (a^2*((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(-(a + b)*(a - b))^(1/2)*(B*b - C*a))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3) - (a^2*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(8*C^2*a^7 - C^2*b^7 + 3*C^2*a*b^6 - 16*C^2*a^6*b - 4*B^2*a^2*b^5 + 12*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 8*B^2*a^5*b^2 - 7*C^2*a^2*b^5 + 13*C^2*a^3*b^4 - 16*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*B*C*a*b^6 - 16*B*C*a^6*b - 12*B*C*a^2*b^5 + 20*B*C*a^3*b^4 - 28*B*C*a^4*b^3 + 32*B*C*a^5*b^2))/b^4 - (a^2*((8*(2*C*b^10 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(-(a + b)*(a - b))^(1/2)*(B*b - C*a))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3)))*(-(a + b)*(a - b))^(1/2)*(B*b - C*a)*2i)/(d*(b^5 - a^2*b^3))","B"
796,1,541,89,2.416383,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x)),x)","\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{2\,B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^2-b^2\right)}-\frac{C\,b\,\sin\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}+\frac{2\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d\,\left(a^2-b^2\right)}-\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d\,\left(a^2-b^2\right)}+\frac{B\,a\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d\,\sqrt{b^2-a^2}}-\frac{B\,a\,\ln\left(\frac{b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d\,\sqrt{b^2-a^2}}-\frac{C\,a^2\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d\,\sqrt{b^2-a^2}}+\frac{C\,a^2\,\ln\left(\frac{b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d\,\sqrt{b^2-a^2}}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{b\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (2*B*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (C*b*sin(c + d*x))/(d*(a^2 - b^2)) + (2*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)) - (2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d*(a^2 - b^2)) + (B*a*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2)))/(b*d*(b^2 - a^2)^(1/2)) - (B*a*log((b*sin(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2)))/(b*d*(b^2 - a^2)^(1/2)) - (C*a^2*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2)))/(b^2*d*(b^2 - a^2)^(1/2)) + (C*a^2*log((b*sin(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2)))/(b^2*d*(b^2 - a^2)^(1/2)) + (C*a^2*sin(c + d*x))/(b*d*(a^2 - b^2))","B"
797,1,344,67,2.979739,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))),x)","\frac{a\,\left(C\,\ln\left(\frac{b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}-C\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}\right)-B\,b\,\ln\left(\frac{b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}+B\,b\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{b\,d\,\left(a^2-b^2\right)}+\frac{2\,C\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d}","Not used",1,"(a*(C*log((b*sin(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(-(a + b)*(a - b))^(1/2) - C*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(b^2 - a^2)^(1/2)) - B*b*log((b*sin(c/2 + (d*x)/2) - a*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(-(a + b)*(a - b))^(1/2) + B*b*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(b^2 - a^2)^(1/2))/(b*d*(a^2 - b^2)) + (2*C*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d)","B"
798,1,342,76,2.948044,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))),x)","\frac{2\,B\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}+\frac{b\,\left(B\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}-B\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}\right)-C\,a\,\ln\left(\frac{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}+C\,a\,\ln\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{a\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*B*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) + (b*(B*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(-(a + b)*(a - b))^(1/2) - B*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(b^2 - a^2)^(1/2)) - C*a*log((a*cos(c/2 + (d*x)/2) + b*cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(-(a + b)*(a - b))^(1/2) + C*a*log((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2) + cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/cos(c/2 + (d*x)/2))*(b^2 - a^2)^(1/2))/(a*d*(a^2 - b^2))","B"
799,1,675,99,3.261470,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))),x)","\frac{B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d\,\left(a^2-b^2\right)}-\frac{C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d\,\left(a^2-b^2\right)}+\frac{B\,a\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}-\frac{B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)}+\frac{C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{a\,d\,\left(a^2-b^2\right)}-\frac{B\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{a\,d\,\left(a^2-b^2\right)}-\frac{C\,b\,\mathrm{atan}\left(\frac{\left(a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a\,b^2-a^3\right)}^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,2{}\mathrm{i}}{a\,d\,\left(a^2-b^2\right)}+\frac{B\,b^2\,\mathrm{atan}\left(\frac{\left(a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a\,b^2-a^3\right)}^2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,2{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)}","Not used",1,"(B*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(d*(a^2 - b^2)) - (C*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(d*(a^2 - b^2)) + (B*a*tan(c + d*x))/(d*(a^2 - b^2)) - (B*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(a^2*d*(a^2 - b^2)) + (C*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(a*d*(a^2 - b^2)) - (B*b^2*tan(c + d*x))/(a*d*(a^2 - b^2)) - (C*b*atan(((a^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)^2))*(-(a + b)*(a - b))^(1/2)*2i)/(a*d*(a^2 - b^2)) + (B*b^2*atan(((a^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)^2))*(-(a + b)*(a - b))^(1/2)*2i)/(a^2*d*(a^2 - b^2))","B"
800,1,4051,143,5.633956,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))),x)","\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,a\,\sin\left(c+d\,x\right)}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{2\,a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2\,a^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,b^2\,\sin\left(c+d\,x\right)}{2\,a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{2\,a\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,b^3\,\mathrm{atan}\left(\frac{\left(B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-B^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,B\,C\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,B\,C\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(B^2\,a^7+2\,B^2\,a^5\,b^2-3\,B^2\,a^3\,b^4-4\,B\,C\,a^6\,b+4\,B\,C\,a^2\,b^5+4\,C^2\,a^5\,b^2-4\,C^2\,a^3\,b^4\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,b^2\,\mathrm{atan}\left(\frac{\left(B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-B^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,B\,C\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,B\,C\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(B^2\,a^7+2\,B^2\,a^5\,b^2-3\,B^2\,a^3\,b^4-4\,B\,C\,a^6\,b+4\,B\,C\,a^2\,b^5+4\,C^2\,a^5\,b^2-4\,C^2\,a^3\,b^4\right)}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{B\,b^3\,\mathrm{atan}\left(\frac{\left(B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-B^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,B\,C\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,B\,C\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(B^2\,a^7+2\,B^2\,a^5\,b^2-3\,B^2\,a^3\,b^4-4\,B\,C\,a^6\,b+4\,B\,C\,a^2\,b^5+4\,C^2\,a^5\,b^2-4\,C^2\,a^3\,b^4\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{C\,b^2\,\mathrm{atan}\left(\frac{\left(B^2\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-B^2\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+3\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,C^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,C^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,C^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,C^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,C^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,B\,C\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,B\,C\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B\,C\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,B\,C\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B\,C\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(B^2\,a^7+2\,B^2\,a^5\,b^2-3\,B^2\,a^3\,b^4-4\,B\,C\,a^6\,b+4\,B\,C\,a^2\,b^5+4\,C^2\,a^5\,b^2-4\,C^2\,a^3\,b^4\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,1{}\mathrm{i}}{a^2\,d\,\left(a^2-b^2\right)\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(C*a*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*a*sin(c + d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(2*a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*b^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/(a^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*b^3*sin(2*c + 2*d*x))/(2*a^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*b^2*sin(2*c + 2*d*x))/(2*a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (C*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b^2*sin(c + d*x))/(2*a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(2*a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*b^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x)*1i)/(a^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*b^3*atan(((B^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - B^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*B*C*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*B*C*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*B*C*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(B^2*a^7 - 3*B^2*a^3*b^4 + 2*B^2*a^5*b^2 - 4*C^2*a^3*b^4 + 4*C^2*a^5*b^2 - 4*B*C*a^6*b + 4*B*C*a^2*b^5)))*(-(a + b)*(a - b))^(1/2)*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*b^2*atan(((B^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - B^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*B*C*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*B*C*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*B*C*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(B^2*a^7 - 3*B^2*a^3*b^4 + 2*B^2*a^5*b^2 - 4*C^2*a^3*b^4 + 4*C^2*a^5*b^2 - 4*B*C*a^6*b + 4*B*C*a^2*b^5)))*(-(a + b)*(a - b))^(1/2)*1i)/(a^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (B*b^3*atan(((B^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - B^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*B*C*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*B*C*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*B*C*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(B^2*a^7 - 3*B^2*a^3*b^4 + 2*B^2*a^5*b^2 - 4*C^2*a^3*b^4 + 4*C^2*a^5*b^2 - 4*B*C*a^6*b + 4*B*C*a^2*b^5)))*cos(2*c + 2*d*x)*(-(a + b)*(a - b))^(1/2)*1i)/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (C*b^2*atan(((B^2*a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*b^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - B^2*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 3*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*C^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*C^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*C^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*C^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*C^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*B*C*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*B*C*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B*C*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*B*C*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B*C*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(B^2*a^7 - 3*B^2*a^3*b^4 + 2*B^2*a^5*b^2 - 4*C^2*a^3*b^4 + 4*C^2*a^5*b^2 - 4*B*C*a^6*b + 4*B*C*a^2*b^5)))*cos(2*c + 2*d*x)*(-(a + b)*(a - b))^(1/2)*1i)/(a^2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2))","B"
801,1,6743,263,10.729288,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^4-2\,B\,b^4+C\,b^4+2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b+3\,C\,a\,b^3-3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^4+6\,C\,a^4+C\,b^4-2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b-3\,C\,a\,b^3+3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-6\,C\,a^4+4\,B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+C\,b^4\right)}{b\,\left(a\,b^2-b^3\right)\,\left(a+b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(3\,a+b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^4}}\right)\,\left(6{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{b^4\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a^2\,\left(\frac{8\,\left(2\,C\,b^{15}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,C\,a^3-2\,B\,a^2\,b-4\,C\,a\,b^2+3\,B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"(atan(((((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(C*a^2*6i + C*b^2*1i - B*a*b*4i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*6i + C*b^2*1i - B*a*b*4i))/(2*b^4))*(C*a^2*6i + C*b^2*1i - B*a*b*4i)*1i)/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(C*a^2*6i + C*b^2*1i - B*a*b*4i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*6i + C*b^2*1i - B*a*b*4i))/(2*b^4))*(C*a^2*6i + C*b^2*1i - B*a*b*4i)*1i)/(2*b^4))/((16*(108*C^3*a^11 - 54*C^3*a^10*b - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 - 216*B*C^2*a^10*b - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(C*a^2*6i + C*b^2*1i - B*a*b*4i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*6i + C*b^2*1i - B*a*b*4i))/(2*b^4))*(C*a^2*6i + C*b^2*1i - B*a*b*4i))/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(C*a^2*6i + C*b^2*1i - B*a*b*4i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*6i + C*b^2*1i - B*a*b*4i))/(2*b^4))*(C*a^2*6i + C*b^2*1i - B*a*b*4i))/(2*b^4)))*(C*a^2*6i + C*b^2*1i - B*a*b*4i)*1i)/(b^4*d) - ((tan(c/2 + (d*x)/2)^5*(6*C*a^4 - 2*B*b^4 + C*b^4 + 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b + 3*C*a*b^3 - 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) + (tan(c/2 + (d*x)/2)*(2*B*b^4 + 6*C*a^4 + C*b^4 - 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b - 3*C*a*b^3 + 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(C*b^4 - 6*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + 4*B*a^3*b))/(b*(a*b^2 - b^3)*(a + b)))/(d*(a + b + tan(c/2 + (d*x)/2)^2*(3*a + b) + tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) + (a^2*atan(((a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*C^3*a^11 - 54*C^3*a^10*b - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 - 216*B*C^2*a^10*b - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^2*((8*tan(c/2 + (d*x)/2)*(72*C^2*a^10 + C^2*b^10 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*C*b^15 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*B*b^3 + 3*C*a^3 - 2*B*a^2*b - 4*C*a*b^2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
802,1,3276,155,6.571422,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a^2\,b-C\,b^3-2\,C\,a^3+C\,a\,b^2+C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,b^3-2\,C\,a^3+B\,a^2\,b+C\,a\,b^2-C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b-2\,C\,a\right)\,1{}\mathrm{i}}{b^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(B\,b\,1{}\mathrm{i}-C\,a\,2{}\mathrm{i}\right)}{b^3\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(-B^3\,a^5\,b^3+B^3\,a^4\,b^4+3\,B^3\,a^3\,b^5-2\,B^3\,a^2\,b^6-2\,B^3\,a\,b^7+6\,B^2\,C\,a^6\,b^2-5\,B^2\,C\,a^5\,b^3-17\,B^2\,C\,a^4\,b^4+9\,B^2\,C\,a^3\,b^5+11\,B^2\,C\,a^2\,b^6-12\,B\,C^2\,a^7\,b+8\,B\,C^2\,a^6\,b^2+32\,B\,C^2\,a^5\,b^3-13\,B\,C^2\,a^4\,b^4-20\,B\,C^2\,a^3\,b^5+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{32\,\left(B\,a^2\,b^{10}-B\,b^{12}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-B\,a^2\,b-3\,C\,a\,b^2+2\,B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1i)*(B*b - 2*C*a)*1i)/(b^3*d) - ((2*tan(c/2 + (d*x)/2)^3*(B*a^2*b - C*b^3 - 2*C*a^3 + C*a*b^2 + C*a^2*b))/(b^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(C*b^3 - 2*C*a^3 + B*a^2*b + C*a*b^2 - C*a^2*b))/(b^2*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) + 2*a*tan(c/2 + (d*x)/2)^2)) - (log(tan(c/2 + (d*x)/2) - 1i)*(B*b*1i - C*a*2i))/(b^3*d) - (a*atan(((a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*C^3*a^8 - 2*B^3*a*b^7 - 4*C^3*a^7*b - 2*B^3*a^2*b^6 + 3*B^3*a^3*b^5 + B^3*a^4*b^4 - B^3*a^5*b^3 + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 - 12*B*C^2*a^7*b - 20*B*C^2*a^3*b^5 - 13*B*C^2*a^4*b^4 + 32*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 11*B^2*C*a^2*b^6 + 9*B^2*C*a^3*b^5 - 17*B^2*C*a^4*b^4 - 5*B^2*C*a^5*b^3 + 6*B^2*C*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(B*a^2*b^10 - B*b^12 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - B*a^2*b - 3*C*a*b^2)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
803,1,3775,122,9.130864,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^2,x)","\frac{2\,C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}-\frac{C\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}}{\frac{64\,\left(B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}+\frac{C\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}\right)}{b^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b\right)}{d\,\left(a+b\right)\,\left(a\,b-b^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(B\,a^2\,b^7-C\,b^9-B\,b^9-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,C\,a\,b^2+B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"(2*C*atan(((C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 + (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2 - (C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 - (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2)/((64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 - 3*B*C^2*a*b^4 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 + (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2 + (C*((C*((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 - (32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2)))/(b^2*d) + (atan(((((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 - 3*B*C^2*a*b^4 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) - (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 4*B*C*a*b^5 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^2*b^7 - C*b^9 - B*b^9 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*C*a*b^2)*2i)/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(C*a^2 - B*a*b))/(d*(a + b)*(a*b - b^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
804,1,113,100,1.989535,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^2),x)","\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a+b}\,\sqrt{a-b}}\right)\,\left(B\,a-C\,b\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b-C\,a\right)}{d\,\left(a+b\right)\,\left(a-b\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*atan((tan(c/2 + (d*x)/2)*(2*a - 2*b))/(2*(a + b)^(1/2)*(a - b)^(1/2)))*(B*a - C*b))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (2*tan(c/2 + (d*x)/2)*(B*b - C*a))/(d*(a + b)*(a - b)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
805,1,3763,133,9.186113,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^2),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^2-C\,a\,b\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{B\,\mathrm{atan}\left(\frac{\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)\,1{}\mathrm{i}}{a^2}-\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)\,1{}\mathrm{i}}{a^2}}{\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)}{a^2}-\frac{64\,\left(2\,B^3\,a^4\,b+2\,B^3\,a^3\,b^2-3\,B^3\,a^2\,b^3-B^3\,a\,b^4+B^3\,b^5-B^2\,C\,a^5-3\,B^2\,C\,a^4\,b+B^2\,C\,a^3\,b^2+B^2\,C\,a^2\,b^3+B\,C^2\,a^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{B\,\left(\frac{B\,\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)}{a^2}}\right)\,2{}\mathrm{i}}{a^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,B^3\,a^4\,b+2\,B^3\,a^3\,b^2-3\,B^3\,a^2\,b^3-B^3\,a\,b^4+B^3\,b^5-B^2\,C\,a^5-3\,B^2\,C\,a^4\,b+B^2\,C\,a^3\,b^2+B^2\,C\,a^2\,b^3+B\,C^2\,a^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^6-2\,B^2\,a^5\,b+3\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3-5\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+2\,B^2\,b^6-4\,B\,C\,a^5\,b+2\,B\,C\,a^3\,b^3+C^2\,a^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(B\,a^4\,b^5-C\,a^9-B\,a^9-3\,B\,a^6\,b^3+B\,a^7\,b^2-C\,a^6\,b^3+C\,a^7\,b^2+2\,B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^3-2\,B\,a^2\,b+B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"- (B*atan(((B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 - (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2 - (B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 + (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2)/((B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 - (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2 - (64*(B^3*b^5 + B*C^2*a^5 - B^2*C*a^5 - B^3*a*b^4 + 2*B^3*a^4*b - 3*B^3*a^2*b^3 + 2*B^3*a^3*b^2 - 3*B^2*C*a^4*b + B^2*C*a^2*b^3 + B^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (B*((B*((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*B*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2 + (32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2))*2i)/(a^2*d) - (atan(((((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(B^3*b^5 + B*C^2*a^5 - B^2*C*a^5 - B^3*a*b^4 + 2*B^3*a^4*b - 3*B^3*a^2*b^3 + 2*B^3*a^3*b^2 - 3*B^2*C*a^4*b + B^2*C*a^2*b^3 + B^2*C*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*a^6 + 2*B^2*b^6 + C^2*a^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b - 5*B^2*a^2*b^4 + 4*B^2*a^3*b^3 + 3*B^2*a^4*b^2 - 4*B*C*a^5*b + 2*B*C*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(B*a^4*b^5 - C*a^9 - B*a^9 - 3*B*a^6*b^3 + B*a^7*b^2 - C*a^6*b^3 + C*a^7*b^2 + 2*B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - 2*B*a^2*b)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(B*b^2 - C*a*b))/(d*(a + b)*(a*b - a^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
806,1,5464,189,9.789353,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^2),x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(B\,a\,b^2-2\,B\,b^3-B\,a^3+B\,a^2\,b+C\,a\,b^2\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,a^3-2\,B\,b^3-B\,a\,b^2+B\,a^2\,b+C\,a\,b^2\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,B\,b-C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b-C\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,\left(2\,B\,b-C\,a\right)}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{\left(2\,B\,b-C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b-C\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,\left(2\,B\,b-C\,a\right)}{a^3}\right)\,1{}\mathrm{i}}{a^3}}{\frac{64\,\left(12\,B^3\,a^4\,b^4+6\,B^3\,a^3\,b^5-20\,B^3\,a^2\,b^6-4\,B^3\,a\,b^7+8\,B^3\,b^8-20\,B^2\,C\,a^5\,b^3-13\,B^2\,C\,a^4\,b^4+32\,B^2\,C\,a^3\,b^5+8\,B^2\,C\,a^2\,b^6-12\,B^2\,C\,a\,b^7+11\,B\,C^2\,a^6\,b^2+9\,B\,C^2\,a^5\,b^3-17\,B\,C^2\,a^4\,b^4-5\,B\,C^2\,a^3\,b^5+6\,B\,C^2\,a^2\,b^6-2\,C^3\,a^7\,b-2\,C^3\,a^6\,b^2+3\,C^3\,a^5\,b^3+C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(2\,B\,b-C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b-C\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,\left(2\,B\,b-C\,a\right)}{a^3}\right)}{a^3}-\frac{\left(2\,B\,b-C\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b-C\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,\left(2\,B\,b-C\,a\right)}{a^3}\right)}{a^3}}\right)\,\left(2\,B\,b-C\,a\right)\,2{}\mathrm{i}}{a^3\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{64\,\left(12\,B^3\,a^4\,b^4+6\,B^3\,a^3\,b^5-20\,B^3\,a^2\,b^6-4\,B^3\,a\,b^7+8\,B^3\,b^8-20\,B^2\,C\,a^5\,b^3-13\,B^2\,C\,a^4\,b^4+32\,B^2\,C\,a^3\,b^5+8\,B^2\,C\,a^2\,b^6-12\,B^2\,C\,a\,b^7+11\,B\,C^2\,a^6\,b^2+9\,B\,C^2\,a^5\,b^3-17\,B\,C^2\,a^4\,b^4-5\,B\,C^2\,a^3\,b^5+6\,B\,C^2\,a^2\,b^6-2\,C^3\,a^7\,b-2\,C^3\,a^6\,b^2+3\,C^3\,a^5\,b^3+C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^6\,b^2-8\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4+16\,B^2\,a^3\,b^5-16\,B^2\,a^2\,b^6-8\,B^2\,a\,b^7+8\,B^2\,b^8-4\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2-8\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4+18\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-8\,B\,C\,a\,b^7+C^2\,a^8-2\,C^2\,a^7\,b+3\,C^2\,a^6\,b^2+4\,C^2\,a^5\,b^3-5\,C^2\,a^4\,b^4-2\,C^2\,a^3\,b^5+2\,C^2\,a^2\,b^6\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(B\,a^7\,b^5-2\,B\,a^6\,b^6-C\,a^{12}+5\,B\,a^8\,b^4-3\,B\,a^9\,b^3-3\,B\,a^{10}\,b^2+C\,a^7\,b^5-3\,C\,a^9\,b^3+C\,a^{10}\,b^2+2\,B\,a^{11}\,b+2\,C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,C\,a^3-3\,B\,a^2\,b-C\,a\,b^2+2\,B\,b^3\right)\,2{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"(atan((((2*B*b - C*a)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(2*B*b - C*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*(2*B*b - C*a))/a^3)*1i)/a^3 + ((2*B*b - C*a)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(2*B*b - C*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*(2*B*b - C*a))/a^3)*1i)/a^3)/((64*(8*B^3*b^8 - 4*B^3*a*b^7 - 2*C^3*a^7*b - 20*B^3*a^2*b^6 + 6*B^3*a^3*b^5 + 12*B^3*a^4*b^4 - C^3*a^3*b^5 + C^3*a^4*b^4 + 3*C^3*a^5*b^3 - 2*C^3*a^6*b^2 - 12*B^2*C*a*b^7 + 6*B*C^2*a^2*b^6 - 5*B*C^2*a^3*b^5 - 17*B*C^2*a^4*b^4 + 9*B*C^2*a^5*b^3 + 11*B*C^2*a^6*b^2 + 8*B^2*C*a^2*b^6 + 32*B^2*C*a^3*b^5 - 13*B^2*C*a^4*b^4 - 20*B^2*C*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + ((2*B*b - C*a)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(2*B*b - C*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*(2*B*b - C*a))/a^3))/a^3 - ((2*B*b - C*a)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(2*B*b - C*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*(2*B*b - C*a))/a^3))/a^3))*(2*B*b - C*a)*2i)/(a^3*d) - ((2*tan(c/2 + (d*x)/2)^3*(B*a*b^2 - 2*B*b^3 - B*a^3 + B*a^2*b + C*a*b^2))/(a^2*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)*(B*a^3 - 2*B*b^3 - B*a*b^2 + B*a^2*b + C*a*b^2))/(a^2*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^4*(a - b) - 2*b*tan(c/2 + (d*x)/2)^2)) + (b*atan(((b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((64*(8*B^3*b^8 - 4*B^3*a*b^7 - 2*C^3*a^7*b - 20*B^3*a^2*b^6 + 6*B^3*a^3*b^5 + 12*B^3*a^4*b^4 - C^3*a^3*b^5 + C^3*a^4*b^4 + 3*C^3*a^5*b^3 - 2*C^3*a^6*b^2 - 12*B^2*C*a*b^7 + 6*B*C^2*a^2*b^6 - 5*B*C^2*a^3*b^5 - 17*B*C^2*a^4*b^4 + 9*B*C^2*a^5*b^3 + 11*B*C^2*a^6*b^2 + 8*B^2*C*a^2*b^6 + 32*B^2*C*a^3*b^5 - 13*B^2*C*a^4*b^4 - 20*B^2*C*a^5*b^3))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(8*B^2*b^8 + C^2*a^8 - 8*B^2*a*b^7 - 2*C^2*a^7*b - 16*B^2*a^2*b^6 + 16*B^2*a^3*b^5 + 5*B^2*a^4*b^4 - 8*B^2*a^5*b^3 + 4*B^2*a^6*b^2 + 2*C^2*a^2*b^6 - 2*C^2*a^3*b^5 - 5*C^2*a^4*b^4 + 4*C^2*a^5*b^3 + 3*C^2*a^6*b^2 - 8*B*C*a*b^7 - 4*B*C*a^7*b + 8*B*C*a^2*b^6 + 18*B*C*a^3*b^5 - 16*B*C*a^4*b^4 - 8*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(B*a^7*b^5 - 2*B*a^6*b^6 - C*a^12 + 5*B*a^8*b^4 - 3*B*a^9*b^3 - 3*B*a^10*b^2 + C*a^7*b^5 - 3*C*a^9*b^3 + C*a^10*b^2 + 2*B*a^11*b + 2*C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*B*b^3 + 2*C*a^3 - 3*B*a^2*b - C*a*b^2)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
807,1,10598,398,13.409717,"\text{Not used}","int((cos(c + d*x)^3*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^6-12\,C\,a^6+C\,b^6-4\,B\,a^2\,b^4-12\,B\,a^3\,b^3+3\,B\,a^4\,b^2-8\,C\,a^2\,b^4+10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+2\,B\,a\,b^5+6\,B\,a^5\,b-5\,C\,a\,b^5-6\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b^7+36\,C\,a^7+3\,C\,b^7-10\,B\,a^2\,b^5+16\,B\,a^3\,b^4+35\,B\,a^4\,b^3-9\,B\,a^5\,b^2+5\,C\,a^2\,b^5+26\,C\,a^3\,b^4-29\,C\,a^4\,b^3-67\,C\,a^5\,b^2-4\,B\,a\,b^6-18\,B\,a^6\,b-4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,C\,b^7-36\,C\,a^7-2\,B\,b^7+10\,B\,a^2\,b^5+16\,B\,a^3\,b^4-35\,B\,a^4\,b^3-9\,B\,a^5\,b^2+5\,C\,a^2\,b^5-26\,C\,a^3\,b^4-29\,C\,a^4\,b^3+67\,C\,a^5\,b^2-4\,B\,a\,b^6+18\,B\,a^6\,b+4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(C\,b^6-12\,C\,a^6-2\,B\,b^6+4\,B\,a^2\,b^4-12\,B\,a^3\,b^3-3\,B\,a^4\,b^2-8\,C\,a^2\,b^4-10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+2\,B\,a\,b^5+6\,B\,a^5\,b+5\,C\,a\,b^5+6\,C\,a^5\,b\right)}{\left(a\,b^4-b^5\right)\,{\left(a+b\right)}^2}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{2\,b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{8\,\left(-216\,B^3\,a^{12}\,b^3+108\,B^3\,a^{11}\,b^4+972\,B^3\,a^{10}\,b^5-486\,B^3\,a^9\,b^6-1728\,B^3\,a^8\,b^7+756\,B^3\,a^7\,b^8+1404\,B^3\,a^6\,b^9-432\,B^3\,a^5\,b^{10}-432\,B^3\,a^4\,b^{11}+1296\,B^2\,C\,a^{13}\,b^2-648\,B^2\,C\,a^{12}\,b^3-5724\,B^2\,C\,a^{11}\,b^4+2808\,B^2\,C\,a^{10}\,b^5+9828\,B^2\,C\,a^9\,b^6-4203\,B^2\,C\,a^8\,b^7-7524\,B^2\,C\,a^7\,b^8+2268\,B^2\,C\,a^6\,b^9+1980\,B^2\,C\,a^5\,b^{10}+144\,B^2\,C\,a^3\,b^{12}-2592\,B\,C^2\,a^{14}\,b+1296\,B\,C^2\,a^{13}\,b^2+11232\,B\,C^2\,a^{12}\,b^3-5400\,B\,C^2\,a^{11}\,b^4-18594\,B\,C^2\,a^{10}\,b^5+7767\,B\,C^2\,a^9\,b^6+13347\,B\,C^2\,a^8\,b^7-3972\,B\,C^2\,a^7\,b^8-2892\,B\,C^2\,a^6\,b^9+9\,B\,C^2\,a^5\,b^{10}-489\,B\,C^2\,a^4\,b^{11}+12\,B\,C^2\,a^3\,b^{12}-12\,B\,C^2\,a^2\,b^{13}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)}{2\,b^5}}\right)\,\left(12{}\mathrm{i}\,C\,a^2-6{}\mathrm{i}\,B\,a\,b+1{}\mathrm{i}\,C\,b^2\right)\,1{}\mathrm{i}}{b^5\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a^2\,\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a^2\,\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}{\frac{8\,\left(-216\,B^3\,a^{12}\,b^3+108\,B^3\,a^{11}\,b^4+972\,B^3\,a^{10}\,b^5-486\,B^3\,a^9\,b^6-1728\,B^3\,a^8\,b^7+756\,B^3\,a^7\,b^8+1404\,B^3\,a^6\,b^9-432\,B^3\,a^5\,b^{10}-432\,B^3\,a^4\,b^{11}+1296\,B^2\,C\,a^{13}\,b^2-648\,B^2\,C\,a^{12}\,b^3-5724\,B^2\,C\,a^{11}\,b^4+2808\,B^2\,C\,a^{10}\,b^5+9828\,B^2\,C\,a^9\,b^6-4203\,B^2\,C\,a^8\,b^7-7524\,B^2\,C\,a^7\,b^8+2268\,B^2\,C\,a^6\,b^9+1980\,B^2\,C\,a^5\,b^{10}+144\,B^2\,C\,a^3\,b^{12}-2592\,B\,C^2\,a^{14}\,b+1296\,B\,C^2\,a^{13}\,b^2+11232\,B\,C^2\,a^{12}\,b^3-5400\,B\,C^2\,a^{11}\,b^4-18594\,B\,C^2\,a^{10}\,b^5+7767\,B\,C^2\,a^9\,b^6+13347\,B\,C^2\,a^8\,b^7-3972\,B\,C^2\,a^7\,b^8-2892\,B\,C^2\,a^6\,b^9+9\,B\,C^2\,a^5\,b^{10}-489\,B\,C^2\,a^4\,b^{11}+12\,B\,C^2\,a^3\,b^{12}-12\,B\,C^2\,a^2\,b^{13}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a^2\,\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a^2\,\left(\frac{4\,\left(4\,C\,b^{21}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-12\,C\,a^5+6\,B\,a^4\,b+29\,C\,a^3\,b^2-15\,B\,a^2\,b^3-20\,C\,a\,b^4+12\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*B*b^6 - 12*C*a^6 + C*b^6 - 4*B*a^2*b^4 - 12*B*a^3*b^3 + 3*B*a^4*b^2 - 8*C*a^2*b^4 + 10*C*a^3*b^3 + 23*C*a^4*b^2 + 2*B*a*b^5 + 6*B*a^5*b - 5*C*a*b^5 - 6*C*a^5*b))/((a + b)*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^3*(2*B*b^7 + 36*C*a^7 + 3*C*b^7 - 10*B*a^2*b^5 + 16*B*a^3*b^4 + 35*B*a^4*b^3 - 9*B*a^5*b^2 + 5*C*a^2*b^5 + 26*C*a^3*b^4 - 29*C*a^4*b^3 - 67*C*a^5*b^2 - 4*B*a*b^6 - 18*B*a^6*b - 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^5*(3*C*b^7 - 36*C*a^7 - 2*B*b^7 + 10*B*a^2*b^5 + 16*B*a^3*b^4 - 35*B*a^4*b^3 - 9*B*a^5*b^2 + 5*C*a^2*b^5 - 26*C*a^3*b^4 - 29*C*a^4*b^3 + 67*C*a^5*b^2 - 4*B*a*b^6 + 18*B*a^6*b + 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^7*(C*b^6 - 12*C*a^6 - 2*B*b^6 + 4*B*a^2*b^4 - 12*B*a^3*b^3 - 3*B*a^4*b^2 - 8*C*a^2*b^4 - 10*C*a^3*b^3 + 23*C*a^4*b^2 + 2*B*a*b^5 + 6*B*a^5*b + 5*C*a*b^5 + 6*C*a^5*b))/((a*b^4 - b^5)*(a + b)^2))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(6*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^2*(4*a*b + 4*a^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 4*a^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan(((((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*tan(c/2 + (d*x)/2)*(C*a^2*12i + C*b^2*1i - B*a*b*6i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*12i + C*b^2*1i - B*a*b*6i))/(2*b^5))*(C*a^2*12i + C*b^2*1i - B*a*b*6i)*1i)/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*tan(c/2 + (d*x)/2)*(C*a^2*12i + C*b^2*1i - B*a*b*6i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*12i + C*b^2*1i - B*a*b*6i))/(2*b^5))*(C*a^2*12i + C*b^2*1i - B*a*b*6i)*1i)/(2*b^5))/((8*(1728*C^3*a^15 - 864*C^3*a^14*b - 432*B^3*a^4*b^11 - 432*B^3*a^5*b^10 + 1404*B^3*a^6*b^9 + 756*B^3*a^7*b^8 - 1728*B^3*a^8*b^7 - 486*B^3*a^9*b^6 + 972*B^3*a^10*b^5 + 108*B^3*a^11*b^4 - 216*B^3*a^12*b^3 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 - 2592*B*C^2*a^14*b - 12*B*C^2*a^2*b^13 + 12*B*C^2*a^3*b^12 - 489*B*C^2*a^4*b^11 + 9*B*C^2*a^5*b^10 - 2892*B*C^2*a^6*b^9 - 3972*B*C^2*a^7*b^8 + 13347*B*C^2*a^8*b^7 + 7767*B*C^2*a^9*b^6 - 18594*B*C^2*a^10*b^5 - 5400*B*C^2*a^11*b^4 + 11232*B*C^2*a^12*b^3 + 1296*B*C^2*a^13*b^2 + 144*B^2*C*a^3*b^12 + 1980*B^2*C*a^5*b^10 + 2268*B^2*C*a^6*b^9 - 7524*B^2*C*a^7*b^8 - 4203*B^2*C*a^8*b^7 + 9828*B^2*C*a^9*b^6 + 2808*B^2*C*a^10*b^5 - 5724*B^2*C*a^11*b^4 - 648*B^2*C*a^12*b^3 + 1296*B^2*C*a^13*b^2))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*tan(c/2 + (d*x)/2)*(C*a^2*12i + C*b^2*1i - B*a*b*6i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*12i + C*b^2*1i - B*a*b*6i))/(2*b^5))*(C*a^2*12i + C*b^2*1i - B*a*b*6i))/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*tan(c/2 + (d*x)/2)*(C*a^2*12i + C*b^2*1i - B*a*b*6i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*12i + C*b^2*1i - B*a*b*6i))/(2*b^5))*(C*a^2*12i + C*b^2*1i - B*a*b*6i))/(2*b^5)))*(C*a^2*12i + C*b^2*1i - B*a*b*6i)*1i)/(b^5*d) + (a^2*atan(((a^2*((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a^2*((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a^2*((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a^2*((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))/((8*(1728*C^3*a^15 - 864*C^3*a^14*b - 432*B^3*a^4*b^11 - 432*B^3*a^5*b^10 + 1404*B^3*a^6*b^9 + 756*B^3*a^7*b^8 - 1728*B^3*a^8*b^7 - 486*B^3*a^9*b^6 + 972*B^3*a^10*b^5 + 108*B^3*a^11*b^4 - 216*B^3*a^12*b^3 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 - 2592*B*C^2*a^14*b - 12*B*C^2*a^2*b^13 + 12*B*C^2*a^3*b^12 - 489*B*C^2*a^4*b^11 + 9*B*C^2*a^5*b^10 - 2892*B*C^2*a^6*b^9 - 3972*B*C^2*a^7*b^8 + 13347*B*C^2*a^8*b^7 + 7767*B*C^2*a^9*b^6 - 18594*B*C^2*a^10*b^5 - 5400*B*C^2*a^11*b^4 + 11232*B*C^2*a^12*b^3 + 1296*B*C^2*a^13*b^2 + 144*B^2*C*a^3*b^12 + 1980*B^2*C*a^5*b^10 + 2268*B^2*C*a^6*b^9 - 7524*B^2*C*a^7*b^8 - 4203*B^2*C*a^8*b^7 + 9828*B^2*C*a^9*b^6 + 2808*B^2*C*a^10*b^5 - 5724*B^2*C*a^11*b^4 - 648*B^2*C*a^12*b^3 + 1296*B^2*C*a^13*b^2))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (a^2*((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a^2*((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a^2*((8*tan(c/2 + (d*x)/2)*(288*C^2*a^14 + C^2*b^14 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a^2*((4*(4*C*b^21 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*B*b^5 - 12*C*a^5 - 15*B*a^2*b^3 + 29*C*a^3*b^2 + 6*B*a^4*b - 20*C*a*b^4)*1i)/(d*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))","B"
808,1,5542,280,8.905244,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^5-2\,C\,b^5+6\,B\,a^2\,b^3+B\,a^3\,b^2+4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-2\,B\,a^4\,b+2\,C\,a\,b^4-3\,C\,a^4\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^5+2\,C\,b^5+6\,B\,a^2\,b^3-B\,a^3\,b^2-4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-2\,B\,a^4\,b+2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,C\,a^6-2\,B\,a^5\,b-13\,C\,a^4\,b^2+5\,B\,a^3\,b^3+6\,C\,a^2\,b^4-2\,C\,b^6\right)}{b\,\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+2\,a\,b-b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^2+2\,a\,b+b^2\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b-3\,C\,a\right)\,1{}\mathrm{i}}{b^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(B\,b\,1{}\mathrm{i}-C\,a\,3{}\mathrm{i}\right)}{b^4\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(-4\,B^3\,a^9\,b^3+2\,B^3\,a^8\,b^4+18\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6-36\,B^3\,a^5\,b^7+26\,B^3\,a^4\,b^8+34\,B^3\,a^3\,b^9-24\,B^3\,a^2\,b^{10}-12\,B^3\,a\,b^{11}+36\,B^2\,C\,a^{10}\,b^2-18\,B^2\,C\,a^9\,b^3-162\,B^2\,C\,a^8\,b^4+105\,B^2\,C\,a^7\,b^5+312\,B^2\,C\,a^6\,b^6-198\,B^2\,C\,a^5\,b^7-282\,B^2\,C\,a^4\,b^8+156\,B^2\,C\,a^3\,b^9+96\,B^2\,C\,a^2\,b^{10}-108\,B\,C^2\,a^{11}\,b+54\,B\,C^2\,a^{10}\,b^2+486\,B\,C^2\,a^9\,b^3-279\,B\,C^2\,a^8\,b^4-900\,B\,C^2\,a^7\,b^5+486\,B\,C^2\,a^6\,b^6+774\,B\,C^2\,a^5\,b^7-324\,B\,C^2\,a^4\,b^8-252\,B\,C^2\,a^3\,b^9+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{a\,\left(\frac{8\,\left(4\,B\,b^{18}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+2\,B\,a^4\,b+15\,C\,a^3\,b^2-5\,B\,a^2\,b^3-12\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(6*C*a^5 - 2*C*b^5 + 6*B*a^2*b^3 + B*a^3*b^2 + 4*C*a^2*b^3 - 12*C*a^3*b^2 - 2*B*a^4*b + 2*C*a*b^4 - 3*C*a^4*b))/((a*b^3 - b^4)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(6*C*a^5 + 2*C*b^5 + 6*B*a^2*b^3 - B*a^3*b^2 - 4*C*a^2*b^3 - 12*C*a^3*b^2 - 2*B*a^4*b + 2*C*a*b^4 + 3*C*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) + (2*tan(c/2 + (d*x)/2)^3*(6*C*a^6 - 2*C*b^6 + 5*B*a^3*b^3 + 6*C*a^2*b^4 - 13*C*a^4*b^2 - 2*B*a^5*b))/(b*(a*b^2 - b^3)*(a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) + (log(tan(c/2 + (d*x)/2) + 1i)*(B*b - 3*C*a)*1i)/(b^4*d) - (log(tan(c/2 + (d*x)/2) - 1i)*(B*b*1i - C*a*3i))/(b^4*d) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(108*C^3*a^12 - 12*B^3*a*b^11 - 54*C^3*a^11*b - 24*B^3*a^2*b^10 + 34*B^3*a^3*b^9 + 26*B^3*a^4*b^8 - 36*B^3*a^5*b^7 - 13*B^3*a^6*b^6 + 18*B^3*a^7*b^5 + 2*B^3*a^8*b^4 - 4*B^3*a^9*b^3 + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 - 108*B*C^2*a^11*b - 252*B*C^2*a^3*b^9 - 324*B*C^2*a^4*b^8 + 774*B*C^2*a^5*b^7 + 486*B*C^2*a^6*b^6 - 900*B*C^2*a^7*b^5 - 279*B*C^2*a^8*b^4 + 486*B*C^2*a^9*b^3 + 54*B*C^2*a^10*b^2 + 96*B^2*C*a^2*b^10 + 156*B^2*C*a^3*b^9 - 282*B^2*C*a^4*b^8 - 198*B^2*C*a^5*b^7 + 312*B^2*C*a^6*b^6 + 105*B^2*C*a^7*b^5 - 162*B^2*C*a^8*b^4 - 18*B^2*C*a^9*b^3 + 36*B^2*C*a^10*b^2))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - (a*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (a*((8*(4*B*b^18 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 5*B*a^2*b^3 + 15*C*a^3*b^2 + 2*B*a^4*b - 12*C*a*b^4)*1i)/(d*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
809,1,6923,211,11.191200,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^4+B\,a^2\,b^2-6\,C\,a^2\,b^2+4\,B\,a\,b^3-C\,a^3\,b\right)}{\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a^4-B\,a^2\,b^2-6\,C\,a^2\,b^2+4\,B\,a\,b^3+C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{2\,C\,\mathrm{atan}\left(-\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}-\frac{C\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}}{-\frac{16\,\left(B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{C\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}\right)}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-2\,C\,a^5+5\,C\,a^3\,b^2+B\,a^2\,b^3-6\,C\,a\,b^4+2\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}","Not used",1,"(2*C*atan(-((C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 - (C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3)/((C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3 - (16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 - 20*B*C^2*a*b^8 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*((C*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4))*1i)/b^3)))/(b^3*d) - ((tan(c/2 + (d*x)/2)^3*(2*C*a^4 + B*a^2*b^2 - 6*C*a^2*b^2 + 4*B*a*b^3 - C*a^3*b))/((a*b^2 - b^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*C*a^4 - B*a^2*b^2 - 6*C*a^2*b^2 + 4*B*a*b^3 + C*a^3*b))/((a + b)*(b^4 - 2*a*b^3 + a^2*b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 - 20*B*C^2*a*b^8 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 24*B*C*a*b^9 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*b^15 + 4*C*b^15 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 6*C*a*b^4)*1i)/(d*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))","B"
810,1,248,180,4.864317,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,a^2+2\,B\,b^2-C\,a^2+B\,a\,b-4\,C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,a^2+2\,B\,b^2+C\,a^2-B\,a\,b-4\,C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(C\,a^2-3\,B\,a\,b+2\,C\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*B*a^2 + 2*B*b^2 - C*a^2 + B*a*b - 4*C*a*b))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(2*B*a^2 + 2*B*b^2 + C*a^2 - B*a*b - 4*C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(C*a^2 + 2*C*b^2 - 3*B*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
811,1,248,164,4.792213,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^2-B\,b^2+2\,C\,b^2-4\,B\,a\,b+C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^2+2\,C\,a^2+2\,C\,b^2-4\,B\,a\,b-C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,B\,a^2-3\,C\,a\,b+B\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*C*a^2 - B*b^2 + 2*C*b^2 - 4*B*a*b + C*a*b))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(B*b^2 + 2*C*a^2 + 2*C*b^2 - 4*B*a*b - C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*B*a^2 + B*b^2 - 3*C*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
812,1,6911,214,10.938755,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b^4-6\,B\,a^2\,b^2+C\,a^2\,b^2-B\,a\,b^3+4\,C\,a^3\,b\right)}{\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^4-6\,B\,a^2\,b^2-C\,a^2\,b^2+B\,a\,b^3+4\,C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{B\,\mathrm{atan}\left(-\frac{\frac{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{8\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)\,1{}\mathrm{i}}{a^3}-\frac{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{8\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)\,1{}\mathrm{i}}{a^3}}{\frac{16\,\left(12\,B^3\,a^8\,b+24\,B^3\,a^7\,b^2-34\,B^3\,a^6\,b^3-26\,B^3\,a^5\,b^4+36\,B^3\,a^4\,b^5+13\,B^3\,a^3\,b^6-18\,B^3\,a^2\,b^7-2\,B^3\,a\,b^8+4\,B^3\,b^9-4\,B^2\,C\,a^9-20\,B^2\,C\,a^8\,b+6\,B^2\,C\,a^7\,b^2+2\,B^2\,C\,a^6\,b^3+2\,B^2\,C\,a^4\,b^5-2\,B^2\,C\,a^3\,b^6-2\,B^2\,C\,a^2\,b^7+4\,B\,C^2\,a^9+4\,B\,C^2\,a^7\,b^2+B\,C^2\,a^5\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{8\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)}{a^3}+\frac{B\,\left(\frac{B\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{8\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)}{a^3}}\right)\,2{}\mathrm{i}}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{16\,\left(12\,B^3\,a^8\,b+24\,B^3\,a^7\,b^2-34\,B^3\,a^6\,b^3-26\,B^3\,a^5\,b^4+36\,B^3\,a^4\,b^5+13\,B^3\,a^3\,b^6-18\,B^3\,a^2\,b^7-2\,B^3\,a\,b^8+4\,B^3\,b^9-4\,B^2\,C\,a^9-20\,B^2\,C\,a^8\,b+6\,B^2\,C\,a^7\,b^2+2\,B^2\,C\,a^6\,b^3+2\,B^2\,C\,a^4\,b^5-2\,B^2\,C\,a^3\,b^6-2\,B^2\,C\,a^2\,b^7+4\,B\,C^2\,a^9+4\,B\,C^2\,a^7\,b^2+B\,C^2\,a^5\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,B^2\,a^{10}-8\,B^2\,a^9\,b+24\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3-52\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5+57\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7-32\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+8\,B^2\,b^{10}-24\,B\,C\,a^9\,b+8\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5-4\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}+4\,C^2\,a^8\,b^2+C^2\,a^6\,b^4\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{15}+4\,C\,a^{15}-4\,B\,a^6\,b^9+2\,B\,a^7\,b^8+18\,B\,a^8\,b^7-4\,B\,a^9\,b^6-36\,B\,a^{10}\,b^5+6\,B\,a^{11}\,b^4+34\,B\,a^{12}\,b^3-8\,B\,a^{13}\,b^2-2\,C\,a^8\,b^7+2\,C\,a^9\,b^6+6\,C\,a^{12}\,b^3-6\,C\,a^{13}\,b^2-12\,B\,a^{14}\,b-4\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,C\,a^5-6\,B\,a^4\,b+C\,a^3\,b^2+5\,B\,a^2\,b^3-2\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*B*b^4 - 6*B*a^2*b^2 + C*a^2*b^2 - B*a*b^3 + 4*C*a^3*b))/((a^2*b - a^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*B*b^4 - 6*B*a^2*b^2 - C*a^2*b^2 + B*a*b^3 + 4*C*a^3*b))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (B*atan(-((B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3 - (B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3)/((16*(4*B^3*b^9 + 4*B*C^2*a^9 - 4*B^2*C*a^9 - 2*B^3*a*b^8 + 12*B^3*a^8*b - 18*B^3*a^2*b^7 + 13*B^3*a^3*b^6 + 36*B^3*a^4*b^5 - 26*B^3*a^5*b^4 - 34*B^3*a^6*b^3 + 24*B^3*a^7*b^2 - 20*B^2*C*a^8*b + B*C^2*a^5*b^4 + 4*B*C^2*a^7*b^2 - 2*B^2*C*a^2*b^7 - 2*B^2*C*a^3*b^6 + 2*B^2*C*a^4*b^5 + 2*B^2*C*a^6*b^3 + 6*B^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 + (B*((B*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*B*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3))*2i)/(a^3*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((16*(4*B^3*b^9 + 4*B*C^2*a^9 - 4*B^2*C*a^9 - 2*B^3*a*b^8 + 12*B^3*a^8*b - 18*B^3*a^2*b^7 + 13*B^3*a^3*b^6 + 36*B^3*a^4*b^5 - 26*B^3*a^5*b^4 - 34*B^3*a^6*b^3 + 24*B^3*a^7*b^2 - 20*B^2*C*a^8*b + B*C^2*a^5*b^4 + 4*B*C^2*a^7*b^2 - 2*B^2*C*a^2*b^7 - 2*B^2*C*a^3*b^6 + 2*B^2*C*a^4*b^5 + 2*B^2*C*a^6*b^3 + 6*B^2*C*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*a^10 + 8*B^2*b^10 + 4*C^2*a^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b - 32*B^2*a^2*b^8 + 32*B^2*a^3*b^7 + 57*B^2*a^4*b^6 - 48*B^2*a^5*b^5 - 52*B^2*a^6*b^4 + 32*B^2*a^7*b^3 + 24*B^2*a^8*b^2 + C^2*a^6*b^4 + 4*C^2*a^8*b^2 - 24*B*C*a^9*b - 4*B*C*a^3*b^7 + 2*B*C*a^5*b^5 + 8*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^15 + 4*C*a^15 - 4*B*a^6*b^9 + 2*B*a^7*b^8 + 18*B*a^8*b^7 - 4*B*a^9*b^6 - 36*B*a^10*b^5 + 6*B*a^11*b^4 + 34*B*a^12*b^3 - 8*B*a^13*b^2 - 2*C*a^8*b^7 + 2*C*a^9*b^6 + 6*C*a^12*b^3 - 6*C*a^13*b^2 - 12*B*a^14*b - 4*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*C*a^5 - 2*B*b^5 + 5*B*a^2*b^3 + C*a^3*b^2 - 6*B*a^4*b)*1i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
813,1,9312,299,14.315804,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,B\,b^5-2\,B\,a^5-12\,B\,a^2\,b^3+4\,B\,a^3\,b^2+C\,a^2\,b^3+6\,C\,a^3\,b^2-3\,B\,a\,b^4+2\,B\,a^4\,b-2\,C\,a\,b^4\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,a^5+6\,B\,b^5-12\,B\,a^2\,b^3-4\,B\,a^3\,b^2-C\,a^2\,b^3+6\,C\,a^3\,b^2+3\,B\,a\,b^4+2\,B\,a^4\,b-2\,C\,a\,b^4\right)}{\left(a+b\right)\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,a^6-6\,B\,a^4\,b^2-5\,C\,a^3\,b^3+13\,B\,a^2\,b^4+2\,C\,a\,b^5-6\,B\,b^6\right)}{a\,\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^2+2\,a\,b+3\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,a\,b-3\,b^2\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B\,b-C\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(3\,B\,b-C\,a\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{\left(3\,B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B\,b-C\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(3\,B\,b-C\,a\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(216\,B^3\,a^8\,b^4+216\,B^3\,a^7\,b^5-702\,B^3\,a^6\,b^6-378\,B^3\,a^5\,b^7+864\,B^3\,a^4\,b^8+243\,B^3\,a^3\,b^9-486\,B^3\,a^2\,b^{10}-54\,B^3\,a\,b^{11}+108\,B^3\,b^{12}-252\,B^2\,C\,a^9\,b^3-324\,B^2\,C\,a^8\,b^4+774\,B^2\,C\,a^7\,b^5+486\,B^2\,C\,a^6\,b^6-900\,B^2\,C\,a^5\,b^7-279\,B^2\,C\,a^4\,b^8+486\,B^2\,C\,a^3\,b^9+54\,B^2\,C\,a^2\,b^{10}-108\,B^2\,C\,a\,b^{11}+96\,B\,C^2\,a^{10}\,b^2+156\,B\,C^2\,a^9\,b^3-282\,B\,C^2\,a^8\,b^4-198\,B\,C^2\,a^7\,b^5+312\,B\,C^2\,a^6\,b^6+105\,B\,C^2\,a^5\,b^7-162\,B\,C^2\,a^4\,b^8-18\,B\,C^2\,a^3\,b^9+36\,B\,C^2\,a^2\,b^{10}-12\,C^3\,a^{11}\,b-24\,C^3\,a^{10}\,b^2+34\,C^3\,a^9\,b^3+26\,C^3\,a^8\,b^4-36\,C^3\,a^7\,b^5-13\,C^3\,a^6\,b^6+18\,C^3\,a^5\,b^7+2\,C^3\,a^4\,b^8-4\,C^3\,a^3\,b^9\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{\left(3\,B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B\,b-C\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(3\,B\,b-C\,a\right)}{a^4}\right)}{a^4}+\frac{\left(3\,B\,b-C\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,B\,b-C\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(3\,B\,b-C\,a\right)}{a^4}\right)}{a^4}}\right)\,\left(3\,B\,b-C\,a\right)\,2{}\mathrm{i}}{a^4\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{16\,\left(216\,B^3\,a^8\,b^4+216\,B^3\,a^7\,b^5-702\,B^3\,a^6\,b^6-378\,B^3\,a^5\,b^7+864\,B^3\,a^4\,b^8+243\,B^3\,a^3\,b^9-486\,B^3\,a^2\,b^{10}-54\,B^3\,a\,b^{11}+108\,B^3\,b^{12}-252\,B^2\,C\,a^9\,b^3-324\,B^2\,C\,a^8\,b^4+774\,B^2\,C\,a^7\,b^5+486\,B^2\,C\,a^6\,b^6-900\,B^2\,C\,a^5\,b^7-279\,B^2\,C\,a^4\,b^8+486\,B^2\,C\,a^3\,b^9+54\,B^2\,C\,a^2\,b^{10}-108\,B^2\,C\,a\,b^{11}+96\,B\,C^2\,a^{10}\,b^2+156\,B\,C^2\,a^9\,b^3-282\,B\,C^2\,a^8\,b^4-198\,B\,C^2\,a^7\,b^5+312\,B\,C^2\,a^6\,b^6+105\,B\,C^2\,a^5\,b^7-162\,B\,C^2\,a^4\,b^8-18\,B\,C^2\,a^3\,b^9+36\,B\,C^2\,a^2\,b^{10}-12\,C^3\,a^{11}\,b-24\,C^3\,a^{10}\,b^2+34\,C^3\,a^9\,b^3+26\,C^3\,a^8\,b^4-36\,C^3\,a^7\,b^5-13\,C^3\,a^6\,b^6+18\,C^3\,a^5\,b^7+2\,C^3\,a^4\,b^8-4\,C^3\,a^3\,b^9\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}-\frac{b\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3+36\,B^2\,a^8\,b^4+288\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6-432\,B^2\,a^5\,b^7+441\,B^2\,a^4\,b^8+288\,B^2\,a^3\,b^9-288\,B^2\,a^2\,b^{10}-72\,B^2\,a\,b^{11}+72\,B^2\,b^{12}-24\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2-72\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4+252\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6-318\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8+192\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-48\,B\,C\,a\,b^{11}+4\,C^2\,a^{12}-8\,C^2\,a^{11}\,b+24\,C^2\,a^{10}\,b^2+32\,C^2\,a^9\,b^3-52\,C^2\,a^8\,b^4-48\,C^2\,a^7\,b^5+57\,C^2\,a^6\,b^6+32\,C^2\,a^5\,b^7-32\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+8\,C^2\,a^2\,b^{10}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{b\,\left(\frac{8\,\left(4\,C\,a^{18}+12\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9-54\,B\,a^{10}\,b^8+24\,B\,a^{11}\,b^7+96\,B\,a^{12}\,b^6-42\,B\,a^{13}\,b^5-78\,B\,a^{14}\,b^4+36\,B\,a^{15}\,b^3+24\,B\,a^{16}\,b^2-4\,C\,a^9\,b^9+2\,C\,a^{10}\,b^8+18\,C\,a^{11}\,b^7-4\,C\,a^{12}\,b^6-36\,C\,a^{13}\,b^5+6\,C\,a^{14}\,b^4+34\,C\,a^{15}\,b^3-8\,C\,a^{16}\,b^2-12\,B\,a^{17}\,b-12\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-6\,C\,a^5+12\,B\,a^4\,b+5\,C\,a^3\,b^2-15\,B\,a^2\,b^3-2\,C\,a\,b^4+6\,B\,b^5\right)\,1{}\mathrm{i}}{d\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(6*B*b^5 - 2*B*a^5 - 12*B*a^2*b^3 + 4*B*a^3*b^2 + C*a^2*b^3 + 6*C*a^3*b^2 - 3*B*a*b^4 + 2*B*a^4*b - 2*C*a*b^4))/((a^3*b - a^4)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*B*a^5 + 6*B*b^5 - 12*B*a^2*b^3 - 4*B*a^3*b^2 - C*a^2*b^3 + 6*C*a^3*b^2 + 3*B*a*b^4 + 2*B*a^4*b - 2*C*a*b^4))/((a + b)*(a^5 - 2*a^4*b + a^3*b^2)) - (2*tan(c/2 + (d*x)/2)^3*(2*B*a^6 - 6*B*b^6 + 13*B*a^2*b^4 - 6*B*a^4*b^2 - 5*C*a^3*b^3 + 2*C*a*b^5))/(a*(a^2*b - a^3)*(a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) + (atan((((3*B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (8*tan(c/2 + (d*x)/2)*(3*B*b - C*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(3*B*b - C*a))/a^4)*1i)/a^4 + ((3*B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (8*tan(c/2 + (d*x)/2)*(3*B*b - C*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(3*B*b - C*a))/a^4)*1i)/a^4)/((16*(108*B^3*b^12 - 54*B^3*a*b^11 - 12*C^3*a^11*b - 486*B^3*a^2*b^10 + 243*B^3*a^3*b^9 + 864*B^3*a^4*b^8 - 378*B^3*a^5*b^7 - 702*B^3*a^6*b^6 + 216*B^3*a^7*b^5 + 216*B^3*a^8*b^4 - 4*C^3*a^3*b^9 + 2*C^3*a^4*b^8 + 18*C^3*a^5*b^7 - 13*C^3*a^6*b^6 - 36*C^3*a^7*b^5 + 26*C^3*a^8*b^4 + 34*C^3*a^9*b^3 - 24*C^3*a^10*b^2 - 108*B^2*C*a*b^11 + 36*B*C^2*a^2*b^10 - 18*B*C^2*a^3*b^9 - 162*B*C^2*a^4*b^8 + 105*B*C^2*a^5*b^7 + 312*B*C^2*a^6*b^6 - 198*B*C^2*a^7*b^5 - 282*B*C^2*a^8*b^4 + 156*B*C^2*a^9*b^3 + 96*B*C^2*a^10*b^2 + 54*B^2*C*a^2*b^10 + 486*B^2*C*a^3*b^9 - 279*B^2*C*a^4*b^8 - 900*B^2*C*a^5*b^7 + 486*B^2*C*a^6*b^6 + 774*B^2*C*a^7*b^5 - 324*B^2*C*a^8*b^4 - 252*B^2*C*a^9*b^3))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - ((3*B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (8*tan(c/2 + (d*x)/2)*(3*B*b - C*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(3*B*b - C*a))/a^4))/a^4 + ((3*B*b - C*a)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (8*tan(c/2 + (d*x)/2)*(3*B*b - C*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(3*B*b - C*a))/a^4))/a^4))*(3*B*b - C*a)*2i)/(a^4*d) + (b*atan(((b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((16*(108*B^3*b^12 - 54*B^3*a*b^11 - 12*C^3*a^11*b - 486*B^3*a^2*b^10 + 243*B^3*a^3*b^9 + 864*B^3*a^4*b^8 - 378*B^3*a^5*b^7 - 702*B^3*a^6*b^6 + 216*B^3*a^7*b^5 + 216*B^3*a^8*b^4 - 4*C^3*a^3*b^9 + 2*C^3*a^4*b^8 + 18*C^3*a^5*b^7 - 13*C^3*a^6*b^6 - 36*C^3*a^7*b^5 + 26*C^3*a^8*b^4 + 34*C^3*a^9*b^3 - 24*C^3*a^10*b^2 - 108*B^2*C*a*b^11 + 36*B*C^2*a^2*b^10 - 18*B*C^2*a^3*b^9 - 162*B*C^2*a^4*b^8 + 105*B*C^2*a^5*b^7 + 312*B*C^2*a^6*b^6 - 198*B*C^2*a^7*b^5 - 282*B*C^2*a^8*b^4 + 156*B*C^2*a^9*b^3 + 96*B*C^2*a^10*b^2 + 54*B^2*C*a^2*b^10 + 486*B^2*C*a^3*b^9 - 279*B^2*C*a^4*b^8 - 900*B^2*C*a^5*b^7 + 486*B^2*C*a^6*b^6 + 774*B^2*C*a^7*b^5 - 324*B^2*C*a^8*b^4 - 252*B^2*C*a^9*b^3))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) - (b*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*b^12 + 4*C^2*a^12 - 72*B^2*a*b^11 - 8*C^2*a^11*b - 288*B^2*a^2*b^10 + 288*B^2*a^3*b^9 + 441*B^2*a^4*b^8 - 432*B^2*a^5*b^7 - 288*B^2*a^6*b^6 + 288*B^2*a^7*b^5 + 36*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 36*B^2*a^10*b^2 + 8*C^2*a^2*b^10 - 8*C^2*a^3*b^9 - 32*C^2*a^4*b^8 + 32*C^2*a^5*b^7 + 57*C^2*a^6*b^6 - 48*C^2*a^7*b^5 - 52*C^2*a^8*b^4 + 32*C^2*a^9*b^3 + 24*C^2*a^10*b^2 - 48*B*C*a*b^11 - 24*B*C*a^11*b + 48*B*C*a^2*b^10 + 192*B*C*a^3*b^9 - 192*B*C*a^4*b^8 - 318*B*C*a^5*b^7 + 288*B*C*a^6*b^6 + 252*B*C*a^7*b^5 - 192*B*C*a^8*b^4 - 72*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (b*((8*(4*C*a^18 + 12*B*a^8*b^10 - 6*B*a^9*b^9 - 54*B*a^10*b^8 + 24*B*a^11*b^7 + 96*B*a^12*b^6 - 42*B*a^13*b^5 - 78*B*a^14*b^4 + 36*B*a^15*b^3 + 24*B*a^16*b^2 - 4*C*a^9*b^9 + 2*C*a^10*b^8 + 18*C*a^11*b^7 - 4*C*a^12*b^6 - 36*C*a^13*b^5 + 6*C*a^14*b^4 + 34*C*a^15*b^3 - 8*C*a^16*b^2 - 12*B*a^17*b - 12*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*B*b^5 - 6*C*a^5 - 15*B*a^2*b^3 + 5*C*a^3*b^2 + 12*B*a^4*b - 2*C*a*b^4)*1i)/(d*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))","B"
814,0,-1,303,0.000000,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
815,0,-1,231,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
816,0,-1,171,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
817,0,-1,178,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
818,0,-1,213,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
819,0,-1,292,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^4, x)","F"
820,0,-1,378,0.000000,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
821,0,-1,297,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
822,0,-1,225,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
823,0,-1,236,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
824,0,-1,232,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
825,0,-1,295,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^4, x)","F"
826,0,-1,375,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^5,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^5, x)","F"
827,0,-1,462,0.000000,"\text{Not used}","int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2), x)","F"
828,0,-1,372,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2), x)","F"
829,0,-1,288,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
830,0,-1,292,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
831,0,-1,296,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^3, x)","F"
832,0,-1,315,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^4,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^4, x)","F"
833,0,-1,376,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^5,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^5, x)","F"
834,0,-1,465,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^6,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^6, x)","F"
835,0,-1,246,0.000000,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
836,1,199,183,2.107056,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,C\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{3\,b\,d}+\frac{2\,B\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)-a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{b\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}+\frac{2\,C\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}\,\left(\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(2\,a^2+b^2\right)-2\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)\right)}{3\,b^2\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*C*sin(c + d*x)*(a + b*cos(c + d*x))^(1/2))/(3*b*d) + (2*B*(ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b) - a*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b)))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(b*d*(a + b*cos(c + d*x))^(1/2)) + (2*C*((a + b*cos(c + d*x))/(a + b))^(1/2)*(ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*(2*a^2 + b^2) - 2*a*ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b)))/(3*b^2*d*(a + b*cos(c + d*x))^(1/2))","B"
837,1,135,130,2.138926,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}+\frac{2\,C\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)-a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{b\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2)) + (2*C*(ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b) - a*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b)))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(b*d*(a + b*cos(c + d*x))^(1/2))","B"
838,0,-1,118,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)), x)","F"
839,0,-1,216,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)), x)","F"
840,0,-1,299,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^(1/2)), x)","F"
841,0,-1,387,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
842,0,-1,262,0.000000,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
843,0,-1,204,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2), x)","F"
844,0,-1,185,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)), x)","F"
845,0,-1,190,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)), x)","F"
846,0,-1,303,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)), x)","F"
847,0,-1,413,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
848,0,-1,331,0.000000,"\text{Not used}","int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
849,0,-1,307,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2), x)","F"
850,0,-1,275,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)), x)","F"
851,0,-1,349,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)), x)","F"
852,0,-1,437,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2)), x)","F"
853,1,177,170,1.053510,"\text{Not used}","int(cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*B*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
854,1,166,140,2.383015,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)),x)","\frac{2\,B\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,B\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*B*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
855,1,128,108,2.241923,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\frac{2\,B\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
856,1,85,75,0.666515,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\frac{2\,C\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}","Not used",1,"(2*C*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d","B"
857,1,96,71,2.691780,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(5/2),x)","\frac{2\,B\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
858,1,150,103,3.332549,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\frac{2\,C\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
859,1,177,140,3.611402,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/cos(c + d*x)^(9/2),x)","\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
860,1,275,264,2.780975,"\text{Not used}","int(cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"- (2*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
861,1,264,223,2.608459,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2,x)","\frac{2\,B\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
862,1,229,182,2.638333,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(1/2),x)","\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,B\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*B*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
863,1,177,140,2.647765,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(3/2),x)","\frac{B\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,B\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(B*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*B*a*b*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
864,1,158,121,2.815087,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(5/2),x)","\frac{C\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*B*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
865,1,194,126,3.532682,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(7/2),x)","\frac{2\,B\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
866,1,227,172,3.934243,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(9/2),x)","\frac{6\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,B\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,B\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*B*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*B*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*B*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
867,1,233,214,4.344407,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(11/2),x)","\frac{30\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,B\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,B\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,C\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(30*B*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*B*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 84*B*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*C*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*C*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*C*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
868,1,364,305,3.030986,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3,x)","\frac{B\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(B*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
869,1,328,255,2.880349,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(1/2),x)","\frac{2\,\left(B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,B\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^3*ellipticE(c/2 + (d*x)/2, 2) + B*a^2*b*ellipticF(c/2 + (d*x)/2, 2) + B*a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*B*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2))","B"
870,1,275,205,2.672130,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(3/2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{2\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,B\,a\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,B\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + C*a^2*b*ellipticF(c/2 + (d*x)/2, 2) + C*a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (2*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*B*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (3*B*a*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*B*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
871,1,248,202,2.745106,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(5/2),x)","\frac{B\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,C\,a\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(B*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*B*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*B*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (3*C*a*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
872,1,255,192,3.736442,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(7/2),x)","\frac{2\,\left(B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{C\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{6\,C\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*b^3*ellipticE(c/2 + (d*x)/2, 2) + 3*B*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + (C*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (6*C*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
873,1,291,204,4.958819,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(9/2),x)","\frac{2\,\left(C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{2\,B\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*b^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*B*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
874,1,311,255,5.197692,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(11/2),x)","\frac{\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,B\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+\frac{6\,B\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"((2*B*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*B*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 2*B*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + (6*B*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5)/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
875,1,304,305,5.942398,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(13/2),x)","\frac{70\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,B\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,B\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,C\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+\frac{6\,C\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(70*B*a^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 210*B*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*B*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 270*B*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + ((2*C*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*C*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 2*C*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + (6*C*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5)/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
876,0,-1,246,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
877,0,-1,182,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
878,0,-1,137,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
879,0,-1,89,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))), x)","F"
880,0,-1,61,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))), x)","F"
881,0,-1,86,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))), x)","F"
882,0,-1,150,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))), x)","F"
883,0,-1,217,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))), x)","F"
884,0,-1,389,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
885,0,-1,303,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
886,0,-1,224,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
887,0,-1,198,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
888,0,-1,200,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
889,0,-1,256,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
890,0,-1,345,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^2), x)","F"
891,0,-1,461,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
892,0,-1,367,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
893,0,-1,344,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
894,0,-1,337,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
895,0,-1,345,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
896,0,-1,420,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
897,0,-1,560,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2), x)","F"
898,0,-1,473,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
899,0,-1,385,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
900,0,-1,351,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2), x)","F"
901,0,-1,284,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2), x)","F"
902,0,-1,350,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(9/2), x)","F"
903,0,-1,433,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(11/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(11/2), x)","F"
904,0,-1,670,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2), x)","F"
905,0,-1,566,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
906,0,-1,472,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
907,0,-1,449,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2), x)","F"
908,0,-1,418,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2), x)","F"
909,0,-1,353,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(9/2), x)","F"
910,0,-1,433,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(11/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(11/2), x)","F"
911,0,-1,779,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2), x)","F"
912,0,-1,664,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
913,0,-1,563,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
914,0,-1,547,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
915,0,-1,536,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2), x)","F"
916,0,-1,493,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2), x)","F"
917,0,-1,434,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(11/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(11/2), x)","F"
918,0,-1,522,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(13/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{13/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(13/2), x)","F"
919,0,-1,622,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(15/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\cos\left(c+d\,x\right)}^{15/2}} \,d x","Not used",1,"int(((B*cos(c + d*x) + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(15/2), x)","F"
920,0,-1,571,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
921,0,-1,479,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
922,0,-1,391,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
923,0,-1,228,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
924,0,-1,230,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
925,0,-1,290,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
926,0,-1,363,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
927,0,-1,620,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
928,0,-1,500,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
929,0,-1,416,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
930,0,-1,284,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
931,0,-1,305,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
932,0,-1,393,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
933,0,-1,674,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
934,0,-1,545,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
935,0,-1,391,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
936,0,-1,429,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
937,0,-1,456,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
938,1,259,156,5.251816,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{x\,\left(A\,a+\frac{3\,B\,b}{4}+\frac{3\,C\,a}{4}\right)}{2}+\frac{\left(2\,A\,b-A\,a+2\,B\,a-\frac{5\,B\,b}{4}-\frac{5\,C\,a}{4}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{16\,A\,b}{3}-2\,A\,a+\frac{16\,B\,a}{3}-\frac{B\,b}{2}-\frac{C\,a}{2}+\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b}{3}+\frac{20\,B\,a}{3}+\frac{116\,C\,b}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,A\,a+\frac{16\,A\,b}{3}+\frac{16\,B\,a}{3}+\frac{B\,b}{2}+\frac{C\,a}{2}+\frac{8\,C\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a+2\,A\,b+2\,B\,a+\frac{5\,B\,b}{4}+\frac{5\,C\,a}{4}+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(x*(A*a + (3*B*b)/4 + (3*C*a)/4))/2 + (tan(c/2 + (d*x)/2)^3*(2*A*a + (16*A*b)/3 + (16*B*a)/3 + (B*b)/2 + (C*a)/2 + (8*C*b)/3) - tan(c/2 + (d*x)/2)^9*(A*a - 2*A*b - 2*B*a + (5*B*b)/4 + (5*C*a)/4 - 2*C*b) - tan(c/2 + (d*x)/2)^7*(2*A*a - (16*A*b)/3 - (16*B*a)/3 + (B*b)/2 + (C*a)/2 - (8*C*b)/3) + tan(c/2 + (d*x)/2)*(A*a + 2*A*b + 2*B*a + (5*B*b)/4 + (5*C*a)/4 + 2*C*b) + tan(c/2 + (d*x)/2)^5*((20*A*b)/3 + (20*B*a)/3 + (116*C*b)/15))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1))","B"
939,1,150,128,1.875261,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{A\,b\,x}{2}+\frac{B\,a\,x}{2}+\frac{3\,C\,b\,x}{8}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,C\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(A*b*x)/2 + (B*a*x)/2 + (3*C*b*x)/8 + (A*a*sin(c + d*x))/d + (3*B*b*sin(c + d*x))/(4*d) + (3*C*a*sin(c + d*x))/(4*d) + (A*b*sin(2*c + 2*d*x))/(4*d) + (B*a*sin(2*c + 2*d*x))/(4*d) + (B*b*sin(3*c + 3*d*x))/(12*d) + (C*a*sin(3*c + 3*d*x))/(12*d) + (C*b*sin(2*c + 2*d*x))/(4*d) + (C*b*sin(4*c + 4*d*x))/(32*d)","B"
940,1,100,80,1.791457,"\text{Not used}","int((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","A\,a\,x+\frac{B\,b\,x}{2}+\frac{C\,a\,x}{2}+\frac{A\,b\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"A*a*x + (B*b*x)/2 + (C*a*x)/2 + (A*b*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (3*C*b*sin(c + d*x))/(4*d) + (B*b*sin(2*c + 2*d*x))/(4*d) + (C*a*sin(2*c + 2*d*x))/(4*d) + (C*b*sin(3*c + 3*d*x))/(12*d)","B"
941,1,156,69,2.073985,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{B\,b\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,\sin\left(c+d\,x\right)}{d}+\frac{2\,A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,A\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(B*b*sin(c + d*x))/d + (C*a*sin(c + d*x))/d + (2*A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*A*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b*sin(2*c + 2*d*x))/(4*d)","B"
942,1,159,52,2.267560,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{A\,a\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,B\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}-\frac{A\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{B\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(A*a*tan(c + d*x))/d - (A*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (2*B*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*b*sin(2*c + 2*d*x))/(2*d*cos(c + d*x))","B"
943,1,164,69,2.342336,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{2\,\left(\frac{A\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+B\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{A\,a\,\sin\left(c+d\,x\right)}{2}+\frac{A\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((A*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + B*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((A*a*sin(c + d*x))/2 + (A*b*sin(2*c + 2*d*x))/2 + (B*a*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
944,1,190,101,5.105332,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A\,b}{2}+\frac{B\,a}{2}+C\,b\right)}{2\,A\,b+2\,B\,a+4\,C\,b}\right)\,\left(A\,b+B\,a+2\,C\,b\right)}{d}-\frac{\left(2\,A\,a-A\,b-B\,a+2\,B\,b+2\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A\,a}{3}-4\,B\,b-4\,C\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+A\,b+B\,a+2\,B\,b+2\,C\,a\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((A*b)/2 + (B*a)/2 + C*b))/(2*A*b + 2*B*a + 4*C*b))*(A*b + B*a + 2*C*b))/d - (tan(c/2 + (d*x)/2)*(2*A*a + A*b + B*a + 2*B*b + 2*C*a) - tan(c/2 + (d*x)/2)^3*((4*A*a)/3 + 4*B*b + 4*C*a) + tan(c/2 + (d*x)/2)^5*(2*A*a - A*b - B*a + 2*B*b + 2*C*a))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
945,1,256,137,5.289875,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A\,a}{8}+\frac{B\,b}{2}+\frac{C\,a}{2}\right)}{\frac{3\,A\,a}{2}+2\,B\,b+2\,C\,a}\right)\,\left(\frac{3\,A\,a}{4}+B\,b+C\,a\right)}{d}+\frac{\left(\frac{5\,A\,a}{4}-2\,A\,b-2\,B\,a+B\,b+C\,a-2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a}{4}+\frac{10\,A\,b}{3}+\frac{10\,B\,a}{3}-B\,b-C\,a+6\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,A\,a}{4}-\frac{10\,A\,b}{3}-\frac{10\,B\,a}{3}-B\,b-C\,a-6\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a}{4}+2\,A\,b+2\,B\,a+B\,b+C\,a+2\,C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((3*A*a)/8 + (B*b)/2 + (C*a)/2))/((3*A*a)/2 + 2*B*b + 2*C*a))*((3*A*a)/4 + B*b + C*a))/d + (tan(c/2 + (d*x)/2)^7*((5*A*a)/4 - 2*A*b - 2*B*a + B*b + C*a - 2*C*b) - tan(c/2 + (d*x)/2)^3*((10*A*b)/3 - (3*A*a)/4 + (10*B*a)/3 + B*b + C*a + 6*C*b) + tan(c/2 + (d*x)/2)^5*((3*A*a)/4 + (10*A*b)/3 + (10*B*a)/3 - B*b - C*a + 6*C*b) + tan(c/2 + (d*x)/2)*((5*A*a)/4 + 2*A*b + 2*B*a + B*b + C*a + 2*C*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
946,1,302,165,5.304567,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A\,b}{8}+\frac{3\,B\,a}{8}+\frac{C\,b}{2}\right)}{\frac{3\,A\,b}{2}+\frac{3\,B\,a}{2}+2\,C\,b}\right)\,\left(\frac{3\,A\,b}{4}+\frac{3\,B\,a}{4}+C\,b\right)}{d}-\frac{\left(2\,A\,a-\frac{5\,A\,b}{4}-\frac{5\,B\,a}{4}+2\,B\,b+2\,C\,a-C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{A\,b}{2}-\frac{8\,A\,a}{3}+\frac{B\,a}{2}-\frac{16\,B\,b}{3}-\frac{16\,C\,a}{3}+2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a}{15}+\frac{20\,B\,b}{3}+\frac{20\,C\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a}{3}-\frac{A\,b}{2}-\frac{B\,a}{2}-\frac{16\,B\,b}{3}-\frac{16\,C\,a}{3}-2\,C\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+\frac{5\,A\,b}{4}+\frac{5\,B\,a}{4}+2\,B\,b+2\,C\,a+C\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((3*A*b)/8 + (3*B*a)/8 + (C*b)/2))/((3*A*b)/2 + (3*B*a)/2 + 2*C*b))*((3*A*b)/4 + (3*B*a)/4 + C*b))/d - (tan(c/2 + (d*x)/2)^9*(2*A*a - (5*A*b)/4 - (5*B*a)/4 + 2*B*b + 2*C*a - C*b) - tan(c/2 + (d*x)/2)^3*((8*A*a)/3 + (A*b)/2 + (B*a)/2 + (16*B*b)/3 + (16*C*a)/3 + 2*C*b) - tan(c/2 + (d*x)/2)^7*((8*A*a)/3 - (A*b)/2 - (B*a)/2 + (16*B*b)/3 + (16*C*a)/3 - 2*C*b) + tan(c/2 + (d*x)/2)*(2*A*a + (5*A*b)/4 + (5*B*a)/4 + 2*B*b + 2*C*a + C*b) + tan(c/2 + (d*x)/2)^5*((116*A*a)/15 + (20*B*b)/3 + (20*C*a)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
947,1,256,224,2.443046,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{30\,B\,a^2\,\sin\left(2\,c+2\,d\,x\right)+10\,A\,b^2\,\sin\left(3\,c+3\,d\,x\right)+30\,B\,b^2\,\sin\left(2\,c+2\,d\,x\right)+10\,C\,a^2\,\sin\left(3\,c+3\,d\,x\right)+\frac{15\,B\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{25\,C\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,C\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{2}+120\,A\,a^2\,\sin\left(c+d\,x\right)+90\,A\,b^2\,\sin\left(c+d\,x\right)+90\,C\,a^2\,\sin\left(c+d\,x\right)+75\,C\,b^2\,\sin\left(c+d\,x\right)+60\,A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)+20\,B\,a\,b\,\sin\left(3\,c+3\,d\,x\right)+60\,C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)+\frac{15\,C\,a\,b\,\sin\left(4\,c+4\,d\,x\right)}{2}+60\,B\,a^2\,d\,x+45\,B\,b^2\,d\,x+180\,B\,a\,b\,\sin\left(c+d\,x\right)+120\,A\,a\,b\,d\,x+90\,C\,a\,b\,d\,x}{120\,d}","Not used",1,"(30*B*a^2*sin(2*c + 2*d*x) + 10*A*b^2*sin(3*c + 3*d*x) + 30*B*b^2*sin(2*c + 2*d*x) + 10*C*a^2*sin(3*c + 3*d*x) + (15*B*b^2*sin(4*c + 4*d*x))/4 + (25*C*b^2*sin(3*c + 3*d*x))/2 + (3*C*b^2*sin(5*c + 5*d*x))/2 + 120*A*a^2*sin(c + d*x) + 90*A*b^2*sin(c + d*x) + 90*C*a^2*sin(c + d*x) + 75*C*b^2*sin(c + d*x) + 60*A*a*b*sin(2*c + 2*d*x) + 20*B*a*b*sin(3*c + 3*d*x) + 60*C*a*b*sin(2*c + 2*d*x) + (15*C*a*b*sin(4*c + 4*d*x))/2 + 60*B*a^2*d*x + 45*B*b^2*d*x + 180*B*a*b*sin(c + d*x) + 120*A*a*b*d*x + 90*C*a*b*d*x)/(120*d)","B"
948,1,214,191,1.980625,"\text{Not used}","int((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","A\,a^2\,x+\frac{A\,b^2\,x}{2}+\frac{C\,a^2\,x}{2}+\frac{3\,C\,b^2\,x}{8}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+B\,a\,b\,x+\frac{A\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{2\,A\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{B\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}","Not used",1,"A*a^2*x + (A*b^2*x)/2 + (C*a^2*x)/2 + (3*C*b^2*x)/8 + (B*a^2*sin(c + d*x))/d + (3*B*b^2*sin(c + d*x))/(4*d) + B*a*b*x + (A*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*sin(2*c + 2*d*x))/(4*d) + (B*b^2*sin(3*c + 3*d*x))/(12*d) + (C*b^2*sin(2*c + 2*d*x))/(4*d) + (C*b^2*sin(4*c + 4*d*x))/(32*d) + (2*A*a*b*sin(c + d*x))/d + (3*C*a*b*sin(c + d*x))/(2*d) + (B*a*b*sin(2*c + 2*d*x))/(2*d) + (C*a*b*sin(3*c + 3*d*x))/(6*d)","B"
949,1,263,134,2.291161,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{A\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{2\,A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{2\,B\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{4\,A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{C\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"(A*b^2*sin(c + d*x))/d + (C*a^2*sin(c + d*x))/d + (3*C*b^2*sin(c + d*x))/(4*d) + (2*A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (B*b^2*sin(2*c + 2*d*x))/(4*d) + (C*b^2*sin(3*c + 3*d*x))/(12*d) + (2*B*a*b*sin(c + d*x))/d + (4*A*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (C*a*b*sin(2*c + 2*d*x))/(2*d)","B"
950,1,274,126,2.382213,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{B\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{2\,C\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{C\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}-\frac{B\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}}{d}-\frac{C\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,1{}\mathrm{i}}{d}-\frac{A\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}-\frac{B\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,4{}\mathrm{i}}{d}","Not used",1,"(B*b^2*sin(c + d*x))/d - (B*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (A*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*a^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (C*b^2*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/d + (A*a^2*sin(c + d*x))/(d*cos(c + d*x)) + (2*C*a*b*sin(c + d*x))/d - (A*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d - (B*a*b*atanh((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (C*b^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
951,1,257,118,3.166758,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{2\,\left(\frac{A\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+A\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+B\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+C\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,B\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,C\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\right)}{d}+\frac{\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{C\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{2}+\frac{C\,b^2\,\sin\left(c+d\,x\right)}{4}+A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"(2*((A*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + A*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + B*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + C*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*B*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*C*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((B*a^2*sin(2*c + 2*d*x))/2 + (C*b^2*sin(3*c + 3*d*x))/4 + (A*a^2*sin(c + d*x))/2 + (C*b^2*sin(c + d*x))/4 + A*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
952,1,512,141,3.228988,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\frac{\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{A\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{C\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{2}+\frac{A\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{C\,a^2\,\sin\left(c+d\,x\right)}{4}+\frac{A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,B\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}+\frac{3\,B\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{3\,C\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{B\,a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{B\,a\,b\,\sin\left(c+d\,x\right)}{2}+\frac{C\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,A\,a\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+3\,C\,a\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{A\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+C\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"((A*a^2*sin(3*c + 3*d*x))/6 + (B*a^2*sin(2*c + 2*d*x))/4 + (A*b^2*sin(3*c + 3*d*x))/4 + (C*a^2*sin(3*c + 3*d*x))/4 + (A*a^2*sin(c + d*x))/2 + (A*b^2*sin(c + d*x))/4 + (C*a^2*sin(c + d*x))/4 + (A*a*b*sin(2*c + 2*d*x))/2 + (B*a*b*sin(3*c + 3*d*x))/2 + (3*B*a^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + (3*B*b^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (3*C*b^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (B*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (B*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (B*a*b*sin(c + d*x))/2 + (C*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (3*A*a*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 3*C*a*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (A*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + C*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
953,1,389,184,5.309520,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{\left(\frac{5\,A\,a^2}{4}+A\,b^2-2\,B\,a^2-2\,B\,b^2+C\,a^2-4\,A\,a\,b+2\,B\,a\,b-4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a^2}{4}-A\,b^2+\frac{10\,B\,a^2}{3}+6\,B\,b^2-C\,a^2+\frac{20\,A\,a\,b}{3}-2\,B\,a\,b+12\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,A\,a^2}{4}-A\,b^2-\frac{10\,B\,a^2}{3}-6\,B\,b^2-C\,a^2-\frac{20\,A\,a\,b}{3}-2\,B\,a\,b-12\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a^2}{4}+A\,b^2+2\,B\,a^2+2\,B\,b^2+C\,a^2+4\,A\,a\,b+2\,B\,a\,b+4\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,A\,a^2}{8}+\frac{A\,b^2}{2}+\frac{C\,a^2}{2}+C\,b^2+B\,a\,b\right)}{\frac{3\,A\,a^2}{2}+2\,A\,b^2+2\,C\,a^2+4\,C\,b^2+4\,B\,a\,b}\right)\,\left(\frac{3\,A\,a^2}{4}+A\,b^2+C\,a^2+2\,C\,b^2+2\,B\,a\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*((5*A*a^2)/4 + A*b^2 - 2*B*a^2 - 2*B*b^2 + C*a^2 - 4*A*a*b + 2*B*a*b - 4*C*a*b) - tan(c/2 + (d*x)/2)^3*(A*b^2 - (3*A*a^2)/4 + (10*B*a^2)/3 + 6*B*b^2 + C*a^2 + (20*A*a*b)/3 + 2*B*a*b + 12*C*a*b) + tan(c/2 + (d*x)/2)^5*((3*A*a^2)/4 - A*b^2 + (10*B*a^2)/3 + 6*B*b^2 - C*a^2 + (20*A*a*b)/3 - 2*B*a*b + 12*C*a*b) + tan(c/2 + (d*x)/2)*((5*A*a^2)/4 + A*b^2 + 2*B*a^2 + 2*B*b^2 + C*a^2 + 4*A*a*b + 2*B*a*b + 4*C*a*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*((3*A*a^2)/8 + (A*b^2)/2 + (C*a^2)/2 + C*b^2 + B*a*b))/((3*A*a^2)/2 + 2*A*b^2 + 2*C*a^2 + 4*C*b^2 + 4*B*a*b))*((3*A*a^2)/4 + A*b^2 + C*a^2 + 2*C*b^2 + 2*B*a*b))/d","B"
954,1,455,232,5.168588,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,B\,a^2}{8}+\frac{B\,b^2}{2}+\frac{3\,A\,a\,b}{4}+C\,a\,b\right)}{\frac{3\,B\,a^2}{2}+2\,B\,b^2+3\,A\,a\,b+4\,C\,a\,b}\right)\,\left(\frac{3\,B\,a^2}{4}+B\,b^2+\frac{3\,A\,a\,b}{2}+2\,C\,a\,b\right)}{d}-\frac{\left(2\,A\,a^2+2\,A\,b^2-\frac{5\,B\,a^2}{4}-B\,b^2+2\,C\,a^2+2\,C\,b^2-\frac{5\,A\,a\,b}{2}+4\,B\,a\,b-2\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{B\,a^2}{2}-\frac{16\,A\,b^2}{3}-\frac{8\,A\,a^2}{3}+2\,B\,b^2-\frac{16\,C\,a^2}{3}-8\,C\,b^2+A\,a\,b-\frac{32\,B\,a\,b}{3}+4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^2}{15}+\frac{20\,A\,b^2}{3}+\frac{20\,C\,a^2}{3}+12\,C\,b^2+\frac{40\,B\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a^2}{3}-\frac{16\,A\,b^2}{3}-\frac{B\,a^2}{2}-2\,B\,b^2-\frac{16\,C\,a^2}{3}-8\,C\,b^2-A\,a\,b-\frac{32\,B\,a\,b}{3}-4\,C\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+\frac{5\,B\,a^2}{4}+B\,b^2+2\,C\,a^2+2\,C\,b^2+\frac{5\,A\,a\,b}{2}+4\,B\,a\,b+2\,C\,a\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((3*B*a^2)/8 + (B*b^2)/2 + (3*A*a*b)/4 + C*a*b))/((3*B*a^2)/2 + 2*B*b^2 + 3*A*a*b + 4*C*a*b))*((3*B*a^2)/4 + B*b^2 + (3*A*a*b)/2 + 2*C*a*b))/d - (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + (5*B*a^2)/4 + B*b^2 + 2*C*a^2 + 2*C*b^2 + (5*A*a*b)/2 + 4*B*a*b + 2*C*a*b) + tan(c/2 + (d*x)/2)^9*(2*A*a^2 + 2*A*b^2 - (5*B*a^2)/4 - B*b^2 + 2*C*a^2 + 2*C*b^2 - (5*A*a*b)/2 + 4*B*a*b - 2*C*a*b) - tan(c/2 + (d*x)/2)^3*((8*A*a^2)/3 + (16*A*b^2)/3 + (B*a^2)/2 + 2*B*b^2 + (16*C*a^2)/3 + 8*C*b^2 + A*a*b + (32*B*a*b)/3 + 4*C*a*b) - tan(c/2 + (d*x)/2)^7*((8*A*a^2)/3 + (16*A*b^2)/3 - (B*a^2)/2 - 2*B*b^2 + (16*C*a^2)/3 + 8*C*b^2 - A*a*b + (32*B*a*b)/3 - 4*C*a*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^2)/15 + (20*A*b^2)/3 + (20*C*a^2)/3 + 12*C*b^2 + (40*B*a*b)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
955,1,471,327,3.791923,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{3\,A\,b^3\,x}{8}+\frac{B\,a^3\,x}{2}+\frac{5\,C\,b^3\,x}{16}+\frac{3\,A\,a^2\,b\,x}{2}+\frac{9\,B\,a\,b^2\,x}{8}+\frac{9\,C\,a^2\,b\,x}{8}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,B\,b^3\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,C\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{5\,B\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{C\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{15\,C\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,C\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{C\,b^3\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{3\,A\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,B\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,B\,a\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,C\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,C\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{16\,d}+\frac{3\,C\,a^2\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,C\,a\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{9\,A\,a\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{9\,B\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{15\,C\,a\,b^2\,\sin\left(c+d\,x\right)}{8\,d}","Not used",1,"(3*A*b^3*x)/8 + (B*a^3*x)/2 + (5*C*b^3*x)/16 + (3*A*a^2*b*x)/2 + (9*B*a*b^2*x)/8 + (9*C*a^2*b*x)/8 + (A*a^3*sin(c + d*x))/d + (5*B*b^3*sin(c + d*x))/(8*d) + (3*C*a^3*sin(c + d*x))/(4*d) + (A*b^3*sin(2*c + 2*d*x))/(4*d) + (B*a^3*sin(2*c + 2*d*x))/(4*d) + (A*b^3*sin(4*c + 4*d*x))/(32*d) + (5*B*b^3*sin(3*c + 3*d*x))/(48*d) + (C*a^3*sin(3*c + 3*d*x))/(12*d) + (B*b^3*sin(5*c + 5*d*x))/(80*d) + (15*C*b^3*sin(2*c + 2*d*x))/(64*d) + (3*C*b^3*sin(4*c + 4*d*x))/(64*d) + (C*b^3*sin(6*c + 6*d*x))/(192*d) + (3*A*a^2*b*sin(2*c + 2*d*x))/(4*d) + (A*a*b^2*sin(3*c + 3*d*x))/(4*d) + (3*B*a*b^2*sin(2*c + 2*d*x))/(4*d) + (B*a^2*b*sin(3*c + 3*d*x))/(4*d) + (3*B*a*b^2*sin(4*c + 4*d*x))/(32*d) + (3*C*a^2*b*sin(2*c + 2*d*x))/(4*d) + (5*C*a*b^2*sin(3*c + 3*d*x))/(16*d) + (3*C*a^2*b*sin(4*c + 4*d*x))/(32*d) + (3*C*a*b^2*sin(5*c + 5*d*x))/(80*d) + (9*A*a*b^2*sin(c + d*x))/(4*d) + (9*B*a^2*b*sin(c + d*x))/(4*d) + (15*C*a*b^2*sin(c + d*x))/(8*d)","B"
956,1,359,277,2.646603,"\text{Not used}","int((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","A\,a^3\,x+\frac{3\,B\,b^3\,x}{8}+\frac{C\,a^3\,x}{2}+\frac{3\,A\,a\,b^2\,x}{2}+\frac{3\,B\,a^2\,b\,x}{2}+\frac{9\,C\,a\,b^2\,x}{8}+\frac{3\,A\,b^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,C\,b^3\,\sin\left(c+d\,x\right)}{8\,d}+\frac{A\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{5\,C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{C\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{3\,A\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,C\,a\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,A\,a^2\,b\,\sin\left(c+d\,x\right)}{d}+\frac{9\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{9\,C\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"A*a^3*x + (3*B*b^3*x)/8 + (C*a^3*x)/2 + (3*A*a*b^2*x)/2 + (3*B*a^2*b*x)/2 + (9*C*a*b^2*x)/8 + (3*A*b^3*sin(c + d*x))/(4*d) + (B*a^3*sin(c + d*x))/d + (5*C*b^3*sin(c + d*x))/(8*d) + (A*b^3*sin(3*c + 3*d*x))/(12*d) + (B*b^3*sin(2*c + 2*d*x))/(4*d) + (C*a^3*sin(2*c + 2*d*x))/(4*d) + (B*b^3*sin(4*c + 4*d*x))/(32*d) + (5*C*b^3*sin(3*c + 3*d*x))/(48*d) + (C*b^3*sin(5*c + 5*d*x))/(80*d) + (3*A*a*b^2*sin(2*c + 2*d*x))/(4*d) + (3*B*a^2*b*sin(2*c + 2*d*x))/(4*d) + (B*a*b^2*sin(3*c + 3*d*x))/(4*d) + (3*C*a*b^2*sin(2*c + 2*d*x))/(4*d) + (C*a^2*b*sin(3*c + 3*d*x))/(4*d) + (3*C*a*b^2*sin(4*c + 4*d*x))/(32*d) + (3*A*a^2*b*sin(c + d*x))/d + (9*B*a*b^2*sin(c + d*x))/(4*d) + (9*C*a^2*b*sin(c + d*x))/(4*d)","B"
957,1,3250,207,4.322044,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\left(2\,B\,b^3-A\,b^3+2\,C\,a^3-\frac{5\,C\,b^3}{4}+6\,A\,a\,b^2-3\,B\,a\,b^2+6\,B\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{10\,B\,b^3}{3}-A\,b^3+6\,C\,a^3+\frac{3\,C\,b^3}{4}+18\,A\,a\,b^2-3\,B\,a\,b^2+18\,B\,a^2\,b+10\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(A\,b^3+\frac{10\,B\,b^3}{3}+6\,C\,a^3-\frac{3\,C\,b^3}{4}+18\,A\,a\,b^2+3\,B\,a\,b^2+18\,B\,a^2\,b+10\,C\,a\,b^2+3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,b^3+2\,B\,b^3+2\,C\,a^3+\frac{5\,C\,b^3}{4}+6\,A\,a\,b^2+3\,B\,a\,b^2+6\,B\,a^2\,b+6\,C\,a\,b^2+3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{\left(\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)+\left(\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)\right)\,\left(\frac{A\,b^3\,1{}\mathrm{i}}{2}+B\,a^3\,1{}\mathrm{i}+\frac{C\,b^3\,3{}\mathrm{i}}{8}+A\,a^2\,b\,3{}\mathrm{i}+\frac{B\,a\,b^2\,3{}\mathrm{i}}{2}+\frac{C\,a^2\,b\,3{}\mathrm{i}}{2}\right)+64\,A\,B^2\,a^9-64\,A^2\,B\,a^9-192\,A^3\,a^8\,b+16\,A^3\,a^3\,b^6+192\,A^3\,a^5\,b^4-32\,A^3\,a^6\,b^3+576\,A^3\,a^7\,b^2+384\,A^2\,B\,a^8\,b-96\,A^2\,C\,a^8\,b+144\,A\,B^2\,a^5\,b^4+192\,A\,B^2\,a^7\,b^2+96\,A^2\,B\,a^4\,b^5+640\,A^2\,B\,a^6\,b^3-96\,A^2\,B\,a^7\,b^2+9\,A\,C^2\,a^3\,b^6+72\,A\,C^2\,a^5\,b^4+144\,A\,C^2\,a^7\,b^2+24\,A^2\,C\,a^3\,b^6+240\,A^2\,C\,a^5\,b^4-24\,A^2\,C\,a^6\,b^3+576\,A^2\,C\,a^7\,b^2+192\,A\,B\,C\,a^8\,b+72\,A\,B\,C\,a^4\,b^5+336\,A\,B\,C\,a^6\,b^3}\right)\,\left(A\,b^3+2\,B\,a^3+\frac{3\,C\,b^3}{4}+6\,A\,a^2\,b+3\,B\,a\,b^2+3\,C\,a^2\,b\right)}{d}-\frac{A\,a^3\,\mathrm{atan}\left(\frac{A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\right)\,1{}\mathrm{i}+A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\right)\,1{}\mathrm{i}}{64\,A\,B^2\,a^9-64\,A^2\,B\,a^9-192\,A^3\,a^8\,b+A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\right)-A\,a^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^6+288\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+8\,A^2\,b^6+192\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+48\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+120\,A\,C\,a^2\,b^4+12\,A\,C\,b^6+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4+96\,B\,C\,a^5\,b+168\,B\,C\,a^3\,b^3+36\,B\,C\,a\,b^5+72\,C^2\,a^4\,b^2+36\,C^2\,a^2\,b^4+\frac{9\,C^2\,b^6}{2}\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+12\,C\,b^3+96\,A\,a^2\,b+48\,B\,a\,b^2+48\,C\,a^2\,b\right)\right)+16\,A^3\,a^3\,b^6+192\,A^3\,a^5\,b^4-32\,A^3\,a^6\,b^3+576\,A^3\,a^7\,b^2+384\,A^2\,B\,a^8\,b-96\,A^2\,C\,a^8\,b+144\,A\,B^2\,a^5\,b^4+192\,A\,B^2\,a^7\,b^2+96\,A^2\,B\,a^4\,b^5+640\,A^2\,B\,a^6\,b^3-96\,A^2\,B\,a^7\,b^2+9\,A\,C^2\,a^3\,b^6+72\,A\,C^2\,a^5\,b^4+144\,A\,C^2\,a^7\,b^2+24\,A^2\,C\,a^3\,b^6+240\,A^2\,C\,a^5\,b^4-24\,A^2\,C\,a^6\,b^3+576\,A^2\,C\,a^7\,b^2+192\,A\,B\,C\,a^8\,b+72\,A\,B\,C\,a^4\,b^5+336\,A\,B\,C\,a^6\,b^3}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(2*B*b^3 - A*b^3 + 2*C*a^3 - (5*C*b^3)/4 + 6*A*a*b^2 - 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 - 3*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(A*b^3 + (10*B*b^3)/3 + 6*C*a^3 - (3*C*b^3)/4 + 18*A*a*b^2 + 3*B*a*b^2 + 18*B*a^2*b + 10*C*a*b^2 + 3*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((10*B*b^3)/3 - A*b^3 + 6*C*a^3 + (3*C*b^3)/4 + 18*A*a*b^2 - 3*B*a*b^2 + 18*B*a^2*b + 10*C*a*b^2 - 3*C*a^2*b) + tan(c/2 + (d*x)/2)*(A*b^3 + 2*B*b^3 + 2*C*a^3 + (5*C*b^3)/4 + 6*A*a*b^2 + 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atan(((((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) + tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2)*1i - (((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) - tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2)*1i)/((((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) + tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2) + (((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b) - tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + (C*b^3*3i)/8 + A*a^2*b*3i + (B*a*b^2*3i)/2 + (C*a^2*b*3i)/2) + 64*A*B^2*a^9 - 64*A^2*B*a^9 - 192*A^3*a^8*b + 16*A^3*a^3*b^6 + 192*A^3*a^5*b^4 - 32*A^3*a^6*b^3 + 576*A^3*a^7*b^2 + 384*A^2*B*a^8*b - 96*A^2*C*a^8*b + 144*A*B^2*a^5*b^4 + 192*A*B^2*a^7*b^2 + 96*A^2*B*a^4*b^5 + 640*A^2*B*a^6*b^3 - 96*A^2*B*a^7*b^2 + 9*A*C^2*a^3*b^6 + 72*A*C^2*a^5*b^4 + 144*A*C^2*a^7*b^2 + 24*A^2*C*a^3*b^6 + 240*A^2*C*a^5*b^4 - 24*A^2*C*a^6*b^3 + 576*A^2*C*a^7*b^2 + 192*A*B*C*a^8*b + 72*A*B*C*a^4*b^5 + 336*A*B*C*a^6*b^3))*(A*b^3 + 2*B*a^3 + (3*C*b^3)/4 + 6*A*a^2*b + 3*B*a*b^2 + 3*C*a^2*b))/d - (A*a^3*atan((A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) + A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b))*1i + A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) - A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b))*1i)/(64*A*B^2*a^9 - 64*A^2*B*a^9 - 192*A^3*a^8*b + A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) + A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b)) - A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + (9*C^2*b^6)/2 + 96*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 72*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 36*C^2*a^2*b^4 + 72*C^2*a^4*b^2 + 12*A*C*b^6 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 36*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 120*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 168*B*C*a^3*b^3) - A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 12*C*b^3 + 96*A*a^2*b + 48*B*a*b^2 + 48*C*a^2*b)) + 16*A^3*a^3*b^6 + 192*A^3*a^5*b^4 - 32*A^3*a^6*b^3 + 576*A^3*a^7*b^2 + 384*A^2*B*a^8*b - 96*A^2*C*a^8*b + 144*A*B^2*a^5*b^4 + 192*A*B^2*a^7*b^2 + 96*A^2*B*a^4*b^5 + 640*A^2*B*a^6*b^3 - 96*A^2*B*a^7*b^2 + 9*A*C^2*a^3*b^6 + 72*A*C^2*a^5*b^4 + 144*A*C^2*a^7*b^2 + 24*A^2*C*a^3*b^6 + 240*A^2*C*a^5*b^4 - 24*A^2*C*a^6*b^3 + 576*A^2*C*a^7*b^2 + 192*A*B*C*a^8*b + 72*A*B*C*a^4*b^5 + 336*A*B*C*a^6*b^3))*2i)/d","B"
958,1,2470,192,4.000378,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\left(2\,A\,a^3-2\,A\,b^3+B\,b^3-2\,C\,b^3-6\,B\,a\,b^2+3\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a^3-2\,A\,b^3-B\,b^3+\frac{2\,C\,b^3}{3}-6\,B\,a\,b^2-3\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,a^3+2\,A\,b^3-B\,b^3-\frac{2\,C\,b^3}{3}+6\,B\,a\,b^2-3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+2\,A\,b^3+B\,b^3+2\,C\,b^3+6\,B\,a\,b^2+3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(B\,a^3+3\,A\,b\,a^2\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(B\,a^3+3\,A\,b\,a^2\right)\,1{}\mathrm{i}-\left(\left(B\,a^3+3\,A\,b\,a^2\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(B\,a^3+3\,A\,b\,a^2\right)\,1{}\mathrm{i}}{\left(\left(B\,a^3+3\,A\,b\,a^2\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(B\,a^3+3\,A\,b\,a^2\right)+\left(\left(B\,a^3+3\,A\,b\,a^2\right)\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)\right)\,\left(B\,a^3+3\,A\,b\,a^2\right)+64\,B\,C^2\,a^9-64\,B^2\,C\,a^9-192\,B^3\,a^8\,b+1728\,A^3\,a^4\,b^5-1728\,A^3\,a^5\,b^4+16\,B^3\,a^3\,b^6+192\,B^3\,a^5\,b^4-32\,B^3\,a^6\,b^3+576\,B^3\,a^7\,b^2+192\,A\,C^2\,a^8\,b+384\,B^2\,C\,a^8\,b+48\,A\,B^2\,a^2\,b^7+768\,A\,B^2\,a^4\,b^5-192\,A\,B^2\,a^5\,b^4+2880\,A\,B^2\,a^6\,b^3-1344\,A\,B^2\,a^7\,b^2+576\,A^2\,B\,a^3\,b^6-288\,A^2\,B\,a^4\,b^5+4032\,A^2\,B\,a^5\,b^4-2880\,A^2\,B\,a^6\,b^3+432\,A\,C^2\,a^4\,b^5+576\,A\,C^2\,a^6\,b^3+1728\,A^2\,C\,a^4\,b^5-864\,A^2\,C\,a^5\,b^4+1152\,A^2\,C\,a^6\,b^3-576\,A^2\,C\,a^7\,b^2+144\,B\,C^2\,a^5\,b^4+192\,B\,C^2\,a^7\,b^2+96\,B^2\,C\,a^4\,b^5+640\,B^2\,C\,a^6\,b^3-96\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a^8\,b+288\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^5\,b^4-576\,A\,B\,C\,a^6\,b^3+1536\,A\,B\,C\,a^7\,b^2}\right)\,\left(2{}\mathrm{i}\,B\,a^3+6{}\mathrm{i}\,A\,b\,a^2\right)}{d}+\frac{\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}+C\,a^3\,1{}\mathrm{i}+A\,a\,b^2\,3{}\mathrm{i}+B\,a^2\,b\,3{}\mathrm{i}+\frac{C\,a\,b^2\,3{}\mathrm{i}}{2}\right)\,\left(288\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+192\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+192\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+32\,B^2\,a^6+288\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+8\,B^2\,b^6+192\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+48\,B\,C\,a\,b^5+32\,C^2\,a^6+96\,C^2\,a^4\,b^2+72\,C^2\,a^2\,b^4\right)}{2\,{\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}+C\,a^3\,1{}\mathrm{i}+A\,a\,b^2\,3{}\mathrm{i}+B\,a^2\,b\,3{}\mathrm{i}+\frac{C\,a\,b^2\,3{}\mathrm{i}}{2}\right)}^2\,\left(32\,B\,a^3+16\,B\,b^3+32\,C\,a^3+96\,A\,a\,b^2+96\,A\,a^2\,b+96\,B\,a^2\,b+48\,C\,a\,b^2\right)+64\,B\,C^2\,a^9-64\,B^2\,C\,a^9-192\,B^3\,a^8\,b+1728\,A^3\,a^4\,b^5-1728\,A^3\,a^5\,b^4+16\,B^3\,a^3\,b^6+192\,B^3\,a^5\,b^4-32\,B^3\,a^6\,b^3+576\,B^3\,a^7\,b^2+192\,A\,C^2\,a^8\,b+384\,B^2\,C\,a^8\,b+48\,A\,B^2\,a^2\,b^7+768\,A\,B^2\,a^4\,b^5-192\,A\,B^2\,a^5\,b^4+2880\,A\,B^2\,a^6\,b^3-1344\,A\,B^2\,a^7\,b^2+576\,A^2\,B\,a^3\,b^6-288\,A^2\,B\,a^4\,b^5+4032\,A^2\,B\,a^5\,b^4-2880\,A^2\,B\,a^6\,b^3+432\,A\,C^2\,a^4\,b^5+576\,A\,C^2\,a^6\,b^3+1728\,A^2\,C\,a^4\,b^5-864\,A^2\,C\,a^5\,b^4+1152\,A^2\,C\,a^6\,b^3-576\,A^2\,C\,a^7\,b^2+144\,B\,C^2\,a^5\,b^4+192\,B\,C^2\,a^7\,b^2+96\,B^2\,C\,a^4\,b^5+640\,B^2\,C\,a^6\,b^3-96\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a^8\,b+288\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^5\,b^4-576\,A\,B\,C\,a^6\,b^3+1536\,A\,B\,C\,a^7\,b^2}\right)\,\left(B\,b^3\,1{}\mathrm{i}+C\,a^3\,2{}\mathrm{i}+A\,a\,b^2\,6{}\mathrm{i}+B\,a^2\,b\,6{}\mathrm{i}+C\,a\,b^2\,3{}\mathrm{i}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^3 + 2*A*b^3 + B*b^3 + 2*C*b^3 + 6*B*a*b^2 + 3*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^7*(2*A*b^3 - 2*A*a^3 - B*b^3 + 2*C*b^3 + 6*B*a*b^2 - 3*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(6*A*a^3 + 2*A*b^3 - B*b^3 - (2*C*b^3)/3 + 6*B*a*b^2 - 3*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^5*(2*A*b^3 - 6*A*a^3 + B*b^3 - (2*C*b^3)/3 + 6*B*a*b^2 + 3*C*a*b^2 + 6*C*a^2*b))/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + 1)) - (atan((((B*a^3 + 3*A*a^2*b)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2) + tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*(B*a^3 + 3*A*a^2*b)*1i - ((B*a^3 + 3*A*a^2*b)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2) - tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*(B*a^3 + 3*A*a^2*b)*1i)/(((B*a^3 + 3*A*a^2*b)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2) + tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*(B*a^3 + 3*A*a^2*b) + ((B*a^3 + 3*A*a^2*b)*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2) - tan(c/2 + (d*x)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*(B*a^3 + 3*A*a^2*b) + 64*B*C^2*a^9 - 64*B^2*C*a^9 - 192*B^3*a^8*b + 1728*A^3*a^4*b^5 - 1728*A^3*a^5*b^4 + 16*B^3*a^3*b^6 + 192*B^3*a^5*b^4 - 32*B^3*a^6*b^3 + 576*B^3*a^7*b^2 + 192*A*C^2*a^8*b + 384*B^2*C*a^8*b + 48*A*B^2*a^2*b^7 + 768*A*B^2*a^4*b^5 - 192*A*B^2*a^5*b^4 + 2880*A*B^2*a^6*b^3 - 1344*A*B^2*a^7*b^2 + 576*A^2*B*a^3*b^6 - 288*A^2*B*a^4*b^5 + 4032*A^2*B*a^5*b^4 - 2880*A^2*B*a^6*b^3 + 432*A*C^2*a^4*b^5 + 576*A*C^2*a^6*b^3 + 1728*A^2*C*a^4*b^5 - 864*A^2*C*a^5*b^4 + 1152*A^2*C*a^6*b^3 - 576*A^2*C*a^7*b^2 + 144*B*C^2*a^5*b^4 + 192*B*C^2*a^7*b^2 + 96*B^2*C*a^4*b^5 + 640*B^2*C*a^6*b^3 - 96*B^2*C*a^7*b^2 - 384*A*B*C*a^8*b + 288*A*B*C*a^3*b^6 + 2496*A*B*C*a^5*b^4 - 576*A*B*C*a^6*b^3 + 1536*A*B*C*a^7*b^2))*(B*a^3*2i + A*a^2*b*6i))/d + (atanh((2*tan(c/2 + (d*x)/2)*((B*b^3*1i)/2 + C*a^3*1i + A*a*b^2*3i + B*a^2*b*3i + (C*a*b^2*3i)/2)*(32*B^2*a^6 + 8*B^2*b^6 + 32*C^2*a^6 + 288*A^2*a^2*b^4 + 288*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 72*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 96*A*B*a*b^5 + 192*A*B*a^5*b + 48*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 320*B*C*a^3*b^3))/(2*((B*b^3*1i)/2 + C*a^3*1i + A*a*b^2*3i + B*a^2*b*3i + (C*a*b^2*3i)/2)^2*(32*B*a^3 + 16*B*b^3 + 32*C*a^3 + 96*A*a*b^2 + 96*A*a^2*b + 96*B*a^2*b + 48*C*a*b^2) + 64*B*C^2*a^9 - 64*B^2*C*a^9 - 192*B^3*a^8*b + 1728*A^3*a^4*b^5 - 1728*A^3*a^5*b^4 + 16*B^3*a^3*b^6 + 192*B^3*a^5*b^4 - 32*B^3*a^6*b^3 + 576*B^3*a^7*b^2 + 192*A*C^2*a^8*b + 384*B^2*C*a^8*b + 48*A*B^2*a^2*b^7 + 768*A*B^2*a^4*b^5 - 192*A*B^2*a^5*b^4 + 2880*A*B^2*a^6*b^3 - 1344*A*B^2*a^7*b^2 + 576*A^2*B*a^3*b^6 - 288*A^2*B*a^4*b^5 + 4032*A^2*B*a^5*b^4 - 2880*A^2*B*a^6*b^3 + 432*A*C^2*a^4*b^5 + 576*A*C^2*a^6*b^3 + 1728*A^2*C*a^4*b^5 - 864*A^2*C*a^5*b^4 + 1152*A^2*C*a^6*b^3 - 576*A^2*C*a^7*b^2 + 144*B*C^2*a^5*b^4 + 192*B*C^2*a^7*b^2 + 96*B^2*C*a^4*b^5 + 640*B^2*C*a^6*b^3 - 96*B^2*C*a^7*b^2 - 384*A*B*C*a^8*b + 288*A*B*C*a^3*b^6 + 2496*A*B*C*a^5*b^4 - 576*A*B*C*a^6*b^3 + 1536*A*B*C*a^7*b^2))*(B*b^3*1i + C*a^3*2i + A*a*b^2*6i + B*a^2*b*6i + C*a*b^2*3i))/d","B"
959,1,3879,204,4.648253,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{\left(A\,a^3-2\,B\,a^3+2\,B\,b^3-C\,b^3-6\,A\,a^2\,b+6\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(3\,A\,a^3-2\,B\,a^3-2\,B\,b^3+3\,C\,b^3-6\,A\,a^2\,b-6\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(3\,A\,a^3+2\,B\,a^3-2\,B\,b^3-3\,C\,b^3+6\,A\,a^2\,b-6\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a^3+2\,B\,a^3+2\,B\,b^3+C\,b^3+6\,A\,a^2\,b+6\,C\,a\,b^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)\,1{}\mathrm{i}}{\left(\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)+\left(\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)\right)\,\left(\frac{A\,a^3}{2}+C\,a^3+3\,A\,a\,b^2+3\,B\,a^2\,b\right)+192\,A^3\,a\,b^8-192\,C^3\,a^8\,b-576\,A^3\,a^2\,b^7+32\,A^3\,a^3\,b^6-192\,A^3\,a^4\,b^5-16\,A^3\,a^6\,b^3+1728\,B^3\,a^4\,b^5-1728\,B^3\,a^5\,b^4+16\,C^3\,a^3\,b^6+192\,C^3\,a^5\,b^4-32\,C^3\,a^6\,b^3+576\,C^3\,a^7\,b^2+48\,A\,C^2\,a\,b^8-192\,A\,C^2\,a^8\,b+192\,A^2\,C\,a\,b^8-48\,A^2\,C\,a^8\,b+2880\,A\,B^2\,a^3\,b^6-4032\,A\,B^2\,a^4\,b^5+288\,A\,B^2\,a^5\,b^4-576\,A\,B^2\,a^6\,b^3+1344\,A^2\,B\,a^2\,b^7-2880\,A^2\,B\,a^3\,b^6+192\,A^2\,B\,a^4\,b^5-768\,A^2\,B\,a^5\,b^4-48\,A^2\,B\,a^7\,b^2+648\,A\,C^2\,a^3\,b^6-192\,A\,C^2\,a^4\,b^5+2208\,A\,C^2\,a^5\,b^4-1248\,A\,C^2\,a^6\,b^3+288\,A\,C^2\,a^7\,b^2-288\,A^2\,C\,a^2\,b^7+1248\,A^2\,C\,a^3\,b^6-2208\,A^2\,C\,a^4\,b^5+192\,A^2\,C\,a^5\,b^4-648\,A^2\,C\,a^6\,b^3+48\,B\,C^2\,a^2\,b^7+768\,B\,C^2\,a^4\,b^5-192\,B\,C^2\,a^5\,b^4+2880\,B\,C^2\,a^6\,b^3-1344\,B\,C^2\,a^7\,b^2+576\,B^2\,C\,a^3\,b^6-288\,B^2\,C\,a^4\,b^5+4032\,B^2\,C\,a^5\,b^4-2880\,B^2\,C\,a^6\,b^3+768\,A\,B\,C\,a^2\,b^7-576\,A\,B\,C\,a^3\,b^6+5088\,A\,B\,C\,a^4\,b^5-5088\,A\,B\,C\,a^5\,b^4+576\,A\,B\,C\,a^6\,b^3-768\,A\,B\,C\,a^7\,b^2}\right)\,\left(A\,a^3\,1{}\mathrm{i}+C\,a^3\,2{}\mathrm{i}+A\,a\,b^2\,6{}\mathrm{i}+B\,a^2\,b\,6{}\mathrm{i}\right)}{d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)-\frac{b\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)}{2}+\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)+\frac{b\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)}{2}}{192\,A^3\,a\,b^8-192\,C^3\,a^8\,b-576\,A^3\,a^2\,b^7+32\,A^3\,a^3\,b^6-192\,A^3\,a^4\,b^5-16\,A^3\,a^6\,b^3+1728\,B^3\,a^4\,b^5-1728\,B^3\,a^5\,b^4+16\,C^3\,a^3\,b^6+192\,C^3\,a^5\,b^4-32\,C^3\,a^6\,b^3+576\,C^3\,a^7\,b^2+48\,A\,C^2\,a\,b^8-192\,A\,C^2\,a^8\,b+192\,A^2\,C\,a\,b^8-48\,A^2\,C\,a^8\,b+2880\,A\,B^2\,a^3\,b^6-4032\,A\,B^2\,a^4\,b^5+288\,A\,B^2\,a^5\,b^4-576\,A\,B^2\,a^6\,b^3+1344\,A^2\,B\,a^2\,b^7-2880\,A^2\,B\,a^3\,b^6+192\,A^2\,B\,a^4\,b^5-768\,A^2\,B\,a^5\,b^4-48\,A^2\,B\,a^7\,b^2+648\,A\,C^2\,a^3\,b^6-192\,A\,C^2\,a^4\,b^5+2208\,A\,C^2\,a^5\,b^4-1248\,A\,C^2\,a^6\,b^3+288\,A\,C^2\,a^7\,b^2-288\,A^2\,C\,a^2\,b^7+1248\,A^2\,C\,a^3\,b^6-2208\,A^2\,C\,a^4\,b^5+192\,A^2\,C\,a^5\,b^4-648\,A^2\,C\,a^6\,b^3+48\,B\,C^2\,a^2\,b^7+768\,B\,C^2\,a^4\,b^5-192\,B\,C^2\,a^5\,b^4+2880\,B\,C^2\,a^6\,b^3-1344\,B\,C^2\,a^7\,b^2+576\,B^2\,C\,a^3\,b^6-288\,B^2\,C\,a^4\,b^5+4032\,B^2\,C\,a^5\,b^4-2880\,B^2\,C\,a^6\,b^3+768\,A\,B\,C\,a^2\,b^7-576\,A\,B\,C\,a^3\,b^6+5088\,A\,B\,C\,a^4\,b^5-5088\,A\,B\,C\,a^5\,b^4+576\,A\,B\,C\,a^6\,b^3-768\,A\,B\,C\,a^7\,b^2-\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)-\frac{b\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)\,1{}\mathrm{i}}{2}+\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6+96\,A^2\,a^4\,b^2+288\,A^2\,a^2\,b^4+32\,A^2\,b^6+96\,A\,B\,a^5\,b+576\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+32\,A\,C\,a^6+192\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+32\,A\,C\,b^6+288\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+192\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+96\,B\,C\,a\,b^5+32\,C^2\,a^6+288\,C^2\,a^4\,b^2+96\,C^2\,a^2\,b^4+8\,C^2\,b^6\right)+\frac{b\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)\,\left(16\,A\,a^3+32\,A\,b^3+32\,C\,a^3+16\,C\,b^3+96\,A\,a\,b^2+96\,B\,a\,b^2+96\,B\,a^2\,b+96\,C\,a^2\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)\,1{}\mathrm{i}}{2}}\right)\,\left(2\,A\,b^2+6\,C\,a^2+C\,b^2+6\,B\,a\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(A*a^3 - 2*B*a^3 + 2*B*b^3 - C*b^3 - 6*A*a^2*b + 6*C*a*b^2) + tan(c/2 + (d*x)/2)^3*(3*A*a^3 + 2*B*a^3 - 2*B*b^3 - 3*C*b^3 + 6*A*a^2*b - 6*C*a*b^2) - tan(c/2 + (d*x)/2)^5*(2*B*a^3 - 3*A*a^3 + 2*B*b^3 - 3*C*b^3 + 6*A*a^2*b + 6*C*a*b^2) + tan(c/2 + (d*x)/2)*(A*a^3 + 2*B*a^3 + 2*B*b^3 + C*b^3 + 6*A*a^2*b + 6*C*a*b^2))/(d*(tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^4 + 1)) - (atan(((((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b)*1i - (((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b)*1i)/((((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b) + (((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3))*((A*a^3)/2 + C*a^3 + 3*A*a*b^2 + 3*B*a^2*b) + 192*A^3*a*b^8 - 192*C^3*a^8*b - 576*A^3*a^2*b^7 + 32*A^3*a^3*b^6 - 192*A^3*a^4*b^5 - 16*A^3*a^6*b^3 + 1728*B^3*a^4*b^5 - 1728*B^3*a^5*b^4 + 16*C^3*a^3*b^6 + 192*C^3*a^5*b^4 - 32*C^3*a^6*b^3 + 576*C^3*a^7*b^2 + 48*A*C^2*a*b^8 - 192*A*C^2*a^8*b + 192*A^2*C*a*b^8 - 48*A^2*C*a^8*b + 2880*A*B^2*a^3*b^6 - 4032*A*B^2*a^4*b^5 + 288*A*B^2*a^5*b^4 - 576*A*B^2*a^6*b^3 + 1344*A^2*B*a^2*b^7 - 2880*A^2*B*a^3*b^6 + 192*A^2*B*a^4*b^5 - 768*A^2*B*a^5*b^4 - 48*A^2*B*a^7*b^2 + 648*A*C^2*a^3*b^6 - 192*A*C^2*a^4*b^5 + 2208*A*C^2*a^5*b^4 - 1248*A*C^2*a^6*b^3 + 288*A*C^2*a^7*b^2 - 288*A^2*C*a^2*b^7 + 1248*A^2*C*a^3*b^6 - 2208*A^2*C*a^4*b^5 + 192*A^2*C*a^5*b^4 - 648*A^2*C*a^6*b^3 + 48*B*C^2*a^2*b^7 + 768*B*C^2*a^4*b^5 - 192*B*C^2*a^5*b^4 + 2880*B*C^2*a^6*b^3 - 1344*B*C^2*a^7*b^2 + 576*B^2*C*a^3*b^6 - 288*B^2*C*a^4*b^5 + 4032*B^2*C*a^5*b^4 - 2880*B^2*C*a^6*b^3 + 768*A*B*C*a^2*b^7 - 576*A*B*C*a^3*b^6 + 5088*A*B*C*a^4*b^5 - 5088*A*B*C*a^5*b^4 + 576*A*B*C*a^6*b^3 - 768*A*B*C*a^7*b^2))*(A*a^3*1i + C*a^3*2i + A*a*b^2*6i + B*a^2*b*6i))/d - (b*atan(((b*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) - (b*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b))/2 + (b*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) + (b*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b))/2)/(192*A^3*a*b^8 - 192*C^3*a^8*b - (b*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) - (b*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b)*1i)/2 + (b*(tan(c/2 + (d*x)/2)*(8*A^2*a^6 + 32*A^2*b^6 + 32*C^2*a^6 + 8*C^2*b^6 + 288*A^2*a^2*b^4 + 96*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 288*B^2*a^4*b^2 + 96*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 32*A*C*a^6 + 32*A*C*b^6 + 192*A*B*a*b^5 + 96*A*B*a^5*b + 96*B*C*a*b^5 + 192*B*C*a^5*b + 576*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 192*A*C*a^4*b^2 + 576*B*C*a^3*b^3) + (b*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b)*(16*A*a^3 + 32*A*b^3 + 32*C*a^3 + 16*C*b^3 + 96*A*a*b^2 + 96*B*a*b^2 + 96*B*a^2*b + 96*C*a^2*b)*1i)/2)*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b)*1i)/2 - 576*A^3*a^2*b^7 + 32*A^3*a^3*b^6 - 192*A^3*a^4*b^5 - 16*A^3*a^6*b^3 + 1728*B^3*a^4*b^5 - 1728*B^3*a^5*b^4 + 16*C^3*a^3*b^6 + 192*C^3*a^5*b^4 - 32*C^3*a^6*b^3 + 576*C^3*a^7*b^2 + 48*A*C^2*a*b^8 - 192*A*C^2*a^8*b + 192*A^2*C*a*b^8 - 48*A^2*C*a^8*b + 2880*A*B^2*a^3*b^6 - 4032*A*B^2*a^4*b^5 + 288*A*B^2*a^5*b^4 - 576*A*B^2*a^6*b^3 + 1344*A^2*B*a^2*b^7 - 2880*A^2*B*a^3*b^6 + 192*A^2*B*a^4*b^5 - 768*A^2*B*a^5*b^4 - 48*A^2*B*a^7*b^2 + 648*A*C^2*a^3*b^6 - 192*A*C^2*a^4*b^5 + 2208*A*C^2*a^5*b^4 - 1248*A*C^2*a^6*b^3 + 288*A*C^2*a^7*b^2 - 288*A^2*C*a^2*b^7 + 1248*A^2*C*a^3*b^6 - 2208*A^2*C*a^4*b^5 + 192*A^2*C*a^5*b^4 - 648*A^2*C*a^6*b^3 + 48*B*C^2*a^2*b^7 + 768*B*C^2*a^4*b^5 - 192*B*C^2*a^5*b^4 + 2880*B*C^2*a^6*b^3 - 1344*B*C^2*a^7*b^2 + 576*B^2*C*a^3*b^6 - 288*B^2*C*a^4*b^5 + 4032*B^2*C*a^5*b^4 - 2880*B^2*C*a^6*b^3 + 768*A*B*C*a^2*b^7 - 576*A*B*C*a^3*b^6 + 5088*A*B*C*a^4*b^5 - 5088*A*B*C*a^5*b^4 + 576*A*B*C*a^6*b^3 - 768*A*B*C*a^7*b^2))*(2*A*b^2 + 6*C*a^2 + C*b^2 + 6*B*a*b))/d","B"
960,1,2437,196,4.032985,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","-\frac{\left(2\,A\,a^3-B\,a^3+2\,C\,a^3-2\,C\,b^3+6\,A\,a\,b^2-3\,A\,a^2\,b+6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{2\,A\,a^3}{3}-B\,a^3-2\,C\,a^3+6\,C\,b^3-6\,A\,a\,b^2-3\,A\,a^2\,b-6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{2\,A\,a^3}{3}+B\,a^3-2\,C\,a^3-6\,C\,b^3-6\,A\,a\,b^2+3\,A\,a^2\,b-6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+B\,a^3+2\,C\,a^3+2\,C\,b^3+6\,A\,a\,b^2+3\,A\,a^2\,b+6\,B\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atanh}\left(\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^3+\frac{B\,a^3}{2}+\frac{3\,A\,a^2\,b}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)}{64\,A^2\,B\,b^9-64\,A\,B^2\,b^9-2\,{\left(A\,b^3+\frac{B\,a^3}{2}+\frac{3\,A\,a^2\,b}{2}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)}^2\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)-192\,B^3\,a\,b^8+576\,B^3\,a^2\,b^7-32\,B^3\,a^3\,b^6+192\,B^3\,a^4\,b^5+16\,B^3\,a^6\,b^3-1728\,C^3\,a^4\,b^5+1728\,C^3\,a^5\,b^4+384\,A\,B^2\,a\,b^8+192\,A^2\,C\,a\,b^8-96\,A\,B^2\,a^2\,b^7+640\,A\,B^2\,a^3\,b^6+96\,A\,B^2\,a^5\,b^4+192\,A^2\,B\,a^2\,b^7+144\,A^2\,B\,a^4\,b^5-576\,A\,C^2\,a^2\,b^7+1152\,A\,C^2\,a^3\,b^6-864\,A\,C^2\,a^4\,b^5+1728\,A\,C^2\,a^5\,b^4+576\,A^2\,C\,a^3\,b^6+432\,A^2\,C\,a^5\,b^4-2880\,B\,C^2\,a^3\,b^6+4032\,B\,C^2\,a^4\,b^5-288\,B\,C^2\,a^5\,b^4+576\,B\,C^2\,a^6\,b^3-1344\,B^2\,C\,a^2\,b^7+2880\,B^2\,C\,a^3\,b^6-192\,B^2\,C\,a^4\,b^5+768\,B^2\,C\,a^5\,b^4+48\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a\,b^8+1536\,A\,B\,C\,a^2\,b^7-576\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^4\,b^5+288\,A\,B\,C\,a^6\,b^3}\right)\,\left(2\,A\,b^3+B\,a^3+3\,A\,a^2\,b+6\,B\,a\,b^2+6\,C\,a^2\,b\right)}{d}+\frac{2\,b^2\,\mathrm{atan}\left(\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)-b^2\,\left(B\,b+3\,C\,a\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b+3\,C\,a\right)+b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)+b^2\,\left(B\,b+3\,C\,a\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b+3\,C\,a\right)}{64\,A^2\,B\,b^9-64\,A\,B^2\,b^9-192\,B^3\,a\,b^8+576\,B^3\,a^2\,b^7-32\,B^3\,a^3\,b^6+192\,B^3\,a^4\,b^5+16\,B^3\,a^6\,b^3-1728\,C^3\,a^4\,b^5+1728\,C^3\,a^5\,b^4+384\,A\,B^2\,a\,b^8+192\,A^2\,C\,a\,b^8-96\,A\,B^2\,a^2\,b^7+640\,A\,B^2\,a^3\,b^6+96\,A\,B^2\,a^5\,b^4+192\,A^2\,B\,a^2\,b^7+144\,A^2\,B\,a^4\,b^5-576\,A\,C^2\,a^2\,b^7+1152\,A\,C^2\,a^3\,b^6-864\,A\,C^2\,a^4\,b^5+1728\,A\,C^2\,a^5\,b^4+576\,A^2\,C\,a^3\,b^6+432\,A^2\,C\,a^5\,b^4-2880\,B\,C^2\,a^3\,b^6+4032\,B\,C^2\,a^4\,b^5-288\,B\,C^2\,a^5\,b^4+576\,B\,C^2\,a^6\,b^3-1344\,B^2\,C\,a^2\,b^7+2880\,B^2\,C\,a^3\,b^6-192\,B^2\,C\,a^4\,b^5+768\,B^2\,C\,a^5\,b^4+48\,B^2\,C\,a^7\,b^2-384\,A\,B\,C\,a\,b^8+1536\,A\,B\,C\,a^2\,b^7-576\,A\,B\,C\,a^3\,b^6+2496\,A\,B\,C\,a^4\,b^5+288\,A\,B\,C\,a^6\,b^3+b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)-b^2\,\left(B\,b+3\,C\,a\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b+3\,C\,a\right)\,1{}\mathrm{i}-b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^4\,b^2+96\,A^2\,a^2\,b^4+32\,A^2\,b^6+48\,A\,B\,a^5\,b+320\,A\,B\,a^3\,b^3+192\,A\,B\,a\,b^5+288\,A\,C\,a^4\,b^2+192\,A\,C\,a^2\,b^4+8\,B^2\,a^6+96\,B^2\,a^4\,b^2+288\,B^2\,a^2\,b^4+32\,B^2\,b^6+96\,B\,C\,a^5\,b+576\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+288\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4\right)+b^2\,\left(B\,b+3\,C\,a\right)\,\left(32\,A\,b^3+16\,B\,a^3+32\,B\,b^3+48\,A\,a^2\,b+96\,B\,a\,b^2+96\,C\,a\,b^2+96\,C\,a^2\,b\right)\,1{}\mathrm{i}\right)\,\left(B\,b+3\,C\,a\right)\,1{}\mathrm{i}}\right)\,\left(B\,b+3\,C\,a\right)}{d}","Not used",1,"(2*b^2*atan((b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3) - b^2*(B*b + 3*C*a)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b)*1i)*(B*b + 3*C*a) + b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3) + b^2*(B*b + 3*C*a)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b)*1i)*(B*b + 3*C*a))/(64*A^2*B*b^9 - 64*A*B^2*b^9 - 192*B^3*a*b^8 + 576*B^3*a^2*b^7 - 32*B^3*a^3*b^6 + 192*B^3*a^4*b^5 + 16*B^3*a^6*b^3 - 1728*C^3*a^4*b^5 + 1728*C^3*a^5*b^4 + b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3) - b^2*(B*b + 3*C*a)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b)*1i)*(B*b + 3*C*a)*1i - b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3) + b^2*(B*b + 3*C*a)*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b)*1i)*(B*b + 3*C*a)*1i + 384*A*B^2*a*b^8 + 192*A^2*C*a*b^8 - 96*A*B^2*a^2*b^7 + 640*A*B^2*a^3*b^6 + 96*A*B^2*a^5*b^4 + 192*A^2*B*a^2*b^7 + 144*A^2*B*a^4*b^5 - 576*A*C^2*a^2*b^7 + 1152*A*C^2*a^3*b^6 - 864*A*C^2*a^4*b^5 + 1728*A*C^2*a^5*b^4 + 576*A^2*C*a^3*b^6 + 432*A^2*C*a^5*b^4 - 2880*B*C^2*a^3*b^6 + 4032*B*C^2*a^4*b^5 - 288*B*C^2*a^5*b^4 + 576*B*C^2*a^6*b^3 - 1344*B^2*C*a^2*b^7 + 2880*B^2*C*a^3*b^6 - 192*B^2*C*a^4*b^5 + 768*B^2*C*a^5*b^4 + 48*B^2*C*a^7*b^2 - 384*A*B*C*a*b^8 + 1536*A*B*C*a^2*b^7 - 576*A*B*C*a^3*b^6 + 2496*A*B*C*a^4*b^5 + 288*A*B*C*a^6*b^3))*(B*b + 3*C*a))/d - (atanh((2*tan(c/2 + (d*x)/2)*(A*b^3 + (B*a^3)/2 + (3*A*a^2*b)/2 + 3*B*a*b^2 + 3*C*a^2*b)*(32*A^2*b^6 + 8*B^2*a^6 + 32*B^2*b^6 + 96*A^2*a^2*b^4 + 72*A^2*a^4*b^2 + 288*B^2*a^2*b^4 + 96*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 288*C^2*a^4*b^2 + 192*A*B*a*b^5 + 48*A*B*a^5*b + 192*B*C*a*b^5 + 96*B*C*a^5*b + 320*A*B*a^3*b^3 + 192*A*C*a^2*b^4 + 288*A*C*a^4*b^2 + 576*B*C*a^3*b^3))/(64*A^2*B*b^9 - 64*A*B^2*b^9 - 2*(A*b^3 + (B*a^3)/2 + (3*A*a^2*b)/2 + 3*B*a*b^2 + 3*C*a^2*b)^2*(32*A*b^3 + 16*B*a^3 + 32*B*b^3 + 48*A*a^2*b + 96*B*a*b^2 + 96*C*a*b^2 + 96*C*a^2*b) - 192*B^3*a*b^8 + 576*B^3*a^2*b^7 - 32*B^3*a^3*b^6 + 192*B^3*a^4*b^5 + 16*B^3*a^6*b^3 - 1728*C^3*a^4*b^5 + 1728*C^3*a^5*b^4 + 384*A*B^2*a*b^8 + 192*A^2*C*a*b^8 - 96*A*B^2*a^2*b^7 + 640*A*B^2*a^3*b^6 + 96*A*B^2*a^5*b^4 + 192*A^2*B*a^2*b^7 + 144*A^2*B*a^4*b^5 - 576*A*C^2*a^2*b^7 + 1152*A*C^2*a^3*b^6 - 864*A*C^2*a^4*b^5 + 1728*A*C^2*a^5*b^4 + 576*A^2*C*a^3*b^6 + 432*A^2*C*a^5*b^4 - 2880*B*C^2*a^3*b^6 + 4032*B*C^2*a^4*b^5 - 288*B*C^2*a^5*b^4 + 576*B*C^2*a^6*b^3 - 1344*B^2*C*a^2*b^7 + 2880*B^2*C*a^3*b^6 - 192*B^2*C*a^4*b^5 + 768*B^2*C*a^5*b^4 + 48*B^2*C*a^7*b^2 - 384*A*B*C*a*b^8 + 1536*A*B*C*a^2*b^7 - 576*A*B*C*a^3*b^6 + 2496*A*B*C*a^4*b^5 + 288*A*B*C*a^6*b^3))*(2*A*b^3 + B*a^3 + 3*A*a^2*b + 6*B*a*b^2 + 6*C*a^2*b))/d - (tan(c/2 + (d*x)/2)*(2*A*a^3 + B*a^3 + 2*C*a^3 + 2*C*b^3 + 6*A*a*b^2 + 3*A*a^2*b + 6*B*a^2*b) + tan(c/2 + (d*x)/2)^7*(2*A*a^3 - B*a^3 + 2*C*a^3 - 2*C*b^3 + 6*A*a*b^2 - 3*A*a^2*b + 6*B*a^2*b) - tan(c/2 + (d*x)/2)^3*(2*C*a^3 - B*a^3 - (2*A*a^3)/3 + 6*C*b^3 + 6*A*a*b^2 - 3*A*a^2*b + 6*B*a^2*b) - tan(c/2 + (d*x)/2)^5*(B*a^3 - (2*A*a^3)/3 + 2*C*a^3 - 6*C*b^3 + 6*A*a*b^2 + 3*A*a^2*b + 6*B*a^2*b))/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 - 1))","B"
961,1,3210,223,4.343063,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)\,1{}\mathrm{i}-\left(\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)\,1{}\mathrm{i}}{64\,B^2\,C\,b^9-\left(\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)-64\,B\,C^2\,b^9-\left(\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^3}{8}+B\,b^3+\frac{C\,a^3}{2}+\frac{3\,A\,a\,b^2}{2}+\frac{3\,B\,a^2\,b}{2}+3\,C\,a\,b^2\right)-192\,C^3\,a\,b^8+576\,C^3\,a^2\,b^7-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3-96\,A\,C^2\,a\,b^8+384\,B\,C^2\,a\,b^8+576\,A\,C^2\,a^2\,b^7-24\,A\,C^2\,a^3\,b^6+240\,A\,C^2\,a^4\,b^5+24\,A\,C^2\,a^6\,b^3+144\,A^2\,C\,a^2\,b^7+72\,A^2\,C\,a^4\,b^5+9\,A^2\,C\,a^6\,b^3-96\,B\,C^2\,a^2\,b^7+640\,B\,C^2\,a^3\,b^6+96\,B\,C^2\,a^5\,b^4+192\,B^2\,C\,a^2\,b^7+144\,B^2\,C\,a^4\,b^5+192\,A\,B\,C\,a\,b^8+336\,A\,B\,C\,a^3\,b^6+72\,A\,B\,C\,a^5\,b^4}\right)\,\left(\frac{A\,a^3\,3{}\mathrm{i}}{4}+B\,b^3\,2{}\mathrm{i}+C\,a^3\,1{}\mathrm{i}+A\,a\,b^2\,3{}\mathrm{i}+B\,a^2\,b\,3{}\mathrm{i}+C\,a\,b^2\,6{}\mathrm{i}\right)}{d}-\frac{\left(2\,A\,b^3-\frac{5\,A\,a^3}{4}+2\,B\,a^3-C\,a^3-3\,A\,a\,b^2+6\,A\,a^2\,b+6\,B\,a\,b^2-3\,B\,a^2\,b+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(C\,a^3-6\,A\,b^3-\frac{10\,B\,a^3}{3}-\frac{3\,A\,a^3}{4}+3\,A\,a\,b^2-10\,A\,a^2\,b-18\,B\,a\,b^2+3\,B\,a^2\,b-18\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,b^3-\frac{3\,A\,a^3}{4}+\frac{10\,B\,a^3}{3}+C\,a^3+3\,A\,a\,b^2+10\,A\,a^2\,b+18\,B\,a\,b^2+3\,B\,a^2\,b+18\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-\frac{5\,A\,a^3}{4}-2\,A\,b^3-2\,B\,a^3-C\,a^3-3\,A\,a\,b^2-6\,A\,a^2\,b-6\,B\,a\,b^2-3\,B\,a^2\,b-6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,C\,b^3\,\mathrm{atan}\left(\frac{C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)}{64\,B^2\,C\,b^9-64\,B\,C^2\,b^9-192\,C^3\,a\,b^8+576\,C^3\,a^2\,b^7-32\,C^3\,a^3\,b^6+192\,C^3\,a^4\,b^5+16\,C^3\,a^6\,b^3-96\,A\,C^2\,a\,b^8+384\,B\,C^2\,a\,b^8+576\,A\,C^2\,a^2\,b^7-24\,A\,C^2\,a^3\,b^6+240\,A\,C^2\,a^4\,b^5+24\,A\,C^2\,a^6\,b^3+144\,A^2\,C\,a^2\,b^7+72\,A^2\,C\,a^4\,b^5+9\,A^2\,C\,a^6\,b^3-96\,B\,C^2\,a^2\,b^7+640\,B\,C^2\,a^3\,b^6+96\,B\,C^2\,a^5\,b^4+192\,B^2\,C\,a^2\,b^7+144\,B^2\,C\,a^4\,b^5+192\,A\,B\,C\,a\,b^8+336\,A\,B\,C\,a^3\,b^6+72\,A\,B\,C\,a^5\,b^4+C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)-C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-C\,b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^6}{2}+36\,A^2\,a^4\,b^2+72\,A^2\,a^2\,b^4+36\,A\,B\,a^5\,b+168\,A\,B\,a^3\,b^3+96\,A\,B\,a\,b^5+12\,A\,C\,a^6+120\,A\,C\,a^4\,b^2+288\,A\,C\,a^2\,b^4+72\,B^2\,a^4\,b^2+96\,B^2\,a^2\,b^4+32\,B^2\,b^6+48\,B\,C\,a^5\,b+320\,B\,C\,a^3\,b^3+192\,B\,C\,a\,b^5+8\,C^2\,a^6+96\,C^2\,a^4\,b^2+288\,C^2\,a^2\,b^4+32\,C^2\,b^6\right)+C\,b^3\,\left(12\,A\,a^3+32\,B\,b^3+16\,C\,a^3+32\,C\,b^3+48\,A\,a\,b^2+48\,B\,a^2\,b+96\,C\,a\,b^2\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)}{d}","Not used",1,"(atan(((((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) + tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2)*1i - (((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) - tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2)*1i)/(64*B^2*C*b^9 - (((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) - tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2) - 64*B*C^2*b^9 - (((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2)*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2) + tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3))*((3*A*a^3)/8 + B*b^3 + (C*a^3)/2 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2 + 3*C*a*b^2) - 192*C^3*a*b^8 + 576*C^3*a^2*b^7 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 - 96*A*C^2*a*b^8 + 384*B*C^2*a*b^8 + 576*A*C^2*a^2*b^7 - 24*A*C^2*a^3*b^6 + 240*A*C^2*a^4*b^5 + 24*A*C^2*a^6*b^3 + 144*A^2*C*a^2*b^7 + 72*A^2*C*a^4*b^5 + 9*A^2*C*a^6*b^3 - 96*B*C^2*a^2*b^7 + 640*B*C^2*a^3*b^6 + 96*B*C^2*a^5*b^4 + 192*B^2*C*a^2*b^7 + 144*B^2*C*a^4*b^5 + 192*A*B*C*a*b^8 + 336*A*B*C*a^3*b^6 + 72*A*B*C*a^5*b^4))*((A*a^3*3i)/4 + B*b^3*2i + C*a^3*1i + A*a*b^2*3i + B*a^2*b*3i + C*a*b^2*6i))/d - (tan(c/2 + (d*x)/2)^7*(2*A*b^3 - (5*A*a^3)/4 + 2*B*a^3 - C*a^3 - 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 - 3*B*a^2*b + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^3*(6*A*b^3 - (3*A*a^3)/4 + (10*B*a^3)/3 + C*a^3 + 3*A*a*b^2 + 10*A*a^2*b + 18*B*a*b^2 + 3*B*a^2*b + 18*C*a^2*b) - tan(c/2 + (d*x)/2)^5*((3*A*a^3)/4 + 6*A*b^3 + (10*B*a^3)/3 - C*a^3 - 3*A*a*b^2 + 10*A*a^2*b + 18*B*a*b^2 - 3*B*a^2*b + 18*C*a^2*b) - tan(c/2 + (d*x)/2)*((5*A*a^3)/4 + 2*A*b^3 + 2*B*a^3 + C*a^3 + 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 + 3*B*a^2*b + 6*C*a^2*b))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (2*C*b^3*atan((C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) - C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2)*1i) + C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) + C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2)*1i))/(64*B^2*C*b^9 - 64*B*C^2*b^9 - 192*C^3*a*b^8 + C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) - C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2)*1i)*1i - C*b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^6)/2 + 32*B^2*b^6 + 8*C^2*a^6 + 32*C^2*b^6 + 72*A^2*a^2*b^4 + 36*A^2*a^4*b^2 + 96*B^2*a^2*b^4 + 72*B^2*a^4*b^2 + 288*C^2*a^2*b^4 + 96*C^2*a^4*b^2 + 12*A*C*a^6 + 96*A*B*a*b^5 + 36*A*B*a^5*b + 192*B*C*a*b^5 + 48*B*C*a^5*b + 168*A*B*a^3*b^3 + 288*A*C*a^2*b^4 + 120*A*C*a^4*b^2 + 320*B*C*a^3*b^3) + C*b^3*(12*A*a^3 + 32*B*b^3 + 16*C*a^3 + 32*C*b^3 + 48*A*a*b^2 + 48*B*a^2*b + 96*C*a*b^2)*1i)*1i + 576*C^3*a^2*b^7 - 32*C^3*a^3*b^6 + 192*C^3*a^4*b^5 + 16*C^3*a^6*b^3 - 96*A*C^2*a*b^8 + 384*B*C^2*a*b^8 + 576*A*C^2*a^2*b^7 - 24*A*C^2*a^3*b^6 + 240*A*C^2*a^4*b^5 + 24*A*C^2*a^6*b^3 + 144*A^2*C*a^2*b^7 + 72*A^2*C*a^4*b^5 + 9*A^2*C*a^6*b^3 - 96*B*C^2*a^2*b^7 + 640*B*C^2*a^3*b^6 + 96*B*C^2*a^5*b^4 + 192*B^2*C*a^2*b^7 + 144*B^2*C*a^4*b^5 + 192*A*B*C*a*b^8 + 336*A*B*C*a^3*b^6 + 72*A*B*C*a^5*b^4)))/d","B"
962,1,601,278,3.884928,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A\,b^3}{2}+\frac{3\,B\,a^3}{8}+C\,b^3+\frac{9\,A\,a^2\,b}{8}+\frac{3\,B\,a\,b^2}{2}+\frac{3\,C\,a^2\,b}{2}\right)}{2\,A\,b^3+\frac{3\,B\,a^3}{2}+4\,C\,b^3+\frac{9\,A\,a^2\,b}{2}+6\,B\,a\,b^2+6\,C\,a^2\,b}\right)\,\left(A\,b^3+\frac{3\,B\,a^3}{4}+2\,C\,b^3+\frac{9\,A\,a^2\,b}{4}+3\,B\,a\,b^2+3\,C\,a^2\,b\right)}{d}-\frac{\left(2\,A\,a^3-A\,b^3-\frac{5\,B\,a^3}{4}+2\,B\,b^3+2\,C\,a^3+6\,A\,a\,b^2-\frac{15\,A\,a^2\,b}{4}-3\,B\,a\,b^2+6\,B\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,A\,b^3-\frac{8\,A\,a^3}{3}+\frac{B\,a^3}{2}-8\,B\,b^3-\frac{16\,C\,a^3}{3}-16\,A\,a\,b^2+\frac{3\,A\,a^2\,b}{2}+6\,B\,a\,b^2-16\,B\,a^2\,b-24\,C\,a\,b^2+6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^3}{15}+12\,B\,b^3+\frac{20\,C\,a^3}{3}+20\,A\,a\,b^2+20\,B\,a^2\,b+36\,C\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a^3}{3}-2\,A\,b^3-\frac{B\,a^3}{2}-8\,B\,b^3-\frac{16\,C\,a^3}{3}-16\,A\,a\,b^2-\frac{3\,A\,a^2\,b}{2}-6\,B\,a\,b^2-16\,B\,a^2\,b-24\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^3+A\,b^3+\frac{5\,B\,a^3}{4}+2\,B\,b^3+2\,C\,a^3+6\,A\,a\,b^2+\frac{15\,A\,a^2\,b}{4}+3\,B\,a\,b^2+6\,B\,a^2\,b+6\,C\,a\,b^2+3\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((A*b^3)/2 + (3*B*a^3)/8 + C*b^3 + (9*A*a^2*b)/8 + (3*B*a*b^2)/2 + (3*C*a^2*b)/2))/(2*A*b^3 + (3*B*a^3)/2 + 4*C*b^3 + (9*A*a^2*b)/2 + 6*B*a*b^2 + 6*C*a^2*b))*(A*b^3 + (3*B*a^3)/4 + 2*C*b^3 + (9*A*a^2*b)/4 + 3*B*a*b^2 + 3*C*a^2*b))/d - (tan(c/2 + (d*x)/2)*(2*A*a^3 + A*b^3 + (5*B*a^3)/4 + 2*B*b^3 + 2*C*a^3 + 6*A*a*b^2 + (15*A*a^2*b)/4 + 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 + 3*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^3)/15 + 12*B*b^3 + (20*C*a^3)/3 + 20*A*a*b^2 + 20*B*a^2*b + 36*C*a*b^2) + tan(c/2 + (d*x)/2)^9*(2*A*a^3 - A*b^3 - (5*B*a^3)/4 + 2*B*b^3 + 2*C*a^3 + 6*A*a*b^2 - (15*A*a^2*b)/4 - 3*B*a*b^2 + 6*B*a^2*b + 6*C*a*b^2 - 3*C*a^2*b) - tan(c/2 + (d*x)/2)^3*((8*A*a^3)/3 + 2*A*b^3 + (B*a^3)/2 + 8*B*b^3 + (16*C*a^3)/3 + 16*A*a*b^2 + (3*A*a^2*b)/2 + 6*B*a*b^2 + 16*B*a^2*b + 24*C*a*b^2 + 6*C*a^2*b) - tan(c/2 + (d*x)/2)^7*((8*A*a^3)/3 - 2*A*b^3 - (B*a^3)/2 + 8*B*b^3 + (16*C*a^3)/3 + 16*A*a*b^2 - (3*A*a^2*b)/2 - 6*B*a*b^2 + 16*B*a^2*b + 24*C*a*b^2 - 6*C*a^2*b))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
963,1,766,336,3.980430,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^7,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,A\,a^3}{16}+\frac{B\,b^3}{2}+\frac{3\,C\,a^3}{8}+\frac{9\,A\,a\,b^2}{8}+\frac{9\,B\,a^2\,b}{8}+\frac{3\,C\,a\,b^2}{2}\right)}{\frac{5\,A\,a^3}{4}+2\,B\,b^3+\frac{3\,C\,a^3}{2}+\frac{9\,A\,a\,b^2}{2}+\frac{9\,B\,a^2\,b}{2}+6\,C\,a\,b^2}\right)\,\left(\frac{5\,A\,a^3}{8}+B\,b^3+\frac{3\,C\,a^3}{4}+\frac{9\,A\,a\,b^2}{4}+\frac{9\,B\,a^2\,b}{4}+3\,C\,a\,b^2\right)}{d}+\frac{\left(\frac{11\,A\,a^3}{8}-2\,A\,b^3-2\,B\,a^3+B\,b^3+\frac{5\,C\,a^3}{4}-2\,C\,b^3+\frac{15\,A\,a\,b^2}{4}-6\,A\,a^2\,b-6\,B\,a\,b^2+\frac{15\,B\,a^2\,b}{4}+3\,C\,a\,b^2-6\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{5\,A\,a^3}{24}+\frac{22\,A\,b^3}{3}+\frac{14\,B\,a^3}{3}-3\,B\,b^3-\frac{7\,C\,a^3}{4}+10\,C\,b^3-\frac{21\,A\,a\,b^2}{4}+14\,A\,a^2\,b+22\,B\,a\,b^2-\frac{21\,B\,a^2\,b}{4}-9\,C\,a\,b^2+22\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{15\,A\,a^3}{4}-12\,A\,b^3-\frac{52\,B\,a^3}{5}+2\,B\,b^3+\frac{C\,a^3}{2}-20\,C\,b^3+\frac{3\,A\,a\,b^2}{2}-\frac{156\,A\,a^2\,b}{5}-36\,B\,a\,b^2+\frac{3\,B\,a^2\,b}{2}+6\,C\,a\,b^2-36\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{15\,A\,a^3}{4}+12\,A\,b^3+\frac{52\,B\,a^3}{5}+2\,B\,b^3+\frac{C\,a^3}{2}+20\,C\,b^3+\frac{3\,A\,a\,b^2}{2}+\frac{156\,A\,a^2\,b}{5}+36\,B\,a\,b^2+\frac{3\,B\,a^2\,b}{2}+6\,C\,a\,b^2+36\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,A\,a^3}{24}-\frac{22\,A\,b^3}{3}-\frac{14\,B\,a^3}{3}-3\,B\,b^3-\frac{7\,C\,a^3}{4}-10\,C\,b^3-\frac{21\,A\,a\,b^2}{4}-14\,A\,a^2\,b-22\,B\,a\,b^2-\frac{21\,B\,a^2\,b}{4}-9\,C\,a\,b^2-22\,C\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,A\,a^3}{8}+2\,A\,b^3+2\,B\,a^3+B\,b^3+\frac{5\,C\,a^3}{4}+2\,C\,b^3+\frac{15\,A\,a\,b^2}{4}+6\,A\,a^2\,b+6\,B\,a\,b^2+\frac{15\,B\,a^2\,b}{4}+3\,C\,a\,b^2+6\,C\,a^2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((5*A*a^3)/16 + (B*b^3)/2 + (3*C*a^3)/8 + (9*A*a*b^2)/8 + (9*B*a^2*b)/8 + (3*C*a*b^2)/2))/((5*A*a^3)/4 + 2*B*b^3 + (3*C*a^3)/2 + (9*A*a*b^2)/2 + (9*B*a^2*b)/2 + 6*C*a*b^2))*((5*A*a^3)/8 + B*b^3 + (3*C*a^3)/4 + (9*A*a*b^2)/4 + (9*B*a^2*b)/4 + 3*C*a*b^2))/d + (tan(c/2 + (d*x)/2)*((11*A*a^3)/8 + 2*A*b^3 + 2*B*a^3 + B*b^3 + (5*C*a^3)/4 + 2*C*b^3 + (15*A*a*b^2)/4 + 6*A*a^2*b + 6*B*a*b^2 + (15*B*a^2*b)/4 + 3*C*a*b^2 + 6*C*a^2*b) + tan(c/2 + (d*x)/2)^11*((11*A*a^3)/8 - 2*A*b^3 - 2*B*a^3 + B*b^3 + (5*C*a^3)/4 - 2*C*b^3 + (15*A*a*b^2)/4 - 6*A*a^2*b - 6*B*a*b^2 + (15*B*a^2*b)/4 + 3*C*a*b^2 - 6*C*a^2*b) - tan(c/2 + (d*x)/2)^3*((22*A*b^3)/3 - (5*A*a^3)/24 + (14*B*a^3)/3 + 3*B*b^3 + (7*C*a^3)/4 + 10*C*b^3 + (21*A*a*b^2)/4 + 14*A*a^2*b + 22*B*a*b^2 + (21*B*a^2*b)/4 + 9*C*a*b^2 + 22*C*a^2*b) + tan(c/2 + (d*x)/2)^9*((5*A*a^3)/24 + (22*A*b^3)/3 + (14*B*a^3)/3 - 3*B*b^3 - (7*C*a^3)/4 + 10*C*b^3 - (21*A*a*b^2)/4 + 14*A*a^2*b + 22*B*a*b^2 - (21*B*a^2*b)/4 - 9*C*a*b^2 + 22*C*a^2*b) + tan(c/2 + (d*x)/2)^5*((15*A*a^3)/4 + 12*A*b^3 + (52*B*a^3)/5 + 2*B*b^3 + (C*a^3)/2 + 20*C*b^3 + (3*A*a*b^2)/2 + (156*A*a^2*b)/5 + 36*B*a*b^2 + (3*B*a^2*b)/2 + 6*C*a*b^2 + 36*C*a^2*b) + tan(c/2 + (d*x)/2)^7*((15*A*a^3)/4 - 12*A*b^3 - (52*B*a^3)/5 + 2*B*b^3 + (C*a^3)/2 - 20*C*b^3 + (3*A*a*b^2)/2 - (156*A*a^2*b)/5 - 36*B*a*b^2 + (3*B*a^2*b)/2 + 6*C*a*b^2 - 36*C*a^2*b))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
964,1,675,445,6.094975,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{B\,a^4\,x}{2}+\frac{5\,B\,b^4\,x}{16}+\frac{3\,A\,a\,b^3\,x}{2}+2\,A\,a^3\,b\,x+\frac{5\,C\,a\,b^3\,x}{4}+\frac{3\,C\,a^3\,b\,x}{2}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{5\,A\,b^4\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,C\,a^4\,\sin\left(c+d\,x\right)}{4\,d}+\frac{35\,C\,b^4\,\sin\left(c+d\,x\right)}{64\,d}+\frac{9\,B\,a^2\,b^2\,x}{4}+\frac{B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,A\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{A\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{15\,B\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{C\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,B\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{B\,b^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{7\,C\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{64\,d}+\frac{7\,C\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{320\,d}+\frac{C\,b^4\,\sin\left(7\,c+7\,d\,x\right)}{448\,d}+\frac{A\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{A\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{A\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{8\,d}+\frac{9\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{5\,B\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{B\,a\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{20\,d}+\frac{15\,C\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{16\,d}+\frac{C\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{3\,C\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{C\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)}{8\,d}+\frac{C\,a\,b^3\,\sin\left(6\,c+6\,d\,x\right)}{48\,d}+\frac{15\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2\,d}+\frac{3\,B\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,B\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{5\,C\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{8\,d}+\frac{3\,C\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{40\,d}+\frac{5\,B\,a\,b^3\,\sin\left(c+d\,x\right)}{2\,d}+\frac{3\,B\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(B*a^4*x)/2 + (5*B*b^4*x)/16 + (3*A*a*b^3*x)/2 + 2*A*a^3*b*x + (5*C*a*b^3*x)/4 + (3*C*a^3*b*x)/2 + (A*a^4*sin(c + d*x))/d + (5*A*b^4*sin(c + d*x))/(8*d) + (3*C*a^4*sin(c + d*x))/(4*d) + (35*C*b^4*sin(c + d*x))/(64*d) + (9*B*a^2*b^2*x)/4 + (B*a^4*sin(2*c + 2*d*x))/(4*d) + (5*A*b^4*sin(3*c + 3*d*x))/(48*d) + (A*b^4*sin(5*c + 5*d*x))/(80*d) + (15*B*b^4*sin(2*c + 2*d*x))/(64*d) + (C*a^4*sin(3*c + 3*d*x))/(12*d) + (3*B*b^4*sin(4*c + 4*d*x))/(64*d) + (B*b^4*sin(6*c + 6*d*x))/(192*d) + (7*C*b^4*sin(3*c + 3*d*x))/(64*d) + (7*C*b^4*sin(5*c + 5*d*x))/(320*d) + (C*b^4*sin(7*c + 7*d*x))/(448*d) + (A*a*b^3*sin(2*c + 2*d*x))/d + (A*a^3*b*sin(2*c + 2*d*x))/d + (A*a*b^3*sin(4*c + 4*d*x))/(8*d) + (9*A*a^2*b^2*sin(c + d*x))/(2*d) + (5*B*a*b^3*sin(3*c + 3*d*x))/(12*d) + (B*a^3*b*sin(3*c + 3*d*x))/(3*d) + (B*a*b^3*sin(5*c + 5*d*x))/(20*d) + (15*C*a*b^3*sin(2*c + 2*d*x))/(16*d) + (C*a^3*b*sin(2*c + 2*d*x))/d + (3*C*a*b^3*sin(4*c + 4*d*x))/(16*d) + (C*a^3*b*sin(4*c + 4*d*x))/(8*d) + (C*a*b^3*sin(6*c + 6*d*x))/(48*d) + (15*C*a^2*b^2*sin(c + d*x))/(4*d) + (A*a^2*b^2*sin(3*c + 3*d*x))/(2*d) + (3*B*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*B*a^2*b^2*sin(4*c + 4*d*x))/(16*d) + (5*C*a^2*b^2*sin(3*c + 3*d*x))/(8*d) + (3*C*a^2*b^2*sin(5*c + 5*d*x))/(40*d) + (5*B*a*b^3*sin(c + d*x))/(2*d) + (3*B*a^3*b*sin(c + d*x))/d","B"
965,1,534,375,4.511770,"\text{Not used}","int((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","A\,a^4\,x+\frac{3\,A\,b^4\,x}{8}+\frac{C\,a^4\,x}{2}+\frac{5\,C\,b^4\,x}{16}+\frac{3\,B\,a\,b^3\,x}{2}+2\,B\,a^3\,b\,x+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{5\,B\,b^4\,\sin\left(c+d\,x\right)}{8\,d}+3\,A\,a^2\,b^2\,x+\frac{9\,C\,a^2\,b^2\,x}{4}+\frac{A\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{C\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,B\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{B\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{15\,C\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,C\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{C\,b^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{A\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{B\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{B\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{B\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{8\,d}+\frac{9\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{5\,C\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{C\,a\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{20\,d}+\frac{3\,A\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{B\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2\,d}+\frac{3\,C\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,C\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{3\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{4\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{d}+\frac{5\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{2\,d}+\frac{3\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"A*a^4*x + (3*A*b^4*x)/8 + (C*a^4*x)/2 + (5*C*b^4*x)/16 + (3*B*a*b^3*x)/2 + 2*B*a^3*b*x + (B*a^4*sin(c + d*x))/d + (5*B*b^4*sin(c + d*x))/(8*d) + 3*A*a^2*b^2*x + (9*C*a^2*b^2*x)/4 + (A*b^4*sin(2*c + 2*d*x))/(4*d) + (A*b^4*sin(4*c + 4*d*x))/(32*d) + (C*a^4*sin(2*c + 2*d*x))/(4*d) + (5*B*b^4*sin(3*c + 3*d*x))/(48*d) + (B*b^4*sin(5*c + 5*d*x))/(80*d) + (15*C*b^4*sin(2*c + 2*d*x))/(64*d) + (3*C*b^4*sin(4*c + 4*d*x))/(64*d) + (C*b^4*sin(6*c + 6*d*x))/(192*d) + (A*a*b^3*sin(3*c + 3*d*x))/(3*d) + (B*a*b^3*sin(2*c + 2*d*x))/d + (B*a^3*b*sin(2*c + 2*d*x))/d + (B*a*b^3*sin(4*c + 4*d*x))/(8*d) + (9*B*a^2*b^2*sin(c + d*x))/(2*d) + (5*C*a*b^3*sin(3*c + 3*d*x))/(12*d) + (C*a^3*b*sin(3*c + 3*d*x))/(3*d) + (C*a*b^3*sin(5*c + 5*d*x))/(20*d) + (3*A*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (B*a^2*b^2*sin(3*c + 3*d*x))/(2*d) + (3*C*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*C*a^2*b^2*sin(4*c + 4*d*x))/(16*d) + (3*A*a*b^3*sin(c + d*x))/d + (4*A*a^3*b*sin(c + d*x))/d + (5*C*a*b^3*sin(c + d*x))/(2*d) + (3*C*a^3*b*sin(c + d*x))/d","B"
966,1,4118,290,5.149052,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)\,1{}\mathrm{i}+\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)-\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(B\,a^4\,1{}\mathrm{i}+\frac{B\,b^4\,3{}\mathrm{i}}{8}+B\,a^2\,b^2\,3{}\mathrm{i}+A\,a\,b^3\,2{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+\frac{C\,a\,b^3\,3{}\mathrm{i}}{2}+C\,a^3\,b\,2{}\mathrm{i}\right)+64\,A\,B^2\,a^{12}-64\,A^2\,B\,a^{12}-256\,A^3\,a^{11}\,b+256\,A^3\,a^6\,b^6+1024\,A^3\,a^8\,b^4-128\,A^3\,a^9\,b^3+1024\,A^3\,a^{10}\,b^2+512\,A^2\,B\,a^{11}\,b-128\,A^2\,C\,a^{11}\,b+9\,A\,B^2\,a^4\,b^8+144\,A\,B^2\,a^6\,b^6+624\,A\,B^2\,a^8\,b^4+384\,A\,B^2\,a^{10}\,b^2+96\,A^2\,B\,a^5\,b^7+960\,A^2\,B\,a^7\,b^5-24\,A^2\,B\,a^8\,b^4+1792\,A^2\,B\,a^9\,b^3-192\,A^2\,B\,a^{10}\,b^2+144\,A\,C^2\,a^6\,b^6+384\,A\,C^2\,a^8\,b^4+256\,A\,C^2\,a^{10}\,b^2+384\,A^2\,C\,a^6\,b^6+1280\,A^2\,C\,a^8\,b^4-96\,A^2\,C\,a^9\,b^3+1024\,A^2\,C\,a^{10}\,b^2+256\,A\,B\,C\,a^{11}\,b+72\,A\,B\,C\,a^5\,b^7+672\,A\,B\,C\,a^7\,b^5+960\,A\,B\,C\,a^9\,b^3}\right)\,\left(2\,B\,a^4+\frac{3\,B\,b^4}{4}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+8\,A\,a^3\,b+3\,C\,a\,b^3+4\,C\,a^3\,b\right)}{d}+\frac{\left(2\,A\,b^4-\frac{5\,B\,b^4}{4}+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2-6\,B\,a^2\,b^2+12\,C\,a^2\,b^2-4\,A\,a\,b^3+8\,B\,a\,b^3+8\,B\,a^3\,b-5\,C\,a\,b^3-4\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{16\,A\,b^4}{3}-\frac{B\,b^4}{2}+8\,C\,a^4+\frac{8\,C\,b^4}{3}+48\,A\,a^2\,b^2-12\,B\,a^2\,b^2+32\,C\,a^2\,b^2-8\,A\,a\,b^3+\frac{64\,B\,a\,b^3}{3}+32\,B\,a^3\,b-2\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,b^4}{3}+12\,C\,a^4+\frac{116\,C\,b^4}{15}+72\,A\,a^2\,b^2+40\,C\,a^2\,b^2+\frac{80\,B\,a\,b^3}{3}+48\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{16\,A\,b^4}{3}+\frac{B\,b^4}{2}+8\,C\,a^4+\frac{8\,C\,b^4}{3}+48\,A\,a^2\,b^2+12\,B\,a^2\,b^2+32\,C\,a^2\,b^2+8\,A\,a\,b^3+\frac{64\,B\,a\,b^3}{3}+32\,B\,a^3\,b+2\,C\,a\,b^3+8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,b^4+\frac{5\,B\,b^4}{4}+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+6\,B\,a^2\,b^2+12\,C\,a^2\,b^2+4\,A\,a\,b^3+8\,B\,a\,b^3+8\,B\,a^3\,b+5\,C\,a\,b^3+4\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{A\,a^4\,\mathrm{atan}\left(\frac{A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,1{}\mathrm{i}}{64\,A\,B^2\,a^{12}-64\,A^2\,B\,a^{12}-256\,A^3\,a^{11}\,b+A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)+A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)-A\,a^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8+512\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+256\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+48\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+192\,A\,C\,a^2\,b^6+32\,B^2\,a^8+192\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+72\,B^2\,a^2\,b^6+\frac{9\,B^2\,b^8}{2}+128\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+336\,B\,C\,a^3\,b^5+36\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+192\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6\right)-A\,a^4\,\left(32\,A\,a^4+32\,B\,a^4+12\,B\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+128\,A\,a^3\,b+48\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)+256\,A^3\,a^6\,b^6+1024\,A^3\,a^8\,b^4-128\,A^3\,a^9\,b^3+1024\,A^3\,a^{10}\,b^2+512\,A^2\,B\,a^{11}\,b-128\,A^2\,C\,a^{11}\,b+9\,A\,B^2\,a^4\,b^8+144\,A\,B^2\,a^6\,b^6+624\,A\,B^2\,a^8\,b^4+384\,A\,B^2\,a^{10}\,b^2+96\,A^2\,B\,a^5\,b^7+960\,A^2\,B\,a^7\,b^5-24\,A^2\,B\,a^8\,b^4+1792\,A^2\,B\,a^9\,b^3-192\,A^2\,B\,a^{10}\,b^2+144\,A\,C^2\,a^6\,b^6+384\,A\,C^2\,a^8\,b^4+256\,A\,C^2\,a^{10}\,b^2+384\,A^2\,C\,a^6\,b^6+1280\,A^2\,C\,a^8\,b^4-96\,A^2\,C\,a^9\,b^3+1024\,A^2\,C\,a^{10}\,b^2+256\,A\,B\,C\,a^{11}\,b+72\,A\,B\,C\,a^5\,b^7+672\,A\,B\,C\,a^7\,b^5+960\,A\,B\,C\,a^9\,b^3}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(atan(((tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + (B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i)*1i + (tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - (B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i)*1i)/((tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + (B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i) - (tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - (B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i)*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*(B*a^4*1i + (B*b^4*3i)/8 + B*a^2*b^2*3i + A*a*b^3*2i + A*a^3*b*4i + (C*a*b^3*3i)/2 + C*a^3*b*2i) + 64*A*B^2*a^12 - 64*A^2*B*a^12 - 256*A^3*a^11*b + 256*A^3*a^6*b^6 + 1024*A^3*a^8*b^4 - 128*A^3*a^9*b^3 + 1024*A^3*a^10*b^2 + 512*A^2*B*a^11*b - 128*A^2*C*a^11*b + 9*A*B^2*a^4*b^8 + 144*A*B^2*a^6*b^6 + 624*A*B^2*a^8*b^4 + 384*A*B^2*a^10*b^2 + 96*A^2*B*a^5*b^7 + 960*A^2*B*a^7*b^5 - 24*A^2*B*a^8*b^4 + 1792*A^2*B*a^9*b^3 - 192*A^2*B*a^10*b^2 + 144*A*C^2*a^6*b^6 + 384*A*C^2*a^8*b^4 + 256*A*C^2*a^10*b^2 + 384*A^2*C*a^6*b^6 + 1280*A^2*C*a^8*b^4 - 96*A^2*C*a^9*b^3 + 1024*A^2*C*a^10*b^2 + 256*A*B*C*a^11*b + 72*A*B*C*a^5*b^7 + 672*A*B*C*a^7*b^5 + 960*A*B*C*a^9*b^3))*(2*B*a^4 + (3*B*b^4)/4 + 6*B*a^2*b^2 + 4*A*a*b^3 + 8*A*a^3*b + 3*C*a*b^3 + 4*C*a^3*b))/d + (tan(c/2 + (d*x)/2)*(2*A*b^4 + (5*B*b^4)/4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + 6*B*a^2*b^2 + 12*C*a^2*b^2 + 4*A*a*b^3 + 8*B*a*b^3 + 8*B*a^3*b + 5*C*a*b^3 + 4*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(2*A*b^4 - (5*B*b^4)/4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 - 6*B*a^2*b^2 + 12*C*a^2*b^2 - 4*A*a*b^3 + 8*B*a*b^3 + 8*B*a^3*b - 5*C*a*b^3 - 4*C*a^3*b) + tan(c/2 + (d*x)/2)^3*((16*A*b^4)/3 + (B*b^4)/2 + 8*C*a^4 + (8*C*b^4)/3 + 48*A*a^2*b^2 + 12*B*a^2*b^2 + 32*C*a^2*b^2 + 8*A*a*b^3 + (64*B*a*b^3)/3 + 32*B*a^3*b + 2*C*a*b^3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((16*A*b^4)/3 - (B*b^4)/2 + 8*C*a^4 + (8*C*b^4)/3 + 48*A*a^2*b^2 - 12*B*a^2*b^2 + 32*C*a^2*b^2 - 8*A*a*b^3 + (64*B*a*b^3)/3 + 32*B*a^3*b - 2*C*a*b^3 - 8*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((20*A*b^4)/3 + 12*C*a^4 + (116*C*b^4)/15 + 72*A*a^2*b^2 + 40*C*a^2*b^2 + (80*B*a*b^3)/3 + 48*B*a^3*b))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (A*a^4*atan((A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*1i + A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b))*1i)/(64*A*B^2*a^12 - 64*A^2*B*a^12 - 256*A^3*a^11*b + A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)) - A*a^4*(tan(c/2 + (d*x)/2)*(32*A^2*a^8 + 32*B^2*a^8 + (9*B^2*b^8)/2 + 128*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 72*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 192*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 48*A*B*a*b^7 + 256*A*B*a^7*b + 36*B*C*a*b^7 + 128*B*C*a^7*b + 480*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 192*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 336*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - A*a^4*(32*A*a^4 + 32*B*a^4 + 12*B*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 128*A*a^3*b + 48*C*a*b^3 + 64*C*a^3*b)) + 256*A^3*a^6*b^6 + 1024*A^3*a^8*b^4 - 128*A^3*a^9*b^3 + 1024*A^3*a^10*b^2 + 512*A^2*B*a^11*b - 128*A^2*C*a^11*b + 9*A*B^2*a^4*b^8 + 144*A*B^2*a^6*b^6 + 624*A*B^2*a^8*b^4 + 384*A*B^2*a^10*b^2 + 96*A^2*B*a^5*b^7 + 960*A^2*B*a^7*b^5 - 24*A^2*B*a^8*b^4 + 1792*A^2*B*a^9*b^3 - 192*A^2*B*a^10*b^2 + 144*A*C^2*a^6*b^6 + 384*A*C^2*a^8*b^4 + 256*A*C^2*a^10*b^2 + 384*A^2*C*a^6*b^6 + 1280*A^2*C*a^8*b^4 - 96*A^2*C*a^9*b^3 + 1024*A^2*C*a^10*b^2 + 256*A*B*C*a^11*b + 72*A*B*C*a^5*b^7 + 672*A*B*C*a^7*b^5 + 960*A*B*C*a^9*b^3))*2i)/d","B"
967,1,4781,273,5.708554,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)\,1{}\mathrm{i}}{\left(\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)+\left(\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(\frac{A\,b^4\,1{}\mathrm{i}}{2}+C\,a^4\,1{}\mathrm{i}+\frac{C\,b^4\,3{}\mathrm{i}}{8}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,3{}\mathrm{i}+B\,a\,b^3\,2{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)+64\,B\,C^2\,a^{12}-64\,B^2\,C\,a^{12}-256\,B^3\,a^{11}\,b+64\,A^3\,a^3\,b^9+1536\,A^3\,a^5\,b^7-512\,A^3\,a^6\,b^6+9216\,A^3\,a^7\,b^5-6144\,A^3\,a^8\,b^4+256\,B^3\,a^6\,b^6+1024\,B^3\,a^8\,b^4-128\,B^3\,a^9\,b^3+1024\,B^3\,a^{10}\,b^2+256\,A\,C^2\,a^{11}\,b+512\,B^2\,C\,a^{11}\,b+1152\,A\,B^2\,a^5\,b^7+5888\,A\,B^2\,a^7\,b^5-1056\,A\,B^2\,a^8\,b^4+7168\,A\,B^2\,a^9\,b^3-2432\,A\,B^2\,a^{10}\,b^2+528\,A^2\,B\,a^4\,b^8+7552\,A^2\,B\,a^6\,b^6-2304\,A^2\,B\,a^7\,b^5+14592\,A^2\,B\,a^8\,b^4-7168\,A^2\,B\,a^9\,b^3+36\,A\,C^2\,a^3\,b^9+576\,A\,C^2\,a^5\,b^7+2496\,A\,C^2\,a^7\,b^5+1536\,A\,C^2\,a^9\,b^3+96\,A^2\,C\,a^3\,b^9+1920\,A^2\,C\,a^5\,b^7-384\,A^2\,C\,a^6\,b^6+9472\,A^2\,C\,a^7\,b^5-3072\,A^2\,C\,a^8\,b^4+3072\,A^2\,C\,a^9\,b^3-1024\,A^2\,C\,a^{10}\,b^2+9\,B\,C^2\,a^4\,b^8+144\,B\,C^2\,a^6\,b^6+624\,B\,C^2\,a^8\,b^4+384\,B\,C^2\,a^{10}\,b^2+96\,B^2\,C\,a^5\,b^7+960\,B^2\,C\,a^7\,b^5-24\,B^2\,C\,a^8\,b^4+1792\,B^2\,C\,a^9\,b^3-192\,B^2\,C\,a^{10}\,b^2-512\,A\,B\,C\,a^{11}\,b+408\,A\,B\,C\,a^4\,b^8+4320\,A\,B\,C\,a^6\,b^6-192\,A\,B\,C\,a^7\,b^5+9536\,A\,B\,C\,a^8\,b^4-1536\,A\,B\,C\,a^9\,b^3+2816\,A\,B\,C\,a^{10}\,b^2}\right)\,\left(A\,b^4+2\,C\,a^4+\frac{3\,C\,b^4}{4}+12\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+8\,B\,a^3\,b\right)}{d}+\frac{\left(2\,A\,a^4+A\,b^4-2\,B\,b^4+\frac{5\,C\,b^4}{4}-12\,B\,a^2\,b^2+6\,C\,a^2\,b^2-8\,A\,a\,b^3+4\,B\,a\,b^3-8\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(8\,A\,a^4-\frac{4\,B\,b^4}{3}-2\,C\,b^4-24\,B\,a^2\,b^2-16\,A\,a\,b^3-\frac{16\,C\,a\,b^3}{3}-16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,A\,a^4-2\,A\,b^4+\frac{3\,C\,b^4}{2}-12\,C\,a^2\,b^2-8\,B\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,A\,a^4+\frac{4\,B\,b^4}{3}-2\,C\,b^4+24\,B\,a^2\,b^2+16\,A\,a\,b^3+\frac{16\,C\,a\,b^3}{3}+16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+A\,b^4+2\,B\,b^4+\frac{5\,C\,b^4}{4}+12\,B\,a^2\,b^2+6\,C\,a^2\,b^2+8\,A\,a\,b^3+4\,B\,a\,b^3+8\,C\,a\,b^3+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(B\,a^4+4\,A\,b\,a^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(B\,a^4+4\,A\,b\,a^3\right)\,1{}\mathrm{i}-\left(\left(B\,a^4+4\,A\,b\,a^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(B\,a^4+4\,A\,b\,a^3\right)\,1{}\mathrm{i}}{\left(\left(B\,a^4+4\,A\,b\,a^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(B\,a^4+4\,A\,b\,a^3\right)+\left(\left(B\,a^4+4\,A\,b\,a^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+32\,C\,a^4+12\,C\,b^4+192\,A\,a^2\,b^2+96\,C\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+8\,A^2\,b^8+256\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+64\,A\,B\,a\,b^7+384\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+240\,A\,C\,a^2\,b^6+12\,A\,C\,b^8+32\,B^2\,a^8+512\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+128\,B^2\,a^2\,b^6+256\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+480\,B\,C\,a^3\,b^5+48\,B\,C\,a\,b^7+32\,C^2\,a^8+192\,C^2\,a^6\,b^2+312\,C^2\,a^4\,b^4+72\,C^2\,a^2\,b^6+\frac{9\,C^2\,b^8}{2}\right)\right)\,\left(B\,a^4+4\,A\,b\,a^3\right)+64\,B\,C^2\,a^{12}-64\,B^2\,C\,a^{12}-256\,B^3\,a^{11}\,b+64\,A^3\,a^3\,b^9+1536\,A^3\,a^5\,b^7-512\,A^3\,a^6\,b^6+9216\,A^3\,a^7\,b^5-6144\,A^3\,a^8\,b^4+256\,B^3\,a^6\,b^6+1024\,B^3\,a^8\,b^4-128\,B^3\,a^9\,b^3+1024\,B^3\,a^{10}\,b^2+256\,A\,C^2\,a^{11}\,b+512\,B^2\,C\,a^{11}\,b+1152\,A\,B^2\,a^5\,b^7+5888\,A\,B^2\,a^7\,b^5-1056\,A\,B^2\,a^8\,b^4+7168\,A\,B^2\,a^9\,b^3-2432\,A\,B^2\,a^{10}\,b^2+528\,A^2\,B\,a^4\,b^8+7552\,A^2\,B\,a^6\,b^6-2304\,A^2\,B\,a^7\,b^5+14592\,A^2\,B\,a^8\,b^4-7168\,A^2\,B\,a^9\,b^3+36\,A\,C^2\,a^3\,b^9+576\,A\,C^2\,a^5\,b^7+2496\,A\,C^2\,a^7\,b^5+1536\,A\,C^2\,a^9\,b^3+96\,A^2\,C\,a^3\,b^9+1920\,A^2\,C\,a^5\,b^7-384\,A^2\,C\,a^6\,b^6+9472\,A^2\,C\,a^7\,b^5-3072\,A^2\,C\,a^8\,b^4+3072\,A^2\,C\,a^9\,b^3-1024\,A^2\,C\,a^{10}\,b^2+9\,B\,C^2\,a^4\,b^8+144\,B\,C^2\,a^6\,b^6+624\,B\,C^2\,a^8\,b^4+384\,B\,C^2\,a^{10}\,b^2+96\,B^2\,C\,a^5\,b^7+960\,B^2\,C\,a^7\,b^5-24\,B^2\,C\,a^8\,b^4+1792\,B^2\,C\,a^9\,b^3-192\,B^2\,C\,a^{10}\,b^2-512\,A\,B\,C\,a^{11}\,b+408\,A\,B\,C\,a^4\,b^8+4320\,A\,B\,C\,a^6\,b^6-192\,A\,B\,C\,a^7\,b^5+9536\,A\,B\,C\,a^8\,b^4-1536\,A\,B\,C\,a^9\,b^3+2816\,A\,B\,C\,a^{10}\,b^2}\right)\,\left(2{}\mathrm{i}\,B\,a^4+8{}\mathrm{i}\,A\,b\,a^3\right)}{d}","Not used",1,"(atan(((((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i)*1i - (((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i)*1i)/((((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i) + (((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((A*b^4*1i)/2 + C*a^4*1i + (C*b^4*3i)/8 + A*a^2*b^2*6i + C*a^2*b^2*3i + B*a*b^3*2i + B*a^3*b*4i) + 64*B*C^2*a^12 - 64*B^2*C*a^12 - 256*B^3*a^11*b + 64*A^3*a^3*b^9 + 1536*A^3*a^5*b^7 - 512*A^3*a^6*b^6 + 9216*A^3*a^7*b^5 - 6144*A^3*a^8*b^4 + 256*B^3*a^6*b^6 + 1024*B^3*a^8*b^4 - 128*B^3*a^9*b^3 + 1024*B^3*a^10*b^2 + 256*A*C^2*a^11*b + 512*B^2*C*a^11*b + 1152*A*B^2*a^5*b^7 + 5888*A*B^2*a^7*b^5 - 1056*A*B^2*a^8*b^4 + 7168*A*B^2*a^9*b^3 - 2432*A*B^2*a^10*b^2 + 528*A^2*B*a^4*b^8 + 7552*A^2*B*a^6*b^6 - 2304*A^2*B*a^7*b^5 + 14592*A^2*B*a^8*b^4 - 7168*A^2*B*a^9*b^3 + 36*A*C^2*a^3*b^9 + 576*A*C^2*a^5*b^7 + 2496*A*C^2*a^7*b^5 + 1536*A*C^2*a^9*b^3 + 96*A^2*C*a^3*b^9 + 1920*A^2*C*a^5*b^7 - 384*A^2*C*a^6*b^6 + 9472*A^2*C*a^7*b^5 - 3072*A^2*C*a^8*b^4 + 3072*A^2*C*a^9*b^3 - 1024*A^2*C*a^10*b^2 + 9*B*C^2*a^4*b^8 + 144*B*C^2*a^6*b^6 + 624*B*C^2*a^8*b^4 + 384*B*C^2*a^10*b^2 + 96*B^2*C*a^5*b^7 + 960*B^2*C*a^7*b^5 - 24*B^2*C*a^8*b^4 + 1792*B^2*C*a^9*b^3 - 192*B^2*C*a^10*b^2 - 512*A*B*C*a^11*b + 408*A*B*C*a^4*b^8 + 4320*A*B*C*a^6*b^6 - 192*A*B*C*a^7*b^5 + 9536*A*B*C*a^8*b^4 - 1536*A*B*C*a^9*b^3 + 2816*A*B*C*a^10*b^2))*(A*b^4 + 2*C*a^4 + (3*C*b^4)/4 + 12*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 8*B*a^3*b))/d + (tan(c/2 + (d*x)/2)*(2*A*a^4 + A*b^4 + 2*B*b^4 + (5*C*b^4)/4 + 12*B*a^2*b^2 + 6*C*a^2*b^2 + 8*A*a*b^3 + 4*B*a*b^3 + 8*C*a*b^3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^3*(8*A*a^4 + (4*B*b^4)/3 - 2*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*C*a*b^3)/3 + 16*C*a^3*b) - tan(c/2 + (d*x)/2)^7*((4*B*b^4)/3 - 8*A*a^4 + 2*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*C*a*b^3)/3 + 16*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + A*b^4 - 2*B*b^4 + (5*C*b^4)/4 - 12*B*a^2*b^2 + 6*C*a^2*b^2 - 8*A*a*b^3 + 4*B*a*b^3 - 8*C*a*b^3 - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^5*(2*A*b^4 - 12*A*a^4 - (3*C*b^4)/2 + 12*C*a^2*b^2 + 8*B*a*b^3))/(d*(3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^10 + 1)) - (atan((((B*a^4 + 4*A*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*a^4 + 4*A*a^3*b)*1i - ((B*a^4 + 4*A*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*a^4 + 4*A*a^3*b)*1i)/(((B*a^4 + 4*A*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*a^4 + 4*A*a^3*b) + ((B*a^4 + 4*A*a^3*b)*(16*A*b^4 + 32*B*a^4 + 32*C*a^4 + 12*C*b^4 + 192*A*a^2*b^2 + 96*C*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 32*C^2*a^8 + (9*C^2*b^8)/2 + 192*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 512*A^2*a^6*b^2 + 128*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 72*C^2*a^2*b^6 + 312*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*b^8 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 48*B*C*a*b^7 + 256*B*C*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 240*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 480*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*(B*a^4 + 4*A*a^3*b) + 64*B*C^2*a^12 - 64*B^2*C*a^12 - 256*B^3*a^11*b + 64*A^3*a^3*b^9 + 1536*A^3*a^5*b^7 - 512*A^3*a^6*b^6 + 9216*A^3*a^7*b^5 - 6144*A^3*a^8*b^4 + 256*B^3*a^6*b^6 + 1024*B^3*a^8*b^4 - 128*B^3*a^9*b^3 + 1024*B^3*a^10*b^2 + 256*A*C^2*a^11*b + 512*B^2*C*a^11*b + 1152*A*B^2*a^5*b^7 + 5888*A*B^2*a^7*b^5 - 1056*A*B^2*a^8*b^4 + 7168*A*B^2*a^9*b^3 - 2432*A*B^2*a^10*b^2 + 528*A^2*B*a^4*b^8 + 7552*A^2*B*a^6*b^6 - 2304*A^2*B*a^7*b^5 + 14592*A^2*B*a^8*b^4 - 7168*A^2*B*a^9*b^3 + 36*A*C^2*a^3*b^9 + 576*A*C^2*a^5*b^7 + 2496*A*C^2*a^7*b^5 + 1536*A*C^2*a^9*b^3 + 96*A^2*C*a^3*b^9 + 1920*A^2*C*a^5*b^7 - 384*A^2*C*a^6*b^6 + 9472*A^2*C*a^7*b^5 - 3072*A^2*C*a^8*b^4 + 3072*A^2*C*a^9*b^3 - 1024*A^2*C*a^10*b^2 + 9*B*C^2*a^4*b^8 + 144*B*C^2*a^6*b^6 + 624*B*C^2*a^8*b^4 + 384*B*C^2*a^10*b^2 + 96*B^2*C*a^5*b^7 + 960*B^2*C*a^7*b^5 - 24*B^2*C*a^8*b^4 + 1792*B^2*C*a^9*b^3 - 192*B^2*C*a^10*b^2 - 512*A*B*C*a^11*b + 408*A*B*C*a^4*b^8 + 4320*A*B*C*a^6*b^6 - 192*A*B*C*a^7*b^5 + 9536*A*B*C*a^8*b^4 - 1536*A*B*C*a^9*b^3 + 2816*A*B*C*a^10*b^2))*(B*a^4*2i + A*a^3*b*8i))/d","B"
968,1,4837,274,5.545786,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\frac{\left(A\,a^4+2\,A\,b^4-2\,B\,a^4-B\,b^4+2\,C\,b^4+12\,C\,a^2\,b^2-8\,A\,a^3\,b+8\,B\,a\,b^3-4\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(4\,A\,a^4-4\,B\,a^4+2\,B\,b^4-\frac{8\,C\,b^4}{3}-16\,A\,a^3\,b+8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a^4-4\,A\,b^4+\frac{4\,C\,b^4}{3}-24\,C\,a^2\,b^2-16\,B\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A\,a^4+4\,B\,a^4-2\,B\,b^4-\frac{8\,C\,b^4}{3}+16\,A\,a^3\,b-8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a^4+2\,A\,b^4+2\,B\,a^4+B\,b^4+2\,C\,b^4+12\,C\,a^2\,b^2+8\,A\,a^3\,b+8\,B\,a\,b^3+4\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)\,1{}\mathrm{i}-\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)\,1{}\mathrm{i}}{\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)+\left(\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{A\,a^4}{2}+C\,a^4+6\,A\,a^2\,b^2+4\,B\,a^3\,b\right)-256\,C^3\,a^{11}\,b+6144\,A^3\,a^4\,b^8-9216\,A^3\,a^5\,b^7+512\,A^3\,a^6\,b^6-1536\,A^3\,a^7\,b^5-64\,A^3\,a^9\,b^3+64\,B^3\,a^3\,b^9+1536\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+9216\,B^3\,a^7\,b^5-6144\,B^3\,a^8\,b^4+256\,C^3\,a^6\,b^6+1024\,C^3\,a^8\,b^4-128\,C^3\,a^9\,b^3+1024\,C^3\,a^{10}\,b^2-256\,A\,C^2\,a^{11}\,b-64\,A^2\,C\,a^{11}\,b+96\,A\,B^2\,a^2\,b^{10}+3336\,A\,B^2\,a^4\,b^8-1536\,A\,B^2\,a^5\,b^7+26304\,A\,B^2\,a^6\,b^6-22656\,A\,B^2\,a^7\,b^5+1152\,A\,B^2\,a^8\,b^4-1536\,A\,B^2\,a^9\,b^3+1536\,A^2\,B\,a^3\,b^9-1152\,A^2\,B\,a^4\,b^8+22656\,A^2\,B\,a^5\,b^7-26304\,A^2\,B\,a^6\,b^6+1536\,A^2\,B\,a^7\,b^5-3336\,A^2\,B\,a^8\,b^4-96\,A^2\,B\,a^{10}\,b^2+1536\,A\,C^2\,a^4\,b^8+7296\,A\,C^2\,a^6\,b^6-1536\,A\,C^2\,a^7\,b^5+8704\,A\,C^2\,a^8\,b^4-3456\,A\,C^2\,a^9\,b^3+512\,A\,C^2\,a^{10}\,b^2+6144\,A^2\,C\,a^4\,b^8-4608\,A^2\,C\,a^5\,b^7+13824\,A^2\,C\,a^6\,b^6-13056\,A^2\,C\,a^7\,b^5+1024\,A^2\,C\,a^8\,b^4-1824\,A^2\,C\,a^9\,b^3+1152\,B\,C^2\,a^5\,b^7+5888\,B\,C^2\,a^7\,b^5-1056\,B\,C^2\,a^8\,b^4+7168\,B\,C^2\,a^9\,b^3-2432\,B\,C^2\,a^{10}\,b^2+528\,B^2\,C\,a^4\,b^8+7552\,B^2\,C\,a^6\,b^6-2304\,B^2\,C\,a^7\,b^5+14592\,B^2\,C\,a^8\,b^4-7168\,B^2\,C\,a^9\,b^3+768\,A\,B\,C\,a^3\,b^9+15168\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+30592\,A\,B\,C\,a^7\,b^5-19488\,A\,B\,C\,a^8\,b^4+1536\,A\,B\,C\,a^9\,b^3-1408\,A\,B\,C\,a^{10}\,b^2}\right)\,\left(A\,a^4\,1{}\mathrm{i}+C\,a^4\,2{}\mathrm{i}+A\,a^2\,b^2\,12{}\mathrm{i}+B\,a^3\,b\,8{}\mathrm{i}\right)}{d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-\frac{b\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)}{2}+\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+\frac{b\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)}{2}}{6144\,A^3\,a^4\,b^8-256\,C^3\,a^{11}\,b-9216\,A^3\,a^5\,b^7+512\,A^3\,a^6\,b^6-1536\,A^3\,a^7\,b^5-64\,A^3\,a^9\,b^3+64\,B^3\,a^3\,b^9+1536\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+9216\,B^3\,a^7\,b^5-6144\,B^3\,a^8\,b^4+256\,C^3\,a^6\,b^6+1024\,C^3\,a^8\,b^4-128\,C^3\,a^9\,b^3+1024\,C^3\,a^{10}\,b^2-256\,A\,C^2\,a^{11}\,b-64\,A^2\,C\,a^{11}\,b+96\,A\,B^2\,a^2\,b^{10}+3336\,A\,B^2\,a^4\,b^8-1536\,A\,B^2\,a^5\,b^7+26304\,A\,B^2\,a^6\,b^6-22656\,A\,B^2\,a^7\,b^5+1152\,A\,B^2\,a^8\,b^4-1536\,A\,B^2\,a^9\,b^3+1536\,A^2\,B\,a^3\,b^9-1152\,A^2\,B\,a^4\,b^8+22656\,A^2\,B\,a^5\,b^7-26304\,A^2\,B\,a^6\,b^6+1536\,A^2\,B\,a^7\,b^5-3336\,A^2\,B\,a^8\,b^4-96\,A^2\,B\,a^{10}\,b^2+1536\,A\,C^2\,a^4\,b^8+7296\,A\,C^2\,a^6\,b^6-1536\,A\,C^2\,a^7\,b^5+8704\,A\,C^2\,a^8\,b^4-3456\,A\,C^2\,a^9\,b^3+512\,A\,C^2\,a^{10}\,b^2+6144\,A^2\,C\,a^4\,b^8-4608\,A^2\,C\,a^5\,b^7+13824\,A^2\,C\,a^6\,b^6-13056\,A^2\,C\,a^7\,b^5+1024\,A^2\,C\,a^8\,b^4-1824\,A^2\,C\,a^9\,b^3+1152\,B\,C^2\,a^5\,b^7+5888\,B\,C^2\,a^7\,b^5-1056\,B\,C^2\,a^8\,b^4+7168\,B\,C^2\,a^9\,b^3-2432\,B\,C^2\,a^{10}\,b^2+528\,B^2\,C\,a^4\,b^8+7552\,B^2\,C\,a^6\,b^6-2304\,B^2\,C\,a^7\,b^5+14592\,B^2\,C\,a^8\,b^4-7168\,B^2\,C\,a^9\,b^3+768\,A\,B\,C\,a^3\,b^9+15168\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+30592\,A\,B\,C\,a^7\,b^5-19488\,A\,B\,C\,a^8\,b^4+1536\,A\,B\,C\,a^9\,b^3-1408\,A\,B\,C\,a^{10}\,b^2-\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)-\frac{b\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)\,1{}\mathrm{i}}{2}+\frac{b\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^8+192\,A^2\,a^6\,b^2+1152\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+128\,A\,B\,a^7\,b+1536\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+32\,A\,C\,a^8+384\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+512\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+8\,B^2\,b^8+256\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+64\,B\,C\,a\,b^7+32\,C^2\,a^8+512\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+128\,C^2\,a^2\,b^6\right)+\frac{b\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)\,\left(16\,A\,a^4+16\,B\,b^4+32\,C\,a^4+192\,A\,a^2\,b^2+192\,B\,a^2\,b^2+128\,A\,a\,b^3+128\,B\,a^3\,b+64\,C\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)\,1{}\mathrm{i}}{2}}\right)\,\left(B\,b^3+8\,C\,a^3+8\,A\,a\,b^2+12\,B\,a^2\,b+4\,C\,a\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(4*A*a^4 + 4*B*a^4 - 2*B*b^4 - (8*C*b^4)/3 + 16*A*a^3*b - 8*C*a*b^3) + tan(c/2 + (d*x)/2)^7*(4*A*a^4 - 4*B*a^4 + 2*B*b^4 - (8*C*b^4)/3 - 16*A*a^3*b + 8*C*a*b^3) + tan(c/2 + (d*x)/2)^9*(A*a^4 + 2*A*b^4 - 2*B*a^4 - B*b^4 + 2*C*b^4 + 12*C*a^2*b^2 - 8*A*a^3*b + 8*B*a*b^3 - 4*C*a*b^3) + tan(c/2 + (d*x)/2)*(A*a^4 + 2*A*b^4 + 2*B*a^4 + B*b^4 + 2*C*b^4 + 12*C*a^2*b^2 + 8*A*a^3*b + 8*B*a*b^3 + 4*C*a*b^3) - tan(c/2 + (d*x)/2)^5*(4*A*b^4 - 6*A*a^4 - (4*C*b^4)/3 + 24*C*a^2*b^2 + 16*B*a*b^3))/(d*(tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (atan(((((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b)*1i - (((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b)*1i)/((((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b) + (((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((A*a^4)/2 + C*a^4 + 6*A*a^2*b^2 + 4*B*a^3*b) - 256*C^3*a^11*b + 6144*A^3*a^4*b^8 - 9216*A^3*a^5*b^7 + 512*A^3*a^6*b^6 - 1536*A^3*a^7*b^5 - 64*A^3*a^9*b^3 + 64*B^3*a^3*b^9 + 1536*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 9216*B^3*a^7*b^5 - 6144*B^3*a^8*b^4 + 256*C^3*a^6*b^6 + 1024*C^3*a^8*b^4 - 128*C^3*a^9*b^3 + 1024*C^3*a^10*b^2 - 256*A*C^2*a^11*b - 64*A^2*C*a^11*b + 96*A*B^2*a^2*b^10 + 3336*A*B^2*a^4*b^8 - 1536*A*B^2*a^5*b^7 + 26304*A*B^2*a^6*b^6 - 22656*A*B^2*a^7*b^5 + 1152*A*B^2*a^8*b^4 - 1536*A*B^2*a^9*b^3 + 1536*A^2*B*a^3*b^9 - 1152*A^2*B*a^4*b^8 + 22656*A^2*B*a^5*b^7 - 26304*A^2*B*a^6*b^6 + 1536*A^2*B*a^7*b^5 - 3336*A^2*B*a^8*b^4 - 96*A^2*B*a^10*b^2 + 1536*A*C^2*a^4*b^8 + 7296*A*C^2*a^6*b^6 - 1536*A*C^2*a^7*b^5 + 8704*A*C^2*a^8*b^4 - 3456*A*C^2*a^9*b^3 + 512*A*C^2*a^10*b^2 + 6144*A^2*C*a^4*b^8 - 4608*A^2*C*a^5*b^7 + 13824*A^2*C*a^6*b^6 - 13056*A^2*C*a^7*b^5 + 1024*A^2*C*a^8*b^4 - 1824*A^2*C*a^9*b^3 + 1152*B*C^2*a^5*b^7 + 5888*B*C^2*a^7*b^5 - 1056*B*C^2*a^8*b^4 + 7168*B*C^2*a^9*b^3 - 2432*B*C^2*a^10*b^2 + 528*B^2*C*a^4*b^8 + 7552*B^2*C*a^6*b^6 - 2304*B^2*C*a^7*b^5 + 14592*B^2*C*a^8*b^4 - 7168*B^2*C*a^9*b^3 + 768*A*B*C*a^3*b^9 + 15168*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 30592*A*B*C*a^7*b^5 - 19488*A*B*C*a^8*b^4 + 1536*A*B*C*a^9*b^3 - 1408*A*B*C*a^10*b^2))*(A*a^4*1i + C*a^4*2i + A*a^2*b^2*12i + B*a^3*b*8i))/d - (b*atan(((b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (b*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2))/2 + (b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (b*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2))/2)/(6144*A^3*a^4*b^8 - 256*C^3*a^11*b - 9216*A^3*a^5*b^7 + 512*A^3*a^6*b^6 - 1536*A^3*a^7*b^5 - 64*A^3*a^9*b^3 + 64*B^3*a^3*b^9 + 1536*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 9216*B^3*a^7*b^5 - 6144*B^3*a^8*b^4 + 256*C^3*a^6*b^6 + 1024*C^3*a^8*b^4 - 128*C^3*a^9*b^3 + 1024*C^3*a^10*b^2 - (b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (b*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2)*1i)/2 + (b*(tan(c/2 + (d*x)/2)*(8*A^2*a^8 + 8*B^2*b^8 + 32*C^2*a^8 + 512*A^2*a^2*b^6 + 1152*A^2*a^4*b^4 + 192*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 512*B^2*a^6*b^2 + 128*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*a^8 + 128*A*B*a*b^7 + 128*A*B*a^7*b + 64*B*C*a*b^7 + 256*B*C*a^7*b + 1536*A*B*a^3*b^5 + 1536*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 384*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (b*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2)*(16*A*a^4 + 16*B*b^4 + 32*C*a^4 + 192*A*a^2*b^2 + 192*B*a^2*b^2 + 128*A*a*b^3 + 128*B*a^3*b + 64*C*a*b^3 + 128*C*a^3*b)*1i)/2)*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2)*1i)/2 - 256*A*C^2*a^11*b - 64*A^2*C*a^11*b + 96*A*B^2*a^2*b^10 + 3336*A*B^2*a^4*b^8 - 1536*A*B^2*a^5*b^7 + 26304*A*B^2*a^6*b^6 - 22656*A*B^2*a^7*b^5 + 1152*A*B^2*a^8*b^4 - 1536*A*B^2*a^9*b^3 + 1536*A^2*B*a^3*b^9 - 1152*A^2*B*a^4*b^8 + 22656*A^2*B*a^5*b^7 - 26304*A^2*B*a^6*b^6 + 1536*A^2*B*a^7*b^5 - 3336*A^2*B*a^8*b^4 - 96*A^2*B*a^10*b^2 + 1536*A*C^2*a^4*b^8 + 7296*A*C^2*a^6*b^6 - 1536*A*C^2*a^7*b^5 + 8704*A*C^2*a^8*b^4 - 3456*A*C^2*a^9*b^3 + 512*A*C^2*a^10*b^2 + 6144*A^2*C*a^4*b^8 - 4608*A^2*C*a^5*b^7 + 13824*A^2*C*a^6*b^6 - 13056*A^2*C*a^7*b^5 + 1024*A^2*C*a^8*b^4 - 1824*A^2*C*a^9*b^3 + 1152*B*C^2*a^5*b^7 + 5888*B*C^2*a^7*b^5 - 1056*B*C^2*a^8*b^4 + 7168*B*C^2*a^9*b^3 - 2432*B*C^2*a^10*b^2 + 528*B^2*C*a^4*b^8 + 7552*B^2*C*a^6*b^6 - 2304*B^2*C*a^7*b^5 + 14592*B^2*C*a^8*b^4 - 7168*B^2*C*a^9*b^3 + 768*A*B*C*a^3*b^9 + 15168*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 30592*A*B*C*a^7*b^5 - 19488*A*B*C*a^8*b^4 + 1536*A*B*C*a^9*b^3 - 1408*A*B*C*a^10*b^2))*(B*b^3 + 8*C*a^3 + 8*A*a*b^2 + 12*B*a^2*b + 4*C*a*b^2))/d","B"
969,1,4849,303,5.728198,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","-\frac{\left(2\,A\,a^4-B\,a^4-2\,B\,b^4+2\,C\,a^4+C\,b^4+12\,A\,a^2\,b^2-4\,A\,a^3\,b+8\,B\,a^3\,b-8\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,A\,a^4}{3}-2\,B\,a^4+4\,B\,b^4-4\,C\,b^4-8\,A\,a^3\,b+16\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{4\,A\,a^4}{3}-4\,C\,a^4+6\,C\,b^4-24\,A\,a^2\,b^2-16\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{8\,A\,a^4}{3}+2\,B\,a^4-4\,B\,b^4-4\,C\,b^4+8\,A\,a^3\,b-16\,C\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+B\,a^4+2\,B\,b^4+2\,C\,a^4+C\,b^4+12\,A\,a^2\,b^2+4\,A\,a^3\,b+8\,B\,a^3\,b+8\,C\,a\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)\,1{}\mathrm{i}-\left(\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)\,1{}\mathrm{i}}{1024\,A^3\,a^2\,b^{10}-\left(\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)-256\,A^3\,a\,b^{11}-\left(\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)\right)\,\left(\frac{B\,a^4}{2}+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,A\,a^3\,b+4\,C\,a^3\,b\right)-128\,A^3\,a^3\,b^9+1024\,A^3\,a^4\,b^8+256\,A^3\,a^6\,b^6-6144\,B^3\,a^4\,b^8+9216\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+1536\,B^3\,a^7\,b^5+64\,B^3\,a^9\,b^3-64\,C^3\,a^3\,b^9-1536\,C^3\,a^5\,b^7+512\,C^3\,a^6\,b^6-9216\,C^3\,a^7\,b^5+6144\,C^3\,a^8\,b^4-64\,A\,C^2\,a\,b^{11}-256\,A^2\,C\,a\,b^{11}-7168\,A\,B^2\,a^3\,b^9+14592\,A\,B^2\,a^4\,b^8-2304\,A\,B^2\,a^5\,b^7+7552\,A\,B^2\,a^6\,b^6+528\,A\,B^2\,a^8\,b^4-2432\,A^2\,B\,a^2\,b^{10}+7168\,A^2\,B\,a^3\,b^9-1056\,A^2\,B\,a^4\,b^8+5888\,A^2\,B\,a^5\,b^7+1152\,A^2\,B\,a^7\,b^5-1824\,A\,C^2\,a^3\,b^9+1024\,A\,C^2\,a^4\,b^8-13056\,A\,C^2\,a^5\,b^7+13824\,A\,C^2\,a^6\,b^6-4608\,A\,C^2\,a^7\,b^5+6144\,A\,C^2\,a^8\,b^4+512\,A^2\,C\,a^2\,b^{10}-3456\,A^2\,C\,a^3\,b^9+8704\,A^2\,C\,a^4\,b^8-1536\,A^2\,C\,a^5\,b^7+7296\,A^2\,C\,a^6\,b^6+1536\,A^2\,C\,a^8\,b^4-96\,B\,C^2\,a^2\,b^{10}-3336\,B\,C^2\,a^4\,b^8+1536\,B\,C^2\,a^5\,b^7-26304\,B\,C^2\,a^6\,b^6+22656\,B\,C^2\,a^7\,b^5-1152\,B\,C^2\,a^8\,b^4+1536\,B\,C^2\,a^9\,b^3-1536\,B^2\,C\,a^3\,b^9+1152\,B^2\,C\,a^4\,b^8-22656\,B^2\,C\,a^5\,b^7+26304\,B^2\,C\,a^6\,b^6-1536\,B^2\,C\,a^7\,b^5+3336\,B^2\,C\,a^8\,b^4+96\,B^2\,C\,a^{10}\,b^2-1408\,A\,B\,C\,a^2\,b^{10}+1536\,A\,B\,C\,a^3\,b^9-19488\,A\,B\,C\,a^4\,b^8+30592\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+15168\,A\,B\,C\,a^7\,b^5+768\,A\,B\,C\,a^9\,b^3}\right)\,\left(B\,a^4\,1{}\mathrm{i}+B\,a^2\,b^2\,12{}\mathrm{i}+A\,a\,b^3\,8{}\mathrm{i}+A\,a^3\,b\,4{}\mathrm{i}+C\,a^3\,b\,8{}\mathrm{i}\right)}{d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)}{2}+\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)}{2}}{1024\,A^3\,a^2\,b^{10}-256\,A^3\,a\,b^{11}-128\,A^3\,a^3\,b^9+1024\,A^3\,a^4\,b^8+256\,A^3\,a^6\,b^6-6144\,B^3\,a^4\,b^8+9216\,B^3\,a^5\,b^7-512\,B^3\,a^6\,b^6+1536\,B^3\,a^7\,b^5+64\,B^3\,a^9\,b^3-64\,C^3\,a^3\,b^9-1536\,C^3\,a^5\,b^7+512\,C^3\,a^6\,b^6-9216\,C^3\,a^7\,b^5+6144\,C^3\,a^8\,b^4-64\,A\,C^2\,a\,b^{11}-256\,A^2\,C\,a\,b^{11}-7168\,A\,B^2\,a^3\,b^9+14592\,A\,B^2\,a^4\,b^8-2304\,A\,B^2\,a^5\,b^7+7552\,A\,B^2\,a^6\,b^6+528\,A\,B^2\,a^8\,b^4-2432\,A^2\,B\,a^2\,b^{10}+7168\,A^2\,B\,a^3\,b^9-1056\,A^2\,B\,a^4\,b^8+5888\,A^2\,B\,a^5\,b^7+1152\,A^2\,B\,a^7\,b^5-1824\,A\,C^2\,a^3\,b^9+1024\,A\,C^2\,a^4\,b^8-13056\,A\,C^2\,a^5\,b^7+13824\,A\,C^2\,a^6\,b^6-4608\,A\,C^2\,a^7\,b^5+6144\,A\,C^2\,a^8\,b^4+512\,A^2\,C\,a^2\,b^{10}-3456\,A^2\,C\,a^3\,b^9+8704\,A^2\,C\,a^4\,b^8-1536\,A^2\,C\,a^5\,b^7+7296\,A^2\,C\,a^6\,b^6+1536\,A^2\,C\,a^8\,b^4-96\,B\,C^2\,a^2\,b^{10}-3336\,B\,C^2\,a^4\,b^8+1536\,B\,C^2\,a^5\,b^7-26304\,B\,C^2\,a^6\,b^6+22656\,B\,C^2\,a^7\,b^5-1152\,B\,C^2\,a^8\,b^4+1536\,B\,C^2\,a^9\,b^3-1536\,B^2\,C\,a^3\,b^9+1152\,B^2\,C\,a^4\,b^8-22656\,B^2\,C\,a^5\,b^7+26304\,B^2\,C\,a^6\,b^6-1536\,B^2\,C\,a^7\,b^5+3336\,B^2\,C\,a^8\,b^4+96\,B^2\,C\,a^{10}\,b^2-1408\,A\,B\,C\,a^2\,b^{10}+1536\,A\,B\,C\,a^3\,b^9-19488\,A\,B\,C\,a^4\,b^8+30592\,A\,B\,C\,a^5\,b^7-6528\,A\,B\,C\,a^6\,b^6+15168\,A\,B\,C\,a^7\,b^5+768\,A\,B\,C\,a^9\,b^3+\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)-\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)\,1{}\mathrm{i}}{2}-\frac{b^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,A^2\,a^6\,b^2+512\,A^2\,a^4\,b^4+512\,A^2\,a^2\,b^6+32\,A^2\,b^8+64\,A\,B\,a^7\,b+896\,A\,B\,a^5\,b^3+1536\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+512\,A\,C\,a^6\,b^2+1024\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+32\,A\,C\,b^8+8\,B^2\,a^8+192\,B^2\,a^6\,b^2+1152\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+128\,B\,C\,a^7\,b+1536\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+128\,B\,C\,a\,b^7+512\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+192\,C^2\,a^2\,b^6+8\,C^2\,b^8\right)+\frac{b^2\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)\,\left(32\,A\,b^4+16\,B\,a^4+16\,C\,b^4+192\,B\,a^2\,b^2+192\,C\,a^2\,b^2+128\,A\,a\,b^3+64\,A\,a^3\,b+128\,B\,a\,b^3+128\,C\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)\,1{}\mathrm{i}}{2}}\right)\,\left(2\,A\,b^2+12\,C\,a^2+C\,b^2+8\,B\,a\,b\right)}{d}","Not used",1,"(atan(((((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b)*1i - (((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b)*1i)/(1024*A^3*a^2*b^10 - (((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) - tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b) - 256*A^3*a*b^11 - (((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b) + tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3))*((B*a^4)/2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 2*A*a^3*b + 4*C*a^3*b) - 128*A^3*a^3*b^9 + 1024*A^3*a^4*b^8 + 256*A^3*a^6*b^6 - 6144*B^3*a^4*b^8 + 9216*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 1536*B^3*a^7*b^5 + 64*B^3*a^9*b^3 - 64*C^3*a^3*b^9 - 1536*C^3*a^5*b^7 + 512*C^3*a^6*b^6 - 9216*C^3*a^7*b^5 + 6144*C^3*a^8*b^4 - 64*A*C^2*a*b^11 - 256*A^2*C*a*b^11 - 7168*A*B^2*a^3*b^9 + 14592*A*B^2*a^4*b^8 - 2304*A*B^2*a^5*b^7 + 7552*A*B^2*a^6*b^6 + 528*A*B^2*a^8*b^4 - 2432*A^2*B*a^2*b^10 + 7168*A^2*B*a^3*b^9 - 1056*A^2*B*a^4*b^8 + 5888*A^2*B*a^5*b^7 + 1152*A^2*B*a^7*b^5 - 1824*A*C^2*a^3*b^9 + 1024*A*C^2*a^4*b^8 - 13056*A*C^2*a^5*b^7 + 13824*A*C^2*a^6*b^6 - 4608*A*C^2*a^7*b^5 + 6144*A*C^2*a^8*b^4 + 512*A^2*C*a^2*b^10 - 3456*A^2*C*a^3*b^9 + 8704*A^2*C*a^4*b^8 - 1536*A^2*C*a^5*b^7 + 7296*A^2*C*a^6*b^6 + 1536*A^2*C*a^8*b^4 - 96*B*C^2*a^2*b^10 - 3336*B*C^2*a^4*b^8 + 1536*B*C^2*a^5*b^7 - 26304*B*C^2*a^6*b^6 + 22656*B*C^2*a^7*b^5 - 1152*B*C^2*a^8*b^4 + 1536*B*C^2*a^9*b^3 - 1536*B^2*C*a^3*b^9 + 1152*B^2*C*a^4*b^8 - 22656*B^2*C*a^5*b^7 + 26304*B^2*C*a^6*b^6 - 1536*B^2*C*a^7*b^5 + 3336*B^2*C*a^8*b^4 + 96*B^2*C*a^10*b^2 - 1408*A*B*C*a^2*b^10 + 1536*A*B*C*a^3*b^9 - 19488*A*B*C*a^4*b^8 + 30592*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 15168*A*B*C*a^7*b^5 + 768*A*B*C*a^9*b^3))*(B*a^4*1i + B*a^2*b^2*12i + A*a*b^3*8i + A*a^3*b*4i + C*a^3*b*8i))/d - (tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 + 2*B*a^4 - 4*B*b^4 - 4*C*b^4 + 8*A*a^3*b - 16*C*a*b^3) + tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 - 2*B*a^4 + 4*B*b^4 - 4*C*b^4 - 8*A*a^3*b + 16*C*a*b^3) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 - B*a^4 - 2*B*b^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 - 4*A*a^3*b + 8*B*a^3*b - 8*C*a*b^3) + tan(c/2 + (d*x)/2)*(2*A*a^4 + B*a^4 + 2*B*b^4 + 2*C*a^4 + C*b^4 + 12*A*a^2*b^2 + 4*A*a^3*b + 8*B*a^3*b + 8*C*a*b^3) - tan(c/2 + (d*x)/2)^5*(4*C*a^4 - (4*A*a^4)/3 - 6*C*b^4 + 24*A*a^2*b^2 + 16*B*a^3*b))/(d*(tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) + (b^2*atan(((b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b))/2 + (b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b))/2)/((b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) - (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b)*1i)/2 - 256*A^3*a*b^11 - (b^2*(tan(c/2 + (d*x)/2)*(32*A^2*b^8 + 8*B^2*a^8 + 8*C^2*b^8 + 512*A^2*a^2*b^6 + 512*A^2*a^4*b^4 + 128*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 1152*B^2*a^4*b^4 + 192*B^2*a^6*b^2 + 192*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 512*C^2*a^6*b^2 + 32*A*C*b^8 + 256*A*B*a*b^7 + 64*A*B*a^7*b + 128*B*C*a*b^7 + 128*B*C*a^7*b + 1536*A*B*a^3*b^5 + 896*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1024*A*C*a^4*b^4 + 512*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 1536*B*C*a^5*b^3) + (b^2*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b)*(32*A*b^4 + 16*B*a^4 + 16*C*b^4 + 192*B*a^2*b^2 + 192*C*a^2*b^2 + 128*A*a*b^3 + 64*A*a^3*b + 128*B*a*b^3 + 128*C*a^3*b)*1i)/2)*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b)*1i)/2 + 1024*A^3*a^2*b^10 - 128*A^3*a^3*b^9 + 1024*A^3*a^4*b^8 + 256*A^3*a^6*b^6 - 6144*B^3*a^4*b^8 + 9216*B^3*a^5*b^7 - 512*B^3*a^6*b^6 + 1536*B^3*a^7*b^5 + 64*B^3*a^9*b^3 - 64*C^3*a^3*b^9 - 1536*C^3*a^5*b^7 + 512*C^3*a^6*b^6 - 9216*C^3*a^7*b^5 + 6144*C^3*a^8*b^4 - 64*A*C^2*a*b^11 - 256*A^2*C*a*b^11 - 7168*A*B^2*a^3*b^9 + 14592*A*B^2*a^4*b^8 - 2304*A*B^2*a^5*b^7 + 7552*A*B^2*a^6*b^6 + 528*A*B^2*a^8*b^4 - 2432*A^2*B*a^2*b^10 + 7168*A^2*B*a^3*b^9 - 1056*A^2*B*a^4*b^8 + 5888*A^2*B*a^5*b^7 + 1152*A^2*B*a^7*b^5 - 1824*A*C^2*a^3*b^9 + 1024*A*C^2*a^4*b^8 - 13056*A*C^2*a^5*b^7 + 13824*A*C^2*a^6*b^6 - 4608*A*C^2*a^7*b^5 + 6144*A*C^2*a^8*b^4 + 512*A^2*C*a^2*b^10 - 3456*A^2*C*a^3*b^9 + 8704*A^2*C*a^4*b^8 - 1536*A^2*C*a^5*b^7 + 7296*A^2*C*a^6*b^6 + 1536*A^2*C*a^8*b^4 - 96*B*C^2*a^2*b^10 - 3336*B*C^2*a^4*b^8 + 1536*B*C^2*a^5*b^7 - 26304*B*C^2*a^6*b^6 + 22656*B*C^2*a^7*b^5 - 1152*B*C^2*a^8*b^4 + 1536*B*C^2*a^9*b^3 - 1536*B^2*C*a^3*b^9 + 1152*B^2*C*a^4*b^8 - 22656*B^2*C*a^5*b^7 + 26304*B^2*C*a^6*b^6 - 1536*B^2*C*a^7*b^5 + 3336*B^2*C*a^8*b^4 + 96*B^2*C*a^10*b^2 - 1408*A*B*C*a^2*b^10 + 1536*A*B*C*a^3*b^9 - 19488*A*B*C*a^4*b^8 + 30592*A*B*C*a^5*b^7 - 6528*A*B*C*a^6*b^6 + 15168*A*B*C*a^7*b^5 + 768*A*B*C*a^9*b^3))*(2*A*b^2 + 12*C*a^2 + C*b^2 + 8*B*a*b))/d","B"
970,1,4710,293,5.845116,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\frac{\mathrm{atan}\left(\frac{\left(\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)\,1{}\mathrm{i}-\left(\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)\,1{}\mathrm{i}}{64\,A^2\,B\,b^{12}-\left(\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)-64\,A\,B^2\,b^{12}-\left(\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)\right)\,\left(\frac{3\,A\,a^4}{8}+A\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+6\,C\,a^2\,b^2+4\,B\,a\,b^3+2\,B\,a^3\,b\right)-256\,B^3\,a\,b^{11}+1024\,B^3\,a^2\,b^{10}-128\,B^3\,a^3\,b^9+1024\,B^3\,a^4\,b^8+256\,B^3\,a^6\,b^6-6144\,C^3\,a^4\,b^8+9216\,C^3\,a^5\,b^7-512\,C^3\,a^6\,b^6+1536\,C^3\,a^7\,b^5+64\,C^3\,a^9\,b^3+512\,A\,B^2\,a\,b^{11}+256\,A^2\,C\,a\,b^{11}-192\,A\,B^2\,a^2\,b^{10}+1792\,A\,B^2\,a^3\,b^9-24\,A\,B^2\,a^4\,b^8+960\,A\,B^2\,a^5\,b^7+96\,A\,B^2\,a^7\,b^5+384\,A^2\,B\,a^2\,b^{10}+624\,A^2\,B\,a^4\,b^8+144\,A^2\,B\,a^6\,b^6+9\,A^2\,B\,a^8\,b^4-1024\,A\,C^2\,a^2\,b^{10}+3072\,A\,C^2\,a^3\,b^9-3072\,A\,C^2\,a^4\,b^8+9472\,A\,C^2\,a^5\,b^7-384\,A\,C^2\,a^6\,b^6+1920\,A\,C^2\,a^7\,b^5+96\,A\,C^2\,a^9\,b^3+1536\,A^2\,C\,a^3\,b^9+2496\,A^2\,C\,a^5\,b^7+576\,A^2\,C\,a^7\,b^5+36\,A^2\,C\,a^9\,b^3-7168\,B\,C^2\,a^3\,b^9+14592\,B\,C^2\,a^4\,b^8-2304\,B\,C^2\,a^5\,b^7+7552\,B\,C^2\,a^6\,b^6+528\,B\,C^2\,a^8\,b^4-2432\,B^2\,C\,a^2\,b^{10}+7168\,B^2\,C\,a^3\,b^9-1056\,B^2\,C\,a^4\,b^8+5888\,B^2\,C\,a^5\,b^7+1152\,B^2\,C\,a^7\,b^5-512\,A\,B\,C\,a\,b^{11}+2816\,A\,B\,C\,a^2\,b^{10}-1536\,A\,B\,C\,a^3\,b^9+9536\,A\,B\,C\,a^4\,b^8-192\,A\,B\,C\,a^5\,b^7+4320\,A\,B\,C\,a^6\,b^6+408\,A\,B\,C\,a^8\,b^4}\right)\,\left(\frac{A\,a^4\,3{}\mathrm{i}}{4}+A\,b^4\,2{}\mathrm{i}+C\,a^4\,1{}\mathrm{i}+A\,a^2\,b^2\,6{}\mathrm{i}+C\,a^2\,b^2\,12{}\mathrm{i}+B\,a\,b^3\,8{}\mathrm{i}+B\,a^3\,b\,4{}\mathrm{i}\right)}{d}+\frac{\left(\frac{5\,A\,a^4}{4}-2\,B\,a^4+C\,a^4+2\,C\,b^4+6\,A\,a^2\,b^2-12\,B\,a^2\,b^2-8\,A\,a\,b^3-8\,A\,a^3\,b+4\,B\,a^3\,b-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,A\,a^4+\frac{4\,B\,a^4}{3}-8\,C\,b^4+24\,B\,a^2\,b^2+16\,A\,a\,b^3+\frac{16\,A\,a^3\,b}{3}+16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,A\,a^4}{2}-2\,C\,a^4+12\,C\,b^4-12\,A\,a^2\,b^2-8\,B\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,A\,a^4-\frac{4\,B\,a^4}{3}-8\,C\,b^4-24\,B\,a^2\,b^2-16\,A\,a\,b^3-\frac{16\,A\,a^3\,b}{3}-16\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,A\,a^4}{4}+2\,B\,a^4+C\,a^4+2\,C\,b^4+6\,A\,a^2\,b^2+12\,B\,a^2\,b^2+8\,A\,a\,b^3+8\,A\,a^3\,b+4\,B\,a^3\,b+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,b^3\,\mathrm{atan}\left(\frac{b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)-b^3\,\left(B\,b+4\,C\,a\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)\,1{}\mathrm{i}\right)\,\left(B\,b+4\,C\,a\right)+b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)+b^3\,\left(B\,b+4\,C\,a\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)\,1{}\mathrm{i}\right)\,\left(B\,b+4\,C\,a\right)}{64\,A^2\,B\,b^{12}-64\,A\,B^2\,b^{12}-256\,B^3\,a\,b^{11}+1024\,B^3\,a^2\,b^{10}-128\,B^3\,a^3\,b^9+1024\,B^3\,a^4\,b^8+256\,B^3\,a^6\,b^6-6144\,C^3\,a^4\,b^8+9216\,C^3\,a^5\,b^7-512\,C^3\,a^6\,b^6+1536\,C^3\,a^7\,b^5+64\,C^3\,a^9\,b^3+512\,A\,B^2\,a\,b^{11}+256\,A^2\,C\,a\,b^{11}-192\,A\,B^2\,a^2\,b^{10}+1792\,A\,B^2\,a^3\,b^9-24\,A\,B^2\,a^4\,b^8+960\,A\,B^2\,a^5\,b^7+96\,A\,B^2\,a^7\,b^5+384\,A^2\,B\,a^2\,b^{10}+624\,A^2\,B\,a^4\,b^8+144\,A^2\,B\,a^6\,b^6+9\,A^2\,B\,a^8\,b^4-1024\,A\,C^2\,a^2\,b^{10}+3072\,A\,C^2\,a^3\,b^9-3072\,A\,C^2\,a^4\,b^8+9472\,A\,C^2\,a^5\,b^7-384\,A\,C^2\,a^6\,b^6+1920\,A\,C^2\,a^7\,b^5+96\,A\,C^2\,a^9\,b^3+1536\,A^2\,C\,a^3\,b^9+2496\,A^2\,C\,a^5\,b^7+576\,A^2\,C\,a^7\,b^5+36\,A^2\,C\,a^9\,b^3-7168\,B\,C^2\,a^3\,b^9+14592\,B\,C^2\,a^4\,b^8-2304\,B\,C^2\,a^5\,b^7+7552\,B\,C^2\,a^6\,b^6+528\,B\,C^2\,a^8\,b^4-2432\,B^2\,C\,a^2\,b^{10}+7168\,B^2\,C\,a^3\,b^9-1056\,B^2\,C\,a^4\,b^8+5888\,B^2\,C\,a^5\,b^7+1152\,B^2\,C\,a^7\,b^5-512\,A\,B\,C\,a\,b^{11}+2816\,A\,B\,C\,a^2\,b^{10}-1536\,A\,B\,C\,a^3\,b^9+9536\,A\,B\,C\,a^4\,b^8-192\,A\,B\,C\,a^5\,b^7+4320\,A\,B\,C\,a^6\,b^6+408\,A\,B\,C\,a^8\,b^4+b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)-b^3\,\left(B\,b+4\,C\,a\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)\,1{}\mathrm{i}\right)\,\left(B\,b+4\,C\,a\right)\,1{}\mathrm{i}-b^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{9\,A^2\,a^8}{2}+72\,A^2\,a^6\,b^2+312\,A^2\,a^4\,b^4+192\,A^2\,a^2\,b^6+32\,A^2\,b^8+48\,A\,B\,a^7\,b+480\,A\,B\,a^5\,b^3+896\,A\,B\,a^3\,b^5+256\,A\,B\,a\,b^7+12\,A\,C\,a^8+240\,A\,C\,a^6\,b^2+1184\,A\,C\,a^4\,b^4+384\,A\,C\,a^2\,b^6+128\,B^2\,a^6\,b^2+512\,B^2\,a^4\,b^4+512\,B^2\,a^2\,b^6+32\,B^2\,b^8+64\,B\,C\,a^7\,b+896\,B\,C\,a^5\,b^3+1536\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+8\,C^2\,a^8+192\,C^2\,a^6\,b^2+1152\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6\right)+b^3\,\left(B\,b+4\,C\,a\right)\,\left(12\,A\,a^4+32\,A\,b^4+32\,B\,b^4+16\,C\,a^4+96\,A\,a^2\,b^2+192\,C\,a^2\,b^2+128\,B\,a\,b^3+64\,B\,a^3\,b+128\,C\,a\,b^3\right)\,1{}\mathrm{i}\right)\,\left(B\,b+4\,C\,a\right)\,1{}\mathrm{i}}\right)\,\left(B\,b+4\,C\,a\right)}{d}","Not used",1,"(atan(((((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) + tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b)*1i - (((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) - tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b)*1i)/(64*A^2*B*b^12 - (((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) - tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b) - 64*A*B^2*b^12 - (((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3) + tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3))*((3*A*a^4)/8 + A*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 2*B*a^3*b) - 256*B^3*a*b^11 + 1024*B^3*a^2*b^10 - 128*B^3*a^3*b^9 + 1024*B^3*a^4*b^8 + 256*B^3*a^6*b^6 - 6144*C^3*a^4*b^8 + 9216*C^3*a^5*b^7 - 512*C^3*a^6*b^6 + 1536*C^3*a^7*b^5 + 64*C^3*a^9*b^3 + 512*A*B^2*a*b^11 + 256*A^2*C*a*b^11 - 192*A*B^2*a^2*b^10 + 1792*A*B^2*a^3*b^9 - 24*A*B^2*a^4*b^8 + 960*A*B^2*a^5*b^7 + 96*A*B^2*a^7*b^5 + 384*A^2*B*a^2*b^10 + 624*A^2*B*a^4*b^8 + 144*A^2*B*a^6*b^6 + 9*A^2*B*a^8*b^4 - 1024*A*C^2*a^2*b^10 + 3072*A*C^2*a^3*b^9 - 3072*A*C^2*a^4*b^8 + 9472*A*C^2*a^5*b^7 - 384*A*C^2*a^6*b^6 + 1920*A*C^2*a^7*b^5 + 96*A*C^2*a^9*b^3 + 1536*A^2*C*a^3*b^9 + 2496*A^2*C*a^5*b^7 + 576*A^2*C*a^7*b^5 + 36*A^2*C*a^9*b^3 - 7168*B*C^2*a^3*b^9 + 14592*B*C^2*a^4*b^8 - 2304*B*C^2*a^5*b^7 + 7552*B*C^2*a^6*b^6 + 528*B*C^2*a^8*b^4 - 2432*B^2*C*a^2*b^10 + 7168*B^2*C*a^3*b^9 - 1056*B^2*C*a^4*b^8 + 5888*B^2*C*a^5*b^7 + 1152*B^2*C*a^7*b^5 - 512*A*B*C*a*b^11 + 2816*A*B*C*a^2*b^10 - 1536*A*B*C*a^3*b^9 + 9536*A*B*C*a^4*b^8 - 192*A*B*C*a^5*b^7 + 4320*A*B*C*a^6*b^6 + 408*A*B*C*a^8*b^4))*((A*a^4*3i)/4 + A*b^4*2i + C*a^4*1i + A*a^2*b^2*6i + C*a^2*b^2*12i + B*a*b^3*8i + B*a^3*b*4i))/d + (tan(c/2 + (d*x)/2)*((5*A*a^4)/4 + 2*B*a^4 + C*a^4 + 2*C*b^4 + 6*A*a^2*b^2 + 12*B*a^2*b^2 + 8*A*a*b^3 + 8*A*a^3*b + 4*B*a^3*b + 8*C*a^3*b) - tan(c/2 + (d*x)/2)^3*((4*B*a^4)/3 - 2*A*a^4 + 8*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*A*a^3*b)/3 + 16*C*a^3*b) + tan(c/2 + (d*x)/2)^7*(2*A*a^4 + (4*B*a^4)/3 - 8*C*b^4 + 24*B*a^2*b^2 + 16*A*a*b^3 + (16*A*a^3*b)/3 + 16*C*a^3*b) + tan(c/2 + (d*x)/2)^9*((5*A*a^4)/4 - 2*B*a^4 + C*a^4 + 2*C*b^4 + 6*A*a^2*b^2 - 12*B*a^2*b^2 - 8*A*a*b^3 - 8*A*a^3*b + 4*B*a^3*b - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^5*(2*C*a^4 - (3*A*a^4)/2 - 12*C*b^4 + 12*A*a^2*b^2 + 8*B*a^3*b))/(d*(2*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (2*b^3*atan((b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3) - b^3*(B*b + 4*C*a)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3)*1i)*(B*b + 4*C*a) + b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3) + b^3*(B*b + 4*C*a)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3)*1i)*(B*b + 4*C*a))/(64*A^2*B*b^12 - 64*A*B^2*b^12 - 256*B^3*a*b^11 + 1024*B^3*a^2*b^10 - 128*B^3*a^3*b^9 + 1024*B^3*a^4*b^8 + 256*B^3*a^6*b^6 - 6144*C^3*a^4*b^8 + 9216*C^3*a^5*b^7 - 512*C^3*a^6*b^6 + 1536*C^3*a^7*b^5 + 64*C^3*a^9*b^3 + b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3) - b^3*(B*b + 4*C*a)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3)*1i)*(B*b + 4*C*a)*1i - b^3*(tan(c/2 + (d*x)/2)*((9*A^2*a^8)/2 + 32*A^2*b^8 + 32*B^2*b^8 + 8*C^2*a^8 + 192*A^2*a^2*b^6 + 312*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 512*B^2*a^2*b^6 + 512*B^2*a^4*b^4 + 128*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 1152*C^2*a^4*b^4 + 192*C^2*a^6*b^2 + 12*A*C*a^8 + 256*A*B*a*b^7 + 48*A*B*a^7*b + 256*B*C*a*b^7 + 64*B*C*a^7*b + 896*A*B*a^3*b^5 + 480*A*B*a^5*b^3 + 384*A*C*a^2*b^6 + 1184*A*C*a^4*b^4 + 240*A*C*a^6*b^2 + 1536*B*C*a^3*b^5 + 896*B*C*a^5*b^3) + b^3*(B*b + 4*C*a)*(12*A*a^4 + 32*A*b^4 + 32*B*b^4 + 16*C*a^4 + 96*A*a^2*b^2 + 192*C*a^2*b^2 + 128*B*a*b^3 + 64*B*a^3*b + 128*C*a*b^3)*1i)*(B*b + 4*C*a)*1i + 512*A*B^2*a*b^11 + 256*A^2*C*a*b^11 - 192*A*B^2*a^2*b^10 + 1792*A*B^2*a^3*b^9 - 24*A*B^2*a^4*b^8 + 960*A*B^2*a^5*b^7 + 96*A*B^2*a^7*b^5 + 384*A^2*B*a^2*b^10 + 624*A^2*B*a^4*b^8 + 144*A^2*B*a^6*b^6 + 9*A^2*B*a^8*b^4 - 1024*A*C^2*a^2*b^10 + 3072*A*C^2*a^3*b^9 - 3072*A*C^2*a^4*b^8 + 9472*A*C^2*a^5*b^7 - 384*A*C^2*a^6*b^6 + 1920*A*C^2*a^7*b^5 + 96*A*C^2*a^9*b^3 + 1536*A^2*C*a^3*b^9 + 2496*A^2*C*a^5*b^7 + 576*A^2*C*a^7*b^5 + 36*A^2*C*a^9*b^3 - 7168*B*C^2*a^3*b^9 + 14592*B*C^2*a^4*b^8 - 2304*B*C^2*a^5*b^7 + 7552*B*C^2*a^6*b^6 + 528*B*C^2*a^8*b^4 - 2432*B^2*C*a^2*b^10 + 7168*B^2*C*a^3*b^9 - 1056*B^2*C*a^4*b^8 + 5888*B^2*C*a^5*b^7 + 1152*B^2*C*a^7*b^5 - 512*A*B*C*a*b^11 + 2816*A*B*C*a^2*b^10 - 1536*A*B*C*a^3*b^9 + 9536*A*B*C*a^4*b^8 - 192*A*B*C*a^5*b^7 + 4320*A*B*C*a^6*b^6 + 408*A*B*C*a^8*b^4))*(B*b + 4*C*a))/d","B"
971,1,4068,314,5.373473,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","-\frac{\left(2\,A\,a^4+2\,A\,b^4-\frac{5\,B\,a^4}{4}+2\,C\,a^4+12\,A\,a^2\,b^2-6\,B\,a^2\,b^2+12\,C\,a^2\,b^2-4\,A\,a\,b^3-5\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,a^3\,b-4\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{B\,a^4}{2}-8\,A\,b^4-\frac{8\,A\,a^4}{3}-\frac{16\,C\,a^4}{3}-32\,A\,a^2\,b^2+12\,B\,a^2\,b^2-48\,C\,a^2\,b^2+8\,A\,a\,b^3+2\,A\,a^3\,b-32\,B\,a\,b^3-\frac{64\,B\,a^3\,b}{3}+8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^4}{15}+12\,A\,b^4+\frac{20\,C\,a^4}{3}+40\,A\,a^2\,b^2+72\,C\,a^2\,b^2+48\,B\,a\,b^3+\frac{80\,B\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,A\,a^4}{3}-8\,A\,b^4-\frac{B\,a^4}{2}-\frac{16\,C\,a^4}{3}-32\,A\,a^2\,b^2-12\,B\,a^2\,b^2-48\,C\,a^2\,b^2-8\,A\,a\,b^3-2\,A\,a^3\,b-32\,B\,a\,b^3-\frac{64\,B\,a^3\,b}{3}-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+\frac{5\,B\,a^4}{4}+2\,C\,a^4+12\,A\,a^2\,b^2+6\,B\,a^2\,b^2+12\,C\,a^2\,b^2+4\,A\,a\,b^3+5\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,a^3\,b+4\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{\mathrm{atan}\left(\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)\,1{}\mathrm{i}+\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)\,1{}\mathrm{i}}{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)-\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\right)\,\left(\frac{3\,B\,a^4}{8}+B\,b^4+3\,B\,a^2\,b^2+2\,A\,a\,b^3+\frac{3\,A\,a^3\,b}{2}+4\,C\,a\,b^3+2\,C\,a^3\,b\right)-64\,B\,C^2\,b^{12}+64\,B^2\,C\,b^{12}-256\,C^3\,a\,b^{11}+1024\,C^3\,a^2\,b^{10}-128\,C^3\,a^3\,b^9+1024\,C^3\,a^4\,b^8+256\,C^3\,a^6\,b^6-128\,A\,C^2\,a\,b^{11}+512\,B\,C^2\,a\,b^{11}+1024\,A\,C^2\,a^2\,b^{10}-96\,A\,C^2\,a^3\,b^9+1280\,A\,C^2\,a^4\,b^8+384\,A\,C^2\,a^6\,b^6+256\,A^2\,C\,a^2\,b^{10}+384\,A^2\,C\,a^4\,b^8+144\,A^2\,C\,a^6\,b^6-192\,B\,C^2\,a^2\,b^{10}+1792\,B\,C^2\,a^3\,b^9-24\,B\,C^2\,a^4\,b^8+960\,B\,C^2\,a^5\,b^7+96\,B\,C^2\,a^7\,b^5+384\,B^2\,C\,a^2\,b^{10}+624\,B^2\,C\,a^4\,b^8+144\,B^2\,C\,a^6\,b^6+9\,B^2\,C\,a^8\,b^4+256\,A\,B\,C\,a\,b^{11}+960\,A\,B\,C\,a^3\,b^9+672\,A\,B\,C\,a^5\,b^7+72\,A\,B\,C\,a^7\,b^5}\right)\,\left(\frac{B\,a^4\,3{}\mathrm{i}}{4}+B\,b^4\,2{}\mathrm{i}+B\,a^2\,b^2\,6{}\mathrm{i}+A\,a\,b^3\,4{}\mathrm{i}+A\,a^3\,b\,3{}\mathrm{i}+C\,a\,b^3\,8{}\mathrm{i}+C\,a^3\,b\,4{}\mathrm{i}\right)}{d}+\frac{2\,C\,b^4\,\mathrm{atan}\left(\frac{C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)+C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)}{64\,B^2\,C\,b^{12}-64\,B\,C^2\,b^{12}-256\,C^3\,a\,b^{11}+1024\,C^3\,a^2\,b^{10}-128\,C^3\,a^3\,b^9+1024\,C^3\,a^4\,b^8+256\,C^3\,a^6\,b^6-128\,A\,C^2\,a\,b^{11}+512\,B\,C^2\,a\,b^{11}+1024\,A\,C^2\,a^2\,b^{10}-96\,A\,C^2\,a^3\,b^9+1280\,A\,C^2\,a^4\,b^8+384\,A\,C^2\,a^6\,b^6+256\,A^2\,C\,a^2\,b^{10}+384\,A^2\,C\,a^4\,b^8+144\,A^2\,C\,a^6\,b^6-192\,B\,C^2\,a^2\,b^{10}+1792\,B\,C^2\,a^3\,b^9-24\,B\,C^2\,a^4\,b^8+960\,B\,C^2\,a^5\,b^7+96\,B\,C^2\,a^7\,b^5+384\,B^2\,C\,a^2\,b^{10}+624\,B^2\,C\,a^4\,b^8+144\,B^2\,C\,a^6\,b^6+9\,B^2\,C\,a^8\,b^4+256\,A\,B\,C\,a\,b^{11}+960\,A\,B\,C\,a^3\,b^9+672\,A\,B\,C\,a^5\,b^7+72\,A\,B\,C\,a^7\,b^5+C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)-C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-C\,b^4\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^6\,b^2+192\,A^2\,a^4\,b^4+128\,A^2\,a^2\,b^6+36\,A\,B\,a^7\,b+336\,A\,B\,a^5\,b^3+480\,A\,B\,a^3\,b^5+128\,A\,B\,a\,b^7+192\,A\,C\,a^6\,b^2+640\,A\,C\,a^4\,b^4+512\,A\,C\,a^2\,b^6+\frac{9\,B^2\,a^8}{2}+72\,B^2\,a^6\,b^2+312\,B^2\,a^4\,b^4+192\,B^2\,a^2\,b^6+32\,B^2\,b^8+48\,B\,C\,a^7\,b+480\,B\,C\,a^5\,b^3+896\,B\,C\,a^3\,b^5+256\,B\,C\,a\,b^7+128\,C^2\,a^6\,b^2+512\,C^2\,a^4\,b^4+512\,C^2\,a^2\,b^6+32\,C^2\,b^8\right)+C\,b^4\,\left(12\,B\,a^4+32\,B\,b^4+32\,C\,b^4+96\,B\,a^2\,b^2+64\,A\,a\,b^3+48\,A\,a^3\,b+128\,C\,a\,b^3+64\,C\,a^3\,b\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)}{d}","Not used",1,"(atan(((tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + ((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b)*1i + (tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - ((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b)*1i)/((tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - ((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b) - (tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + ((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b)*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b))*((3*B*a^4)/8 + B*b^4 + 3*B*a^2*b^2 + 2*A*a*b^3 + (3*A*a^3*b)/2 + 4*C*a*b^3 + 2*C*a^3*b) - 64*B*C^2*b^12 + 64*B^2*C*b^12 - 256*C^3*a*b^11 + 1024*C^3*a^2*b^10 - 128*C^3*a^3*b^9 + 1024*C^3*a^4*b^8 + 256*C^3*a^6*b^6 - 128*A*C^2*a*b^11 + 512*B*C^2*a*b^11 + 1024*A*C^2*a^2*b^10 - 96*A*C^2*a^3*b^9 + 1280*A*C^2*a^4*b^8 + 384*A*C^2*a^6*b^6 + 256*A^2*C*a^2*b^10 + 384*A^2*C*a^4*b^8 + 144*A^2*C*a^6*b^6 - 192*B*C^2*a^2*b^10 + 1792*B*C^2*a^3*b^9 - 24*B*C^2*a^4*b^8 + 960*B*C^2*a^5*b^7 + 96*B*C^2*a^7*b^5 + 384*B^2*C*a^2*b^10 + 624*B^2*C*a^4*b^8 + 144*B^2*C*a^6*b^6 + 9*B^2*C*a^8*b^4 + 256*A*B*C*a*b^11 + 960*A*B*C*a^3*b^9 + 672*A*B*C*a^5*b^7 + 72*A*B*C*a^7*b^5))*((B*a^4*3i)/4 + B*b^4*2i + B*a^2*b^2*6i + A*a*b^3*4i + A*a^3*b*3i + C*a*b^3*8i + C*a^3*b*4i))/d - (tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + (5*B*a^4)/4 + 2*C*a^4 + 12*A*a^2*b^2 + 6*B*a^2*b^2 + 12*C*a^2*b^2 + 4*A*a*b^3 + 5*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b + 4*C*a^3*b) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + 2*A*b^4 - (5*B*a^4)/4 + 2*C*a^4 + 12*A*a^2*b^2 - 6*B*a^2*b^2 + 12*C*a^2*b^2 - 4*A*a*b^3 - 5*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b - 4*C*a^3*b) - tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 + 8*A*b^4 + (B*a^4)/2 + (16*C*a^4)/3 + 32*A*a^2*b^2 + 12*B*a^2*b^2 + 48*C*a^2*b^2 + 8*A*a*b^3 + 2*A*a^3*b + 32*B*a*b^3 + (64*B*a^3*b)/3 + 8*C*a^3*b) - tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 + 8*A*b^4 - (B*a^4)/2 + (16*C*a^4)/3 + 32*A*a^2*b^2 - 12*B*a^2*b^2 + 48*C*a^2*b^2 - 8*A*a*b^3 - 2*A*a^3*b + 32*B*a*b^3 + (64*B*a^3*b)/3 - 8*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^4)/15 + 12*A*b^4 + (20*C*a^4)/3 + 40*A*a^2*b^2 + 72*C*a^2*b^2 + 48*B*a*b^3 + (80*B*a^3*b)/3))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) + (2*C*b^4*atan((C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i) + C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i))/(64*B^2*C*b^12 - 64*B*C^2*b^12 - 256*C^3*a*b^11 + C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) - C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i)*1i - C*b^4*(tan(c/2 + (d*x)/2)*((9*B^2*a^8)/2 + 32*B^2*b^8 + 32*C^2*b^8 + 128*A^2*a^2*b^6 + 192*A^2*a^4*b^4 + 72*A^2*a^6*b^2 + 192*B^2*a^2*b^6 + 312*B^2*a^4*b^4 + 72*B^2*a^6*b^2 + 512*C^2*a^2*b^6 + 512*C^2*a^4*b^4 + 128*C^2*a^6*b^2 + 128*A*B*a*b^7 + 36*A*B*a^7*b + 256*B*C*a*b^7 + 48*B*C*a^7*b + 480*A*B*a^3*b^5 + 336*A*B*a^5*b^3 + 512*A*C*a^2*b^6 + 640*A*C*a^4*b^4 + 192*A*C*a^6*b^2 + 896*B*C*a^3*b^5 + 480*B*C*a^5*b^3) + C*b^4*(12*B*a^4 + 32*B*b^4 + 32*C*b^4 + 96*B*a^2*b^2 + 64*A*a*b^3 + 48*A*a^3*b + 128*C*a*b^3 + 64*C*a^3*b)*1i)*1i + 1024*C^3*a^2*b^10 - 128*C^3*a^3*b^9 + 1024*C^3*a^4*b^8 + 256*C^3*a^6*b^6 - 128*A*C^2*a*b^11 + 512*B*C^2*a*b^11 + 1024*A*C^2*a^2*b^10 - 96*A*C^2*a^3*b^9 + 1280*A*C^2*a^4*b^8 + 384*A*C^2*a^6*b^6 + 256*A^2*C*a^2*b^10 + 384*A^2*C*a^4*b^8 + 144*A^2*C*a^6*b^6 - 192*B*C^2*a^2*b^10 + 1792*B*C^2*a^3*b^9 - 24*B*C^2*a^4*b^8 + 960*B*C^2*a^5*b^7 + 96*B*C^2*a^7*b^5 + 384*B^2*C*a^2*b^10 + 624*B^2*C*a^4*b^8 + 144*B^2*C*a^6*b^6 + 9*B^2*C*a^8*b^4 + 256*A*B*C*a*b^11 + 960*A*B*C*a^3*b^9 + 672*A*B*C*a^5*b^7 + 72*A*B*C*a^7*b^5)))/d","B"
972,1,942,381,3.921825,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^7,x)","\frac{\left(\frac{11\,A\,a^4}{8}+A\,b^4-2\,B\,a^4-2\,B\,b^4+\frac{5\,C\,a^4}{4}+\frac{15\,A\,a^2\,b^2}{2}-12\,B\,a^2\,b^2+6\,C\,a^2\,b^2-8\,A\,a\,b^3-8\,A\,a^3\,b+4\,B\,a\,b^3+5\,B\,a^3\,b-8\,C\,a\,b^3-8\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{5\,A\,a^4}{24}-3\,A\,b^4+\frac{14\,B\,a^4}{3}+10\,B\,b^4-\frac{7\,C\,a^4}{4}-\frac{21\,A\,a^2\,b^2}{2}+44\,B\,a^2\,b^2-18\,C\,a^2\,b^2+\frac{88\,A\,a\,b^3}{3}+\frac{56\,A\,a^3\,b}{3}-12\,B\,a\,b^3-7\,B\,a^3\,b+40\,C\,a\,b^3+\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{15\,A\,a^4}{4}+2\,A\,b^4-\frac{52\,B\,a^4}{5}-20\,B\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2-72\,B\,a^2\,b^2+12\,C\,a^2\,b^2-48\,A\,a\,b^3-\frac{208\,A\,a^3\,b}{5}+8\,B\,a\,b^3+2\,B\,a^3\,b-80\,C\,a\,b^3-48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{15\,A\,a^4}{4}+2\,A\,b^4+\frac{52\,B\,a^4}{5}+20\,B\,b^4+\frac{C\,a^4}{2}+3\,A\,a^2\,b^2+72\,B\,a^2\,b^2+12\,C\,a^2\,b^2+48\,A\,a\,b^3+\frac{208\,A\,a^3\,b}{5}+8\,B\,a\,b^3+2\,B\,a^3\,b+80\,C\,a\,b^3+48\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,A\,a^4}{24}-3\,A\,b^4-\frac{14\,B\,a^4}{3}-10\,B\,b^4-\frac{7\,C\,a^4}{4}-\frac{21\,A\,a^2\,b^2}{2}-44\,B\,a^2\,b^2-18\,C\,a^2\,b^2-\frac{88\,A\,a\,b^3}{3}-\frac{56\,A\,a^3\,b}{3}-12\,B\,a\,b^3-7\,B\,a^3\,b-40\,C\,a\,b^3-\frac{88\,C\,a^3\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,A\,a^4}{8}+A\,b^4+2\,B\,a^4+2\,B\,b^4+\frac{5\,C\,a^4}{4}+\frac{15\,A\,a^2\,b^2}{2}+12\,B\,a^2\,b^2+6\,C\,a^2\,b^2+8\,A\,a\,b^3+8\,A\,a^3\,b+4\,B\,a\,b^3+5\,B\,a^3\,b+8\,C\,a\,b^3+8\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,A\,a^4}{16}+\frac{A\,b^4}{2}+\frac{3\,C\,a^4}{8}+C\,b^4+\frac{9\,A\,a^2\,b^2}{4}+3\,C\,a^2\,b^2+2\,B\,a\,b^3+\frac{3\,B\,a^3\,b}{2}\right)}{\frac{5\,A\,a^4}{4}+2\,A\,b^4+\frac{3\,C\,a^4}{2}+4\,C\,b^4+9\,A\,a^2\,b^2+12\,C\,a^2\,b^2+8\,B\,a\,b^3+6\,B\,a^3\,b}\right)\,\left(\frac{5\,A\,a^4}{8}+A\,b^4+\frac{3\,C\,a^4}{4}+2\,C\,b^4+\frac{9\,A\,a^2\,b^2}{2}+6\,C\,a^2\,b^2+4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((11*A*a^4)/8 + A*b^4 + 2*B*a^4 + 2*B*b^4 + (5*C*a^4)/4 + (15*A*a^2*b^2)/2 + 12*B*a^2*b^2 + 6*C*a^2*b^2 + 8*A*a*b^3 + 8*A*a^3*b + 4*B*a*b^3 + 5*B*a^3*b + 8*C*a*b^3 + 8*C*a^3*b) + tan(c/2 + (d*x)/2)^11*((11*A*a^4)/8 + A*b^4 - 2*B*a^4 - 2*B*b^4 + (5*C*a^4)/4 + (15*A*a^2*b^2)/2 - 12*B*a^2*b^2 + 6*C*a^2*b^2 - 8*A*a*b^3 - 8*A*a^3*b + 4*B*a*b^3 + 5*B*a^3*b - 8*C*a*b^3 - 8*C*a^3*b) - tan(c/2 + (d*x)/2)^3*(3*A*b^4 - (5*A*a^4)/24 + (14*B*a^4)/3 + 10*B*b^4 + (7*C*a^4)/4 + (21*A*a^2*b^2)/2 + 44*B*a^2*b^2 + 18*C*a^2*b^2 + (88*A*a*b^3)/3 + (56*A*a^3*b)/3 + 12*B*a*b^3 + 7*B*a^3*b + 40*C*a*b^3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^9*((5*A*a^4)/24 - 3*A*b^4 + (14*B*a^4)/3 + 10*B*b^4 - (7*C*a^4)/4 - (21*A*a^2*b^2)/2 + 44*B*a^2*b^2 - 18*C*a^2*b^2 + (88*A*a*b^3)/3 + (56*A*a^3*b)/3 - 12*B*a*b^3 - 7*B*a^3*b + 40*C*a*b^3 + (88*C*a^3*b)/3) + tan(c/2 + (d*x)/2)^5*((15*A*a^4)/4 + 2*A*b^4 + (52*B*a^4)/5 + 20*B*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 + 72*B*a^2*b^2 + 12*C*a^2*b^2 + 48*A*a*b^3 + (208*A*a^3*b)/5 + 8*B*a*b^3 + 2*B*a^3*b + 80*C*a*b^3 + 48*C*a^3*b) + tan(c/2 + (d*x)/2)^7*((15*A*a^4)/4 + 2*A*b^4 - (52*B*a^4)/5 - 20*B*b^4 + (C*a^4)/2 + 3*A*a^2*b^2 - 72*B*a^2*b^2 + 12*C*a^2*b^2 - 48*A*a*b^3 - (208*A*a^3*b)/5 + 8*B*a*b^3 + 2*B*a^3*b - 80*C*a*b^3 - 48*C*a^3*b))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (atanh((4*tan(c/2 + (d*x)/2)*((5*A*a^4)/16 + (A*b^4)/2 + (3*C*a^4)/8 + C*b^4 + (9*A*a^2*b^2)/4 + 3*C*a^2*b^2 + 2*B*a*b^3 + (3*B*a^3*b)/2))/((5*A*a^4)/4 + 2*A*b^4 + (3*C*a^4)/2 + 4*C*b^4 + 9*A*a^2*b^2 + 12*C*a^2*b^2 + 8*B*a*b^3 + 6*B*a^3*b))*((5*A*a^4)/8 + A*b^4 + (3*C*a^4)/4 + 2*C*b^4 + (9*A*a^2*b^2)/2 + 6*C*a^2*b^2 + 4*B*a*b^3 + 3*B*a^3*b))/d","B"
973,1,1044,454,4.235923,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^8,x)","\frac{\mathrm{atanh}\left(\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,B\,a^4}{16}+\frac{B\,b^4}{2}+\frac{9\,B\,a^2\,b^2}{4}+\frac{3\,A\,a\,b^3}{2}+\frac{5\,A\,a^3\,b}{4}+2\,C\,a\,b^3+\frac{3\,C\,a^3\,b}{2}\right)}{\frac{5\,B\,a^4}{4}+2\,B\,b^4+9\,B\,a^2\,b^2+6\,A\,a\,b^3+5\,A\,a^3\,b+8\,C\,a\,b^3+6\,C\,a^3\,b}\right)\,\left(\frac{5\,B\,a^4}{8}+B\,b^4+\frac{9\,B\,a^2\,b^2}{2}+3\,A\,a\,b^3+\frac{5\,A\,a^3\,b}{2}+4\,C\,a\,b^3+3\,C\,a^3\,b\right)}{d}-\frac{\left(2\,A\,a^4+2\,A\,b^4-\frac{11\,B\,a^4}{8}-B\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2-\frac{15\,B\,a^2\,b^2}{2}+12\,C\,a^2\,b^2-5\,A\,a\,b^3-\frac{11\,A\,a^3\,b}{2}+8\,B\,a\,b^3+8\,B\,a^3\,b-4\,C\,a\,b^3-5\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{7\,B\,a^4}{6}-\frac{28\,A\,b^4}{3}-4\,A\,a^4+4\,B\,b^4-\frac{20\,C\,a^4}{3}-12\,C\,b^4-40\,A\,a^2\,b^2+18\,B\,a^2\,b^2-56\,C\,a^2\,b^2+12\,A\,a\,b^3+\frac{14\,A\,a^3\,b}{3}-\frac{112\,B\,a\,b^3}{3}-\frac{80\,B\,a^3\,b}{3}+16\,C\,a\,b^3+12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{86\,A\,a^4}{5}+\frac{58\,A\,b^4}{3}-\frac{85\,B\,a^4}{24}-5\,B\,b^4+\frac{226\,C\,a^4}{15}+30\,C\,b^4+\frac{452\,A\,a^2\,b^2}{5}-\frac{27\,B\,a^2\,b^2}{2}+116\,C\,a^2\,b^2-9\,A\,a\,b^3-\frac{85\,A\,a^3\,b}{6}+\frac{232\,B\,a\,b^3}{3}+\frac{904\,B\,a^3\,b}{15}-20\,C\,a\,b^3-9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{424\,A\,a^4}{35}-24\,A\,b^4-\frac{104\,C\,a^4}{5}-40\,C\,b^4-\frac{624\,A\,a^2\,b^2}{5}-144\,C\,a^2\,b^2-96\,B\,a\,b^3-\frac{416\,B\,a^3\,b}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{86\,A\,a^4}{5}+\frac{58\,A\,b^4}{3}+\frac{85\,B\,a^4}{24}+5\,B\,b^4+\frac{226\,C\,a^4}{15}+30\,C\,b^4+\frac{452\,A\,a^2\,b^2}{5}+\frac{27\,B\,a^2\,b^2}{2}+116\,C\,a^2\,b^2+9\,A\,a\,b^3+\frac{85\,A\,a^3\,b}{6}+\frac{232\,B\,a\,b^3}{3}+\frac{904\,B\,a^3\,b}{15}+20\,C\,a\,b^3+9\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,A\,a^4-\frac{28\,A\,b^4}{3}-\frac{7\,B\,a^4}{6}-4\,B\,b^4-\frac{20\,C\,a^4}{3}-12\,C\,b^4-40\,A\,a^2\,b^2-18\,B\,a^2\,b^2-56\,C\,a^2\,b^2-12\,A\,a\,b^3-\frac{14\,A\,a^3\,b}{3}-\frac{112\,B\,a\,b^3}{3}-\frac{80\,B\,a^3\,b}{3}-16\,C\,a\,b^3-12\,C\,a^3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^4+2\,A\,b^4+\frac{11\,B\,a^4}{8}+B\,b^4+2\,C\,a^4+2\,C\,b^4+12\,A\,a^2\,b^2+\frac{15\,B\,a^2\,b^2}{2}+12\,C\,a^2\,b^2+5\,A\,a\,b^3+\frac{11\,A\,a^3\,b}{2}+8\,B\,a\,b^3+8\,B\,a^3\,b+4\,C\,a\,b^3+5\,C\,a^3\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((5*B*a^4)/16 + (B*b^4)/2 + (9*B*a^2*b^2)/4 + (3*A*a*b^3)/2 + (5*A*a^3*b)/4 + 2*C*a*b^3 + (3*C*a^3*b)/2))/((5*B*a^4)/4 + 2*B*b^4 + 9*B*a^2*b^2 + 6*A*a*b^3 + 5*A*a^3*b + 8*C*a*b^3 + 6*C*a^3*b))*((5*B*a^4)/8 + B*b^4 + (9*B*a^2*b^2)/2 + 3*A*a*b^3 + (5*A*a^3*b)/2 + 4*C*a*b^3 + 3*C*a^3*b))/d - (tan(c/2 + (d*x)/2)^13*(2*A*a^4 + 2*A*b^4 - (11*B*a^4)/8 - B*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 - (15*B*a^2*b^2)/2 + 12*C*a^2*b^2 - 5*A*a*b^3 - (11*A*a^3*b)/2 + 8*B*a*b^3 + 8*B*a^3*b - 4*C*a*b^3 - 5*C*a^3*b) - tan(c/2 + (d*x)/2)^3*(4*A*a^4 + (28*A*b^4)/3 + (7*B*a^4)/6 + 4*B*b^4 + (20*C*a^4)/3 + 12*C*b^4 + 40*A*a^2*b^2 + 18*B*a^2*b^2 + 56*C*a^2*b^2 + 12*A*a*b^3 + (14*A*a^3*b)/3 + (112*B*a*b^3)/3 + (80*B*a^3*b)/3 + 16*C*a*b^3 + 12*C*a^3*b) - tan(c/2 + (d*x)/2)^11*(4*A*a^4 + (28*A*b^4)/3 - (7*B*a^4)/6 - 4*B*b^4 + (20*C*a^4)/3 + 12*C*b^4 + 40*A*a^2*b^2 - 18*B*a^2*b^2 + 56*C*a^2*b^2 - 12*A*a*b^3 - (14*A*a^3*b)/3 + (112*B*a*b^3)/3 + (80*B*a^3*b)/3 - 16*C*a*b^3 - 12*C*a^3*b) + tan(c/2 + (d*x)/2)^5*((86*A*a^4)/5 + (58*A*b^4)/3 + (85*B*a^4)/24 + 5*B*b^4 + (226*C*a^4)/15 + 30*C*b^4 + (452*A*a^2*b^2)/5 + (27*B*a^2*b^2)/2 + 116*C*a^2*b^2 + 9*A*a*b^3 + (85*A*a^3*b)/6 + (232*B*a*b^3)/3 + (904*B*a^3*b)/15 + 20*C*a*b^3 + 9*C*a^3*b) + tan(c/2 + (d*x)/2)^9*((86*A*a^4)/5 + (58*A*b^4)/3 - (85*B*a^4)/24 - 5*B*b^4 + (226*C*a^4)/15 + 30*C*b^4 + (452*A*a^2*b^2)/5 - (27*B*a^2*b^2)/2 + 116*C*a^2*b^2 - 9*A*a*b^3 - (85*A*a^3*b)/6 + (232*B*a*b^3)/3 + (904*B*a^3*b)/15 - 20*C*a*b^3 - 9*C*a^3*b) - tan(c/2 + (d*x)/2)^7*((424*A*a^4)/35 + 24*A*b^4 + (104*C*a^4)/5 + 40*C*b^4 + (624*A*a^2*b^2)/5 + 144*C*a^2*b^2 + 96*B*a*b^3 + (416*B*a^3*b)/5) + tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + (11*B*a^4)/8 + B*b^4 + 2*C*a^4 + 2*C*b^4 + 12*A*a^2*b^2 + (15*B*a^2*b^2)/2 + 12*C*a^2*b^2 + 5*A*a*b^3 + (11*A*a^3*b)/2 + 8*B*a*b^3 + 8*B*a^3*b + 4*C*a*b^3 + 5*C*a^3*b))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
974,1,325,256,2.433373,"\text{Not used}","int((a + b*cos(c + d*x))^3*(C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x)),x)","\frac{3\,B\,b^5\,x}{8}-C\,a^5\,x+B\,a^4\,b\,x+\frac{9\,C\,a\,b^4\,x}{8}+\frac{5\,C\,b^5\,\sin\left(c+d\,x\right)}{8\,d}+3\,B\,a^2\,b^3\,x-C\,a^3\,b^2\,x+\frac{B\,b^5\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b^5\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{5\,C\,b^5\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{C\,b^5\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{B\,a\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{4\,B\,a^3\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,C\,a\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,C\,a\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,C\,a^2\,b^3\,\sin\left(c+d\,x\right)}{2\,d}+\frac{3\,B\,a^2\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}-\frac{C\,a^3\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{C\,a^2\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{3\,B\,a\,b^4\,\sin\left(c+d\,x\right)}{d}-\frac{3\,C\,a^4\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*B*b^5*x)/8 - C*a^5*x + B*a^4*b*x + (9*C*a*b^4*x)/8 + (5*C*b^5*sin(c + d*x))/(8*d) + 3*B*a^2*b^3*x - C*a^3*b^2*x + (B*b^5*sin(2*c + 2*d*x))/(4*d) + (B*b^5*sin(4*c + 4*d*x))/(32*d) + (5*C*b^5*sin(3*c + 3*d*x))/(48*d) + (C*b^5*sin(5*c + 5*d*x))/(80*d) + (B*a*b^4*sin(3*c + 3*d*x))/(3*d) + (4*B*a^3*b^2*sin(c + d*x))/d + (3*C*a*b^4*sin(2*c + 2*d*x))/(4*d) + (3*C*a*b^4*sin(4*c + 4*d*x))/(32*d) + (3*C*a^2*b^3*sin(c + d*x))/(2*d) + (3*B*a^2*b^3*sin(2*c + 2*d*x))/(2*d) - (C*a^3*b^2*sin(2*c + 2*d*x))/(2*d) + (C*a^2*b^3*sin(3*c + 3*d*x))/(6*d) + (3*B*a*b^4*sin(c + d*x))/d - (3*C*a^4*b*sin(c + d*x))/d","B"
975,1,187,176,2.018765,"\text{Not used}","int((a + b*cos(c + d*x))^2*(C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x)),x)","\frac{3\,C\,b^4\,x}{8}-C\,a^4\,x+\frac{3\,B\,a\,b^3\,x}{2}+B\,a^3\,b\,x+\frac{3\,B\,b^4\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{C\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}+\frac{3\,C\,a\,b^3\,\sin\left(c+d\,x\right)}{2\,d}-\frac{2\,C\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*C*b^4*x)/8 - C*a^4*x + (3*B*a*b^3*x)/2 + B*a^3*b*x + (3*B*b^4*sin(c + d*x))/(4*d) + (B*b^4*sin(3*c + 3*d*x))/(12*d) + (C*b^4*sin(2*c + 2*d*x))/(4*d) + (C*b^4*sin(4*c + 4*d*x))/(32*d) + (3*B*a*b^3*sin(2*c + 2*d*x))/(4*d) + (3*B*a^2*b^2*sin(c + d*x))/d + (C*a*b^3*sin(3*c + 3*d*x))/(6*d) + (3*C*a*b^3*sin(c + d*x))/(2*d) - (2*C*a^3*b*sin(c + d*x))/d","B"
976,1,132,120,1.927867,"\text{Not used}","int((a + b*cos(c + d*x))*(C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x)),x)","\frac{B\,b^3\,x}{2}-C\,a^3\,x+B\,a^2\,b\,x+\frac{C\,a\,b^2\,x}{2}+\frac{3\,C\,b^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{C\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{C\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{2\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{d}-\frac{C\,a^2\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(B*b^3*x)/2 - C*a^3*x + B*a^2*b*x + (C*a*b^2*x)/2 + (3*C*b^3*sin(c + d*x))/(4*d) + (B*b^3*sin(2*c + 2*d*x))/(4*d) + (C*b^3*sin(3*c + 3*d*x))/(12*d) + (C*a*b^2*sin(2*c + 2*d*x))/(4*d) + (2*B*a*b^2*sin(c + d*x))/d - (C*a^2*b*sin(c + d*x))/d","B"
977,1,9661,279,10.809504,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,A\,b^3-8\,B\,b^3+8\,C\,a^3+5\,C\,b^3+8\,A\,a\,b^2-4\,B\,a\,b^2-8\,B\,a^2\,b+8\,C\,a\,b^2+4\,C\,a^2\,b\right)}{4\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(72\,C\,a^3-40\,B\,b^3-12\,A\,b^3+9\,C\,b^3+72\,A\,a\,b^2+12\,B\,a\,b^2-72\,B\,a^2\,b+40\,C\,a\,b^2-12\,C\,a^2\,b\right)}{12\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,A\,b^3-40\,B\,b^3+72\,C\,a^3-9\,C\,b^3+72\,A\,a\,b^2-12\,B\,a\,b^2-72\,B\,a^2\,b+40\,C\,a\,b^2+12\,C\,a^2\,b\right)}{12\,b^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3+8\,B\,b^3-8\,C\,a^3+5\,C\,b^3-8\,A\,a\,b^2-4\,B\,a\,b^2+8\,B\,a^2\,b-8\,C\,a\,b^2+4\,C\,a^2\,b\right)}{4\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}}{\frac{64\,A^3\,a^8\,b^6-96\,A^3\,a^7\,b^7+96\,A^3\,a^6\,b^8-80\,A^3\,a^5\,b^9+32\,A^3\,a^4\,b^{10}-16\,A^3\,a^3\,b^{11}-192\,A^2\,B\,a^9\,b^5+288\,A^2\,B\,a^8\,b^6-288\,A^2\,B\,a^7\,b^7+240\,A^2\,B\,a^6\,b^8-96\,A^2\,B\,a^5\,b^9+48\,A^2\,B\,a^4\,b^{10}+192\,A^2\,C\,a^{10}\,b^4-288\,A^2\,C\,a^9\,b^5+288\,A^2\,C\,a^8\,b^6-264\,A^2\,C\,a^7\,b^7+168\,A^2\,C\,a^6\,b^8-120\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}-24\,A^2\,C\,a^3\,b^{11}+192\,A\,B^2\,a^{10}\,b^4-288\,A\,B^2\,a^9\,b^5+288\,A\,B^2\,a^8\,b^6-240\,A\,B^2\,a^7\,b^7+96\,A\,B^2\,a^6\,b^8-48\,A\,B^2\,a^5\,b^9-384\,A\,B\,C\,a^{11}\,b^3+576\,A\,B\,C\,a^{10}\,b^4-576\,A\,B\,C\,a^9\,b^5+528\,A\,B\,C\,a^8\,b^6-336\,A\,B\,C\,a^7\,b^7+240\,A\,B\,C\,a^6\,b^8-96\,A\,B\,C\,a^5\,b^9+48\,A\,B\,C\,a^4\,b^{10}+192\,A\,C^2\,a^{12}\,b^2-288\,A\,C^2\,a^{11}\,b^3+288\,A\,C^2\,a^{10}\,b^4-288\,A\,C^2\,a^9\,b^5+240\,A\,C^2\,a^8\,b^6-192\,A\,C^2\,a^7\,b^7+96\,A\,C^2\,a^6\,b^8-57\,A\,C^2\,a^5\,b^9+18\,A\,C^2\,a^4\,b^{10}-9\,A\,C^2\,a^3\,b^{11}-64\,B^3\,a^{11}\,b^3+96\,B^3\,a^{10}\,b^4-96\,B^3\,a^9\,b^5+80\,B^3\,a^8\,b^6-32\,B^3\,a^7\,b^7+16\,B^3\,a^6\,b^8+192\,B^2\,C\,a^{12}\,b^2-288\,B^2\,C\,a^{11}\,b^3+288\,B^2\,C\,a^{10}\,b^4-264\,B^2\,C\,a^9\,b^5+168\,B^2\,C\,a^8\,b^6-120\,B^2\,C\,a^7\,b^7+48\,B^2\,C\,a^6\,b^8-24\,B^2\,C\,a^5\,b^9-192\,B\,C^2\,a^{13}\,b+288\,B\,C^2\,a^{12}\,b^2-288\,B\,C^2\,a^{11}\,b^3+288\,B\,C^2\,a^{10}\,b^4-240\,B\,C^2\,a^9\,b^5+192\,B\,C^2\,a^8\,b^6-96\,B\,C^2\,a^7\,b^7+57\,B\,C^2\,a^6\,b^8-18\,B\,C^2\,a^5\,b^9+9\,B\,C^2\,a^4\,b^{10}+64\,C^3\,a^{14}-96\,C^3\,a^{13}\,b+96\,C^3\,a^{12}\,b^2-104\,C^3\,a^{11}\,b^3+104\,C^3\,a^{10}\,b^4-88\,C^3\,a^9\,b^5+48\,C^3\,a^8\,b^6-33\,C^3\,a^7\,b^7+18\,C^3\,a^6\,b^8-9\,C^3\,a^5\,b^9}{b^{12}}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{b^5}-\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{2\,b^{13}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{b^5}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)}{b^5}}\right)\,\left(b^2\,\left(A\,a^2\,1{}\mathrm{i}+\frac{C\,a^2\,1{}\mathrm{i}}{2}\right)+C\,a^4\,1{}\mathrm{i}+b^4\,\left(\frac{A\,1{}\mathrm{i}}{2}+\frac{C\,3{}\mathrm{i}}{8}\right)-\frac{B\,a\,b^3\,1{}\mathrm{i}}{2}-B\,a^3\,b\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^5\,d}-\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^7-a^2\,b^5}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^7-a^2\,b^5}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^7-a^2\,b^5}}{\frac{64\,A^3\,a^8\,b^6-96\,A^3\,a^7\,b^7+96\,A^3\,a^6\,b^8-80\,A^3\,a^5\,b^9+32\,A^3\,a^4\,b^{10}-16\,A^3\,a^3\,b^{11}-192\,A^2\,B\,a^9\,b^5+288\,A^2\,B\,a^8\,b^6-288\,A^2\,B\,a^7\,b^7+240\,A^2\,B\,a^6\,b^8-96\,A^2\,B\,a^5\,b^9+48\,A^2\,B\,a^4\,b^{10}+192\,A^2\,C\,a^{10}\,b^4-288\,A^2\,C\,a^9\,b^5+288\,A^2\,C\,a^8\,b^6-264\,A^2\,C\,a^7\,b^7+168\,A^2\,C\,a^6\,b^8-120\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}-24\,A^2\,C\,a^3\,b^{11}+192\,A\,B^2\,a^{10}\,b^4-288\,A\,B^2\,a^9\,b^5+288\,A\,B^2\,a^8\,b^6-240\,A\,B^2\,a^7\,b^7+96\,A\,B^2\,a^6\,b^8-48\,A\,B^2\,a^5\,b^9-384\,A\,B\,C\,a^{11}\,b^3+576\,A\,B\,C\,a^{10}\,b^4-576\,A\,B\,C\,a^9\,b^5+528\,A\,B\,C\,a^8\,b^6-336\,A\,B\,C\,a^7\,b^7+240\,A\,B\,C\,a^6\,b^8-96\,A\,B\,C\,a^5\,b^9+48\,A\,B\,C\,a^4\,b^{10}+192\,A\,C^2\,a^{12}\,b^2-288\,A\,C^2\,a^{11}\,b^3+288\,A\,C^2\,a^{10}\,b^4-288\,A\,C^2\,a^9\,b^5+240\,A\,C^2\,a^8\,b^6-192\,A\,C^2\,a^7\,b^7+96\,A\,C^2\,a^6\,b^8-57\,A\,C^2\,a^5\,b^9+18\,A\,C^2\,a^4\,b^{10}-9\,A\,C^2\,a^3\,b^{11}-64\,B^3\,a^{11}\,b^3+96\,B^3\,a^{10}\,b^4-96\,B^3\,a^9\,b^5+80\,B^3\,a^8\,b^6-32\,B^3\,a^7\,b^7+16\,B^3\,a^6\,b^8+192\,B^2\,C\,a^{12}\,b^2-288\,B^2\,C\,a^{11}\,b^3+288\,B^2\,C\,a^{10}\,b^4-264\,B^2\,C\,a^9\,b^5+168\,B^2\,C\,a^8\,b^6-120\,B^2\,C\,a^7\,b^7+48\,B^2\,C\,a^6\,b^8-24\,B^2\,C\,a^5\,b^9-192\,B\,C^2\,a^{13}\,b+288\,B\,C^2\,a^{12}\,b^2-288\,B\,C^2\,a^{11}\,b^3+288\,B\,C^2\,a^{10}\,b^4-240\,B\,C^2\,a^9\,b^5+192\,B\,C^2\,a^8\,b^6-96\,B\,C^2\,a^7\,b^7+57\,B\,C^2\,a^6\,b^8-18\,B\,C^2\,a^5\,b^9+9\,B\,C^2\,a^4\,b^{10}+64\,C^3\,a^{14}-96\,C^3\,a^{13}\,b+96\,C^3\,a^{12}\,b^2-104\,C^3\,a^{11}\,b^3+104\,C^3\,a^{10}\,b^4-88\,C^3\,a^9\,b^5+48\,C^3\,a^8\,b^6-33\,C^3\,a^7\,b^7+18\,C^3\,a^6\,b^8-9\,C^3\,a^5\,b^9}{b^{12}}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}+\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^7-a^2\,b^5}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^7-a^2\,b^5}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,A^2\,a^7\,b^4+256\,A^2\,a^6\,b^5-256\,A^2\,a^5\,b^6+256\,A^2\,a^4\,b^7-208\,A^2\,a^3\,b^8+112\,A^2\,a^2\,b^9-48\,A^2\,a\,b^{10}+16\,A^2\,b^{11}+256\,A\,B\,a^8\,b^3-512\,A\,B\,a^7\,b^4+512\,A\,B\,a^6\,b^5-512\,A\,B\,a^5\,b^6+416\,A\,B\,a^4\,b^7-224\,A\,B\,a^3\,b^8+96\,A\,B\,a^2\,b^9-32\,A\,B\,a\,b^{10}-256\,A\,C\,a^9\,b^2+512\,A\,C\,a^8\,b^3-512\,A\,C\,a^7\,b^4+512\,A\,C\,a^6\,b^5-464\,A\,C\,a^5\,b^6+368\,A\,C\,a^4\,b^7-264\,A\,C\,a^3\,b^8+152\,A\,C\,a^2\,b^9-72\,A\,C\,a\,b^{10}+24\,A\,C\,b^{11}-128\,B^2\,a^9\,b^2+256\,B^2\,a^8\,b^3-256\,B^2\,a^7\,b^4+256\,B^2\,a^6\,b^5-208\,B^2\,a^5\,b^6+112\,B^2\,a^4\,b^7-48\,B^2\,a^3\,b^8+16\,B^2\,a^2\,b^9+256\,B\,C\,a^{10}\,b-512\,B\,C\,a^9\,b^2+512\,B\,C\,a^8\,b^3-512\,B\,C\,a^7\,b^4+464\,B\,C\,a^6\,b^5-368\,B\,C\,a^5\,b^6+264\,B\,C\,a^4\,b^7-152\,B\,C\,a^3\,b^8+72\,B\,C\,a^2\,b^9-24\,B\,C\,a\,b^{10}-128\,C^2\,a^{11}+256\,C^2\,a^{10}\,b-256\,C^2\,a^9\,b^2+256\,C^2\,a^8\,b^3-256\,C^2\,a^7\,b^4+256\,C^2\,a^6\,b^5-216\,C^2\,a^5\,b^6+136\,C^2\,a^4\,b^7-81\,C^2\,a^3\,b^8+51\,C^2\,a^2\,b^9-27\,C^2\,a\,b^{10}+9\,C^2\,b^{11}\right)}{2\,b^8}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{16\,A\,b^{16}+12\,C\,b^{16}+16\,A\,a^2\,b^{14}-48\,A\,a^3\,b^{13}+32\,A\,a^4\,b^{12}+16\,B\,a^2\,b^{14}-16\,B\,a^3\,b^{13}+48\,B\,a^4\,b^{12}-32\,B\,a^5\,b^{11}+4\,C\,a^2\,b^{14}-4\,C\,a^3\,b^{13}+16\,C\,a^4\,b^{12}-48\,C\,a^5\,b^{11}+32\,C\,a^6\,b^{10}-16\,A\,a\,b^{15}-16\,B\,a\,b^{15}-12\,C\,a\,b^{15}}{b^{12}}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^3\,b^{10}-256\,a^2\,b^{11}+128\,a\,b^{12}\right)}{2\,b^8\,\left(b^7-a^2\,b^5\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^7-a^2\,b^5}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^7-a^2\,b^5}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^7-a^2\,b^5\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^7*(4*A*b^3 - 8*B*b^3 + 8*C*a^3 + 5*C*b^3 + 8*A*a*b^2 - 4*B*a*b^2 - 8*B*a^2*b + 8*C*a*b^2 + 4*C*a^2*b))/(4*b^4) + (tan(c/2 + (d*x)/2)^3*(72*C*a^3 - 40*B*b^3 - 12*A*b^3 + 9*C*b^3 + 72*A*a*b^2 + 12*B*a*b^2 - 72*B*a^2*b + 40*C*a*b^2 - 12*C*a^2*b))/(12*b^4) + (tan(c/2 + (d*x)/2)^5*(12*A*b^3 - 40*B*b^3 + 72*C*a^3 - 9*C*b^3 + 72*A*a*b^2 - 12*B*a*b^2 - 72*B*a^2*b + 40*C*a*b^2 + 12*C*a^2*b))/(12*b^4) - (tan(c/2 + (d*x)/2)*(4*A*b^3 + 8*B*b^3 - 8*C*a^3 + 5*C*b^3 - 8*A*a*b^2 - 4*B*a*b^2 + 8*B*a^2*b - 8*C*a*b^2 + 4*C*a^2*b))/(4*b^4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (atan(((((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) + (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 - (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i)*1i)/b^5 + (((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) - (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 + (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i)*1i)/b^5)/((64*C^3*a^14 - 96*C^3*a^13*b - 16*A^3*a^3*b^11 + 32*A^3*a^4*b^10 - 80*A^3*a^5*b^9 + 96*A^3*a^6*b^8 - 96*A^3*a^7*b^7 + 64*A^3*a^8*b^6 + 16*B^3*a^6*b^8 - 32*B^3*a^7*b^7 + 80*B^3*a^8*b^6 - 96*B^3*a^9*b^5 + 96*B^3*a^10*b^4 - 64*B^3*a^11*b^3 - 9*C^3*a^5*b^9 + 18*C^3*a^6*b^8 - 33*C^3*a^7*b^7 + 48*C^3*a^8*b^6 - 88*C^3*a^9*b^5 + 104*C^3*a^10*b^4 - 104*C^3*a^11*b^3 + 96*C^3*a^12*b^2 - 192*B*C^2*a^13*b - 48*A*B^2*a^5*b^9 + 96*A*B^2*a^6*b^8 - 240*A*B^2*a^7*b^7 + 288*A*B^2*a^8*b^6 - 288*A*B^2*a^9*b^5 + 192*A*B^2*a^10*b^4 + 48*A^2*B*a^4*b^10 - 96*A^2*B*a^5*b^9 + 240*A^2*B*a^6*b^8 - 288*A^2*B*a^7*b^7 + 288*A^2*B*a^8*b^6 - 192*A^2*B*a^9*b^5 - 9*A*C^2*a^3*b^11 + 18*A*C^2*a^4*b^10 - 57*A*C^2*a^5*b^9 + 96*A*C^2*a^6*b^8 - 192*A*C^2*a^7*b^7 + 240*A*C^2*a^8*b^6 - 288*A*C^2*a^9*b^5 + 288*A*C^2*a^10*b^4 - 288*A*C^2*a^11*b^3 + 192*A*C^2*a^12*b^2 - 24*A^2*C*a^3*b^11 + 48*A^2*C*a^4*b^10 - 120*A^2*C*a^5*b^9 + 168*A^2*C*a^6*b^8 - 264*A^2*C*a^7*b^7 + 288*A^2*C*a^8*b^6 - 288*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4 + 9*B*C^2*a^4*b^10 - 18*B*C^2*a^5*b^9 + 57*B*C^2*a^6*b^8 - 96*B*C^2*a^7*b^7 + 192*B*C^2*a^8*b^6 - 240*B*C^2*a^9*b^5 + 288*B*C^2*a^10*b^4 - 288*B*C^2*a^11*b^3 + 288*B*C^2*a^12*b^2 - 24*B^2*C*a^5*b^9 + 48*B^2*C*a^6*b^8 - 120*B^2*C*a^7*b^7 + 168*B^2*C*a^8*b^6 - 264*B^2*C*a^9*b^5 + 288*B^2*C*a^10*b^4 - 288*B^2*C*a^11*b^3 + 192*B^2*C*a^12*b^2 + 48*A*B*C*a^4*b^10 - 96*A*B*C*a^5*b^9 + 240*A*B*C*a^6*b^8 - 336*A*B*C*a^7*b^7 + 528*A*B*C*a^8*b^6 - 576*A*B*C*a^9*b^5 + 576*A*B*C*a^10*b^4 - 384*A*B*C*a^11*b^3)/b^12 + (((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) + (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 - (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/b^5 - (((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) - (((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 + (tan(c/2 + (d*x)/2)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/(2*b^13))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/b^5)*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i))/b^5))*(b^2*(A*a^2*1i + (C*a^2*1i)/2) + C*a^4*1i + b^4*((A*1i)/2 + (C*3i)/8) - (B*a*b^3*1i)/2 - B*a^3*b*1i)*2i)/(b^5*d) - (a^3*atan(((a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) + (a^3*(-(a + b)*(a - b))^(1/2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 - (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5)))*(A*b^2 + C*a^2 - B*a*b))/(b^7 - a^2*b^5))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^7 - a^2*b^5) + (a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) - (a^3*(-(a + b)*(a - b))^(1/2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 + (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5)))*(A*b^2 + C*a^2 - B*a*b))/(b^7 - a^2*b^5))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^7 - a^2*b^5))/((64*C^3*a^14 - 96*C^3*a^13*b - 16*A^3*a^3*b^11 + 32*A^3*a^4*b^10 - 80*A^3*a^5*b^9 + 96*A^3*a^6*b^8 - 96*A^3*a^7*b^7 + 64*A^3*a^8*b^6 + 16*B^3*a^6*b^8 - 32*B^3*a^7*b^7 + 80*B^3*a^8*b^6 - 96*B^3*a^9*b^5 + 96*B^3*a^10*b^4 - 64*B^3*a^11*b^3 - 9*C^3*a^5*b^9 + 18*C^3*a^6*b^8 - 33*C^3*a^7*b^7 + 48*C^3*a^8*b^6 - 88*C^3*a^9*b^5 + 104*C^3*a^10*b^4 - 104*C^3*a^11*b^3 + 96*C^3*a^12*b^2 - 192*B*C^2*a^13*b - 48*A*B^2*a^5*b^9 + 96*A*B^2*a^6*b^8 - 240*A*B^2*a^7*b^7 + 288*A*B^2*a^8*b^6 - 288*A*B^2*a^9*b^5 + 192*A*B^2*a^10*b^4 + 48*A^2*B*a^4*b^10 - 96*A^2*B*a^5*b^9 + 240*A^2*B*a^6*b^8 - 288*A^2*B*a^7*b^7 + 288*A^2*B*a^8*b^6 - 192*A^2*B*a^9*b^5 - 9*A*C^2*a^3*b^11 + 18*A*C^2*a^4*b^10 - 57*A*C^2*a^5*b^9 + 96*A*C^2*a^6*b^8 - 192*A*C^2*a^7*b^7 + 240*A*C^2*a^8*b^6 - 288*A*C^2*a^9*b^5 + 288*A*C^2*a^10*b^4 - 288*A*C^2*a^11*b^3 + 192*A*C^2*a^12*b^2 - 24*A^2*C*a^3*b^11 + 48*A^2*C*a^4*b^10 - 120*A^2*C*a^5*b^9 + 168*A^2*C*a^6*b^8 - 264*A^2*C*a^7*b^7 + 288*A^2*C*a^8*b^6 - 288*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4 + 9*B*C^2*a^4*b^10 - 18*B*C^2*a^5*b^9 + 57*B*C^2*a^6*b^8 - 96*B*C^2*a^7*b^7 + 192*B*C^2*a^8*b^6 - 240*B*C^2*a^9*b^5 + 288*B*C^2*a^10*b^4 - 288*B*C^2*a^11*b^3 + 288*B*C^2*a^12*b^2 - 24*B^2*C*a^5*b^9 + 48*B^2*C*a^6*b^8 - 120*B^2*C*a^7*b^7 + 168*B^2*C*a^8*b^6 - 264*B^2*C*a^9*b^5 + 288*B^2*C*a^10*b^4 - 288*B^2*C*a^11*b^3 + 192*B^2*C*a^12*b^2 + 48*A*B*C*a^4*b^10 - 96*A*B*C*a^5*b^9 + 240*A*B*C*a^6*b^8 - 336*A*B*C*a^7*b^7 + 528*A*B*C*a^8*b^6 - 576*A*B*C*a^9*b^5 + 576*A*B*C*a^10*b^4 - 384*A*B*C*a^11*b^3)/b^12 + (a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) + (a^3*(-(a + b)*(a - b))^(1/2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 - (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5)))*(A*b^2 + C*a^2 - B*a*b))/(b^7 - a^2*b^5))*(A*b^2 + C*a^2 - B*a*b))/(b^7 - a^2*b^5) - (a^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(16*A^2*b^11 - 128*C^2*a^11 + 9*C^2*b^11 - 48*A^2*a*b^10 - 27*C^2*a*b^10 + 256*C^2*a^10*b + 112*A^2*a^2*b^9 - 208*A^2*a^3*b^8 + 256*A^2*a^4*b^7 - 256*A^2*a^5*b^6 + 256*A^2*a^6*b^5 - 128*A^2*a^7*b^4 + 16*B^2*a^2*b^9 - 48*B^2*a^3*b^8 + 112*B^2*a^4*b^7 - 208*B^2*a^5*b^6 + 256*B^2*a^6*b^5 - 256*B^2*a^7*b^4 + 256*B^2*a^8*b^3 - 128*B^2*a^9*b^2 + 51*C^2*a^2*b^9 - 81*C^2*a^3*b^8 + 136*C^2*a^4*b^7 - 216*C^2*a^5*b^6 + 256*C^2*a^6*b^5 - 256*C^2*a^7*b^4 + 256*C^2*a^8*b^3 - 256*C^2*a^9*b^2 + 24*A*C*b^11 - 32*A*B*a*b^10 - 72*A*C*a*b^10 - 24*B*C*a*b^10 + 256*B*C*a^10*b + 96*A*B*a^2*b^9 - 224*A*B*a^3*b^8 + 416*A*B*a^4*b^7 - 512*A*B*a^5*b^6 + 512*A*B*a^6*b^5 - 512*A*B*a^7*b^4 + 256*A*B*a^8*b^3 + 152*A*C*a^2*b^9 - 264*A*C*a^3*b^8 + 368*A*C*a^4*b^7 - 464*A*C*a^5*b^6 + 512*A*C*a^6*b^5 - 512*A*C*a^7*b^4 + 512*A*C*a^8*b^3 - 256*A*C*a^9*b^2 + 72*B*C*a^2*b^9 - 152*B*C*a^3*b^8 + 264*B*C*a^4*b^7 - 368*B*C*a^5*b^6 + 464*B*C*a^6*b^5 - 512*B*C*a^7*b^4 + 512*B*C*a^8*b^3 - 512*B*C*a^9*b^2))/(2*b^8) - (a^3*(-(a + b)*(a - b))^(1/2)*((16*A*b^16 + 12*C*b^16 + 16*A*a^2*b^14 - 48*A*a^3*b^13 + 32*A*a^4*b^12 + 16*B*a^2*b^14 - 16*B*a^3*b^13 + 48*B*a^4*b^12 - 32*B*a^5*b^11 + 4*C*a^2*b^14 - 4*C*a^3*b^13 + 16*C*a^4*b^12 - 48*C*a^5*b^11 + 32*C*a^6*b^10 - 16*A*a*b^15 - 16*B*a*b^15 - 12*C*a*b^15)/b^12 + (a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a*b^12 - 256*a^2*b^11 + 128*a^3*b^10))/(2*b^8*(b^7 - a^2*b^5)))*(A*b^2 + C*a^2 - B*a*b))/(b^7 - a^2*b^5))*(A*b^2 + C*a^2 - B*a*b))/(b^7 - a^2*b^5)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(b^7 - a^2*b^5))","B"
978,1,7119,206,9.564297,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^2-B\,b^2+2\,C\,a^2+2\,C\,b^2-2\,B\,a\,b+C\,a\,b\right)}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^2+3\,C\,a^2+C\,b^2-3\,B\,a\,b\right)}{3\,b^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^2+B\,b^2+2\,C\,a^2+2\,C\,b^2-2\,B\,a\,b-C\,a\,b\right)}{b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^{10}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^4}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^{10}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^4}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^2\,B\,a^6\,b^5+14\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+4\,A^2\,B\,a^3\,b^8+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,B^2\,a^7\,b^4-16\,A\,B^2\,a^6\,b^5+12\,A\,B^2\,a^5\,b^6-9\,A\,B^2\,a^4\,b^7+2\,A\,B^2\,a^3\,b^8-A\,B^2\,a^2\,b^9-24\,A\,B\,C\,a^8\,b^3+32\,A\,B\,C\,a^7\,b^4-24\,A\,B\,C\,a^6\,b^5+18\,A\,B\,C\,a^5\,b^6-4\,A\,B\,C\,a^4\,b^7+2\,A\,B\,C\,a^3\,b^8+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^{10}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^4}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^4}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^{10}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^4}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)}{b^4}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,1{}\mathrm{i}-b^2\,\left(A\,a\,1{}\mathrm{i}+\frac{C\,a\,1{}\mathrm{i}}{2}\right)+B\,a^2\,b\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^4\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^2\,B\,a^6\,b^5+14\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+4\,A^2\,B\,a^3\,b^8+12\,A^2\,C\,a^7\,b^4-14\,A^2\,C\,a^6\,b^5+6\,A^2\,C\,a^5\,b^6-4\,A^2\,C\,a^4\,b^7+12\,A\,B^2\,a^7\,b^4-16\,A\,B^2\,a^6\,b^5+12\,A\,B^2\,a^5\,b^6-9\,A\,B^2\,a^4\,b^7+2\,A\,B^2\,a^3\,b^8-A\,B^2\,a^2\,b^9-24\,A\,B\,C\,a^8\,b^3+32\,A\,B\,C\,a^7\,b^4-24\,A\,B\,C\,a^6\,b^5+18\,A\,B\,C\,a^5\,b^6-4\,A\,B\,C\,a^4\,b^7+2\,A\,B\,C\,a^3\,b^8+12\,A\,C^2\,a^9\,b^2-16\,A\,C^2\,a^8\,b^3+12\,A\,C^2\,a^7\,b^4-9\,A\,C^2\,a^6\,b^5+2\,A\,C^2\,a^5\,b^6-A\,C^2\,a^4\,b^7-4\,B^3\,a^8\,b^3+6\,B^3\,a^7\,b^4-6\,B^3\,a^6\,b^5+5\,B^3\,a^5\,b^6-2\,B^3\,a^4\,b^7+B^3\,a^3\,b^8+12\,B^2\,C\,a^9\,b^2-18\,B^2\,C\,a^8\,b^3+18\,B^2\,C\,a^7\,b^4-15\,B^2\,C\,a^6\,b^5+6\,B^2\,C\,a^5\,b^6-3\,B^2\,C\,a^4\,b^7-12\,B\,C^2\,a^{10}\,b+18\,B\,C^2\,a^9\,b^2-18\,B\,C^2\,a^8\,b^3+15\,B\,C^2\,a^7\,b^4-6\,B\,C^2\,a^6\,b^5+3\,B\,C^2\,a^5\,b^6+4\,C^3\,a^{11}-6\,C^3\,a^{10}\,b+6\,C^3\,a^9\,b^2-5\,C^3\,a^8\,b^3+2\,C^3\,a^7\,b^4-C^3\,a^6\,b^5\right)}{b^9}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-12\,A^2\,a^3\,b^6+4\,A^2\,a^2\,b^7+16\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+28\,A\,B\,a^4\,b^5-20\,A\,B\,a^3\,b^6+12\,A\,B\,a^2\,b^7-4\,A\,B\,a\,b^8-16\,A\,C\,a^7\,b^2+32\,A\,C\,a^6\,b^3-28\,A\,C\,a^5\,b^4+20\,A\,C\,a^4\,b^5-12\,A\,C\,a^3\,b^6+4\,A\,C\,a^2\,b^7-8\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-13\,B^2\,a^3\,b^6+7\,B^2\,a^2\,b^7-3\,B^2\,a\,b^8+B^2\,b^9+16\,B\,C\,a^8\,b-32\,B\,C\,a^7\,b^2+32\,B\,C\,a^6\,b^3-32\,B\,C\,a^5\,b^4+26\,B\,C\,a^4\,b^5-14\,B\,C\,a^3\,b^6+6\,B\,C\,a^2\,b^7-2\,B\,C\,a\,b^8-8\,C^2\,a^9+16\,C^2\,a^8\,b-16\,C^2\,a^7\,b^2+16\,C^2\,a^6\,b^3-13\,C^2\,a^5\,b^4+7\,C^2\,a^4\,b^5-3\,C^2\,a^3\,b^6+C^2\,a^2\,b^7\right)}{b^6}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^3\,b^{10}-8\,A\,a^2\,b^{11}-2\,B\,b^{13}-2\,B\,a^2\,b^{11}+6\,B\,a^3\,b^{10}-4\,B\,a^4\,b^9-2\,C\,a^2\,b^{11}+2\,C\,a^3\,b^{10}-6\,C\,a^4\,b^9+4\,C\,a^5\,b^8+4\,A\,a\,b^{12}+2\,B\,a\,b^{12}+2\,C\,a\,b^{12}\right)}{b^9}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)}{b^6\,\left(b^6-a^2\,b^4\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^6-a^2\,b^4}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(2*A*b^2 - B*b^2 + 2*C*a^2 + 2*C*b^2 - 2*B*a*b + C*a*b))/b^3 + (4*tan(c/2 + (d*x)/2)^3*(3*A*b^2 + 3*C*a^2 + C*b^2 - 3*B*a*b))/(3*b^3) + (tan(c/2 + (d*x)/2)*(2*A*b^2 + B*b^2 + 2*C*a^2 + 2*C*b^2 - 2*B*a*b - C*a*b))/b^3)/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) + (atan(((((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^10)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^4)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i)*1i)/b^4 + (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^10)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^4)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i)*1i)/b^4)/((16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b - A*B^2*a^2*b^9 + 2*A*B^2*a^3*b^8 - 9*A*B^2*a^4*b^7 + 12*A*B^2*a^5*b^6 - 16*A*B^2*a^6*b^5 + 12*A*B^2*a^7*b^4 + 4*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 14*A^2*B*a^5*b^6 - 12*A^2*B*a^6*b^5 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4 + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2 + 2*A*B*C*a^3*b^8 - 4*A*B*C*a^4*b^7 + 18*A*B*C*a^5*b^6 - 24*A*B*C*a^6*b^5 + 32*A*B*C*a^7*b^4 - 24*A*B*C*a^8*b^3))/b^9 + (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^10)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^4)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^4 - (((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*tan(c/2 + (d*x)/2)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^10)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^4)*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i))/b^4))*((B*b^3*1i)/2 - C*a^3*1i - b^2*(A*a*1i + (C*a*1i)/2) + B*a^2*b*1i)*2i)/(b^4*d) + (a^2*atan(((a^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^6 - a^2*b^4) + (a^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^6 - a^2*b^4))/((16*(4*C^3*a^11 - 6*C^3*a^10*b - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 + B^3*a^3*b^8 - 2*B^3*a^4*b^7 + 5*B^3*a^5*b^6 - 6*B^3*a^6*b^5 + 6*B^3*a^7*b^4 - 4*B^3*a^8*b^3 - C^3*a^6*b^5 + 2*C^3*a^7*b^4 - 5*C^3*a^8*b^3 + 6*C^3*a^9*b^2 - 12*B*C^2*a^10*b - A*B^2*a^2*b^9 + 2*A*B^2*a^3*b^8 - 9*A*B^2*a^4*b^7 + 12*A*B^2*a^5*b^6 - 16*A*B^2*a^6*b^5 + 12*A*B^2*a^7*b^4 + 4*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 14*A^2*B*a^5*b^6 - 12*A^2*B*a^6*b^5 - A*C^2*a^4*b^7 + 2*A*C^2*a^5*b^6 - 9*A*C^2*a^6*b^5 + 12*A*C^2*a^7*b^4 - 16*A*C^2*a^8*b^3 + 12*A*C^2*a^9*b^2 - 4*A^2*C*a^4*b^7 + 6*A^2*C*a^5*b^6 - 14*A^2*C*a^6*b^5 + 12*A^2*C*a^7*b^4 + 3*B*C^2*a^5*b^6 - 6*B*C^2*a^6*b^5 + 15*B*C^2*a^7*b^4 - 18*B*C^2*a^8*b^3 + 18*B*C^2*a^9*b^2 - 3*B^2*C*a^4*b^7 + 6*B^2*C*a^5*b^6 - 15*B^2*C*a^6*b^5 + 18*B^2*C*a^7*b^4 - 18*B^2*C*a^8*b^3 + 12*B^2*C*a^9*b^2 + 2*A*B*C*a^3*b^8 - 4*A*B*C*a^4*b^7 + 18*A*B*C*a^5*b^6 - 24*A*B*C*a^6*b^5 + 32*A*B*C*a^7*b^4 - 24*A*B*C*a^8*b^3))/b^9 + (a^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 + (a^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4) - (a^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(B^2*b^9 - 8*C^2*a^9 - 3*B^2*a*b^8 + 16*C^2*a^8*b + 4*A^2*a^2*b^7 - 12*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 8*A^2*a^5*b^4 + 7*B^2*a^2*b^7 - 13*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 8*B^2*a^7*b^2 + C^2*a^2*b^7 - 3*C^2*a^3*b^6 + 7*C^2*a^4*b^5 - 13*C^2*a^5*b^4 + 16*C^2*a^6*b^3 - 16*C^2*a^7*b^2 - 4*A*B*a*b^8 - 2*B*C*a*b^8 + 16*B*C*a^8*b + 12*A*B*a^2*b^7 - 20*A*B*a^3*b^6 + 28*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 16*A*B*a^6*b^3 + 4*A*C*a^2*b^7 - 12*A*C*a^3*b^6 + 20*A*C*a^4*b^5 - 28*A*C*a^5*b^4 + 32*A*C*a^6*b^3 - 16*A*C*a^7*b^2 + 6*B*C*a^2*b^7 - 14*B*C*a^3*b^6 + 26*B*C*a^4*b^5 - 32*B*C*a^5*b^4 + 32*B*C*a^6*b^3 - 32*B*C*a^7*b^2))/b^6 - (a^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^3*b^10 - 8*A*a^2*b^11 - 2*B*b^13 - 2*B*a^2*b^11 + 6*B*a^3*b^10 - 4*B*a^4*b^9 - 2*C*a^2*b^11 + 2*C*a^3*b^10 - 6*C*a^4*b^9 + 4*C*a^5*b^8 + 4*A*a*b^12 + 2*B*a*b^12 + 2*C*a*b^12))/b^9 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4))*(A*b^2 + C*a^2 - B*a*b))/(b^6 - a^2*b^4)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(b^6 - a^2*b^4))","B"
979,1,5594,144,9.009761,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b-2\,C\,a+C\,b\right)}{b^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a-2\,B\,b+C\,b\right)}{b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^7}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^7}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^3}}{\frac{16\,\left(4\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7-12\,A^2\,B\,a^3\,b^5+12\,A^2\,B\,a^2\,b^6+12\,A^2\,C\,a^4\,b^4-14\,A^2\,C\,a^3\,b^5+6\,A^2\,C\,a^2\,b^6-4\,A^2\,C\,a\,b^7+12\,A\,B^2\,a^4\,b^4-12\,A\,B^2\,a^3\,b^5-24\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-12\,A\,B\,C\,a^3\,b^5+8\,A\,B\,C\,a^2\,b^6+12\,A\,C^2\,a^6\,b^2-16\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4-9\,A\,C^2\,a^3\,b^5+2\,A\,C^2\,a^2\,b^6-A\,C^2\,a\,b^7-4\,B^3\,a^5\,b^3+4\,B^3\,a^4\,b^4+12\,B^2\,C\,a^6\,b^2-14\,B^2\,C\,a^5\,b^3+6\,B^2\,C\,a^4\,b^4-4\,B^2\,C\,a^3\,b^5-12\,B\,C^2\,a^7\,b+16\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3+9\,B\,C^2\,a^4\,b^4-2\,B\,C^2\,a^3\,b^5+B\,C^2\,a^2\,b^6+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^7}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^7}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^3}}\right)\,\left(1{}\mathrm{i}\,C\,a^2-1{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^3\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}}{\frac{16\,\left(4\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7-12\,A^2\,B\,a^3\,b^5+12\,A^2\,B\,a^2\,b^6+12\,A^2\,C\,a^4\,b^4-14\,A^2\,C\,a^3\,b^5+6\,A^2\,C\,a^2\,b^6-4\,A^2\,C\,a\,b^7+12\,A\,B^2\,a^4\,b^4-12\,A\,B^2\,a^3\,b^5-24\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-12\,A\,B\,C\,a^3\,b^5+8\,A\,B\,C\,a^2\,b^6+12\,A\,C^2\,a^6\,b^2-16\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4-9\,A\,C^2\,a^3\,b^5+2\,A\,C^2\,a^2\,b^6-A\,C^2\,a\,b^7-4\,B^3\,a^5\,b^3+4\,B^3\,a^4\,b^4+12\,B^2\,C\,a^6\,b^2-14\,B^2\,C\,a^5\,b^3+6\,B^2\,C\,a^4\,b^4-4\,B^2\,C\,a^3\,b^5-12\,B\,C^2\,a^7\,b+16\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3+9\,B\,C^2\,a^4\,b^4-2\,B\,C^2\,a^3\,b^5+B\,C^2\,a^2\,b^6+4\,C^3\,a^8-6\,C^3\,a^7\,b+6\,C^3\,a^6\,b^2-5\,C^3\,a^5\,b^3+2\,C^3\,a^4\,b^4-C^3\,a^3\,b^5\right)}{b^6}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}+\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^3\,b^4+16\,A^2\,a^2\,b^5-12\,A^2\,a\,b^6+4\,A^2\,b^7+16\,A\,B\,a^4\,b^3-32\,A\,B\,a^3\,b^4+24\,A\,B\,a^2\,b^5-8\,A\,B\,a\,b^6-16\,A\,C\,a^5\,b^2+32\,A\,C\,a^4\,b^3-28\,A\,C\,a^3\,b^4+20\,A\,C\,a^2\,b^5-12\,A\,C\,a\,b^6+4\,A\,C\,b^7-8\,B^2\,a^5\,b^2+16\,B^2\,a^4\,b^3-12\,B^2\,a^3\,b^4+4\,B^2\,a^2\,b^5+16\,B\,C\,a^6\,b-32\,B\,C\,a^5\,b^2+28\,B\,C\,a^4\,b^3-20\,B\,C\,a^3\,b^4+12\,B\,C\,a^2\,b^5-4\,B\,C\,a\,b^6-8\,C^2\,a^7+16\,C^2\,a^6\,b-16\,C^2\,a^5\,b^2+16\,C^2\,a^4\,b^3-13\,C^2\,a^3\,b^4+7\,C^2\,a^2\,b^5-3\,C^2\,a\,b^6+C^2\,b^7\right)}{b^4}-\frac{a\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,b^{10}+2\,C\,b^{10}+4\,A\,a^2\,b^8+8\,B\,a^2\,b^8-4\,B\,a^3\,b^7+2\,C\,a^2\,b^8-6\,C\,a^3\,b^7+4\,C\,a^4\,b^6-8\,A\,a\,b^9-4\,B\,a\,b^9-2\,C\,a\,b^9\right)}{b^6}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^3\,b^6-16\,a^2\,b^7+8\,a\,b^8\right)}{b^4\,\left(b^5-a^2\,b^3\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{b^5-a^2\,b^3}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(b^5-a^2\,b^3\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*B*b - 2*C*a + C*b))/b^2 - (tan(c/2 + (d*x)/2)^3*(2*C*a - 2*B*b + C*b))/b^2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^7)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i)*1i)/b^3 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^7)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i)*1i)/b^3)/((16*(4*C^3*a^8 - 4*A^3*a*b^7 - 6*C^3*a^7*b + 4*A^3*a^2*b^6 + 4*B^3*a^4*b^4 - 4*B^3*a^5*b^3 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - A*C^2*a*b^7 - 4*A^2*C*a*b^7 - 12*B*C^2*a^7*b - 12*A*B^2*a^3*b^5 + 12*A*B^2*a^4*b^4 + 12*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 2*A*C^2*a^2*b^6 - 9*A*C^2*a^3*b^5 + 12*A*C^2*a^4*b^4 - 16*A*C^2*a^5*b^3 + 12*A*C^2*a^6*b^2 + 6*A^2*C*a^2*b^6 - 14*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 + B*C^2*a^2*b^6 - 2*B*C^2*a^3*b^5 + 9*B*C^2*a^4*b^4 - 12*B*C^2*a^5*b^3 + 16*B*C^2*a^6*b^2 - 4*B^2*C*a^3*b^5 + 6*B^2*C*a^4*b^4 - 14*B^2*C*a^5*b^3 + 12*B^2*C*a^6*b^2 + 8*A*B*C*a^2*b^6 - 12*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 24*A*B*C*a^5*b^3))/b^6 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^7)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^3 - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*tan(c/2 + (d*x)/2)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^7)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^3)*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i))/b^3))*(C*a^2*1i + b^2*(A*1i + (C*1i)/2) - B*a*b*1i)*2i)/(b^3*d) - (a*atan(((a*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (a*(-(a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*a*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^5 - a^2*b^3) + (a*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (a*(-(a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*a*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b)*1i)/(b^5 - a^2*b^3))/((16*(4*C^3*a^8 - 4*A^3*a*b^7 - 6*C^3*a^7*b + 4*A^3*a^2*b^6 + 4*B^3*a^4*b^4 - 4*B^3*a^5*b^3 - C^3*a^3*b^5 + 2*C^3*a^4*b^4 - 5*C^3*a^5*b^3 + 6*C^3*a^6*b^2 - A*C^2*a*b^7 - 4*A^2*C*a*b^7 - 12*B*C^2*a^7*b - 12*A*B^2*a^3*b^5 + 12*A*B^2*a^4*b^4 + 12*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 2*A*C^2*a^2*b^6 - 9*A*C^2*a^3*b^5 + 12*A*C^2*a^4*b^4 - 16*A*C^2*a^5*b^3 + 12*A*C^2*a^6*b^2 + 6*A^2*C*a^2*b^6 - 14*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 + B*C^2*a^2*b^6 - 2*B*C^2*a^3*b^5 + 9*B*C^2*a^4*b^4 - 12*B*C^2*a^5*b^3 + 16*B*C^2*a^6*b^2 - 4*B^2*C*a^3*b^5 + 6*B^2*C*a^4*b^4 - 14*B^2*C*a^5*b^3 + 12*B^2*C*a^6*b^2 + 8*A*B*C*a^2*b^6 - 12*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 24*A*B*C*a^5*b^3))/b^6 + (a*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 + (a*(-(a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 - (8*a*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3) - (a*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^7 - 8*C^2*a^7 + C^2*b^7 - 12*A^2*a*b^6 - 3*C^2*a*b^6 + 16*C^2*a^6*b + 16*A^2*a^2*b^5 - 8*A^2*a^3*b^4 + 4*B^2*a^2*b^5 - 12*B^2*a^3*b^4 + 16*B^2*a^4*b^3 - 8*B^2*a^5*b^2 + 7*C^2*a^2*b^5 - 13*C^2*a^3*b^4 + 16*C^2*a^4*b^3 - 16*C^2*a^5*b^2 + 4*A*C*b^7 - 8*A*B*a*b^6 - 12*A*C*a*b^6 - 4*B*C*a*b^6 + 16*B*C*a^6*b + 24*A*B*a^2*b^5 - 32*A*B*a^3*b^4 + 16*A*B*a^4*b^3 + 20*A*C*a^2*b^5 - 28*A*C*a^3*b^4 + 32*A*C*a^4*b^3 - 16*A*C*a^5*b^2 + 12*B*C*a^2*b^5 - 20*B*C*a^3*b^4 + 28*B*C*a^4*b^3 - 32*B*C*a^5*b^2))/b^4 - (a*(-(a + b)*(a - b))^(1/2)*((8*(4*A*b^10 + 2*C*b^10 + 4*A*a^2*b^8 + 8*B*a^2*b^8 - 4*B*a^3*b^7 + 2*C*a^2*b^8 - 6*C*a^3*b^7 + 4*C*a^4*b^6 - 8*A*a*b^9 - 4*B*a*b^9 - 2*C*a*b^9))/b^6 + (8*a*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3)))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3))*(A*b^2 + C*a^2 - B*a*b))/(b^5 - a^2*b^3)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(b^5 - a^2*b^3))","B"
980,1,4410,97,5.141552,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x)),x)","\frac{2\,B\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(b^4-a^2\,b^2\right)}+\frac{2\,C\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(b^4-a^2\,b^2\right)}+\frac{C\,b^3\,\sin\left(c+d\,x\right)}{d\,\left(b^4-a^2\,b^2\right)}-\frac{C\,a^2\,b\,\sin\left(c+d\,x\right)}{d\,\left(b^4-a^2\,b^2\right)}+\frac{A\,b^2\,\mathrm{atan}\left(\frac{-A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-B^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A^2\,a\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-A^2\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-B^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}+B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-C^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}+A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+B\,C\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}-B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-A\,B\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}+A\,B\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,B\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,B\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}-A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+B\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,6{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^5\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b^7+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{d\,\left(b^4-a^2\,b^2\right)}+\frac{C\,a^2\,\mathrm{atan}\left(\frac{-A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-B^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A^2\,a\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-A^2\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-B^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}+B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-C^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}+A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+B\,C\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}-B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-A\,B\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}+A\,B\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,B\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,B\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}-A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+B\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,6{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^5\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b^7+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{d\,\left(b^4-a^2\,b^2\right)}-\frac{2\,B\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(b^4-a^2\,b^2\right)}-\frac{2\,C\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(b^4-a^2\,b^2\right)}-\frac{B\,a\,b\,\mathrm{atan}\left(\frac{-A^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-B^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}+C^2\,a^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A^2\,a\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-A^2\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+A^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+A^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+B^2\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,2{}\mathrm{i}-B^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}+B^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-C^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}+C^2\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-C^2\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}+A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+B\,C\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}-B\,C\,a^6\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}-A\,B\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}+A\,B\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,B\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,B\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-A\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}\,4{}\mathrm{i}-A\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+A\,C\,a^5\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-B\,C\,a^3\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}+B\,C\,a^4\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,6{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A^2\,b^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^6\,b^2-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^4\,b^4+2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,C\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^5\,b^3+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a^3\,b^5-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b^7+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^6\,b^2-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^4\,b^4+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2\,b^6}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{d\,\left(b^4-a^2\,b^2\right)}","Not used",1,"(2*B*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(b^4 - a^2*b^2)) + (2*C*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(b^4 - a^2*b^2)) + (C*b^3*sin(c + d*x))/(d*(b^4 - a^2*b^2)) - (C*a^2*b*sin(c + d*x))/(d*(b^4 - a^2*b^2)) + (A*b^2*atan((C^2*a^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - B^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A^2*a*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - A^2*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - B^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i + B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - C^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i + A*B*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + B*C*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i - B*C*a^6*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - A*B*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i + A*B*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*B*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*B*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i - A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + B*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*6i)/(A^2*b^8*cos(c/2 + (d*x)/2) + B^2*b^8*cos(c/2 + (d*x)/2) - 2*A^2*a^2*b^6*cos(c/2 + (d*x)/2) + A^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*B^2*a^2*b^6*cos(c/2 + (d*x)/2) + B^2*a^4*b^4*cos(c/2 + (d*x)/2) + C^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*C^2*a^4*b^4*cos(c/2 + (d*x)/2) + C^2*a^6*b^2*cos(c/2 + (d*x)/2) + 4*A*B*a^3*b^5*cos(c/2 + (d*x)/2) - 2*A*B*a^5*b^3*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2) + 4*B*C*a^3*b^5*cos(c/2 + (d*x)/2) - 2*B*C*a^5*b^3*cos(c/2 + (d*x)/2) - 2*A*B*a*b^7*cos(c/2 + (d*x)/2) - 2*B*C*a*b^7*cos(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i)/(d*(b^4 - a^2*b^2)) + (C*a^2*atan((C^2*a^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - B^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A^2*a*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - A^2*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - B^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i + B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - C^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i + A*B*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + B*C*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i - B*C*a^6*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - A*B*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i + A*B*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*B*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*B*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i - A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + B*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*6i)/(A^2*b^8*cos(c/2 + (d*x)/2) + B^2*b^8*cos(c/2 + (d*x)/2) - 2*A^2*a^2*b^6*cos(c/2 + (d*x)/2) + A^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*B^2*a^2*b^6*cos(c/2 + (d*x)/2) + B^2*a^4*b^4*cos(c/2 + (d*x)/2) + C^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*C^2*a^4*b^4*cos(c/2 + (d*x)/2) + C^2*a^6*b^2*cos(c/2 + (d*x)/2) + 4*A*B*a^3*b^5*cos(c/2 + (d*x)/2) - 2*A*B*a^5*b^3*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2) + 4*B*C*a^3*b^5*cos(c/2 + (d*x)/2) - 2*B*C*a^5*b^3*cos(c/2 + (d*x)/2) - 2*A*B*a*b^7*cos(c/2 + (d*x)/2) - 2*B*C*a*b^7*cos(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i)/(d*(b^4 - a^2*b^2)) - (2*B*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(b^4 - a^2*b^2)) - (2*C*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(b^4 - a^2*b^2)) - (B*a*b*atan((C^2*a^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - B^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - A^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A^2*a*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - A^2*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + A^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + A^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + B^2*a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*2i - B^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i + B^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - C^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i + C^2*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - C^2*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i + A*B*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + B*C*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^4*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i - B*C*a^6*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i - A*B*a^2*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i + A*B*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*B*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*B*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - A*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^3*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2)*4i - A*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + A*C*a^5*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i - B*C*a^3*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*2i + B*C*a^4*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*6i)/(A^2*b^8*cos(c/2 + (d*x)/2) + B^2*b^8*cos(c/2 + (d*x)/2) - 2*A^2*a^2*b^6*cos(c/2 + (d*x)/2) + A^2*a^4*b^4*cos(c/2 + (d*x)/2) - 2*B^2*a^2*b^6*cos(c/2 + (d*x)/2) + B^2*a^4*b^4*cos(c/2 + (d*x)/2) + C^2*a^2*b^6*cos(c/2 + (d*x)/2) - 2*C^2*a^4*b^4*cos(c/2 + (d*x)/2) + C^2*a^6*b^2*cos(c/2 + (d*x)/2) + 4*A*B*a^3*b^5*cos(c/2 + (d*x)/2) - 2*A*B*a^5*b^3*cos(c/2 + (d*x)/2) + 2*A*C*a^2*b^6*cos(c/2 + (d*x)/2) - 4*A*C*a^4*b^4*cos(c/2 + (d*x)/2) + 2*A*C*a^6*b^2*cos(c/2 + (d*x)/2) + 4*B*C*a^3*b^5*cos(c/2 + (d*x)/2) - 2*B*C*a^5*b^3*cos(c/2 + (d*x)/2) - 2*A*B*a*b^7*cos(c/2 + (d*x)/2) - 2*B*C*a*b^7*cos(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i)/(d*(b^4 - a^2*b^2))","B"
981,1,18201,94,12.160925,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))),x)","\frac{2\,C\,\mathrm{atan}\left(\frac{16384\,C^5\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}+\frac{16384\,C^5\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,B^2\,C^3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,B\,C^4\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-16384\,A^4\,C\,a\,b^5+16384\,A^4\,C\,b^6+32768\,A^3\,B\,C\,a^2\,b^4-32768\,A^3\,B\,C\,a\,b^5-32768\,A^3\,C^2\,a^3\,b^3+32768\,A^3\,C^2\,a^2\,b^4-16384\,A^2\,B^2\,C\,a^3\,b^3+16384\,A^2\,B^2\,C\,a^2\,b^4+32768\,A^2\,B\,C^2\,a^4\,b^2-32768\,A^2\,B\,C^2\,a^3\,b^3-32768\,A^2\,C^3\,a^3\,b^3+32768\,A^2\,C^3\,a^2\,b^4+32768\,A\,B\,C^3\,a^4\,b^2-32768\,A\,B\,C^3\,a^3\,b^3-32768\,A\,C^4\,a^5\,b+32768\,A\,C^4\,a^4\,b^2-16384\,B^2\,C^3\,a^5\,b+16384\,B^2\,C^3\,a^4\,b^2+32768\,B\,C^4\,a^6-32768\,B\,C^4\,a^5\,b-16384\,C^5\,a^5\,b+16384\,C^5\,a^4\,b^2}+\frac{32768\,A\,C^4\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}+\frac{32768\,B\,C^4\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}+\frac{32768\,A\,C^4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,A^4\,C\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,B^2\,C^3\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^5+32768\,A\,C^4\,a^5+32768\,B\,C^4\,a^5-16384\,A^4\,C\,b^5-16384\,C^5\,a^4\,b+16384\,B^2\,C^3\,a^5-32768\,A^2\,C^3\,a^2\,b^3+32768\,A^2\,C^3\,a^3\,b^2-32768\,A^3\,C^2\,a^2\,b^3+32768\,A^3\,C^2\,a^3\,b^2-32768\,A\,C^4\,a^4\,b+16384\,A^4\,C\,a\,b^4-16384\,B^2\,C^3\,a^4\,b-\frac{32768\,B\,C^4\,a^6}{b}+32768\,A\,B\,C^3\,a^3\,b^2-32768\,A^2\,B\,C^2\,a^4\,b-32768\,A^3\,B\,C\,a^2\,b^3+32768\,A^2\,B\,C^2\,a^3\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^3+16384\,A^2\,B^2\,C\,a^3\,b^2-32768\,A\,B\,C^3\,a^4\,b+32768\,A^3\,B\,C\,a\,b^4}-\frac{16384\,A^4\,C\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A^2\,B\,C^2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{32768\,A^2\,C^3\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{32768\,A^3\,C^2\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A^2\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A^3\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,B^2\,C\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A\,B\,C^3\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,C^5\,a^4+32768\,A\,C^4\,a^4+16384\,A^4\,C\,b^4+16384\,B^2\,C^3\,a^4-\frac{16384\,C^5\,a^5}{b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2-\frac{16384\,B^2\,C^3\,a^5}{b}+32768\,A\,B\,C^3\,a^4-16384\,A^4\,C\,a\,b^3+32768\,A^2\,B\,C^2\,a^4-32768\,A^2\,C^3\,a^3\,b-32768\,A^3\,C^2\,a^3\,b-\frac{32768\,A\,C^4\,a^5}{b}-\frac{32768\,B\,C^4\,a^5}{b}+\frac{32768\,B\,C^4\,a^6}{b^2}-32768\,A^2\,B\,C^2\,a^3\,b-16384\,A^2\,B^2\,C\,a^3\,b+32768\,A^3\,B\,C\,a^2\,b^2+16384\,A^2\,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\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{32768\,A\,B\,C^3\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{16384\,A\,B^2\,C^2\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}-\frac{32768\,A^2\,B\,C^2\,a\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}+\frac{16384\,A\,B^2\,C^2\,a^2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16384\,A^5\,b^4+16384\,A\,C^4\,a^4+32768\,A^4\,C\,b^4+16384\,A^3\,B^2\,b^4-\frac{16384\,A^5\,b^5}{a}-\frac{16384\,A^3\,B^2\,b^5}{a}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+32768\,A^3\,B\,C\,b^4-16384\,A\,C^4\,a^3\,b+32768\,A^2\,B\,C^2\,b^4-\frac{32768\,A^4\,B\,b^5}{a}+\frac{32768\,A^4\,B\,b^6}{a^2}-32768\,A^2\,C^3\,a\,b^3-32768\,A^3\,C^2\,a\,b^3-\frac{32768\,A^4\,C\,b^5}{a}+32768\,A\,B\,C^3\,a^2\,b^2-16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3+16384\,A\,B^2\,C^2\,a^2\,b^2-32768\,A\,B\,C^3\,a^3\,b-32768\,A^3\,B\,C\,a\,b^3}\right)}{a\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,C^3\,a^6-24576\,A^3\,b^6+8192\,A^2\,B\,b^6-8192\,B\,C^2\,a^6+49152\,A^3\,a\,b^5-49152\,C^3\,a^5\,b-32768\,A^3\,a^2\,b^4+8192\,A^3\,a^3\,b^3-8192\,C^3\,a^3\,b^3+32768\,C^3\,a^4\,b^2-8192\,A\,B^2\,a\,b^5+16384\,A^2\,B\,a\,b^5+8192\,A\,C^2\,a^5\,b-8192\,A^2\,C\,a\,b^5-16384\,B\,C^2\,a^5\,b+8192\,B^2\,C\,a^5\,b+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}+8192\,A\,B^2\,a^2\,b^4-49152\,A^2\,B\,a^2\,b^4+32768\,A^2\,B\,a^3\,b^3-8192\,A^2\,B\,a^4\,b^2+24576\,A\,C^2\,a^2\,b^4-65536\,A\,C^2\,a^3\,b^3+32768\,A\,C^2\,a^4\,b^2-32768\,A^2\,C\,a^2\,b^4+65536\,A^2\,C\,a^3\,b^3-24576\,A^2\,C\,a^4\,b^2+8192\,B\,C^2\,a^2\,b^4-32768\,B\,C^2\,a^3\,b^3+49152\,B\,C^2\,a^4\,b^2-8192\,B^2\,C\,a^4\,b^2+16384\,A\,B\,C\,a^2\,b^4-16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a\,b^3-a^3\,b}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A^3\,b^6-24576\,C^3\,a^6-8192\,A^2\,B\,b^6+8192\,B\,C^2\,a^6-49152\,A^3\,a\,b^5+49152\,C^3\,a^5\,b+32768\,A^3\,a^2\,b^4-8192\,A^3\,a^3\,b^3+8192\,C^3\,a^3\,b^3-32768\,C^3\,a^4\,b^2+8192\,A\,B^2\,a\,b^5-16384\,A^2\,B\,a\,b^5-8192\,A\,C^2\,a^5\,b+8192\,A^2\,C\,a\,b^5+16384\,B\,C^2\,a^5\,b-8192\,B^2\,C\,a^5\,b+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}-8192\,A\,B^2\,a^2\,b^4+49152\,A^2\,B\,a^2\,b^4-32768\,A^2\,B\,a^3\,b^3+8192\,A^2\,B\,a^4\,b^2-24576\,A\,C^2\,a^2\,b^4+65536\,A\,C^2\,a^3\,b^3-32768\,A\,C^2\,a^4\,b^2+32768\,A^2\,C\,a^2\,b^4-65536\,A^2\,C\,a^3\,b^3+24576\,A^2\,C\,a^4\,b^2-8192\,B\,C^2\,a^2\,b^4+32768\,B\,C^2\,a^3\,b^3-49152\,B\,C^2\,a^4\,b^2+8192\,B^2\,C\,a^4\,b^2-16384\,A\,B\,C\,a^2\,b^4+16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a\,b^3-a^3\,b}}{49152\,A^2\,C^3\,a^4-16384\,A^4\,C\,b^4-16384\,A\,C^4\,a^4+49152\,A^3\,C^2\,b^4-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,C^3\,a^6-24576\,A^3\,b^6+8192\,A^2\,B\,b^6-8192\,B\,C^2\,a^6+49152\,A^3\,a\,b^5-49152\,C^3\,a^5\,b-32768\,A^3\,a^2\,b^4+8192\,A^3\,a^3\,b^3-8192\,C^3\,a^3\,b^3+32768\,C^3\,a^4\,b^2-8192\,A\,B^2\,a\,b^5+16384\,A^2\,B\,a\,b^5+8192\,A\,C^2\,a^5\,b-8192\,A^2\,C\,a\,b^5-16384\,B\,C^2\,a^5\,b+8192\,B^2\,C\,a^5\,b+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}+8192\,A\,B^2\,a^2\,b^4-49152\,A^2\,B\,a^2\,b^4+32768\,A^2\,B\,a^3\,b^3-8192\,A^2\,B\,a^4\,b^2+24576\,A\,C^2\,a^2\,b^4-65536\,A\,C^2\,a^3\,b^3+32768\,A\,C^2\,a^4\,b^2-32768\,A^2\,C\,a^2\,b^4+65536\,A^2\,C\,a^3\,b^3-24576\,A^2\,C\,a^4\,b^2+8192\,B\,C^2\,a^2\,b^4-32768\,B\,C^2\,a^3\,b^3+49152\,B\,C^2\,a^4\,b^2-8192\,B^2\,C\,a^4\,b^2+16384\,A\,B\,C\,a^2\,b^4-16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8192\,A^4\,a\,b^4+8192\,A^4\,b^5+16384\,A^3\,B\,a^2\,b^3-16384\,A^3\,B\,a\,b^4-16384\,A^3\,C\,a^3\,b^2+16384\,A^3\,C\,a^2\,b^3-8192\,A^2\,B^2\,a^3\,b^2+8192\,A^2\,B^2\,a^2\,b^3+16384\,A^2\,B\,C\,a^4\,b-16384\,A^2\,B\,C\,a^3\,b^2-16384\,A^2\,C^2\,a^5+49152\,A^2\,C^2\,a^4\,b-81920\,A^2\,C^2\,a^3\,b^2+81920\,A^2\,C^2\,a^2\,b^3-49152\,A^2\,C^2\,a\,b^4+16384\,A^2\,C^2\,b^5+16384\,A\,B\,C^2\,a^2\,b^3-16384\,A\,B\,C^2\,a\,b^4-16384\,A\,C^3\,a^3\,b^2+16384\,A\,C^3\,a^2\,b^3-8192\,B^2\,C^2\,a^3\,b^2+8192\,B^2\,C^2\,a^2\,b^3+16384\,B\,C^3\,a^4\,b-16384\,B\,C^3\,a^3\,b^2-8192\,C^4\,a^5+8192\,C^4\,a^4\,b\right)+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A^3\,b^6-24576\,C^3\,a^6-8192\,A^2\,B\,b^6+8192\,B\,C^2\,a^6-49152\,A^3\,a\,b^5+49152\,C^3\,a^5\,b+32768\,A^3\,a^2\,b^4-8192\,A^3\,a^3\,b^3+8192\,C^3\,a^3\,b^3-32768\,C^3\,a^4\,b^2+8192\,A\,B^2\,a\,b^5-16384\,A^2\,B\,a\,b^5-8192\,A\,C^2\,a^5\,b+8192\,A^2\,C\,a\,b^5+16384\,B\,C^2\,a^5\,b-8192\,B^2\,C\,a^5\,b+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16384\,A^2\,a^5\,b^2+49152\,A^2\,a^4\,b^3-65536\,A^2\,a^3\,b^4+65536\,A^2\,a^2\,b^5-49152\,A^2\,a\,b^6+16384\,A^2\,b^7-16384\,A\,B\,a^4\,b^3+16384\,A\,B\,a^3\,b^4+16384\,A\,B\,a^2\,b^5-16384\,A\,B\,a\,b^6+16384\,A\,C\,a^5\,b^2-16384\,A\,C\,a^4\,b^3-16384\,A\,C\,a^3\,b^4+16384\,A\,C\,a^2\,b^5+8192\,B^2\,a^5\,b^2-8192\,B^2\,a^4\,b^3-8192\,B^2\,a^3\,b^4+8192\,B^2\,a^2\,b^5-16384\,B\,C\,a^6\,b+16384\,B\,C\,a^5\,b^2+16384\,B\,C\,a^4\,b^3-16384\,B\,C\,a^3\,b^4+16384\,C^2\,a^7-49152\,C^2\,a^6\,b+65536\,C^2\,a^5\,b^2-65536\,C^2\,a^4\,b^3+49152\,C^2\,a^3\,b^4-16384\,C^2\,a^2\,b^5\right)-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(24576\,A\,a^2\,b^6-57344\,A\,a^3\,b^5+40960\,A\,a^4\,b^4-8192\,A\,a^5\,b^3+8192\,B\,a^2\,b^6-32768\,B\,a^3\,b^5+49152\,B\,a^4\,b^4-32768\,B\,a^5\,b^3+8192\,B\,a^6\,b^2-8192\,C\,a^3\,b^5+40960\,C\,a^4\,b^4-57344\,C\,a^5\,b^3+24576\,C\,a^6\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(-16384\,a^7\,b^2+49152\,a^6\,b^3-65536\,a^5\,b^4+65536\,a^4\,b^5-49152\,a^3\,b^6+16384\,a^2\,b^7\right)}{a\,b^3-a^3\,b}\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}-8192\,A\,B^2\,a^2\,b^4+49152\,A^2\,B\,a^2\,b^4-32768\,A^2\,B\,a^3\,b^3+8192\,A^2\,B\,a^4\,b^2-24576\,A\,C^2\,a^2\,b^4+65536\,A\,C^2\,a^3\,b^3-32768\,A\,C^2\,a^4\,b^2+32768\,A^2\,C\,a^2\,b^4-65536\,A^2\,C\,a^3\,b^3+24576\,A^2\,C\,a^4\,b^2-8192\,B\,C^2\,a^2\,b^4+32768\,B\,C^2\,a^3\,b^3-49152\,B\,C^2\,a^4\,b^2+8192\,B^2\,C\,a^4\,b^2-16384\,A\,B\,C\,a^2\,b^4+16384\,A\,B\,C\,a^4\,b^2\right)}{a\,b^3-a^3\,b}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a\,b^3-a^3\,b}+32768\,A^2\,C^3\,a^2\,b^2+32768\,A^3\,C^2\,a^2\,b^2+16384\,A\,C^4\,a^3\,b+16384\,A^4\,C\,a\,b^3-16384\,A^2\,B\,C^2\,a^4-16384\,A^2\,B\,C^2\,b^4+16384\,A^2\,C^3\,a\,b^3-98304\,A^2\,C^3\,a^3\,b-98304\,A^3\,C^2\,a\,b^3+16384\,A^3\,C^2\,a^3\,b-32768\,A\,B\,C^3\,a^2\,b^2+16384\,A\,B^2\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a\,b^3-32768\,A^2\,B\,C^2\,a^3\,b+16384\,A^2\,B^2\,C\,a^3\,b-32768\,A^3\,B\,C\,a^2\,b^2-16384\,A\,B^2\,C^2\,a^2\,b^2+98304\,A^2\,B\,C^2\,a^2\,b^2-16384\,A^2\,B^2\,C\,a^2\,b^2+32768\,A\,B\,C^3\,a^3\,b+32768\,A^3\,B\,C\,a\,b^3}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a\,b^3-a^3\,b\right)}","Not used",1,"(2*C*atan((16384*C^5*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) + (16384*C^5*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*B^2*C^3*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*B*C^4*a^6*tan(c/2 + (d*x)/2))/(32768*B*C^4*a^6 + 16384*A^4*C*b^6 - 16384*C^5*a^5*b + 16384*C^5*a^4*b^2 + 32768*A^2*C^3*a^2*b^4 - 32768*A^2*C^3*a^3*b^3 + 32768*A^3*C^2*a^2*b^4 - 32768*A^3*C^2*a^3*b^3 + 16384*B^2*C^3*a^4*b^2 - 32768*A*C^4*a^5*b - 16384*A^4*C*a*b^5 - 32768*B*C^4*a^5*b + 32768*A*C^4*a^4*b^2 - 16384*B^2*C^3*a^5*b - 32768*A*B*C^3*a^3*b^3 + 32768*A*B*C^3*a^4*b^2 + 32768*A^3*B*C*a^2*b^4 - 32768*A^2*B*C^2*a^3*b^3 + 32768*A^2*B*C^2*a^4*b^2 + 16384*A^2*B^2*C*a^2*b^4 - 16384*A^2*B^2*C*a^3*b^3 - 32768*A^3*B*C*a*b^5) + (32768*A*C^4*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) + (32768*B*C^4*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) + (32768*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*B^2*C^3*a^5*tan(c/2 + (d*x)/2))/(16384*C^5*a^5 + 32768*A*C^4*a^5 + 32768*B*C^4*a^5 - 16384*A^4*C*b^5 - 16384*C^5*a^4*b + 16384*B^2*C^3*a^5 - 32768*A^2*C^3*a^2*b^3 + 32768*A^2*C^3*a^3*b^2 - 32768*A^3*C^2*a^2*b^3 + 32768*A^3*C^2*a^3*b^2 - 32768*A*C^4*a^4*b + 16384*A^4*C*a*b^4 - 16384*B^2*C^3*a^4*b - (32768*B*C^4*a^6)/b + 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a^4*b - 32768*A^3*B*C*a^2*b^3 + 32768*A^2*B*C^2*a^3*b^2 - 16384*A^2*B^2*C*a^2*b^3 + 16384*A^2*B^2*C*a^3*b^2 - 32768*A*B*C^3*a^4*b + 32768*A^3*B*C*a*b^4) - (16384*A^4*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^2*B*C^2*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*C^2*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A*B*C^3*a^4*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A^2*B^2*C*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A*B*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*B*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*B*C^2*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (16384*A^2*B^2*C*a^3*b*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*B*C*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*C^5*a^4 + 32768*A*C^4*a^4 + 16384*A^4*C*b^4 + 16384*B^2*C^3*a^4 - (16384*C^5*a^5)/b + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 - (16384*B^2*C^3*a^5)/b + 32768*A*B*C^3*a^4 - 16384*A^4*C*a*b^3 + 32768*A^2*B*C^2*a^4 - 32768*A^2*C^3*a^3*b - 32768*A^3*C^2*a^3*b - (32768*A*C^4*a^5)/b - (32768*B*C^4*a^5)/b + (32768*B*C^4*a^6)/b^2 - 32768*A^2*B*C^2*a^3*b - 16384*A^2*B^2*C*a^3*b + 32768*A^3*B*C*a^2*b^2 + 16384*A^2*B^2*C*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3)))/(b*d) + (2*A*atanh((16384*A^5*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (16384*A^5*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^4*B*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (32768*A^4*C*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (16384*A*C^4*a^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^4*C*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A^3*B^2*b^5*tan(c/2 + (d*x)/2))/(16384*A^5*b^5 - 16384*A*C^4*a^5 + 32768*A^4*B*b^5 + 32768*A^4*C*b^5 - 16384*A^5*a*b^4 + 16384*A^3*B^2*b^5 + 32768*A^2*C^3*a^2*b^3 - 32768*A^2*C^3*a^3*b^2 + 32768*A^3*C^2*a^2*b^3 - 32768*A^3*C^2*a^3*b^2 + 16384*A*C^4*a^4*b - 32768*A^4*C*a*b^4 - 16384*A^3*B^2*a*b^4 - (32768*A^4*B*b^6)/a - 32768*A*B*C^3*a^3*b^2 - 32768*A^2*B*C^2*a*b^4 + 32768*A^3*B*C*a^2*b^3 + 16384*A*B^2*C^2*a^2*b^3 - 16384*A*B^2*C^2*a^3*b^2 + 32768*A^2*B*C^2*a^2*b^3 + 32768*A*B*C^3*a^4*b - 32768*A^3*B*C*a*b^4) + (16384*A^3*B^2*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^4*B*b^6*tan(c/2 + (d*x)/2))/(16384*A*C^4*a^6 + 32768*A^4*B*b^6 - 16384*A^5*a*b^5 + 16384*A^5*a^2*b^4 + 16384*A^3*B^2*a^2*b^4 - 32768*A^2*C^3*a^3*b^3 + 32768*A^2*C^3*a^4*b^2 - 32768*A^3*C^2*a^3*b^3 + 32768*A^3*C^2*a^4*b^2 - 32768*A^4*B*a*b^5 - 16384*A*C^4*a^5*b - 32768*A^4*C*a*b^5 - 16384*A^3*B^2*a*b^5 + 32768*A^4*C*a^2*b^4 + 32768*A*B*C^3*a^4*b^2 + 32768*A^3*B*C*a^2*b^4 - 32768*A^3*B*C*a^3*b^3 - 16384*A*B^2*C^2*a^3*b^3 + 16384*A*B^2*C^2*a^4*b^2 + 32768*A^2*B*C^2*a^2*b^4 - 32768*A^2*B*C^2*a^3*b^3 - 32768*A*B*C^3*a^5*b) + (32768*A^2*B*C^2*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*C^3*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^2*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A^3*B*C*b^4*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (16384*A*C^4*a^3*b*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A*B*C^3*a^3*b*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^3*B*C*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (32768*A*B*C^3*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (16384*A*B^2*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) - (32768*A^2*B*C^2*a*b^3*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3) + (16384*A*B^2*C^2*a^2*b^2*tan(c/2 + (d*x)/2))/(16384*A^5*b^4 + 16384*A*C^4*a^4 + 32768*A^4*C*b^4 + 16384*A^3*B^2*b^4 - (16384*A^5*b^5)/a - (16384*A^3*B^2*b^5)/a + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 32768*A^3*B*C*b^4 - 16384*A*C^4*a^3*b + 32768*A^2*B*C^2*b^4 - (32768*A^4*B*b^5)/a + (32768*A^4*B*b^6)/a^2 - 32768*A^2*C^3*a*b^3 - 32768*A^3*C^2*a*b^3 - (32768*A^4*C*b^5)/a + 32768*A*B*C^3*a^2*b^2 - 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 + 16384*A*B^2*C^2*a^2*b^2 - 32768*A*B*C^3*a^3*b - 32768*A^3*B*C*a*b^3)))/(a*d) - (atan((((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) + ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*C^3*a^6 - 24576*A^3*b^6 + 8192*A^2*B*b^6 - 8192*B*C^2*a^6 + 49152*A^3*a*b^5 - 49152*C^3*a^5*b - 32768*A^3*a^2*b^4 + 8192*A^3*a^3*b^3 - 8192*C^3*a^3*b^3 + 32768*C^3*a^4*b^2 - 8192*A*B^2*a*b^5 + 16384*A^2*B*a*b^5 + 8192*A*C^2*a^5*b - 8192*A^2*C*a*b^5 - 16384*B*C^2*a^5*b + 8192*B^2*C*a^5*b + ((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) + ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 - (tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) + 8192*A*B^2*a^2*b^4 - 49152*A^2*B*a^2*b^4 + 32768*A^2*B*a^3*b^3 - 8192*A^2*B*a^4*b^2 + 24576*A*C^2*a^2*b^4 - 65536*A*C^2*a^3*b^3 + 32768*A*C^2*a^4*b^2 - 32768*A^2*C*a^2*b^4 + 65536*A^2*C*a^3*b^3 - 24576*A^2*C*a^4*b^2 + 8192*B*C^2*a^2*b^4 - 32768*B*C^2*a^3*b^3 + 49152*B*C^2*a^4*b^2 - 8192*B^2*C*a^4*b^2 + 16384*A*B*C*a^2*b^4 - 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a*b^3 - a^3*b) + ((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) + ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A^3*b^6 - 24576*C^3*a^6 - 8192*A^2*B*b^6 + 8192*B*C^2*a^6 - 49152*A^3*a*b^5 + 49152*C^3*a^5*b + 32768*A^3*a^2*b^4 - 8192*A^3*a^3*b^3 + 8192*C^3*a^3*b^3 - 32768*C^3*a^4*b^2 + 8192*A*B^2*a*b^5 - 16384*A^2*B*a*b^5 - 8192*A*C^2*a^5*b + 8192*A^2*C*a*b^5 + 16384*B*C^2*a^5*b - 8192*B^2*C*a^5*b + ((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) - ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 + (tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) - 8192*A*B^2*a^2*b^4 + 49152*A^2*B*a^2*b^4 - 32768*A^2*B*a^3*b^3 + 8192*A^2*B*a^4*b^2 - 24576*A*C^2*a^2*b^4 + 65536*A*C^2*a^3*b^3 - 32768*A*C^2*a^4*b^2 + 32768*A^2*C*a^2*b^4 - 65536*A^2*C*a^3*b^3 + 24576*A^2*C*a^4*b^2 - 8192*B*C^2*a^2*b^4 + 32768*B*C^2*a^3*b^3 - 49152*B*C^2*a^4*b^2 + 8192*B^2*C*a^4*b^2 - 16384*A*B*C*a^2*b^4 + 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a*b^3 - a^3*b))/(49152*A^2*C^3*a^4 - 16384*A^4*C*b^4 - 16384*A*C^4*a^4 + 49152*A^3*C^2*b^4 - ((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) + ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*C^3*a^6 - 24576*A^3*b^6 + 8192*A^2*B*b^6 - 8192*B*C^2*a^6 + 49152*A^3*a*b^5 - 49152*C^3*a^5*b - 32768*A^3*a^2*b^4 + 8192*A^3*a^3*b^3 - 8192*C^3*a^3*b^3 + 32768*C^3*a^4*b^2 - 8192*A*B^2*a*b^5 + 16384*A^2*B*a*b^5 + 8192*A*C^2*a^5*b - 8192*A^2*C*a*b^5 - 16384*B*C^2*a^5*b + 8192*B^2*C*a^5*b + ((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) + ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 - (tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) + 8192*A*B^2*a^2*b^4 - 49152*A^2*B*a^2*b^4 + 32768*A^2*B*a^3*b^3 - 8192*A^2*B*a^4*b^2 + 24576*A*C^2*a^2*b^4 - 65536*A*C^2*a^3*b^3 + 32768*A*C^2*a^4*b^2 - 32768*A^2*C*a^2*b^4 + 65536*A^2*C*a^3*b^3 - 24576*A^2*C*a^4*b^2 + 8192*B*C^2*a^2*b^4 - 32768*B*C^2*a^3*b^3 + 49152*B*C^2*a^4*b^2 - 8192*B^2*C*a^4*b^2 + 16384*A*B*C*a^2*b^4 - 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) + ((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(8192*A^4*b^5 - 8192*C^4*a^5 - 8192*A^4*a*b^4 + 8192*C^4*a^4*b - 16384*A^2*C^2*a^5 + 16384*A^2*C^2*b^5 + 8192*A^2*B^2*a^2*b^3 - 8192*A^2*B^2*a^3*b^2 + 81920*A^2*C^2*a^2*b^3 - 81920*A^2*C^2*a^3*b^2 + 8192*B^2*C^2*a^2*b^3 - 8192*B^2*C^2*a^3*b^2 - 16384*A^3*B*a*b^4 + 16384*B*C^3*a^4*b + 16384*A^3*B*a^2*b^3 + 16384*A*C^3*a^2*b^3 - 16384*A*C^3*a^3*b^2 - 49152*A^2*C^2*a*b^4 + 49152*A^2*C^2*a^4*b + 16384*A^3*C*a^2*b^3 - 16384*A^3*C*a^3*b^2 - 16384*B*C^3*a^3*b^2 + 16384*A*B*C^2*a^2*b^3 - 16384*A^2*B*C*a^3*b^2 - 16384*A*B*C^2*a*b^4 + 16384*A^2*B*C*a^4*b) + ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A^3*b^6 - 24576*C^3*a^6 - 8192*A^2*B*b^6 + 8192*B*C^2*a^6 - 49152*A^3*a*b^5 + 49152*C^3*a^5*b + 32768*A^3*a^2*b^4 - 8192*A^3*a^3*b^3 + 8192*C^3*a^3*b^3 - 32768*C^3*a^4*b^2 + 8192*A*B^2*a*b^5 - 16384*A^2*B*a*b^5 - 8192*A*C^2*a^5*b + 8192*A^2*C*a*b^5 + 16384*B*C^2*a^5*b - 8192*B^2*C*a^5*b + ((-(a + b)*(a - b))^(1/2)*(tan(c/2 + (d*x)/2)*(16384*A^2*b^7 + 16384*C^2*a^7 - 49152*A^2*a*b^6 - 49152*C^2*a^6*b + 65536*A^2*a^2*b^5 - 65536*A^2*a^3*b^4 + 49152*A^2*a^4*b^3 - 16384*A^2*a^5*b^2 + 8192*B^2*a^2*b^5 - 8192*B^2*a^3*b^4 - 8192*B^2*a^4*b^3 + 8192*B^2*a^5*b^2 - 16384*C^2*a^2*b^5 + 49152*C^2*a^3*b^4 - 65536*C^2*a^4*b^3 + 65536*C^2*a^5*b^2 - 16384*A*B*a*b^6 - 16384*B*C*a^6*b + 16384*A*B*a^2*b^5 + 16384*A*B*a^3*b^4 - 16384*A*B*a^4*b^3 + 16384*A*C*a^2*b^5 - 16384*A*C*a^3*b^4 - 16384*A*C*a^4*b^3 + 16384*A*C*a^5*b^2 - 16384*B*C*a^3*b^4 + 16384*B*C*a^4*b^3 + 16384*B*C*a^5*b^2) - ((-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(24576*A*a^2*b^6 - 57344*A*a^3*b^5 + 40960*A*a^4*b^4 - 8192*A*a^5*b^3 + 8192*B*a^2*b^6 - 32768*B*a^3*b^5 + 49152*B*a^4*b^4 - 32768*B*a^5*b^3 + 8192*B*a^6*b^2 - 8192*C*a^3*b^5 + 40960*C*a^4*b^4 - 57344*C*a^5*b^3 + 24576*C*a^6*b^2 + (tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(16384*a^2*b^7 - 49152*a^3*b^6 + 65536*a^4*b^5 - 65536*a^5*b^4 + 49152*a^6*b^3 - 16384*a^7*b^2))/(a*b^3 - a^3*b)))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) - 8192*A*B^2*a^2*b^4 + 49152*A^2*B*a^2*b^4 - 32768*A^2*B*a^3*b^3 + 8192*A^2*B*a^4*b^2 - 24576*A*C^2*a^2*b^4 + 65536*A*C^2*a^3*b^3 - 32768*A*C^2*a^4*b^2 + 32768*A^2*C*a^2*b^4 - 65536*A^2*C*a^3*b^3 + 24576*A^2*C*a^4*b^2 - 8192*B*C^2*a^2*b^4 + 32768*B*C^2*a^3*b^3 - 49152*B*C^2*a^4*b^2 + 8192*B^2*C*a^4*b^2 - 16384*A*B*C*a^2*b^4 + 16384*A*B*C*a^4*b^2))/(a*b^3 - a^3*b))*(A*b^2 + C*a^2 - B*a*b))/(a*b^3 - a^3*b) + 32768*A^2*C^3*a^2*b^2 + 32768*A^3*C^2*a^2*b^2 + 16384*A*C^4*a^3*b + 16384*A^4*C*a*b^3 - 16384*A^2*B*C^2*a^4 - 16384*A^2*B*C^2*b^4 + 16384*A^2*C^3*a*b^3 - 98304*A^2*C^3*a^3*b - 98304*A^3*C^2*a*b^3 + 16384*A^3*C^2*a^3*b - 32768*A*B*C^3*a^2*b^2 + 16384*A*B^2*C^2*a*b^3 - 32768*A^2*B*C^2*a*b^3 - 32768*A^2*B*C^2*a^3*b + 16384*A^2*B^2*C*a^3*b - 32768*A^3*B*C*a^2*b^2 - 16384*A*B^2*C^2*a^2*b^2 + 98304*A^2*B*C^2*a^2*b^2 - 16384*A^2*B^2*C*a^2*b^2 + 32768*A*B*C^3*a^3*b + 32768*A^3*B*C*a*b^3))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a*b^3 - a^3*b))","B"
982,1,3483,107,8.088716,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))),x)","-\frac{2\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}+\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b-B\,a\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}-\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b-B\,a\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{\frac{64\,\left(-A^3\,a\,b^4+A^3\,b^5+3\,A^2\,B\,a^2\,b^3-3\,A^2\,B\,a\,b^4-A^2\,C\,a^3\,b^2+A^2\,C\,a\,b^4-3\,A\,B^2\,a^3\,b^2+3\,A\,B^2\,a^2\,b^3+2\,A\,B\,C\,a^4\,b-2\,A\,B\,C\,a^2\,b^3-A\,C^2\,a^4\,b+A\,C^2\,a^3\,b^2+B^3\,a^4\,b-B^3\,a^3\,b^2-B^2\,C\,a^5+B^2\,C\,a^3\,b^2+B\,C^2\,a^5-B\,C^2\,a^4\,b\right)}{a^3}+\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}+\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b-B\,a\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)}{a^2}-\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}-\frac{\left(A\,b-B\,a\right)\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b-B\,a\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^4}\right)}{a^2}\right)}{a^2}}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{a^2\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^4-a^2\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^4-a^2\,b^2}}{\frac{64\,\left(-A^3\,a\,b^4+A^3\,b^5+3\,A^2\,B\,a^2\,b^3-3\,A^2\,B\,a\,b^4-A^2\,C\,a^3\,b^2+A^2\,C\,a\,b^4-3\,A\,B^2\,a^3\,b^2+3\,A\,B^2\,a^2\,b^3+2\,A\,B\,C\,a^4\,b-2\,A\,B\,C\,a^2\,b^3-A\,C^2\,a^4\,b+A\,C^2\,a^3\,b^2+B^3\,a^4\,b-B^3\,a^3\,b^2-B^2\,C\,a^5+B^2\,C\,a^3\,b^2+B\,C^2\,a^5-B\,C^2\,a^4\,b\right)}{a^3}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^4-a^2\,b^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^3\,b^2+3\,A^2\,a^2\,b^3-4\,A^2\,a\,b^4+2\,A^2\,b^5+2\,A\,B\,a^4\,b-6\,A\,B\,a^3\,b^2+8\,A\,B\,a^2\,b^3-4\,A\,B\,a\,b^4-2\,A\,C\,a^3\,b^2+2\,A\,C\,a^2\,b^3-B^2\,a^5+3\,B^2\,a^4\,b-4\,B^2\,a^3\,b^2+2\,B^2\,a^2\,b^3+2\,B\,C\,a^4\,b-2\,B\,C\,a^3\,b^2-C^2\,a^5+C^2\,a^4\,b\right)}{a^2}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{32\,\left(B\,a^7+C\,a^7-A\,a^4\,b^3+2\,A\,a^5\,b^2+B\,a^5\,b^2+C\,a^5\,b^2-A\,a^6\,b-2\,B\,a^6\,b-2\,C\,a^6\,b\right)}{a^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(2\,a^6\,b-4\,a^5\,b^2+2\,a^4\,b^3\right)}{a^2\,\left(a^4-a^2\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^4-a^2\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^4-a^2\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}","Not used",1,"(atan((((A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 + ((A*b - B*a)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 - (32*tan(c/2 + (d*x)/2)*(A*b - B*a)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2)*1i)/a^2 + ((A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 - ((A*b - B*a)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 + (32*tan(c/2 + (d*x)/2)*(A*b - B*a)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2)*1i)/a^2)/((64*(A^3*b^5 + B*C^2*a^5 - B^2*C*a^5 - A^3*a*b^4 + B^3*a^4*b - B^3*a^3*b^2 - 3*A^2*B*a*b^4 - A*C^2*a^4*b + A^2*C*a*b^4 - B*C^2*a^4*b + 3*A*B^2*a^2*b^3 - 3*A*B^2*a^3*b^2 + 3*A^2*B*a^2*b^3 + A*C^2*a^3*b^2 - A^2*C*a^3*b^2 + B^2*C*a^3*b^2 + 2*A*B*C*a^4*b - 2*A*B*C*a^2*b^3))/a^3 + ((A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 + ((A*b - B*a)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 - (32*tan(c/2 + (d*x)/2)*(A*b - B*a)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2))/a^2 - ((A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 - ((A*b - B*a)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 + (32*tan(c/2 + (d*x)/2)*(A*b - B*a)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/a^4))/a^2))/a^2))*(A*b - B*a)*2i)/(a^2*d) + (atan((((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 + ((-(a + b)*(a - b))^(1/2)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 - (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^4 - a^2*b^2) + ((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 - ((-(a + b)*(a - b))^(1/2)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 + (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^4 - a^2*b^2))/((64*(A^3*b^5 + B*C^2*a^5 - B^2*C*a^5 - A^3*a*b^4 + B^3*a^4*b - B^3*a^3*b^2 - 3*A^2*B*a*b^4 - A*C^2*a^4*b + A^2*C*a*b^4 - B*C^2*a^4*b + 3*A*B^2*a^2*b^3 - 3*A*B^2*a^3*b^2 + 3*A^2*B*a^2*b^3 + A*C^2*a^3*b^2 - A^2*C*a^3*b^2 + B^2*C*a^3*b^2 + 2*A*B*C*a^4*b - 2*A*B*C*a^2*b^3))/a^3 + ((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 + ((-(a + b)*(a - b))^(1/2)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 - (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^4 - a^2*b^2) - ((-(a + b)*(a - b))^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*A^2*b^5 - B^2*a^5 - C^2*a^5 - 4*A^2*a*b^4 + 3*B^2*a^4*b + C^2*a^4*b + 3*A^2*a^2*b^3 - A^2*a^3*b^2 + 2*B^2*a^2*b^3 - 4*B^2*a^3*b^2 - 4*A*B*a*b^4 + 2*A*B*a^4*b + 2*B*C*a^4*b + 8*A*B*a^2*b^3 - 6*A*B*a^3*b^2 + 2*A*C*a^2*b^3 - 2*A*C*a^3*b^2 - 2*B*C*a^3*b^2))/a^2 - ((-(a + b)*(a - b))^(1/2)*((32*(B*a^7 + C*a^7 - A*a^4*b^3 + 2*A*a^5*b^2 + B*a^5*b^2 + C*a^5*b^2 - A*a^6*b - 2*B*a^6*b - 2*C*a^6*b))/a^3 + (32*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(2*a^6*b + 2*a^4*b^3 - 4*a^5*b^2))/(a^2*(a^4 - a^2*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^4 - a^2*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^4 - a^2*b^2)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a^4 - a^2*b^2)) - (2*A*tan(c/2 + (d*x)/2))/(a*d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
983,1,5502,154,8.758761,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a-2\,A\,b+2\,B\,a\right)}{a^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a+2\,A\,b-2\,B\,a\right)}{a^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^3}}{\frac{16\,\left(-A^3\,a^5\,b^3+2\,A^3\,a^4\,b^4-5\,A^3\,a^3\,b^5+6\,A^3\,a^2\,b^6-6\,A^3\,a\,b^7+4\,A^3\,b^8+A^2\,B\,a^6\,b^2-2\,A^2\,B\,a^5\,b^3+9\,A^2\,B\,a^4\,b^4-12\,A^2\,B\,a^3\,b^5+16\,A^2\,B\,a^2\,b^6-12\,A^2\,B\,a\,b^7-A^2\,C\,a^7\,b+2\,A^2\,C\,a^6\,b^2-9\,A^2\,C\,a^5\,b^3+12\,A^2\,C\,a^4\,b^4-16\,A^2\,C\,a^3\,b^5+12\,A^2\,C\,a^2\,b^6-4\,A\,B^2\,a^5\,b^3+6\,A\,B^2\,a^4\,b^4-14\,A\,B^2\,a^3\,b^5+12\,A\,B^2\,a^2\,b^6+8\,A\,B\,C\,a^6\,b^2-12\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-24\,A\,B\,C\,a^3\,b^5-4\,A\,C^2\,a^7\,b+6\,A\,C^2\,a^6\,b^2-14\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4+4\,B^3\,a^4\,b^4-4\,B^3\,a^3\,b^5-12\,B^2\,C\,a^5\,b^3+12\,B^2\,C\,a^4\,b^4+12\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3-4\,C^3\,a^7\,b+4\,C^3\,a^6\,b^2\right)}{a^6}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)}{a^3}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)}{a^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)}{a^3}}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{a^3\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^5-a^3\,b^2}}{\frac{16\,\left(-A^3\,a^5\,b^3+2\,A^3\,a^4\,b^4-5\,A^3\,a^3\,b^5+6\,A^3\,a^2\,b^6-6\,A^3\,a\,b^7+4\,A^3\,b^8+A^2\,B\,a^6\,b^2-2\,A^2\,B\,a^5\,b^3+9\,A^2\,B\,a^4\,b^4-12\,A^2\,B\,a^3\,b^5+16\,A^2\,B\,a^2\,b^6-12\,A^2\,B\,a\,b^7-A^2\,C\,a^7\,b+2\,A^2\,C\,a^6\,b^2-9\,A^2\,C\,a^5\,b^3+12\,A^2\,C\,a^4\,b^4-16\,A^2\,C\,a^3\,b^5+12\,A^2\,C\,a^2\,b^6-4\,A\,B^2\,a^5\,b^3+6\,A\,B^2\,a^4\,b^4-14\,A\,B^2\,a^3\,b^5+12\,A\,B^2\,a^2\,b^6+8\,A\,B\,C\,a^6\,b^2-12\,A\,B\,C\,a^5\,b^3+28\,A\,B\,C\,a^4\,b^4-24\,A\,B\,C\,a^3\,b^5-4\,A\,C^2\,a^7\,b+6\,A\,C^2\,a^6\,b^2-14\,A\,C^2\,a^5\,b^3+12\,A\,C^2\,a^4\,b^4+4\,B^3\,a^4\,b^4-4\,B^3\,a^3\,b^5-12\,B^2\,C\,a^5\,b^3+12\,B^2\,C\,a^4\,b^4+12\,B\,C^2\,a^6\,b^2-12\,B\,C^2\,a^5\,b^3-4\,C^3\,a^7\,b+4\,C^3\,a^6\,b^2\right)}{a^6}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}+\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^7-3\,A^2\,a^6\,b+7\,A^2\,a^5\,b^2-13\,A^2\,a^4\,b^3+16\,A^2\,a^3\,b^4-16\,A^2\,a^2\,b^5+16\,A^2\,a\,b^6-8\,A^2\,b^7-4\,A\,B\,a^6\,b+12\,A\,B\,a^5\,b^2-20\,A\,B\,a^4\,b^3+28\,A\,B\,a^3\,b^4-32\,A\,B\,a^2\,b^5+16\,A\,B\,a\,b^6+4\,A\,C\,a^7-12\,A\,C\,a^6\,b+20\,A\,C\,a^5\,b^2-28\,A\,C\,a^4\,b^3+32\,A\,C\,a^3\,b^4-16\,A\,C\,a^2\,b^5+4\,B^2\,a^5\,b^2-12\,B^2\,a^4\,b^3+16\,B^2\,a^3\,b^4-8\,B^2\,a^2\,b^5-8\,B\,C\,a^6\,b+24\,B\,C\,a^5\,b^2-32\,B\,C\,a^4\,b^3+16\,B\,C\,a^3\,b^4+4\,C^2\,a^7-12\,C^2\,a^6\,b+16\,C^2\,a^5\,b^2-8\,C^2\,a^4\,b^3\right)}{a^4}-\frac{b\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,A\,a^{10}+4\,C\,a^{10}+4\,A\,a^6\,b^4-6\,A\,a^7\,b^3+2\,A\,a^8\,b^2-4\,B\,a^7\,b^3+8\,B\,a^8\,b^2+4\,C\,a^8\,b^2-2\,A\,a^9\,b-4\,B\,a^9\,b-8\,C\,a^9\,b\right)}{a^6}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^8\,b-16\,a^7\,b^2+8\,a^6\,b^3\right)}{a^4\,\left(a^5-a^3\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^5-a^3\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^5-a^3\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(A*a - 2*A*b + 2*B*a))/a^2 + (tan(c/2 + (d*x)/2)^3*(A*a + 2*A*b - 2*B*a))/a^2)/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (atan(((((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*tan(c/2 + (d*x)/2)*(A*b^2 + a^2*(A/2 + C) - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*b^2 + a^2*(A/2 + C) - B*a*b))/a^3)*(A*b^2 + a^2*(A/2 + C) - B*a*b)*1i)/a^3 + (((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*tan(c/2 + (d*x)/2)*(A*b^2 + a^2*(A/2 + C) - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*b^2 + a^2*(A/2 + C) - B*a*b))/a^3)*(A*b^2 + a^2*(A/2 + C) - B*a*b)*1i)/a^3)/((16*(4*A^3*b^8 - 6*A^3*a*b^7 - 4*C^3*a^7*b + 6*A^3*a^2*b^6 - 5*A^3*a^3*b^5 + 2*A^3*a^4*b^4 - A^3*a^5*b^3 - 4*B^3*a^3*b^5 + 4*B^3*a^4*b^4 + 4*C^3*a^6*b^2 - 12*A^2*B*a*b^7 - 4*A*C^2*a^7*b - A^2*C*a^7*b + 12*A*B^2*a^2*b^6 - 14*A*B^2*a^3*b^5 + 6*A*B^2*a^4*b^4 - 4*A*B^2*a^5*b^3 + 16*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 9*A^2*B*a^4*b^4 - 2*A^2*B*a^5*b^3 + A^2*B*a^6*b^2 + 12*A*C^2*a^4*b^4 - 14*A*C^2*a^5*b^3 + 6*A*C^2*a^6*b^2 + 12*A^2*C*a^2*b^6 - 16*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 - 9*A^2*C*a^5*b^3 + 2*A^2*C*a^6*b^2 - 12*B*C^2*a^5*b^3 + 12*B*C^2*a^6*b^2 + 12*B^2*C*a^4*b^4 - 12*B^2*C*a^5*b^3 - 24*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 12*A*B*C*a^5*b^3 + 8*A*B*C*a^6*b^2))/a^6 - (((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*tan(c/2 + (d*x)/2)*(A*b^2 + a^2*(A/2 + C) - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*b^2 + a^2*(A/2 + C) - B*a*b))/a^3)*(A*b^2 + a^2*(A/2 + C) - B*a*b))/a^3 + (((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*tan(c/2 + (d*x)/2)*(A*b^2 + a^2*(A/2 + C) - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/a^7)*(A*b^2 + a^2*(A/2 + C) - B*a*b))/a^3)*(A*b^2 + a^2*(A/2 + C) - B*a*b))/a^3))*(A*b^2 + a^2*(A/2 + C) - B*a*b)*2i)/(a^3*d) + (b*atan(((b*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (b*(-(a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^5 - a^3*b^2) + (b*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (b*(-(a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^5 - a^3*b^2))/((16*(4*A^3*b^8 - 6*A^3*a*b^7 - 4*C^3*a^7*b + 6*A^3*a^2*b^6 - 5*A^3*a^3*b^5 + 2*A^3*a^4*b^4 - A^3*a^5*b^3 - 4*B^3*a^3*b^5 + 4*B^3*a^4*b^4 + 4*C^3*a^6*b^2 - 12*A^2*B*a*b^7 - 4*A*C^2*a^7*b - A^2*C*a^7*b + 12*A*B^2*a^2*b^6 - 14*A*B^2*a^3*b^5 + 6*A*B^2*a^4*b^4 - 4*A*B^2*a^5*b^3 + 16*A^2*B*a^2*b^6 - 12*A^2*B*a^3*b^5 + 9*A^2*B*a^4*b^4 - 2*A^2*B*a^5*b^3 + A^2*B*a^6*b^2 + 12*A*C^2*a^4*b^4 - 14*A*C^2*a^5*b^3 + 6*A*C^2*a^6*b^2 + 12*A^2*C*a^2*b^6 - 16*A^2*C*a^3*b^5 + 12*A^2*C*a^4*b^4 - 9*A^2*C*a^5*b^3 + 2*A^2*C*a^6*b^2 - 12*B*C^2*a^5*b^3 + 12*B*C^2*a^6*b^2 + 12*B^2*C*a^4*b^4 - 12*B^2*C*a^5*b^3 - 24*A*B*C*a^3*b^5 + 28*A*B*C*a^4*b^4 - 12*A*B*C*a^5*b^3 + 8*A*B*C*a^6*b^2))/a^6 - (b*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 + (b*(-(a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2) + (b*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^7 - 8*A^2*b^7 + 4*C^2*a^7 + 16*A^2*a*b^6 - 3*A^2*a^6*b - 12*C^2*a^6*b - 16*A^2*a^2*b^5 + 16*A^2*a^3*b^4 - 13*A^2*a^4*b^3 + 7*A^2*a^5*b^2 - 8*B^2*a^2*b^5 + 16*B^2*a^3*b^4 - 12*B^2*a^4*b^3 + 4*B^2*a^5*b^2 - 8*C^2*a^4*b^3 + 16*C^2*a^5*b^2 + 4*A*C*a^7 + 16*A*B*a*b^6 - 4*A*B*a^6*b - 12*A*C*a^6*b - 8*B*C*a^6*b - 32*A*B*a^2*b^5 + 28*A*B*a^3*b^4 - 20*A*B*a^4*b^3 + 12*A*B*a^5*b^2 - 16*A*C*a^2*b^5 + 32*A*C*a^3*b^4 - 28*A*C*a^4*b^3 + 20*A*C*a^5*b^2 + 16*B*C*a^3*b^4 - 32*B*C*a^4*b^3 + 24*B*C*a^5*b^2))/a^4 - (b*(-(a + b)*(a - b))^(1/2)*((8*(2*A*a^10 + 4*C*a^10 + 4*A*a^6*b^4 - 6*A*a^7*b^3 + 2*A*a^8*b^2 - 4*B*a^7*b^3 + 8*B*a^8*b^2 + 4*C*a^8*b^2 - 2*A*a^9*b - 4*B*a^9*b - 8*C*a^9*b))/a^6 - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^8*b + 8*a^6*b^3 - 16*a^7*b^2))/(a^4*(a^5 - a^3*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^5 - a^3*b^2)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a^5 - a^3*b^2))","B"
984,1,7033,214,10.053928,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^2+2\,A\,b^2+B\,a^2+2\,C\,a^2-A\,a\,b-2\,B\,a\,b\right)}{a^3}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^2+3\,A\,b^2+3\,C\,a^2-3\,B\,a\,b\right)}{3\,a^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^2+2\,A\,b^2-B\,a^2+2\,C\,a^2+A\,a\,b-2\,B\,a\,b\right)}{a^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^{10}}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^4}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)\,1{}\mathrm{i}}{a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^{10}}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^4}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}+3\,A^2\,B\,a^6\,b^5-6\,A^2\,B\,a^5\,b^6+15\,A^2\,B\,a^4\,b^7-18\,A^2\,B\,a^3\,b^8+18\,A^2\,B\,a^2\,b^9-12\,A^2\,B\,a\,b^{10}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-3\,A\,B^2\,a^7\,b^4+6\,A\,B^2\,a^6\,b^5-15\,A\,B^2\,a^5\,b^6+18\,A\,B^2\,a^4\,b^7-18\,A\,B^2\,a^3\,b^8+12\,A\,B^2\,a^2\,b^9+2\,A\,B\,C\,a^8\,b^3-4\,A\,B\,C\,a^7\,b^4+18\,A\,B\,C\,a^6\,b^5-24\,A\,B\,C\,a^5\,b^6+32\,A\,B\,C\,a^4\,b^7-24\,A\,B\,C\,a^3\,b^8-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7+B^3\,a^8\,b^3-2\,B^3\,a^7\,b^4+5\,B^3\,a^6\,b^5-6\,B^3\,a^5\,b^6+6\,B^3\,a^4\,b^7-4\,B^3\,a^3\,b^8-B^2\,C\,a^9\,b^2+2\,B^2\,C\,a^8\,b^3-9\,B^2\,C\,a^7\,b^4+12\,B^2\,C\,a^6\,b^5-16\,B^2\,C\,a^5\,b^6+12\,B^2\,C\,a^4\,b^7+4\,B\,C^2\,a^8\,b^3-6\,B\,C^2\,a^7\,b^4+14\,B\,C^2\,a^6\,b^5-12\,B\,C^2\,a^5\,b^6-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^{10}}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^4}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^{10}}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^4}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)}{a^4}}\right)\,\left(A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(\frac{A\,b}{2}+C\,b\right)-B\,a\,b^2\right)\,2{}\mathrm{i}}{a^4\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(-A^3\,a^5\,b^6+2\,A^3\,a^4\,b^7-5\,A^3\,a^3\,b^8+6\,A^3\,a^2\,b^9-6\,A^3\,a\,b^{10}+4\,A^3\,b^{11}+3\,A^2\,B\,a^6\,b^5-6\,A^2\,B\,a^5\,b^6+15\,A^2\,B\,a^4\,b^7-18\,A^2\,B\,a^3\,b^8+18\,A^2\,B\,a^2\,b^9-12\,A^2\,B\,a\,b^{10}-A^2\,C\,a^7\,b^4+2\,A^2\,C\,a^6\,b^5-9\,A^2\,C\,a^5\,b^6+12\,A^2\,C\,a^4\,b^7-16\,A^2\,C\,a^3\,b^8+12\,A^2\,C\,a^2\,b^9-3\,A\,B^2\,a^7\,b^4+6\,A\,B^2\,a^6\,b^5-15\,A\,B^2\,a^5\,b^6+18\,A\,B^2\,a^4\,b^7-18\,A\,B^2\,a^3\,b^8+12\,A\,B^2\,a^2\,b^9+2\,A\,B\,C\,a^8\,b^3-4\,A\,B\,C\,a^7\,b^4+18\,A\,B\,C\,a^6\,b^5-24\,A\,B\,C\,a^5\,b^6+32\,A\,B\,C\,a^4\,b^7-24\,A\,B\,C\,a^3\,b^8-4\,A\,C^2\,a^7\,b^4+6\,A\,C^2\,a^6\,b^5-14\,A\,C^2\,a^5\,b^6+12\,A\,C^2\,a^4\,b^7+B^3\,a^8\,b^3-2\,B^3\,a^7\,b^4+5\,B^3\,a^6\,b^5-6\,B^3\,a^5\,b^6+6\,B^3\,a^4\,b^7-4\,B^3\,a^3\,b^8-B^2\,C\,a^9\,b^2+2\,B^2\,C\,a^8\,b^3-9\,B^2\,C\,a^7\,b^4+12\,B^2\,C\,a^6\,b^5-16\,B^2\,C\,a^5\,b^6+12\,B^2\,C\,a^4\,b^7+4\,B\,C^2\,a^8\,b^3-6\,B\,C^2\,a^7\,b^4+14\,B\,C^2\,a^6\,b^5-12\,B\,C^2\,a^5\,b^6-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^9}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}+\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-A^2\,a^7\,b^2+3\,A^2\,a^6\,b^3-7\,A^2\,a^5\,b^4+13\,A^2\,a^4\,b^5-16\,A^2\,a^3\,b^6+16\,A^2\,a^2\,b^7-16\,A^2\,a\,b^8+8\,A^2\,b^9+2\,A\,B\,a^8\,b-6\,A\,B\,a^7\,b^2+14\,A\,B\,a^6\,b^3-26\,A\,B\,a^5\,b^4+32\,A\,B\,a^4\,b^5-32\,A\,B\,a^3\,b^6+32\,A\,B\,a^2\,b^7-16\,A\,B\,a\,b^8-4\,A\,C\,a^7\,b^2+12\,A\,C\,a^6\,b^3-20\,A\,C\,a^5\,b^4+28\,A\,C\,a^4\,b^5-32\,A\,C\,a^3\,b^6+16\,A\,C\,a^2\,b^7-B^2\,a^9+3\,B^2\,a^8\,b-7\,B^2\,a^7\,b^2+13\,B^2\,a^6\,b^3-16\,B^2\,a^5\,b^4+16\,B^2\,a^4\,b^5-16\,B^2\,a^3\,b^6+8\,B^2\,a^2\,b^7+4\,B\,C\,a^8\,b-12\,B\,C\,a^7\,b^2+20\,B\,C\,a^6\,b^3-28\,B\,C\,a^5\,b^4+32\,B\,C\,a^4\,b^5-16\,B\,C\,a^3\,b^6-4\,C^2\,a^7\,b^2+12\,C^2\,a^6\,b^3-16\,C^2\,a^5\,b^4+8\,C^2\,a^4\,b^5\right)}{a^6}-\frac{b^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(4\,A\,a^8\,b^5-2\,B\,a^{13}-6\,A\,a^9\,b^4+2\,A\,a^{10}\,b^3-2\,A\,a^{11}\,b^2-4\,B\,a^9\,b^4+6\,B\,a^{10}\,b^3-2\,B\,a^{11}\,b^2+4\,C\,a^{10}\,b^3-8\,C\,a^{11}\,b^2+2\,A\,a^{12}\,b+2\,B\,a^{12}\,b+4\,C\,a^{12}\,b\right)}{a^9}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"(b^2*atan(((b^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (b^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^6 - a^4*b^2) + (b^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (b^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^6 - a^4*b^2))/((16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 - 4*B^3*a^3*b^8 + 6*B^3*a^4*b^7 - 6*B^3*a^5*b^6 + 5*B^3*a^6*b^5 - 2*B^3*a^7*b^4 + B^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*A^2*B*a*b^10 + 12*A*B^2*a^2*b^9 - 18*A*B^2*a^3*b^8 + 18*A*B^2*a^4*b^7 - 15*A*B^2*a^5*b^6 + 6*A*B^2*a^6*b^5 - 3*A*B^2*a^7*b^4 + 18*A^2*B*a^2*b^9 - 18*A^2*B*a^3*b^8 + 15*A^2*B*a^4*b^7 - 6*A^2*B*a^5*b^6 + 3*A^2*B*a^6*b^5 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4 - 12*B*C^2*a^5*b^6 + 14*B*C^2*a^6*b^5 - 6*B*C^2*a^7*b^4 + 4*B*C^2*a^8*b^3 + 12*B^2*C*a^4*b^7 - 16*B^2*C*a^5*b^6 + 12*B^2*C*a^6*b^5 - 9*B^2*C*a^7*b^4 + 2*B^2*C*a^8*b^3 - B^2*C*a^9*b^2 - 24*A*B*C*a^3*b^8 + 32*A*B*C*a^4*b^7 - 24*A*B*C*a^5*b^6 + 18*A*B*C*a^6*b^5 - 4*A*B*C*a^7*b^4 + 2*A*B*C*a^8*b^3))/a^9 - (b^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (b^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2) + (b^2*(-(a + b)*(a - b))^(1/2)*((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (b^2*(-(a + b)*(a - b))^(1/2)*((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^6 - a^4*b^2)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a^6 - a^4*b^2)) - (atan(-((((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^10)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^4)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2)*1i)/a^4 + (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^10)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^4)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2)*1i)/a^4)/((16*(4*A^3*b^11 - 6*A^3*a*b^10 + 6*A^3*a^2*b^9 - 5*A^3*a^3*b^8 + 2*A^3*a^4*b^7 - A^3*a^5*b^6 - 4*B^3*a^3*b^8 + 6*B^3*a^4*b^7 - 6*B^3*a^5*b^6 + 5*B^3*a^6*b^5 - 2*B^3*a^7*b^4 + B^3*a^8*b^3 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*A^2*B*a*b^10 + 12*A*B^2*a^2*b^9 - 18*A*B^2*a^3*b^8 + 18*A*B^2*a^4*b^7 - 15*A*B^2*a^5*b^6 + 6*A*B^2*a^6*b^5 - 3*A*B^2*a^7*b^4 + 18*A^2*B*a^2*b^9 - 18*A^2*B*a^3*b^8 + 15*A^2*B*a^4*b^7 - 6*A^2*B*a^5*b^6 + 3*A^2*B*a^6*b^5 + 12*A*C^2*a^4*b^7 - 14*A*C^2*a^5*b^6 + 6*A*C^2*a^6*b^5 - 4*A*C^2*a^7*b^4 + 12*A^2*C*a^2*b^9 - 16*A^2*C*a^3*b^8 + 12*A^2*C*a^4*b^7 - 9*A^2*C*a^5*b^6 + 2*A^2*C*a^6*b^5 - A^2*C*a^7*b^4 - 12*B*C^2*a^5*b^6 + 14*B*C^2*a^6*b^5 - 6*B*C^2*a^7*b^4 + 4*B*C^2*a^8*b^3 + 12*B^2*C*a^4*b^7 - 16*B^2*C*a^5*b^6 + 12*B^2*C*a^6*b^5 - 9*B^2*C*a^7*b^4 + 2*B^2*C*a^8*b^3 - B^2*C*a^9*b^2 - 24*A*B*C*a^3*b^8 + 32*A*B*C*a^4*b^7 - 24*A*B*C*a^5*b^6 + 18*A*B*C*a^6*b^5 - 4*A*B*C*a^7*b^4 + 2*A*B*C*a^8*b^3))/a^9 - (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 + (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 - (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^10)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^4)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^4 + (((8*tan(c/2 + (d*x)/2)*(8*A^2*b^9 - B^2*a^9 - 16*A^2*a*b^8 + 3*B^2*a^8*b + 16*A^2*a^2*b^7 - 16*A^2*a^3*b^6 + 13*A^2*a^4*b^5 - 7*A^2*a^5*b^4 + 3*A^2*a^6*b^3 - A^2*a^7*b^2 + 8*B^2*a^2*b^7 - 16*B^2*a^3*b^6 + 16*B^2*a^4*b^5 - 16*B^2*a^5*b^4 + 13*B^2*a^6*b^3 - 7*B^2*a^7*b^2 + 8*C^2*a^4*b^5 - 16*C^2*a^5*b^4 + 12*C^2*a^6*b^3 - 4*C^2*a^7*b^2 - 16*A*B*a*b^8 + 2*A*B*a^8*b + 4*B*C*a^8*b + 32*A*B*a^2*b^7 - 32*A*B*a^3*b^6 + 32*A*B*a^4*b^5 - 26*A*B*a^5*b^4 + 14*A*B*a^6*b^3 - 6*A*B*a^7*b^2 + 16*A*C*a^2*b^7 - 32*A*C*a^3*b^6 + 28*A*C*a^4*b^5 - 20*A*C*a^5*b^4 + 12*A*C*a^6*b^3 - 4*A*C*a^7*b^2 - 16*B*C*a^3*b^6 + 32*B*C*a^4*b^5 - 28*B*C*a^5*b^4 + 20*B*C*a^6*b^3 - 12*B*C*a^7*b^2))/a^6 - (((8*(4*A*a^8*b^5 - 2*B*a^13 - 6*A*a^9*b^4 + 2*A*a^10*b^3 - 2*A*a^11*b^2 - 4*B*a^9*b^4 + 6*B*a^10*b^3 - 2*B*a^11*b^2 + 4*C*a^10*b^3 - 8*C*a^11*b^2 + 2*A*a^12*b + 2*B*a^12*b + 4*C*a^12*b))/a^9 + (8*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^10)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^4)*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2))/a^4))*(A*b^3 - (B*a^3)/2 + a^2*((A*b)/2 + C*b) - B*a*b^2)*2i)/(a^4*d) - ((tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 + 2*C*a^2 - A*a*b - 2*B*a*b))/a^3 - (4*tan(c/2 + (d*x)/2)^3*(A*a^2 + 3*A*b^2 + 3*C*a^2 - 3*B*a*b))/(3*a^3) + (tan(c/2 + (d*x)/2)^5*(2*A*a^2 + 2*A*b^2 - B*a^2 + 2*C*a^2 + A*a*b - 2*B*a*b))/a^3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
985,1,9543,285,11.074973,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^5*(a + b*cos(c + d*x))),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,A\,a^3+8\,A\,b^3-8\,B\,a^3+4\,C\,a^3+4\,A\,a\,b^2+8\,A\,a^2\,b-8\,B\,a\,b^2-4\,B\,a^2\,b+8\,C\,a^2\,b\right)}{4\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,A\,a^3+72\,A\,b^3-40\,B\,a^3-12\,C\,a^3-12\,A\,a\,b^2+40\,A\,a^2\,b-72\,B\,a\,b^2+12\,B\,a^2\,b+72\,C\,a^2\,b\right)}{12\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(72\,A\,b^3-9\,A\,a^3-40\,B\,a^3+12\,C\,a^3+12\,A\,a\,b^2+40\,A\,a^2\,b-72\,B\,a\,b^2-12\,B\,a^2\,b+72\,C\,a^2\,b\right)}{12\,a^4}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A\,a^3-8\,A\,b^3+8\,B\,a^3+4\,C\,a^3+4\,A\,a\,b^2-8\,A\,a^2\,b+8\,B\,a\,b^2-4\,B\,a^2\,b-8\,C\,a^2\,b\right)}{4\,a^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)\,1{}\mathrm{i}}{a^5}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)\,1{}\mathrm{i}}{a^5}}{\frac{-9\,A^3\,a^9\,b^5+18\,A^3\,a^8\,b^6-33\,A^3\,a^7\,b^7+48\,A^3\,a^6\,b^8-88\,A^3\,a^5\,b^9+104\,A^3\,a^4\,b^{10}-104\,A^3\,a^3\,b^{11}+96\,A^3\,a^2\,b^{12}-96\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+9\,A^2\,B\,a^{10}\,b^4-18\,A^2\,B\,a^9\,b^5+57\,A^2\,B\,a^8\,b^6-96\,A^2\,B\,a^7\,b^7+192\,A^2\,B\,a^6\,b^8-240\,A^2\,B\,a^5\,b^9+288\,A^2\,B\,a^4\,b^{10}-288\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-192\,A^2\,B\,a\,b^{13}-9\,A^2\,C\,a^{11}\,b^3+18\,A^2\,C\,a^{10}\,b^4-57\,A^2\,C\,a^9\,b^5+96\,A^2\,C\,a^8\,b^6-192\,A^2\,C\,a^7\,b^7+240\,A^2\,C\,a^6\,b^8-288\,A^2\,C\,a^5\,b^9+288\,A^2\,C\,a^4\,b^{10}-288\,A^2\,C\,a^3\,b^{11}+192\,A^2\,C\,a^2\,b^{12}-24\,A\,B^2\,a^9\,b^5+48\,A\,B^2\,a^8\,b^6-120\,A\,B^2\,a^7\,b^7+168\,A\,B^2\,a^6\,b^8-264\,A\,B^2\,a^5\,b^9+288\,A\,B^2\,a^4\,b^{10}-288\,A\,B^2\,a^3\,b^{11}+192\,A\,B^2\,a^2\,b^{12}+48\,A\,B\,C\,a^{10}\,b^4-96\,A\,B\,C\,a^9\,b^5+240\,A\,B\,C\,a^8\,b^6-336\,A\,B\,C\,a^7\,b^7+528\,A\,B\,C\,a^6\,b^8-576\,A\,B\,C\,a^5\,b^9+576\,A\,B\,C\,a^4\,b^{10}-384\,A\,B\,C\,a^3\,b^{11}-24\,A\,C^2\,a^{11}\,b^3+48\,A\,C^2\,a^{10}\,b^4-120\,A\,C^2\,a^9\,b^5+168\,A\,C^2\,a^8\,b^6-264\,A\,C^2\,a^7\,b^7+288\,A\,C^2\,a^6\,b^8-288\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}+16\,B^3\,a^8\,b^6-32\,B^3\,a^7\,b^7+80\,B^3\,a^6\,b^8-96\,B^3\,a^5\,b^9+96\,B^3\,a^4\,b^{10}-64\,B^3\,a^3\,b^{11}-48\,B^2\,C\,a^9\,b^5+96\,B^2\,C\,a^8\,b^6-240\,B^2\,C\,a^7\,b^7+288\,B^2\,C\,a^6\,b^8-288\,B^2\,C\,a^5\,b^9+192\,B^2\,C\,a^4\,b^{10}+48\,B\,C^2\,a^{10}\,b^4-96\,B\,C^2\,a^9\,b^5+240\,B\,C^2\,a^8\,b^6-288\,B\,C^2\,a^7\,b^7+288\,B\,C^2\,a^6\,b^8-192\,B\,C^2\,a^5\,b^9-16\,C^3\,a^{11}\,b^3+32\,C^3\,a^{10}\,b^4-80\,C^3\,a^9\,b^5+96\,C^3\,a^8\,b^6-96\,C^3\,a^7\,b^7+64\,C^3\,a^6\,b^8}{a^{12}}-\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{a^5}+\frac{\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{2\,a^{13}}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{a^5}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)}{a^5}}\right)\,\left(a^2\,\left(\frac{A\,b^2}{2}+C\,b^2\right)+A\,b^4+a^4\,\left(\frac{3\,A}{8}+\frac{C}{2}\right)-B\,a\,b^3-\frac{B\,a^3\,b}{2}\right)\,2{}\mathrm{i}}{a^5\,d}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}}{\frac{-9\,A^3\,a^9\,b^5+18\,A^3\,a^8\,b^6-33\,A^3\,a^7\,b^7+48\,A^3\,a^6\,b^8-88\,A^3\,a^5\,b^9+104\,A^3\,a^4\,b^{10}-104\,A^3\,a^3\,b^{11}+96\,A^3\,a^2\,b^{12}-96\,A^3\,a\,b^{13}+64\,A^3\,b^{14}+9\,A^2\,B\,a^{10}\,b^4-18\,A^2\,B\,a^9\,b^5+57\,A^2\,B\,a^8\,b^6-96\,A^2\,B\,a^7\,b^7+192\,A^2\,B\,a^6\,b^8-240\,A^2\,B\,a^5\,b^9+288\,A^2\,B\,a^4\,b^{10}-288\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-192\,A^2\,B\,a\,b^{13}-9\,A^2\,C\,a^{11}\,b^3+18\,A^2\,C\,a^{10}\,b^4-57\,A^2\,C\,a^9\,b^5+96\,A^2\,C\,a^8\,b^6-192\,A^2\,C\,a^7\,b^7+240\,A^2\,C\,a^6\,b^8-288\,A^2\,C\,a^5\,b^9+288\,A^2\,C\,a^4\,b^{10}-288\,A^2\,C\,a^3\,b^{11}+192\,A^2\,C\,a^2\,b^{12}-24\,A\,B^2\,a^9\,b^5+48\,A\,B^2\,a^8\,b^6-120\,A\,B^2\,a^7\,b^7+168\,A\,B^2\,a^6\,b^8-264\,A\,B^2\,a^5\,b^9+288\,A\,B^2\,a^4\,b^{10}-288\,A\,B^2\,a^3\,b^{11}+192\,A\,B^2\,a^2\,b^{12}+48\,A\,B\,C\,a^{10}\,b^4-96\,A\,B\,C\,a^9\,b^5+240\,A\,B\,C\,a^8\,b^6-336\,A\,B\,C\,a^7\,b^7+528\,A\,B\,C\,a^6\,b^8-576\,A\,B\,C\,a^5\,b^9+576\,A\,B\,C\,a^4\,b^{10}-384\,A\,B\,C\,a^3\,b^{11}-24\,A\,C^2\,a^{11}\,b^3+48\,A\,C^2\,a^{10}\,b^4-120\,A\,C^2\,a^9\,b^5+168\,A\,C^2\,a^8\,b^6-264\,A\,C^2\,a^7\,b^7+288\,A\,C^2\,a^6\,b^8-288\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}+16\,B^3\,a^8\,b^6-32\,B^3\,a^7\,b^7+80\,B^3\,a^6\,b^8-96\,B^3\,a^5\,b^9+96\,B^3\,a^4\,b^{10}-64\,B^3\,a^3\,b^{11}-48\,B^2\,C\,a^9\,b^5+96\,B^2\,C\,a^8\,b^6-240\,B^2\,C\,a^7\,b^7+288\,B^2\,C\,a^6\,b^8-288\,B^2\,C\,a^5\,b^9+192\,B^2\,C\,a^4\,b^{10}+48\,B\,C^2\,a^{10}\,b^4-96\,B\,C^2\,a^9\,b^5+240\,B\,C^2\,a^8\,b^6-288\,B\,C^2\,a^7\,b^7+288\,B\,C^2\,a^6\,b^8-192\,B\,C^2\,a^5\,b^9-16\,C^3\,a^{11}\,b^3+32\,C^3\,a^{10}\,b^4-80\,C^3\,a^9\,b^5+96\,C^3\,a^8\,b^6-96\,C^3\,a^7\,b^7+64\,C^3\,a^6\,b^8}{a^{12}}-\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^{11}-27\,A^2\,a^{10}\,b+51\,A^2\,a^9\,b^2-81\,A^2\,a^8\,b^3+136\,A^2\,a^7\,b^4-216\,A^2\,a^6\,b^5+256\,A^2\,a^5\,b^6-256\,A^2\,a^4\,b^7+256\,A^2\,a^3\,b^8-256\,A^2\,a^2\,b^9+256\,A^2\,a\,b^{10}-128\,A^2\,b^{11}-24\,A\,B\,a^{10}\,b+72\,A\,B\,a^9\,b^2-152\,A\,B\,a^8\,b^3+264\,A\,B\,a^7\,b^4-368\,A\,B\,a^6\,b^5+464\,A\,B\,a^5\,b^6-512\,A\,B\,a^4\,b^7+512\,A\,B\,a^3\,b^8-512\,A\,B\,a^2\,b^9+256\,A\,B\,a\,b^{10}+24\,A\,C\,a^{11}-72\,A\,C\,a^{10}\,b+152\,A\,C\,a^9\,b^2-264\,A\,C\,a^8\,b^3+368\,A\,C\,a^7\,b^4-464\,A\,C\,a^6\,b^5+512\,A\,C\,a^5\,b^6-512\,A\,C\,a^4\,b^7+512\,A\,C\,a^3\,b^8-256\,A\,C\,a^2\,b^9+16\,B^2\,a^9\,b^2-48\,B^2\,a^8\,b^3+112\,B^2\,a^7\,b^4-208\,B^2\,a^6\,b^5+256\,B^2\,a^5\,b^6-256\,B^2\,a^4\,b^7+256\,B^2\,a^3\,b^8-128\,B^2\,a^2\,b^9-32\,B\,C\,a^{10}\,b+96\,B\,C\,a^9\,b^2-224\,B\,C\,a^8\,b^3+416\,B\,C\,a^7\,b^4-512\,B\,C\,a^6\,b^5+512\,B\,C\,a^5\,b^6-512\,B\,C\,a^4\,b^7+256\,B\,C\,a^3\,b^8+16\,C^2\,a^{11}-48\,C^2\,a^{10}\,b+112\,C^2\,a^9\,b^2-208\,C^2\,a^8\,b^3+256\,C^2\,a^7\,b^4-256\,C^2\,a^6\,b^5+256\,C^2\,a^5\,b^6-128\,C^2\,a^4\,b^7\right)}{2\,a^8}-\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{12\,A\,a^{16}+16\,C\,a^{16}+32\,A\,a^{10}\,b^6-48\,A\,a^{11}\,b^5+16\,A\,a^{12}\,b^4-4\,A\,a^{13}\,b^3+4\,A\,a^{14}\,b^2-32\,B\,a^{11}\,b^5+48\,B\,a^{12}\,b^4-16\,B\,a^{13}\,b^3+16\,B\,a^{14}\,b^2+32\,C\,a^{12}\,b^4-48\,C\,a^{13}\,b^3+16\,C\,a^{14}\,b^2-12\,A\,a^{15}\,b-16\,B\,a^{15}\,b-16\,C\,a^{15}\,b}{a^{12}}-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{a^7-a^5\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(C\,a^2-B\,a\,b+A\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^7*(5*A*a^3 + 8*A*b^3 - 8*B*a^3 + 4*C*a^3 + 4*A*a*b^2 + 8*A*a^2*b - 8*B*a*b^2 - 4*B*a^2*b + 8*C*a^2*b))/(4*a^4) + (tan(c/2 + (d*x)/2)^3*(9*A*a^3 + 72*A*b^3 - 40*B*a^3 - 12*C*a^3 - 12*A*a*b^2 + 40*A*a^2*b - 72*B*a*b^2 + 12*B*a^2*b + 72*C*a^2*b))/(12*a^4) - (tan(c/2 + (d*x)/2)^5*(72*A*b^3 - 9*A*a^3 - 40*B*a^3 + 12*C*a^3 + 12*A*a*b^2 + 40*A*a^2*b - 72*B*a*b^2 - 12*B*a^2*b + 72*C*a^2*b))/(12*a^4) + (tan(c/2 + (d*x)/2)*(5*A*a^3 - 8*A*b^3 + 8*B*a^3 + 4*C*a^3 + 4*A*a*b^2 - 8*A*a^2*b + 8*B*a*b^2 - 4*B*a^2*b - 8*C*a^2*b))/(4*a^4))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atan(((((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/(2*a^13))*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/a^5)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2)*1i)/a^5 + (((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/(2*a^13))*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/a^5)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2)*1i)/a^5)/((64*A^3*b^14 - 96*A^3*a*b^13 + 96*A^3*a^2*b^12 - 104*A^3*a^3*b^11 + 104*A^3*a^4*b^10 - 88*A^3*a^5*b^9 + 48*A^3*a^6*b^8 - 33*A^3*a^7*b^7 + 18*A^3*a^8*b^6 - 9*A^3*a^9*b^5 - 64*B^3*a^3*b^11 + 96*B^3*a^4*b^10 - 96*B^3*a^5*b^9 + 80*B^3*a^6*b^8 - 32*B^3*a^7*b^7 + 16*B^3*a^8*b^6 + 64*C^3*a^6*b^8 - 96*C^3*a^7*b^7 + 96*C^3*a^8*b^6 - 80*C^3*a^9*b^5 + 32*C^3*a^10*b^4 - 16*C^3*a^11*b^3 - 192*A^2*B*a*b^13 + 192*A*B^2*a^2*b^12 - 288*A*B^2*a^3*b^11 + 288*A*B^2*a^4*b^10 - 264*A*B^2*a^5*b^9 + 168*A*B^2*a^6*b^8 - 120*A*B^2*a^7*b^7 + 48*A*B^2*a^8*b^6 - 24*A*B^2*a^9*b^5 + 288*A^2*B*a^2*b^12 - 288*A^2*B*a^3*b^11 + 288*A^2*B*a^4*b^10 - 240*A^2*B*a^5*b^9 + 192*A^2*B*a^6*b^8 - 96*A^2*B*a^7*b^7 + 57*A^2*B*a^8*b^6 - 18*A^2*B*a^9*b^5 + 9*A^2*B*a^10*b^4 + 192*A*C^2*a^4*b^10 - 288*A*C^2*a^5*b^9 + 288*A*C^2*a^6*b^8 - 264*A*C^2*a^7*b^7 + 168*A*C^2*a^8*b^6 - 120*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 - 24*A*C^2*a^11*b^3 + 192*A^2*C*a^2*b^12 - 288*A^2*C*a^3*b^11 + 288*A^2*C*a^4*b^10 - 288*A^2*C*a^5*b^9 + 240*A^2*C*a^6*b^8 - 192*A^2*C*a^7*b^7 + 96*A^2*C*a^8*b^6 - 57*A^2*C*a^9*b^5 + 18*A^2*C*a^10*b^4 - 9*A^2*C*a^11*b^3 - 192*B*C^2*a^5*b^9 + 288*B*C^2*a^6*b^8 - 288*B*C^2*a^7*b^7 + 240*B*C^2*a^8*b^6 - 96*B*C^2*a^9*b^5 + 48*B*C^2*a^10*b^4 + 192*B^2*C*a^4*b^10 - 288*B^2*C*a^5*b^9 + 288*B^2*C*a^6*b^8 - 240*B^2*C*a^7*b^7 + 96*B^2*C*a^8*b^6 - 48*B^2*C*a^9*b^5 - 384*A*B*C*a^3*b^11 + 576*A*B*C*a^4*b^10 - 576*A*B*C*a^5*b^9 + 528*A*B*C*a^6*b^8 - 336*A*B*C*a^7*b^7 + 240*A*B*C*a^8*b^6 - 96*A*B*C*a^9*b^5 + 48*A*B*C*a^10*b^4)/a^12 - (((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/(2*a^13))*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/a^5)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/a^5 + (((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (tan(c/2 + (d*x)/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/(2*a^13))*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/a^5)*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2))/a^5))*(a^2*((A*b^2)/2 + C*b^2) + A*b^4 + a^4*((3*A)/8 + C/2) - B*a*b^3 - (B*a^3*b)/2)*2i)/(a^5*d) + (b^3*atan(((b^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (b^3*(-(a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^7 - a^5*b^2) + (b^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (b^3*(-(a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b)*1i)/(a^7 - a^5*b^2))/((64*A^3*b^14 - 96*A^3*a*b^13 + 96*A^3*a^2*b^12 - 104*A^3*a^3*b^11 + 104*A^3*a^4*b^10 - 88*A^3*a^5*b^9 + 48*A^3*a^6*b^8 - 33*A^3*a^7*b^7 + 18*A^3*a^8*b^6 - 9*A^3*a^9*b^5 - 64*B^3*a^3*b^11 + 96*B^3*a^4*b^10 - 96*B^3*a^5*b^9 + 80*B^3*a^6*b^8 - 32*B^3*a^7*b^7 + 16*B^3*a^8*b^6 + 64*C^3*a^6*b^8 - 96*C^3*a^7*b^7 + 96*C^3*a^8*b^6 - 80*C^3*a^9*b^5 + 32*C^3*a^10*b^4 - 16*C^3*a^11*b^3 - 192*A^2*B*a*b^13 + 192*A*B^2*a^2*b^12 - 288*A*B^2*a^3*b^11 + 288*A*B^2*a^4*b^10 - 264*A*B^2*a^5*b^9 + 168*A*B^2*a^6*b^8 - 120*A*B^2*a^7*b^7 + 48*A*B^2*a^8*b^6 - 24*A*B^2*a^9*b^5 + 288*A^2*B*a^2*b^12 - 288*A^2*B*a^3*b^11 + 288*A^2*B*a^4*b^10 - 240*A^2*B*a^5*b^9 + 192*A^2*B*a^6*b^8 - 96*A^2*B*a^7*b^7 + 57*A^2*B*a^8*b^6 - 18*A^2*B*a^9*b^5 + 9*A^2*B*a^10*b^4 + 192*A*C^2*a^4*b^10 - 288*A*C^2*a^5*b^9 + 288*A*C^2*a^6*b^8 - 264*A*C^2*a^7*b^7 + 168*A*C^2*a^8*b^6 - 120*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 - 24*A*C^2*a^11*b^3 + 192*A^2*C*a^2*b^12 - 288*A^2*C*a^3*b^11 + 288*A^2*C*a^4*b^10 - 288*A^2*C*a^5*b^9 + 240*A^2*C*a^6*b^8 - 192*A^2*C*a^7*b^7 + 96*A^2*C*a^8*b^6 - 57*A^2*C*a^9*b^5 + 18*A^2*C*a^10*b^4 - 9*A^2*C*a^11*b^3 - 192*B*C^2*a^5*b^9 + 288*B*C^2*a^6*b^8 - 288*B*C^2*a^7*b^7 + 240*B*C^2*a^8*b^6 - 96*B*C^2*a^9*b^5 + 48*B*C^2*a^10*b^4 + 192*B^2*C*a^4*b^10 - 288*B^2*C*a^5*b^9 + 288*B^2*C*a^6*b^8 - 240*B^2*C*a^7*b^7 + 96*B^2*C*a^8*b^6 - 48*B^2*C*a^9*b^5 - 384*A*B*C*a^3*b^11 + 576*A*B*C*a^4*b^10 - 576*A*B*C*a^5*b^9 + 528*A*B*C*a^6*b^8 - 336*A*B*C*a^7*b^7 + 240*A*B*C*a^8*b^6 - 96*A*B*C*a^9*b^5 + 48*A*B*C*a^10*b^4)/a^12 - (b^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) + (b^3*(-(a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 + (b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2) + (b^3*(-(a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(9*A^2*a^11 - 128*A^2*b^11 + 16*C^2*a^11 + 256*A^2*a*b^10 - 27*A^2*a^10*b - 48*C^2*a^10*b - 256*A^2*a^2*b^9 + 256*A^2*a^3*b^8 - 256*A^2*a^4*b^7 + 256*A^2*a^5*b^6 - 216*A^2*a^6*b^5 + 136*A^2*a^7*b^4 - 81*A^2*a^8*b^3 + 51*A^2*a^9*b^2 - 128*B^2*a^2*b^9 + 256*B^2*a^3*b^8 - 256*B^2*a^4*b^7 + 256*B^2*a^5*b^6 - 208*B^2*a^6*b^5 + 112*B^2*a^7*b^4 - 48*B^2*a^8*b^3 + 16*B^2*a^9*b^2 - 128*C^2*a^4*b^7 + 256*C^2*a^5*b^6 - 256*C^2*a^6*b^5 + 256*C^2*a^7*b^4 - 208*C^2*a^8*b^3 + 112*C^2*a^9*b^2 + 24*A*C*a^11 + 256*A*B*a*b^10 - 24*A*B*a^10*b - 72*A*C*a^10*b - 32*B*C*a^10*b - 512*A*B*a^2*b^9 + 512*A*B*a^3*b^8 - 512*A*B*a^4*b^7 + 464*A*B*a^5*b^6 - 368*A*B*a^6*b^5 + 264*A*B*a^7*b^4 - 152*A*B*a^8*b^3 + 72*A*B*a^9*b^2 - 256*A*C*a^2*b^9 + 512*A*C*a^3*b^8 - 512*A*C*a^4*b^7 + 512*A*C*a^5*b^6 - 464*A*C*a^6*b^5 + 368*A*C*a^7*b^4 - 264*A*C*a^8*b^3 + 152*A*C*a^9*b^2 + 256*B*C*a^3*b^8 - 512*B*C*a^4*b^7 + 512*B*C*a^5*b^6 - 512*B*C*a^6*b^5 + 416*B*C*a^7*b^4 - 224*B*C*a^8*b^3 + 96*B*C*a^9*b^2))/(2*a^8) - (b^3*(-(a + b)*(a - b))^(1/2)*((12*A*a^16 + 16*C*a^16 + 32*A*a^10*b^6 - 48*A*a^11*b^5 + 16*A*a^12*b^4 - 4*A*a^13*b^3 + 4*A*a^14*b^2 - 32*B*a^11*b^5 + 48*B*a^12*b^4 - 16*B*a^13*b^3 + 16*B*a^14*b^2 + 32*C*a^12*b^4 - 48*C*a^13*b^3 + 16*C*a^14*b^2 - 12*A*a^15*b - 16*B*a^15*b - 16*C*a^15*b)/a^12 - (b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2))*(A*b^2 + C*a^2 - B*a*b))/(a^7 - a^5*b^2)))*(-(a + b)*(a - b))^(1/2)*(A*b^2 + C*a^2 - B*a*b)*2i)/(d*(a^7 - a^5*b^2))","B"
986,1,11768,398,13.282443,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^5+B\,b^5-8\,C\,a^5+2\,C\,b^5-2\,A\,a^2\,b^3-4\,A\,a^3\,b^2-5\,B\,a^2\,b^3+3\,B\,a^3\,b^2+2\,C\,a^2\,b^3+6\,C\,a^3\,b^2+2\,A\,a\,b^4-3\,B\,a\,b^4+6\,B\,a^4\,b-4\,C\,a^4\,b\right)}{b^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,B\,b^5-6\,A\,b^5+72\,C\,a^5+2\,C\,b^5+6\,A\,a^2\,b^3+36\,A\,a^3\,b^2+33\,B\,a^2\,b^3-9\,B\,a^3\,b^2-14\,C\,a^2\,b^3-38\,C\,a^3\,b^2-18\,A\,a\,b^4+9\,B\,a\,b^4-54\,B\,a^4\,b-16\,C\,a\,b^4+12\,C\,a^4\,b\right)}{3\,b^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,b^5-3\,B\,b^5-72\,C\,a^5-6\,A\,b^5+6\,A\,a^2\,b^3-36\,A\,a^3\,b^2-33\,B\,a^2\,b^3-9\,B\,a^3\,b^2-14\,C\,a^2\,b^3+38\,C\,a^3\,b^2+18\,A\,a\,b^4+9\,B\,a\,b^4+54\,B\,a^4\,b+16\,C\,a\,b^4+12\,C\,a^4\,b\right)}{3\,b^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,b^5-B\,b^5+8\,C\,a^5+2\,C\,b^5-2\,A\,a^2\,b^3+4\,A\,a^3\,b^2+5\,B\,a^2\,b^3+3\,B\,a^3\,b^2+2\,C\,a^2\,b^3-6\,C\,a^3\,b^2-2\,A\,a\,b^4-3\,B\,a\,b^4-6\,B\,a^4\,b-4\,C\,a^4\,b\right)}{b^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(4\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a+2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}-\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5}}{\frac{16\,\left(32\,A^3\,a^8\,b^6-16\,A^3\,a^7\,b^7-80\,A^3\,a^6\,b^8+24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}-144\,A^2\,B\,a^9\,b^5+72\,A^2\,B\,a^8\,b^6+336\,A^2\,B\,a^7\,b^7-108\,A^2\,B\,a^6\,b^8-168\,A^2\,B\,a^5\,b^9+6\,A^2\,B\,a^4\,b^{10}-24\,A^2\,B\,a^3\,b^{11}+192\,A^2\,C\,a^{10}\,b^4-96\,A^2\,C\,a^9\,b^5-432\,A^2\,C\,a^8\,b^6+144\,A^2\,C\,a^7\,b^7+192\,A^2\,C\,a^6\,b^8-12\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}+216\,A\,B^2\,a^{10}\,b^4-108\,A\,B^2\,a^9\,b^5-468\,A\,B^2\,a^8\,b^6+162\,A\,B^2\,a^7\,b^7+186\,A\,B^2\,a^6\,b^8-15\,A\,B^2\,a^5\,b^9+63\,A\,B^2\,a^4\,b^{10}-3\,A\,B^2\,a^3\,b^{11}+3\,A\,B^2\,a^2\,b^{12}-576\,A\,B\,C\,a^{11}\,b^3+288\,A\,B\,C\,a^{10}\,b^4+1200\,A\,B\,C\,a^9\,b^5-432\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7+48\,A\,B\,C\,a^6\,b^8-204\,A\,B\,C\,a^5\,b^9+12\,A\,B\,C\,a^4\,b^{10}-12\,A\,B\,C\,a^3\,b^{11}+384\,A\,C^2\,a^{12}\,b^2-192\,A\,C^2\,a^{11}\,b^3-768\,A\,C^2\,a^{10}\,b^4+288\,A\,C^2\,a^9\,b^5+216\,A\,C^2\,a^8\,b^6-36\,A\,C^2\,a^7\,b^7+156\,A\,C^2\,a^6\,b^8-12\,A\,C^2\,a^5\,b^9+12\,A\,C^2\,a^4\,b^{10}-108\,B^3\,a^{11}\,b^3+54\,B^3\,a^{10}\,b^4+216\,B^3\,a^9\,b^5-81\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7+9\,B^3\,a^6\,b^8-41\,B^3\,a^5\,b^9+4\,B^3\,a^4\,b^{10}-4\,B^3\,a^3\,b^{11}+432\,B^2\,C\,a^{12}\,b^2-216\,B^2\,C\,a^{11}\,b^3-828\,B^2\,C\,a^{10}\,b^4+324\,B^2\,C\,a^9\,b^5+192\,B^2\,C\,a^8\,b^6-39\,B^2\,C\,a^7\,b^7+183\,B^2\,C\,a^6\,b^8-21\,B^2\,C\,a^5\,b^9+21\,B^2\,C\,a^4\,b^{10}-576\,B\,C^2\,a^{13}\,b+288\,B\,C^2\,a^{12}\,b^2+1056\,B\,C^2\,a^{11}\,b^3-432\,B\,C^2\,a^{10}\,b^4-180\,B\,C^2\,a^9\,b^5+54\,B\,C^2\,a^8\,b^6-264\,B\,C^2\,a^7\,b^7+36\,B\,C^2\,a^6\,b^8-36\,B\,C^2\,a^5\,b^9+256\,C^3\,a^{14}-128\,C^3\,a^{13}\,b-448\,C^3\,a^{12}\,b^2+192\,C^3\,a^{11}\,b^3+48\,C^3\,a^{10}\,b^4-24\,C^3\,a^9\,b^5+124\,C^3\,a^8\,b^6-20\,C^3\,a^7\,b^7+20\,C^3\,a^6\,b^8\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)}{b^5}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)}{b^5}}\right)\,\left(\frac{B\,b^3\,1{}\mathrm{i}}{2}-C\,a^3\,4{}\mathrm{i}-b^2\,\left(A\,a\,2{}\mathrm{i}+C\,a\,1{}\mathrm{i}\right)+B\,a^2\,b\,3{}\mathrm{i}\right)\,2{}\mathrm{i}}{b^5\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a^2\,\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)\,1{}\mathrm{i}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^2\,\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)\,1{}\mathrm{i}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}{\frac{16\,\left(32\,A^3\,a^8\,b^6-16\,A^3\,a^7\,b^7-80\,A^3\,a^6\,b^8+24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}-144\,A^2\,B\,a^9\,b^5+72\,A^2\,B\,a^8\,b^6+336\,A^2\,B\,a^7\,b^7-108\,A^2\,B\,a^6\,b^8-168\,A^2\,B\,a^5\,b^9+6\,A^2\,B\,a^4\,b^{10}-24\,A^2\,B\,a^3\,b^{11}+192\,A^2\,C\,a^{10}\,b^4-96\,A^2\,C\,a^9\,b^5-432\,A^2\,C\,a^8\,b^6+144\,A^2\,C\,a^7\,b^7+192\,A^2\,C\,a^6\,b^8-12\,A^2\,C\,a^5\,b^9+48\,A^2\,C\,a^4\,b^{10}+216\,A\,B^2\,a^{10}\,b^4-108\,A\,B^2\,a^9\,b^5-468\,A\,B^2\,a^8\,b^6+162\,A\,B^2\,a^7\,b^7+186\,A\,B^2\,a^6\,b^8-15\,A\,B^2\,a^5\,b^9+63\,A\,B^2\,a^4\,b^{10}-3\,A\,B^2\,a^3\,b^{11}+3\,A\,B^2\,a^2\,b^{12}-576\,A\,B\,C\,a^{11}\,b^3+288\,A\,B\,C\,a^{10}\,b^4+1200\,A\,B\,C\,a^9\,b^5-432\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7+48\,A\,B\,C\,a^6\,b^8-204\,A\,B\,C\,a^5\,b^9+12\,A\,B\,C\,a^4\,b^{10}-12\,A\,B\,C\,a^3\,b^{11}+384\,A\,C^2\,a^{12}\,b^2-192\,A\,C^2\,a^{11}\,b^3-768\,A\,C^2\,a^{10}\,b^4+288\,A\,C^2\,a^9\,b^5+216\,A\,C^2\,a^8\,b^6-36\,A\,C^2\,a^7\,b^7+156\,A\,C^2\,a^6\,b^8-12\,A\,C^2\,a^5\,b^9+12\,A\,C^2\,a^4\,b^{10}-108\,B^3\,a^{11}\,b^3+54\,B^3\,a^{10}\,b^4+216\,B^3\,a^9\,b^5-81\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7+9\,B^3\,a^6\,b^8-41\,B^3\,a^5\,b^9+4\,B^3\,a^4\,b^{10}-4\,B^3\,a^3\,b^{11}+432\,B^2\,C\,a^{12}\,b^2-216\,B^2\,C\,a^{11}\,b^3-828\,B^2\,C\,a^{10}\,b^4+324\,B^2\,C\,a^9\,b^5+192\,B^2\,C\,a^8\,b^6-39\,B^2\,C\,a^7\,b^7+183\,B^2\,C\,a^6\,b^8-21\,B^2\,C\,a^5\,b^9+21\,B^2\,C\,a^4\,b^{10}-576\,B\,C^2\,a^{13}\,b+288\,B\,C^2\,a^{12}\,b^2+1056\,B\,C^2\,a^{11}\,b^3-432\,B\,C^2\,a^{10}\,b^4-180\,B\,C^2\,a^9\,b^5+54\,B\,C^2\,a^8\,b^6-264\,B\,C^2\,a^7\,b^7+36\,B\,C^2\,a^6\,b^8-36\,B\,C^2\,a^5\,b^9+256\,C^3\,a^{14}-128\,C^3\,a^{13}\,b-448\,C^3\,a^{12}\,b^2+192\,C^3\,a^{11}\,b^3+48\,C^3\,a^{10}\,b^4-24\,C^3\,a^9\,b^5+124\,C^3\,a^8\,b^6-20\,C^3\,a^7\,b^7+20\,C^3\,a^6\,b^8\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a^2\,\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}-\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^4-32\,A^2\,a^7\,b^5-64\,A^2\,a^6\,b^6+64\,A^2\,a^5\,b^7+20\,A^2\,a^4\,b^8-32\,A^2\,a^3\,b^9+16\,A^2\,a^2\,b^{10}-96\,A\,B\,a^9\,b^3+96\,A\,B\,a^8\,b^4+176\,A\,B\,a^7\,b^5-176\,A\,B\,a^6\,b^6-40\,A\,B\,a^5\,b^7+64\,A\,B\,a^4\,b^8-40\,A\,B\,a^3\,b^9+16\,A\,B\,a^2\,b^{10}-8\,A\,B\,a\,b^{11}+128\,A\,C\,a^{10}\,b^2-128\,A\,C\,a^9\,b^3-224\,A\,C\,a^8\,b^4+224\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6-64\,A\,C\,a^5\,b^7+48\,A\,C\,a^4\,b^8-32\,A\,C\,a^3\,b^9+16\,A\,C\,a^2\,b^{10}+72\,B^2\,a^{10}\,b^2-72\,B^2\,a^9\,b^3-120\,B^2\,a^8\,b^4+120\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6-26\,B^2\,a^5\,b^7+23\,B^2\,a^4\,b^8-20\,B^2\,a^3\,b^9+11\,B^2\,a^2\,b^{10}-2\,B^2\,a\,b^{11}+B^2\,b^{12}-192\,B\,C\,a^{11}\,b+192\,B\,C\,a^{10}\,b^2+304\,B\,C\,a^9\,b^3-304\,B\,C\,a^8\,b^4-28\,B\,C\,a^7\,b^5+40\,B\,C\,a^6\,b^6-52\,B\,C\,a^5\,b^7+64\,B\,C\,a^4\,b^8-36\,B\,C\,a^3\,b^9+8\,B\,C\,a^2\,b^{10}-4\,B\,C\,a\,b^{11}+128\,C^2\,a^{12}-128\,C^2\,a^{11}\,b-192\,C^2\,a^{10}\,b^2+192\,C^2\,a^9\,b^3+8\,C^2\,a^8\,b^4-8\,C^2\,a^7\,b^5+28\,C^2\,a^6\,b^6-48\,C^2\,a^5\,b^7+28\,C^2\,a^4\,b^8-8\,C^2\,a^3\,b^9+4\,C^2\,a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^2\,\left(\frac{8\,\left(2\,B\,b^{18}+12\,A\,a^2\,b^{16}+12\,A\,a^3\,b^{15}-20\,A\,a^4\,b^{14}-4\,A\,a^5\,b^{13}+8\,A\,a^6\,b^{12}+6\,B\,a^2\,b^{16}-16\,B\,a^3\,b^{15}-14\,B\,a^4\,b^{14}+28\,B\,a^5\,b^{13}+6\,B\,a^6\,b^{12}-12\,B\,a^7\,b^{11}-4\,C\,a^3\,b^{15}+20\,C\,a^4\,b^{14}+16\,C\,a^5\,b^{13}-36\,C\,a^6\,b^{12}-8\,C\,a^7\,b^{11}+16\,C\,a^8\,b^{10}-8\,A\,a\,b^{17}-4\,C\,a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^{10}+8\,a^5\,b^{11}+16\,a^4\,b^{12}-16\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-4\,C\,a^4-2\,A\,a^2\,b^2+5\,C\,a^2\,b^2-4\,B\,a\,b^3+3\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(2*A*b^5 + B*b^5 - 8*C*a^5 + 2*C*b^5 - 2*A*a^2*b^3 - 4*A*a^3*b^2 - 5*B*a^2*b^3 + 3*B*a^3*b^2 + 2*C*a^2*b^3 + 6*C*a^3*b^2 + 2*A*a*b^4 - 3*B*a*b^4 + 6*B*a^4*b - 4*C*a^4*b))/(b^4*(a + b)*(a - b)) - (tan(c/2 + (d*x)/2)^3*(3*B*b^5 - 6*A*b^5 + 72*C*a^5 + 2*C*b^5 + 6*A*a^2*b^3 + 36*A*a^3*b^2 + 33*B*a^2*b^3 - 9*B*a^3*b^2 - 14*C*a^2*b^3 - 38*C*a^3*b^2 - 18*A*a*b^4 + 9*B*a*b^4 - 54*B*a^4*b - 16*C*a*b^4 + 12*C*a^4*b))/(3*b^4*(a + b)*(a - b)) + (tan(c/2 + (d*x)/2)^5*(2*C*b^5 - 3*B*b^5 - 72*C*a^5 - 6*A*b^5 + 6*A*a^2*b^3 - 36*A*a^3*b^2 - 33*B*a^2*b^3 - 9*B*a^3*b^2 - 14*C*a^2*b^3 + 38*C*a^3*b^2 + 18*A*a*b^4 + 9*B*a*b^4 + 54*B*a^4*b + 16*C*a*b^4 + 12*C*a^4*b))/(3*b^4*(a + b)*(a - b)) - (tan(c/2 + (d*x)/2)^7*(2*A*b^5 - B*b^5 + 8*C*a^5 + 2*C*b^5 - 2*A*a^2*b^3 + 4*A*a^3*b^2 + 5*B*a^2*b^3 + 3*B*a^3*b^2 + 2*C*a^2*b^3 - 6*C*a^3*b^2 - 2*A*a*b^4 - 3*B*a*b^4 - 6*B*a^4*b - 4*C*a^4*b))/(b^4*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^8*(a - b) + tan(c/2 + (d*x)/2)^2*(4*a + 2*b) + tan(c/2 + (d*x)/2)^6*(4*a - 2*b) + 6*a*tan(c/2 + (d*x)/2)^4)) - (atan(((((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*tan(c/2 + (d*x)/2)*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i))/b^5 + (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i)*1i)/b^5 - (((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*tan(c/2 + (d*x)/2)*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i))/b^5 - (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i)*1i)/b^5)/((16*(256*C^3*a^14 - 128*C^3*a^13*b + 48*A^3*a^4*b^10 + 24*A^3*a^5*b^9 - 80*A^3*a^6*b^8 - 16*A^3*a^7*b^7 + 32*A^3*a^8*b^6 - 4*B^3*a^3*b^11 + 4*B^3*a^4*b^10 - 41*B^3*a^5*b^9 + 9*B^3*a^6*b^8 - 63*B^3*a^7*b^7 - 81*B^3*a^8*b^6 + 216*B^3*a^9*b^5 + 54*B^3*a^10*b^4 - 108*B^3*a^11*b^3 + 20*C^3*a^6*b^8 - 20*C^3*a^7*b^7 + 124*C^3*a^8*b^6 - 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 + 192*C^3*a^11*b^3 - 448*C^3*a^12*b^2 - 576*B*C^2*a^13*b + 3*A*B^2*a^2*b^12 - 3*A*B^2*a^3*b^11 + 63*A*B^2*a^4*b^10 - 15*A*B^2*a^5*b^9 + 186*A*B^2*a^6*b^8 + 162*A*B^2*a^7*b^7 - 468*A*B^2*a^8*b^6 - 108*A*B^2*a^9*b^5 + 216*A*B^2*a^10*b^4 - 24*A^2*B*a^3*b^11 + 6*A^2*B*a^4*b^10 - 168*A^2*B*a^5*b^9 - 108*A^2*B*a^6*b^8 + 336*A^2*B*a^7*b^7 + 72*A^2*B*a^8*b^6 - 144*A^2*B*a^9*b^5 + 12*A*C^2*a^4*b^10 - 12*A*C^2*a^5*b^9 + 156*A*C^2*a^6*b^8 - 36*A*C^2*a^7*b^7 + 216*A*C^2*a^8*b^6 + 288*A*C^2*a^9*b^5 - 768*A*C^2*a^10*b^4 - 192*A*C^2*a^11*b^3 + 384*A*C^2*a^12*b^2 + 48*A^2*C*a^4*b^10 - 12*A^2*C*a^5*b^9 + 192*A^2*C*a^6*b^8 + 144*A^2*C*a^7*b^7 - 432*A^2*C*a^8*b^6 - 96*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4 - 36*B*C^2*a^5*b^9 + 36*B*C^2*a^6*b^8 - 264*B*C^2*a^7*b^7 + 54*B*C^2*a^8*b^6 - 180*B*C^2*a^9*b^5 - 432*B*C^2*a^10*b^4 + 1056*B*C^2*a^11*b^3 + 288*B*C^2*a^12*b^2 + 21*B^2*C*a^4*b^10 - 21*B^2*C*a^5*b^9 + 183*B^2*C*a^6*b^8 - 39*B^2*C*a^7*b^7 + 192*B^2*C*a^8*b^6 + 324*B^2*C*a^9*b^5 - 828*B^2*C*a^10*b^4 - 216*B^2*C*a^11*b^3 + 432*B^2*C*a^12*b^2 - 12*A*B*C*a^3*b^11 + 12*A*B*C*a^4*b^10 - 204*A*B*C*a^5*b^9 + 48*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 - 432*A*B*C*a^8*b^6 + 1200*A*B*C*a^9*b^5 + 288*A*B*C*a^10*b^4 - 576*A*B*C*a^11*b^3))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*tan(c/2 + (d*x)/2)*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i))/b^5 + (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i))/b^5 + (((((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*tan(c/2 + (d*x)/2)*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10))/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i))/b^5 - (8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i))/b^5))*((B*b^3*1i)/2 - C*a^3*4i - b^2*(A*a*2i + C*a*1i) + B*a^2*b*3i)*2i)/(b^5*d) - (a^2*atan(((a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b)*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) + (a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b)*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))/((16*(256*C^3*a^14 - 128*C^3*a^13*b + 48*A^3*a^4*b^10 + 24*A^3*a^5*b^9 - 80*A^3*a^6*b^8 - 16*A^3*a^7*b^7 + 32*A^3*a^8*b^6 - 4*B^3*a^3*b^11 + 4*B^3*a^4*b^10 - 41*B^3*a^5*b^9 + 9*B^3*a^6*b^8 - 63*B^3*a^7*b^7 - 81*B^3*a^8*b^6 + 216*B^3*a^9*b^5 + 54*B^3*a^10*b^4 - 108*B^3*a^11*b^3 + 20*C^3*a^6*b^8 - 20*C^3*a^7*b^7 + 124*C^3*a^8*b^6 - 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 + 192*C^3*a^11*b^3 - 448*C^3*a^12*b^2 - 576*B*C^2*a^13*b + 3*A*B^2*a^2*b^12 - 3*A*B^2*a^3*b^11 + 63*A*B^2*a^4*b^10 - 15*A*B^2*a^5*b^9 + 186*A*B^2*a^6*b^8 + 162*A*B^2*a^7*b^7 - 468*A*B^2*a^8*b^6 - 108*A*B^2*a^9*b^5 + 216*A*B^2*a^10*b^4 - 24*A^2*B*a^3*b^11 + 6*A^2*B*a^4*b^10 - 168*A^2*B*a^5*b^9 - 108*A^2*B*a^6*b^8 + 336*A^2*B*a^7*b^7 + 72*A^2*B*a^8*b^6 - 144*A^2*B*a^9*b^5 + 12*A*C^2*a^4*b^10 - 12*A*C^2*a^5*b^9 + 156*A*C^2*a^6*b^8 - 36*A*C^2*a^7*b^7 + 216*A*C^2*a^8*b^6 + 288*A*C^2*a^9*b^5 - 768*A*C^2*a^10*b^4 - 192*A*C^2*a^11*b^3 + 384*A*C^2*a^12*b^2 + 48*A^2*C*a^4*b^10 - 12*A^2*C*a^5*b^9 + 192*A^2*C*a^6*b^8 + 144*A^2*C*a^7*b^7 - 432*A^2*C*a^8*b^6 - 96*A^2*C*a^9*b^5 + 192*A^2*C*a^10*b^4 - 36*B*C^2*a^5*b^9 + 36*B*C^2*a^6*b^8 - 264*B*C^2*a^7*b^7 + 54*B*C^2*a^8*b^6 - 180*B*C^2*a^9*b^5 - 432*B*C^2*a^10*b^4 + 1056*B*C^2*a^11*b^3 + 288*B*C^2*a^12*b^2 + 21*B^2*C*a^4*b^10 - 21*B^2*C*a^5*b^9 + 183*B^2*C*a^6*b^8 - 39*B^2*C*a^7*b^7 + 192*B^2*C*a^8*b^6 + 324*B^2*C*a^9*b^5 - 828*B^2*C*a^10*b^4 - 216*B^2*C*a^11*b^3 + 432*B^2*C*a^12*b^2 - 12*A*B*C*a^3*b^11 + 12*A*B*C*a^4*b^10 - 204*A*B*C*a^5*b^9 + 48*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 - 432*A*B*C*a^8*b^6 + 1200*A*B*C*a^9*b^5 + 288*A*B*C*a^10*b^4 - 576*A*B*C*a^11*b^3))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) - (a^2*((8*tan(c/2 + (d*x)/2)*(B^2*b^12 + 128*C^2*a^12 - 2*B^2*a*b^11 - 128*C^2*a^11*b + 16*A^2*a^2*b^10 - 32*A^2*a^3*b^9 + 20*A^2*a^4*b^8 + 64*A^2*a^5*b^7 - 64*A^2*a^6*b^6 - 32*A^2*a^7*b^5 + 32*A^2*a^8*b^4 + 11*B^2*a^2*b^10 - 20*B^2*a^3*b^9 + 23*B^2*a^4*b^8 - 26*B^2*a^5*b^7 + 17*B^2*a^6*b^6 + 120*B^2*a^7*b^5 - 120*B^2*a^8*b^4 - 72*B^2*a^9*b^3 + 72*B^2*a^10*b^2 + 4*C^2*a^2*b^10 - 8*C^2*a^3*b^9 + 28*C^2*a^4*b^8 - 48*C^2*a^5*b^7 + 28*C^2*a^6*b^6 - 8*C^2*a^7*b^5 + 8*C^2*a^8*b^4 + 192*C^2*a^9*b^3 - 192*C^2*a^10*b^2 - 8*A*B*a*b^11 - 4*B*C*a*b^11 - 192*B*C*a^11*b + 16*A*B*a^2*b^10 - 40*A*B*a^3*b^9 + 64*A*B*a^4*b^8 - 40*A*B*a^5*b^7 - 176*A*B*a^6*b^6 + 176*A*B*a^7*b^5 + 96*A*B*a^8*b^4 - 96*A*B*a^9*b^3 + 16*A*C*a^2*b^10 - 32*A*C*a^3*b^9 + 48*A*C*a^4*b^8 - 64*A*C*a^5*b^7 + 40*A*C*a^6*b^6 + 224*A*C*a^7*b^5 - 224*A*C*a^8*b^4 - 128*A*C*a^9*b^3 + 128*A*C*a^10*b^2 + 8*B*C*a^2*b^10 - 36*B*C*a^3*b^9 + 64*B*C*a^4*b^8 - 52*B*C*a^5*b^7 + 40*B*C*a^6*b^6 - 28*B*C*a^7*b^5 - 304*B*C*a^8*b^4 + 304*B*C*a^9*b^3 + 192*B*C*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^2*((8*(2*B*b^18 + 12*A*a^2*b^16 + 12*A*a^3*b^15 - 20*A*a^4*b^14 - 4*A*a^5*b^13 + 8*A*a^6*b^12 + 6*B*a^2*b^16 - 16*B*a^3*b^15 - 14*B*a^4*b^14 + 28*B*a^5*b^13 + 6*B*a^6*b^12 - 12*B*a^7*b^11 - 4*C*a^3*b^15 + 20*C*a^4*b^14 + 16*C*a^5*b^13 - 36*C*a^6*b^12 - 8*C*a^7*b^11 + 16*C*a^8*b^10 - 8*A*a*b^17 - 4*C*a*b^17))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^15 - 8*a^2*b^14 - 16*a^3*b^13 + 16*a^4*b^12 + 8*a^5*b^11 - 8*a^6*b^10)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 4*C*a^4 - 2*A*a^2*b^2 + 5*C*a^2*b^2 - 4*B*a*b^3 + 3*B*a^3*b)*2i)/(d*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))","B"
987,1,10024,303,12.381636,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^4+6\,C\,a^4+C\,b^4+2\,A\,a^2\,b^2-2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b-3\,C\,a\,b^3+3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,C\,a^4-2\,B\,b^4+C\,b^4+2\,A\,a^2\,b^2+2\,B\,a^2\,b^2-5\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b+3\,C\,a\,b^3-3\,C\,a^3\,b\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,C\,a^4-C\,b^4+2\,A\,a^2\,b^2-3\,C\,a^2\,b^2+2\,B\,a\,b^3-4\,B\,a^3\,b\right)}{b\,\left(a\,b^2-b^3\right)\,\left(a+b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(3\,a+b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^4}-\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^4}}{-\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}-24\,A^2\,B\,a^6\,b^5+20\,A^2\,B\,a^5\,b^6+68\,A^2\,B\,a^4\,b^7-36\,A^2\,B\,a^3\,b^8-44\,A^2\,B\,a^2\,b^9+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+48\,A\,B^2\,a^7\,b^4-32\,A\,B^2\,a^6\,b^5-128\,A\,B^2\,a^5\,b^6+52\,A\,B^2\,a^4\,b^7+80\,A\,B^2\,a^3\,b^8-144\,A\,B\,C\,a^8\,b^3+96\,A\,B\,C\,a^7\,b^4+360\,A\,B\,C\,a^6\,b^5-152\,A\,B\,C\,a^5\,b^6-188\,A\,B\,C\,a^4\,b^7+4\,A\,B\,C\,a^3\,b^8-28\,A\,B\,C\,a^2\,b^9+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}+\frac{\left(\frac{\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^4}}\right)\,\left(3{}\mathrm{i}\,C\,a^2-2{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,2{}\mathrm{i}}{b^4\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(4\,A^3\,a^5\,b^6-4\,A^3\,a^4\,b^7-12\,A^3\,a^3\,b^8+8\,A^3\,a^2\,b^9+8\,A^3\,a\,b^{10}-24\,A^2\,B\,a^6\,b^5+20\,A^2\,B\,a^5\,b^6+68\,A^2\,B\,a^4\,b^7-36\,A^2\,B\,a^3\,b^8-44\,A^2\,B\,a^2\,b^9+36\,A^2\,C\,a^7\,b^4-30\,A^2\,C\,a^6\,b^5-96\,A^2\,C\,a^5\,b^6+52\,A^2\,C\,a^4\,b^7+52\,A^2\,C\,a^3\,b^8+8\,A^2\,C\,a\,b^{10}+48\,A\,B^2\,a^7\,b^4-32\,A\,B^2\,a^6\,b^5-128\,A\,B^2\,a^5\,b^6+52\,A\,B^2\,a^4\,b^7+80\,A\,B^2\,a^3\,b^8-144\,A\,B\,C\,a^8\,b^3+96\,A\,B\,C\,a^7\,b^4+360\,A\,B\,C\,a^6\,b^5-152\,A\,B\,C\,a^5\,b^6-188\,A\,B\,C\,a^4\,b^7+4\,A\,B\,C\,a^3\,b^8-28\,A\,B\,C\,a^2\,b^9+108\,A\,C^2\,a^9\,b^2-72\,A\,C^2\,a^8\,b^3-252\,A\,C^2\,a^7\,b^4+111\,A\,C^2\,a^6\,b^5+105\,A\,C^2\,a^5\,b^6-5\,A\,C^2\,a^4\,b^7+37\,A\,C^2\,a^3\,b^8-2\,A\,C^2\,a^2\,b^9+2\,A\,C^2\,a\,b^{10}-32\,B^3\,a^8\,b^3+16\,B^3\,a^7\,b^4+80\,B^3\,a^6\,b^5-24\,B^3\,a^5\,b^6-48\,B^3\,a^4\,b^7+144\,B^2\,C\,a^9\,b^2-72\,B^2\,C\,a^8\,b^3-336\,B^2\,C\,a^7\,b^4+108\,B^2\,C\,a^6\,b^5+168\,B^2\,C\,a^5\,b^6-6\,B^2\,C\,a^4\,b^7+24\,B^2\,C\,a^3\,b^8-216\,B\,C^2\,a^{10}\,b+108\,B\,C^2\,a^9\,b^2+468\,B\,C^2\,a^8\,b^3-162\,B\,C^2\,a^7\,b^4-186\,B\,C^2\,a^6\,b^5+15\,B\,C^2\,a^5\,b^6-63\,B\,C^2\,a^4\,b^7+3\,B\,C^2\,a^3\,b^8-3\,B\,C^2\,a^2\,b^9+108\,C^3\,a^{11}-54\,C^3\,a^{10}\,b-216\,C^3\,a^9\,b^2+81\,C^3\,a^8\,b^3+63\,C^3\,a^7\,b^4-9\,C^3\,a^6\,b^5+41\,C^3\,a^5\,b^6-4\,C^3\,a^4\,b^7+4\,C^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^6\,b^4-8\,A^2\,a^5\,b^5-20\,A^2\,a^4\,b^6+16\,A^2\,a^3\,b^7+12\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+4\,A^2\,b^{10}-32\,A\,B\,a^7\,b^3+32\,A\,B\,a^6\,b^4+72\,A\,B\,a^5\,b^5-64\,A\,B\,a^4\,b^6-32\,A\,B\,a^3\,b^7+32\,A\,B\,a^2\,b^8-16\,A\,B\,a\,b^9+48\,A\,C\,a^8\,b^2-48\,A\,C\,a^7\,b^3-100\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5+36\,A\,C\,a^4\,b^6-32\,A\,C\,a^3\,b^7+20\,A\,C\,a^2\,b^8-8\,A\,C\,a\,b^9+4\,A\,C\,b^{10}+32\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3-64\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5+20\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+16\,B^2\,a^2\,b^8-96\,B\,C\,a^9\,b+96\,B\,C\,a^8\,b^2+176\,B\,C\,a^7\,b^3-176\,B\,C\,a^6\,b^4-40\,B\,C\,a^5\,b^5+64\,B\,C\,a^4\,b^6-40\,B\,C\,a^3\,b^7+16\,B\,C\,a^2\,b^8-8\,B\,C\,a\,b^9+72\,C^2\,a^{10}-72\,C^2\,a^9\,b-120\,C^2\,a^8\,b^2+120\,C^2\,a^7\,b^3+17\,C^2\,a^6\,b^4-26\,C^2\,a^5\,b^5+23\,C^2\,a^4\,b^6-20\,C^2\,a^3\,b^7+11\,C^2\,a^2\,b^8-2\,C^2\,a\,b^9+C^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(4\,A\,b^{15}+2\,C\,b^{15}-4\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-4\,A\,a^5\,b^{10}+12\,B\,a^2\,b^{13}+12\,B\,a^3\,b^{12}-20\,B\,a^4\,b^{11}-4\,B\,a^5\,b^{10}+8\,B\,a^6\,b^9+6\,C\,a^2\,b^{13}-16\,C\,a^3\,b^{12}-14\,C\,a^4\,b^{11}+28\,C\,a^5\,b^{10}+6\,C\,a^6\,b^9-12\,C\,a^7\,b^8-8\,A\,a\,b^{14}-8\,B\,a\,b^{14}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,A\,b^4-3\,C\,a^4-A\,a^2\,b^2+4\,C\,a^2\,b^2-3\,B\,a\,b^3+2\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"(atan(-((((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i))/b^4 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i)*1i)/b^4 - (((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i))/b^4 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i)*1i)/b^4)/((((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i))/b^4 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i))/b^4 - (16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 216*B*C^2*a^10*b + 80*A*B^2*a^3*b^8 + 52*A*B^2*a^4*b^7 - 128*A*B^2*a^5*b^6 - 32*A*B^2*a^6*b^5 + 48*A*B^2*a^7*b^4 - 44*A^2*B*a^2*b^9 - 36*A^2*B*a^3*b^8 + 68*A^2*B*a^4*b^7 + 20*A^2*B*a^5*b^6 - 24*A^2*B*a^6*b^5 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4 - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2 - 28*A*B*C*a^2*b^9 + 4*A*B*C*a^3*b^8 - 188*A*B*C*a^4*b^7 - 152*A*B*C*a^5*b^6 + 360*A*B*C*a^6*b^5 + 96*A*B*C*a^7*b^4 - 144*A*B*C*a^8*b^3))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (((((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*tan(c/2 + (d*x)/2)*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6)))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i))/b^4 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i))/b^4))*(C*a^2*3i + b^2*(A*1i + (C*1i)/2) - B*a*b*2i)*2i)/(b^4*d) - ((tan(c/2 + (d*x)/2)*(2*B*b^4 + 6*C*a^4 + C*b^4 + 2*A*a^2*b^2 - 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b - 3*C*a*b^3 + 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(6*C*a^4 - 2*B*b^4 + C*b^4 + 2*A*a^2*b^2 + 2*B*a^2*b^2 - 5*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b + 3*C*a*b^3 - 3*C*a^3*b))/((a*b^3 - b^4)*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(6*C*a^4 - C*b^4 + 2*A*a^2*b^2 - 3*C*a^2*b^2 + 2*B*a*b^3 - 4*B*a^3*b))/(b*(a*b^2 - b^3)*(a + b)))/(d*(a + b + tan(c/2 + (d*x)/2)^2*(3*a + b) + tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*C^3*a^11 + 8*A^3*a*b^10 - 54*C^3*a^10*b + 8*A^3*a^2*b^9 - 12*A^3*a^3*b^8 - 4*A^3*a^4*b^7 + 4*A^3*a^5*b^6 - 48*B^3*a^4*b^7 - 24*B^3*a^5*b^6 + 80*B^3*a^6*b^5 + 16*B^3*a^7*b^4 - 32*B^3*a^8*b^3 + 4*C^3*a^3*b^8 - 4*C^3*a^4*b^7 + 41*C^3*a^5*b^6 - 9*C^3*a^6*b^5 + 63*C^3*a^7*b^4 + 81*C^3*a^8*b^3 - 216*C^3*a^9*b^2 + 2*A*C^2*a*b^10 + 8*A^2*C*a*b^10 - 216*B*C^2*a^10*b + 80*A*B^2*a^3*b^8 + 52*A*B^2*a^4*b^7 - 128*A*B^2*a^5*b^6 - 32*A*B^2*a^6*b^5 + 48*A*B^2*a^7*b^4 - 44*A^2*B*a^2*b^9 - 36*A^2*B*a^3*b^8 + 68*A^2*B*a^4*b^7 + 20*A^2*B*a^5*b^6 - 24*A^2*B*a^6*b^5 - 2*A*C^2*a^2*b^9 + 37*A*C^2*a^3*b^8 - 5*A*C^2*a^4*b^7 + 105*A*C^2*a^5*b^6 + 111*A*C^2*a^6*b^5 - 252*A*C^2*a^7*b^4 - 72*A*C^2*a^8*b^3 + 108*A*C^2*a^9*b^2 + 52*A^2*C*a^3*b^8 + 52*A^2*C*a^4*b^7 - 96*A^2*C*a^5*b^6 - 30*A^2*C*a^6*b^5 + 36*A^2*C*a^7*b^4 - 3*B*C^2*a^2*b^9 + 3*B*C^2*a^3*b^8 - 63*B*C^2*a^4*b^7 + 15*B*C^2*a^5*b^6 - 186*B*C^2*a^6*b^5 - 162*B*C^2*a^7*b^4 + 468*B*C^2*a^8*b^3 + 108*B*C^2*a^9*b^2 + 24*B^2*C*a^3*b^8 - 6*B^2*C*a^4*b^7 + 168*B^2*C*a^5*b^6 + 108*B^2*C*a^6*b^5 - 336*B^2*C*a^7*b^4 - 72*B^2*C*a^8*b^3 + 144*B^2*C*a^9*b^2 - 28*A*B*C*a^2*b^9 + 4*A*B*C*a^3*b^8 - 188*A*B*C*a^4*b^7 - 152*A*B*C*a^5*b^6 + 360*A*B*C*a^6*b^5 + 96*A*B*C*a^7*b^4 - 144*A*B*C*a^8*b^3))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 72*C^2*a^10 + C^2*b^10 - 8*A^2*a*b^9 - 2*C^2*a*b^9 - 72*C^2*a^9*b + 12*A^2*a^2*b^8 + 16*A^2*a^3*b^7 - 20*A^2*a^4*b^6 - 8*A^2*a^5*b^5 + 8*A^2*a^6*b^4 + 16*B^2*a^2*b^8 - 32*B^2*a^3*b^7 + 20*B^2*a^4*b^6 + 64*B^2*a^5*b^5 - 64*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 32*B^2*a^8*b^2 + 11*C^2*a^2*b^8 - 20*C^2*a^3*b^7 + 23*C^2*a^4*b^6 - 26*C^2*a^5*b^5 + 17*C^2*a^6*b^4 + 120*C^2*a^7*b^3 - 120*C^2*a^8*b^2 + 4*A*C*b^10 - 16*A*B*a*b^9 - 8*A*C*a*b^9 - 8*B*C*a*b^9 - 96*B*C*a^9*b + 32*A*B*a^2*b^8 - 32*A*B*a^3*b^7 - 64*A*B*a^4*b^6 + 72*A*B*a^5*b^5 + 32*A*B*a^6*b^4 - 32*A*B*a^7*b^3 + 20*A*C*a^2*b^8 - 32*A*C*a^3*b^7 + 36*A*C*a^4*b^6 + 88*A*C*a^5*b^5 - 100*A*C*a^6*b^4 - 48*A*C*a^7*b^3 + 48*A*C*a^8*b^2 + 16*B*C*a^2*b^8 - 40*B*C*a^3*b^7 + 64*B*C*a^4*b^6 - 40*B*C*a^5*b^5 - 176*B*C*a^6*b^4 + 176*B*C*a^7*b^3 + 96*B*C*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(4*A*b^15 + 2*C*b^15 - 4*A*a^2*b^13 + 12*A*a^3*b^12 - 4*A*a^5*b^10 + 12*B*a^2*b^13 + 12*B*a^3*b^12 - 20*B*a^4*b^11 - 4*B*a^5*b^10 + 8*B*a^6*b^9 + 6*C*a^2*b^13 - 16*C*a^3*b^12 - 14*C*a^4*b^11 + 28*C*a^5*b^10 + 6*C*a^6*b^9 - 12*C*a^7*b^8 - 8*A*a*b^14 - 8*B*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/((a*b^8 + b^9 - a^2*b^7 - a^3*b^6)*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(-(a + b)^3*(a - b)^3)^(1/2)*(2*A*b^4 - 3*C*a^4 - A*a^2*b^2 + 4*C*a^2*b^2 - 3*B*a*b^3 + 2*B*a^3*b)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
988,1,3816,168,6.746790,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,C\,a^3-C\,b^3+A\,a\,b^2-B\,a^2\,b-C\,a\,b^2+C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^3+C\,b^3+A\,a\,b^2-B\,a^2\,b-C\,a\,b^2-C\,a^2\,b\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b-2\,C\,a\right)\,1{}\mathrm{i}}{b^3\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(B\,b\,1{}\mathrm{i}-C\,a\,2{}\mathrm{i}\right)}{b^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(-A^2\,B\,b^8+2\,A^2\,C\,a\,b^7-A\,B^2\,a^3\,b^5-A\,B^2\,a^2\,b^6+3\,A\,B^2\,a\,b^7+A\,B^2\,b^8+4\,A\,B\,C\,a^4\,b^4+4\,A\,B\,C\,a^3\,b^5-10\,A\,B\,C\,a^2\,b^6-4\,A\,B\,C\,a\,b^7-4\,A\,C^2\,a^5\,b^3-4\,A\,C^2\,a^4\,b^4+8\,A\,C^2\,a^3\,b^5+4\,A\,C^2\,a^2\,b^6-B^3\,a^5\,b^3+B^3\,a^4\,b^4+3\,B^3\,a^3\,b^5-2\,B^3\,a^2\,b^6-2\,B^3\,a\,b^7+6\,B^2\,C\,a^6\,b^2-5\,B^2\,C\,a^5\,b^3-17\,B^2\,C\,a^4\,b^4+9\,B^2\,C\,a^3\,b^5+11\,B^2\,C\,a^2\,b^6-12\,B\,C^2\,a^7\,b+8\,B\,C^2\,a^6\,b^2+32\,B\,C^2\,a^5\,b^3-13\,B\,C^2\,a^4\,b^4-20\,B\,C^2\,a^3\,b^5+8\,C^3\,a^8-4\,C^3\,a^7\,b-20\,C^3\,a^6\,b^2+6\,C^3\,a^5\,b^3+12\,C^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^8+2\,A\,B\,a^3\,b^5-4\,A\,B\,a\,b^7-4\,A\,C\,a^4\,b^4+6\,A\,C\,a^2\,b^6+2\,B^2\,a^6\,b^2-2\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4+4\,B^2\,a^3\,b^5+3\,B^2\,a^2\,b^6-2\,B^2\,a\,b^7+B^2\,b^8-8\,B\,C\,a^7\,b+8\,B\,C\,a^6\,b^2+18\,B\,C\,a^5\,b^3-16\,B\,C\,a^4\,b^4-8\,B\,C\,a^3\,b^5+8\,B\,C\,a^2\,b^6-4\,B\,C\,a\,b^7+8\,C^2\,a^8-8\,C^2\,a^7\,b-16\,C^2\,a^6\,b^2+16\,C^2\,a^5\,b^3+5\,C^2\,a^4\,b^4-8\,C^2\,a^3\,b^5+4\,C^2\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{\left(\frac{32\,\left(A\,a^2\,b^{10}-B\,b^{12}-A\,b^{12}-A\,a^3\,b^9+B\,a^2\,b^{10}-3\,B\,a^3\,b^9+B\,a^5\,b^7-3\,C\,a^2\,b^{10}-3\,C\,a^3\,b^9+5\,C\,a^4\,b^8+C\,a^5\,b^7-2\,C\,a^6\,b^6+A\,a\,b^{11}+2\,B\,a\,b^{11}+2\,C\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)}{\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,C\,a^4+B\,a^3\,b+3\,C\,a^2\,b^2-2\,B\,a\,b^3+A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)*(2*C*a^3 - C*b^3 + A*a*b^2 - B*a^2*b - C*a*b^2 + C*a^2*b))/(b^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(2*C*a^3 + C*b^3 + A*a*b^2 - B*a^2*b - C*a*b^2 - C*a^2*b))/(b^2*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) + 2*a*tan(c/2 + (d*x)/2)^2)) + (log(tan(c/2 + (d*x)/2) + 1i)*(B*b - 2*C*a)*1i)/(b^3*d) - (log(tan(c/2 + (d*x)/2) - 1i)*(B*b*1i - C*a*2i))/(b^3*d) - (atan((((-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + ((-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*C^3*a^8 + A*B^2*b^8 - A^2*B*b^8 - 2*B^3*a*b^7 - 4*C^3*a^7*b - 2*B^3*a^2*b^6 + 3*B^3*a^3*b^5 + B^3*a^4*b^4 - B^3*a^5*b^3 + 12*C^3*a^4*b^4 + 6*C^3*a^5*b^3 - 20*C^3*a^6*b^2 + 3*A*B^2*a*b^7 + 2*A^2*C*a*b^7 - 12*B*C^2*a^7*b - A*B^2*a^2*b^6 - A*B^2*a^3*b^5 + 4*A*C^2*a^2*b^6 + 8*A*C^2*a^3*b^5 - 4*A*C^2*a^4*b^4 - 4*A*C^2*a^5*b^3 - 20*B*C^2*a^3*b^5 - 13*B*C^2*a^4*b^4 + 32*B*C^2*a^5*b^3 + 8*B*C^2*a^6*b^2 + 11*B^2*C*a^2*b^6 + 9*B^2*C*a^3*b^5 - 17*B^2*C*a^4*b^4 - 5*B^2*C*a^5*b^3 + 6*B^2*C*a^6*b^2 - 4*A*B*C*a*b^7 - 10*A*B*C*a^2*b^6 + 4*A*B*C*a^3*b^5 + 4*A*B*C*a^4*b^4))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - ((-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + ((-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + B^2*b^8 + 8*C^2*a^8 - 2*B^2*a*b^7 - 8*C^2*a^7*b + 3*B^2*a^2*b^6 + 4*B^2*a^3*b^5 - 5*B^2*a^4*b^4 - 2*B^2*a^5*b^3 + 2*B^2*a^6*b^2 + 4*C^2*a^2*b^6 - 8*C^2*a^3*b^5 + 5*C^2*a^4*b^4 + 16*C^2*a^5*b^3 - 16*C^2*a^6*b^2 - 4*A*B*a*b^7 - 4*B*C*a*b^7 - 8*B*C*a^7*b + 2*A*B*a^3*b^5 + 6*A*C*a^2*b^6 - 4*A*C*a^4*b^4 + 8*B*C*a^2*b^6 - 8*B*C*a^3*b^5 - 16*B*C*a^4*b^4 + 18*B*C*a^5*b^3 + 8*B*C*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (((32*(A*a^2*b^10 - B*b^12 - A*b^12 - A*a^3*b^9 + B*a^2*b^10 - 3*B*a^3*b^9 + B*a^5*b^7 - 3*C*a^2*b^10 - 3*C*a^3*b^9 + 5*C*a^4*b^8 + C*a^5*b^7 - 2*C*a^6*b^6 + A*a*b^11 + 2*B*a*b^11 + 2*C*a*b^11))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6))/((a*b^6 + b^7 - a^2*b^5 - a^3*b^4)*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^4 - 2*C*a^4 + 3*C*a^2*b^2 - 2*B*a*b^3 + B*a^3*b)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
989,1,4556,139,9.402192,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^2,x)","\frac{2\,C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}+\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)}{b^2}}{\frac{64\,\left(A^2\,C\,a^2\,b^3-2\,A\,B\,C\,a\,b^4-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}-\frac{C\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{C\,\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)\,32{}\mathrm{i}}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}\right)\,1{}\mathrm{i}}{b^2}\right)\,1{}\mathrm{i}}{b^2}}\right)}{b^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-b^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(A^2\,C\,a^2\,b^3-2\,A\,B\,C\,a\,b^4-A\,C^2\,a^4\,b-A\,C^2\,a^3\,b^2+3\,A\,C^2\,a^2\,b^3+A\,C^2\,a\,b^4+B^2\,C\,b^5+B\,C^2\,a^3\,b^2+B\,C^2\,a^2\,b^3-3\,B\,C^2\,a\,b^4-B\,C^2\,b^5+C^3\,a^5-C^3\,a^4\,b-3\,C^3\,a^3\,b^2+2\,C^3\,a^2\,b^3+2\,C^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^2\,b^4-2\,A\,B\,a\,b^5-2\,A\,C\,a^4\,b^2+4\,A\,C\,a^2\,b^4+B^2\,b^6+2\,B\,C\,a^3\,b^3-4\,B\,C\,a\,b^5+2\,C^2\,a^6-2\,C^2\,a^5\,b-5\,C^2\,a^4\,b^2+4\,C^2\,a^3\,b^3+3\,C^2\,a^2\,b^4-2\,C^2\,a\,b^5+C^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-C\,b^9-A\,a^2\,b^7-A\,a^3\,b^6-B\,b^9+B\,a^2\,b^7-B\,a^3\,b^6+C\,a^2\,b^7-3\,C\,a^3\,b^6+C\,a^5\,b^4+A\,a\,b^8+B\,a\,b^8+2\,C\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,\left(-2\,a^6\,b^4+2\,a^5\,b^5+4\,a^4\,b^6-4\,a^3\,b^7-2\,a^2\,b^8+2\,a\,b^9\right)}{\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(B\,b^3+C\,a^3-A\,a\,b^2-2\,C\,a\,b^2\right)\,2{}\mathrm{i}}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"(2*C*atan(((C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2))/b^2 + (C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2))/b^2)/((64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b - 3*B*C^2*a*b^4 + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2 - 2*A*B*C*a*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2)*1i)/b^2 - (C*((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (C*((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (C*tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2)*1i)/b^2)))/(b^2*d) + (atan(((((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(C^3*a^5 - B*C^2*b^5 + B^2*C*b^5 + 2*C^3*a*b^4 - C^3*a^4*b + 2*C^3*a^2*b^3 - 3*C^3*a^3*b^2 + A*C^2*a*b^4 - A*C^2*a^4*b - 3*B*C^2*a*b^4 + 3*A*C^2*a^2*b^3 - A*C^2*a^3*b^2 + A^2*C*a^2*b^3 + B*C^2*a^2*b^3 + B*C^2*a^3*b^2 - 2*A*B*C*a*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) - (((32*tan(c/2 + (d*x)/2)*(B^2*b^6 + 2*C^2*a^6 + C^2*b^6 - 2*C^2*a*b^5 - 2*C^2*a^5*b + A^2*a^2*b^4 + 3*C^2*a^2*b^4 + 4*C^2*a^3*b^3 - 5*C^2*a^4*b^2 - 2*A*B*a*b^5 - 4*B*C*a*b^5 + 4*A*C*a^2*b^4 - 2*A*C*a^4*b^2 + 2*B*C*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - C*b^9 - A*a^2*b^7 - A*a^3*b^6 - B*b^9 + B*a^2*b^7 - B*a^3*b^6 + C*a^2*b^7 - 3*C*a^3*b^6 + C*a^5*b^4 + A*a*b^8 + B*a*b^8 + 2*C*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(B*b^3 + C*a^3 - A*a*b^2 - 2*C*a*b^2)*2i)/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2 - B*a*b))/(d*(a + b)*(a*b - b^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
990,1,4548,147,9.417068,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^2),x)","-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(C\,a^2-B\,a\,b+A\,b^2\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5-A^2\,B\,a^5-3\,A^2\,B\,a^4\,b+A^2\,B\,a^3\,b^2+A^2\,B\,a^2\,b^3+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,B^2\,a^5-2\,A\,B\,C\,a^4\,b+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}\right)}{a^2}+\frac{A\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{A\,\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)}{a^2}\right)}{a^2}}\right)\,2{}\mathrm{i}}{a^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,A^3\,a^4\,b+2\,A^3\,a^3\,b^2-3\,A^3\,a^2\,b^3-A^3\,a\,b^4+A^3\,b^5-A^2\,B\,a^5-3\,A^2\,B\,a^4\,b+A^2\,B\,a^3\,b^2+A^2\,B\,a^2\,b^3+A^2\,C\,a^4\,b+3\,A^2\,C\,a^3\,b^2-A^2\,C\,a^2\,b^3-A^2\,C\,a\,b^4+A\,B^2\,a^5-2\,A\,B\,C\,a^4\,b+A\,C^2\,a^3\,b^2\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6-2\,A^2\,a^5\,b+3\,A^2\,a^4\,b^2+4\,A^2\,a^3\,b^3-5\,A^2\,a^2\,b^4-2\,A^2\,a\,b^5+2\,A^2\,b^6-4\,A\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+4\,A\,C\,a^4\,b^2-2\,A\,C\,a^2\,b^4+B^2\,a^6-2\,B\,C\,a^5\,b+C^2\,a^4\,b^2\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{\left(\frac{32\,\left(A\,a^4\,b^5-B\,a^9-A\,a^9-3\,A\,a^6\,b^3+A\,a^7\,b^2-B\,a^6\,b^3+B\,a^7\,b^2+C\,a^5\,b^4-C\,a^6\,b^3-C\,a^7\,b^2+2\,A\,a^8\,b+B\,a^8\,b+C\,a^8\,b\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,\left(2\,a^9\,b-2\,a^8\,b^2-4\,a^7\,b^3+4\,a^6\,b^4+2\,a^5\,b^5-2\,a^4\,b^6\right)}{\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(A\,b^3+B\,a^3-2\,A\,a^2\,b-C\,a^2\,b\right)\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"- (A*atan(((A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2)*1i)/a^2 + (A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2)*1i)/a^2)/((64*(A^3*b^5 + A*B^2*a^5 - A^2*B*a^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - 3*A^2*B*a^4*b - A^2*C*a*b^4 + A^2*C*a^4*b + A^2*B*a^2*b^3 + A^2*B*a^3*b^2 + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2 - 2*A*B*C*a^4*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2))/a^2 + (A*((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (A*((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*A*tan(c/2 + (d*x)/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2))))/a^2))/a^2))*2i)/(a^2*d) - (atan(((((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(A^3*b^5 + A*B^2*a^5 - A^2*B*a^5 - A^3*a*b^4 + 2*A^3*a^4*b - 3*A^3*a^2*b^3 + 2*A^3*a^3*b^2 - 3*A^2*B*a^4*b - A^2*C*a*b^4 + A^2*C*a^4*b + A^2*B*a^2*b^3 + A^2*B*a^3*b^2 + A*C^2*a^3*b^2 - A^2*C*a^2*b^3 + 3*A^2*C*a^3*b^2 - 2*A*B*C*a^4*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (((32*tan(c/2 + (d*x)/2)*(A^2*a^6 + 2*A^2*b^6 + B^2*a^6 - 2*A^2*a*b^5 - 2*A^2*a^5*b - 5*A^2*a^2*b^4 + 4*A^2*a^3*b^3 + 3*A^2*a^4*b^2 + C^2*a^4*b^2 - 4*A*B*a^5*b - 2*B*C*a^5*b + 2*A*B*a^3*b^3 - 2*A*C*a^2*b^4 + 4*A*C*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^4*b^5 - B*a^9 - A*a^9 - 3*A*a^6*b^3 + A*a^7*b^2 - B*a^6*b^3 + B*a^7*b^2 + C*a^5*b^4 - C*a^6*b^3 - C*a^7*b^2 + 2*A*a^8*b + B*a^8*b + C*a^8*b))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(A*b^3 + B*a^3 - 2*A*a^2*b - C*a^2*b)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)) - (2*tan(c/2 + (d*x)/2)*(A*b^2 + C*a^2 - B*a*b))/(d*(a + b)*(a*b - a^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
991,1,6450,211,10.468879,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^2),x)","\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^3-2\,A\,b^3-A\,a\,b^2+A\,a^2\,b+B\,a\,b^2-C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^3+2\,A\,b^3-A\,a\,b^2-A\,a^2\,b-B\,a\,b^2+C\,a^2\,b\right)}{a^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b-B\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b-B\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)\,1{}\mathrm{i}}{a^3}}{\frac{64\,\left(12\,A^3\,a^4\,b^4+6\,A^3\,a^3\,b^5-20\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+8\,A^3\,b^8-20\,A^2\,B\,a^5\,b^3-13\,A^2\,B\,a^4\,b^4+32\,A^2\,B\,a^3\,b^5+8\,A^2\,B\,a^2\,b^6-12\,A^2\,B\,a\,b^7+4\,A^2\,C\,a^6\,b^2+8\,A^2\,C\,a^5\,b^3-4\,A^2\,C\,a^4\,b^4-4\,A^2\,C\,a^3\,b^5+11\,A\,B^2\,a^6\,b^2+9\,A\,B^2\,a^5\,b^3-17\,A\,B^2\,a^4\,b^4-5\,A\,B^2\,a^3\,b^5+6\,A\,B^2\,a^2\,b^6-4\,A\,B\,C\,a^7\,b-10\,A\,B\,C\,a^6\,b^2+4\,A\,B\,C\,a^5\,b^3+4\,A\,B\,C\,a^4\,b^4+2\,A\,C^2\,a^7\,b-2\,B^3\,a^7\,b-2\,B^3\,a^6\,b^2+3\,B^3\,a^5\,b^3+B^3\,a^4\,b^4-B^3\,a^3\,b^5+B^2\,C\,a^8+3\,B^2\,C\,a^7\,b-B^2\,C\,a^6\,b^2-B^2\,C\,a^5\,b^3-B\,C^2\,a^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b-B\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)}{a^3}-\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(2\,A\,b-B\,a\right)\,\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b-B\,a\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)}{a^3}}\right)\,\left(2\,A\,b-B\,a\right)\,2{}\mathrm{i}}{a^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{64\,\left(12\,A^3\,a^4\,b^4+6\,A^3\,a^3\,b^5-20\,A^3\,a^2\,b^6-4\,A^3\,a\,b^7+8\,A^3\,b^8-20\,A^2\,B\,a^5\,b^3-13\,A^2\,B\,a^4\,b^4+32\,A^2\,B\,a^3\,b^5+8\,A^2\,B\,a^2\,b^6-12\,A^2\,B\,a\,b^7+4\,A^2\,C\,a^6\,b^2+8\,A^2\,C\,a^5\,b^3-4\,A^2\,C\,a^4\,b^4-4\,A^2\,C\,a^3\,b^5+11\,A\,B^2\,a^6\,b^2+9\,A\,B^2\,a^5\,b^3-17\,A\,B^2\,a^4\,b^4-5\,A\,B^2\,a^3\,b^5+6\,A\,B^2\,a^2\,b^6-4\,A\,B\,C\,a^7\,b-10\,A\,B\,C\,a^6\,b^2+4\,A\,B\,C\,a^5\,b^3+4\,A\,B\,C\,a^4\,b^4+2\,A\,C^2\,a^7\,b-2\,B^3\,a^7\,b-2\,B^3\,a^6\,b^2+3\,B^3\,a^5\,b^3+B^3\,a^4\,b^4-B^3\,a^3\,b^5+B^2\,C\,a^8+3\,B^2\,C\,a^7\,b-B^2\,C\,a^6\,b^2-B^2\,C\,a^5\,b^3-B\,C^2\,a^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}-\frac{\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^6\,b^2-8\,A^2\,a^5\,b^3+5\,A^2\,a^4\,b^4+16\,A^2\,a^3\,b^5-16\,A^2\,a^2\,b^6-8\,A^2\,a\,b^7+8\,A^2\,b^8-4\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2-8\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4+18\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-8\,A\,B\,a\,b^7+6\,A\,C\,a^6\,b^2-4\,A\,C\,a^4\,b^4+B^2\,a^8-2\,B^2\,a^7\,b+3\,B^2\,a^6\,b^2+4\,B^2\,a^5\,b^3-5\,B^2\,a^4\,b^4-2\,B^2\,a^3\,b^5+2\,B^2\,a^2\,b^6-4\,B\,C\,a^7\,b+2\,B\,C\,a^5\,b^3+C^2\,a^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(A\,a^7\,b^5-C\,a^{12}-2\,A\,a^6\,b^6-B\,a^{12}+5\,A\,a^8\,b^4-3\,A\,a^9\,b^3-3\,A\,a^{10}\,b^2+B\,a^7\,b^5-3\,B\,a^9\,b^3+B\,a^{10}\,b^2-C\,a^9\,b^3+C\,a^{10}\,b^2+2\,A\,a^{11}\,b+2\,B\,a^{11}\,b+C\,a^{11}\,b\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(C\,a^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+B\,a\,b^3-2\,A\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)*(A*a^3 - 2*A*b^3 - A*a*b^2 + A*a^2*b + B*a*b^2 - C*a^2*b))/(a^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(A*a^3 + 2*A*b^3 - A*a*b^2 - A*a^2*b - B*a*b^2 + C*a^2*b))/(a^2*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^4*(a - b) - 2*b*tan(c/2 + (d*x)/2)^2)) + (atan((((2*A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + ((2*A*b - B*a)*((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(2*A*b - B*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3)*1i)/a^3 + ((2*A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - ((2*A*b - B*a)*((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(2*A*b - B*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3)*1i)/a^3)/((64*(8*A^3*b^8 - B*C^2*a^8 + B^2*C*a^8 - 4*A^3*a*b^7 - 2*B^3*a^7*b - 20*A^3*a^2*b^6 + 6*A^3*a^3*b^5 + 12*A^3*a^4*b^4 - B^3*a^3*b^5 + B^3*a^4*b^4 + 3*B^3*a^5*b^3 - 2*B^3*a^6*b^2 - 12*A^2*B*a*b^7 + 2*A*C^2*a^7*b + 3*B^2*C*a^7*b + 6*A*B^2*a^2*b^6 - 5*A*B^2*a^3*b^5 - 17*A*B^2*a^4*b^4 + 9*A*B^2*a^5*b^3 + 11*A*B^2*a^6*b^2 + 8*A^2*B*a^2*b^6 + 32*A^2*B*a^3*b^5 - 13*A^2*B*a^4*b^4 - 20*A^2*B*a^5*b^3 - 4*A^2*C*a^3*b^5 - 4*A^2*C*a^4*b^4 + 8*A^2*C*a^5*b^3 + 4*A^2*C*a^6*b^2 - B^2*C*a^5*b^3 - B^2*C*a^6*b^2 - 4*A*B*C*a^7*b + 4*A*B*C*a^4*b^4 + 4*A*B*C*a^5*b^3 - 10*A*B*C*a^6*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + ((2*A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + ((2*A*b - B*a)*((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(2*A*b - B*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3))/a^3 - ((2*A*b - B*a)*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - ((2*A*b - B*a)*((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(2*A*b - B*a)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3))/a^3))*(2*A*b - B*a)*2i)/(a^3*d) + (atan(((((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((64*(8*A^3*b^8 - B*C^2*a^8 + B^2*C*a^8 - 4*A^3*a*b^7 - 2*B^3*a^7*b - 20*A^3*a^2*b^6 + 6*A^3*a^3*b^5 + 12*A^3*a^4*b^4 - B^3*a^3*b^5 + B^3*a^4*b^4 + 3*B^3*a^5*b^3 - 2*B^3*a^6*b^2 - 12*A^2*B*a*b^7 + 2*A*C^2*a^7*b + 3*B^2*C*a^7*b + 6*A*B^2*a^2*b^6 - 5*A*B^2*a^3*b^5 - 17*A*B^2*a^4*b^4 + 9*A*B^2*a^5*b^3 + 11*A*B^2*a^6*b^2 + 8*A^2*B*a^2*b^6 + 32*A^2*B*a^3*b^5 - 13*A^2*B*a^4*b^4 - 20*A^2*B*a^5*b^3 - 4*A^2*C*a^3*b^5 - 4*A^2*C*a^4*b^4 + 8*A^2*C*a^5*b^3 + 4*A^2*C*a^6*b^2 - B^2*C*a^5*b^3 - B^2*C*a^6*b^2 - 4*A*B*C*a^7*b + 4*A*B*C*a^4*b^4 + 4*A*B*C*a^5*b^3 - 10*A*B*C*a^6*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) - (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^2*a^8 + C^2*a^8 - 8*A^2*a*b^7 - 2*B^2*a^7*b - 16*A^2*a^2*b^6 + 16*A^2*a^3*b^5 + 5*A^2*a^4*b^4 - 8*A^2*a^5*b^3 + 4*A^2*a^6*b^2 + 2*B^2*a^2*b^6 - 2*B^2*a^3*b^5 - 5*B^2*a^4*b^4 + 4*B^2*a^5*b^3 + 3*B^2*a^6*b^2 - 8*A*B*a*b^7 - 4*A*B*a^7*b - 4*B*C*a^7*b + 8*A*B*a^2*b^6 + 18*A*B*a^3*b^5 - 16*A*B*a^4*b^4 - 8*A*B*a^5*b^3 + 8*A*B*a^6*b^2 - 4*A*C*a^4*b^4 + 6*A*C*a^6*b^2 + 2*B*C*a^5*b^3))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(A*a^7*b^5 - C*a^12 - 2*A*a^6*b^6 - B*a^12 + 5*A*a^8*b^4 - 3*A*a^9*b^3 - 3*A*a^10*b^2 + B*a^7*b^5 - 3*B*a^9*b^3 + B*a^10*b^2 - C*a^9*b^3 + C*a^10*b^2 + 2*A*a^11*b + 2*B*a^11*b + C*a^11*b))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/((a^6*b + a^7 - a^4*b^3 - a^5*b^2)*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(C*a^4 - 2*A*b^4 + 3*A*a^2*b^2 + B*a*b^3 - 2*B*a^3*b)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
992,1,9931,307,12.357473,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^2),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^4+6\,A\,b^4+2\,B\,a^4-5\,A\,a^2\,b^2-2\,B\,a^2\,b^2+2\,C\,a^2\,b^2+3\,A\,a\,b^3-3\,A\,a^3\,b-4\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A\,a^4+6\,A\,b^4-2\,B\,a^4-5\,A\,a^2\,b^2+2\,B\,a^2\,b^2+2\,C\,a^2\,b^2-3\,A\,a\,b^3+3\,A\,a^3\,b-4\,B\,a\,b^3+2\,B\,a^3\,b\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a^4-6\,A\,b^4+3\,A\,a^2\,b^2-2\,C\,a^2\,b^2+4\,B\,a\,b^3-2\,B\,a^3\,b\right)}{a\,\left(a^2\,b-a^3\right)\,\left(a+b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-a-3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}-3\,A^2\,B\,a^9\,b^2+3\,A^2\,B\,a^8\,b^3-63\,A^2\,B\,a^7\,b^4+15\,A^2\,B\,a^6\,b^5-186\,A^2\,B\,a^5\,b^6-162\,A^2\,B\,a^4\,b^7+468\,A^2\,B\,a^3\,b^8+108\,A^2\,B\,a^2\,b^9-216\,A^2\,B\,a\,b^{10}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+24\,A\,B^2\,a^8\,b^3-6\,A\,B^2\,a^7\,b^4+168\,A\,B^2\,a^6\,b^5+108\,A\,B^2\,a^5\,b^6-336\,A\,B^2\,a^4\,b^7-72\,A\,B^2\,a^3\,b^8+144\,A\,B^2\,a^2\,b^9-28\,A\,B\,C\,a^9\,b^2+4\,A\,B\,C\,a^8\,b^3-188\,A\,B\,C\,a^7\,b^4-152\,A\,B\,C\,a^6\,b^5+360\,A\,B\,C\,a^5\,b^6+96\,A\,B\,C\,a^4\,b^7-144\,A\,B\,C\,a^3\,b^8+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7-48\,B^3\,a^7\,b^4-24\,B^3\,a^6\,b^5+80\,B^3\,a^5\,b^6+16\,B^3\,a^4\,b^7-32\,B^3\,a^3\,b^8+80\,B^2\,C\,a^8\,b^3+52\,B^2\,C\,a^7\,b^4-128\,B^2\,C\,a^6\,b^5-32\,B^2\,C\,a^5\,b^6+48\,B^2\,C\,a^4\,b^7-44\,B\,C^2\,a^9\,b^2-36\,B\,C^2\,a^8\,b^3+68\,B\,C^2\,a^7\,b^4+20\,B\,C^2\,a^6\,b^5-24\,B\,C^2\,a^5\,b^6+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)}{a^4}+\frac{\left(\frac{\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{a^4\,\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)}{a^4}}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-2\,B\,a\,b+3\,A\,b^2\right)\,2{}\mathrm{i}}{a^4\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{16\,\left(4\,A^3\,a^8\,b^3-4\,A^3\,a^7\,b^4+41\,A^3\,a^6\,b^5-9\,A^3\,a^5\,b^6+63\,A^3\,a^4\,b^7+81\,A^3\,a^3\,b^8-216\,A^3\,a^2\,b^9-54\,A^3\,a\,b^{10}+108\,A^3\,b^{11}-3\,A^2\,B\,a^9\,b^2+3\,A^2\,B\,a^8\,b^3-63\,A^2\,B\,a^7\,b^4+15\,A^2\,B\,a^6\,b^5-186\,A^2\,B\,a^5\,b^6-162\,A^2\,B\,a^4\,b^7+468\,A^2\,B\,a^3\,b^8+108\,A^2\,B\,a^2\,b^9-216\,A^2\,B\,a\,b^{10}+2\,A^2\,C\,a^{10}\,b-2\,A^2\,C\,a^9\,b^2+37\,A^2\,C\,a^8\,b^3-5\,A^2\,C\,a^7\,b^4+105\,A^2\,C\,a^6\,b^5+111\,A^2\,C\,a^5\,b^6-252\,A^2\,C\,a^4\,b^7-72\,A^2\,C\,a^3\,b^8+108\,A^2\,C\,a^2\,b^9+24\,A\,B^2\,a^8\,b^3-6\,A\,B^2\,a^7\,b^4+168\,A\,B^2\,a^6\,b^5+108\,A\,B^2\,a^5\,b^6-336\,A\,B^2\,a^4\,b^7-72\,A\,B^2\,a^3\,b^8+144\,A\,B^2\,a^2\,b^9-28\,A\,B\,C\,a^9\,b^2+4\,A\,B\,C\,a^8\,b^3-188\,A\,B\,C\,a^7\,b^4-152\,A\,B\,C\,a^6\,b^5+360\,A\,B\,C\,a^5\,b^6+96\,A\,B\,C\,a^4\,b^7-144\,A\,B\,C\,a^3\,b^8+8\,A\,C^2\,a^{10}\,b+52\,A\,C^2\,a^8\,b^3+52\,A\,C^2\,a^7\,b^4-96\,A\,C^2\,a^6\,b^5-30\,A\,C^2\,a^5\,b^6+36\,A\,C^2\,a^4\,b^7-48\,B^3\,a^7\,b^4-24\,B^3\,a^6\,b^5+80\,B^3\,a^5\,b^6+16\,B^3\,a^4\,b^7-32\,B^3\,a^3\,b^8+80\,B^2\,C\,a^8\,b^3+52\,B^2\,C\,a^7\,b^4-128\,B^2\,C\,a^6\,b^5-32\,B^2\,C\,a^5\,b^6+48\,B^2\,C\,a^4\,b^7-44\,B\,C^2\,a^9\,b^2-36\,B\,C^2\,a^8\,b^3+68\,B\,C^2\,a^7\,b^4+20\,B\,C^2\,a^6\,b^5-24\,B\,C^2\,a^5\,b^6+8\,C^3\,a^{10}\,b+8\,C^3\,a^9\,b^2-12\,C^3\,a^8\,b^3-4\,C^3\,a^7\,b^4+4\,C^3\,a^6\,b^5\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{10}-2\,A^2\,a^9\,b+11\,A^2\,a^8\,b^2-20\,A^2\,a^7\,b^3+23\,A^2\,a^6\,b^4-26\,A^2\,a^5\,b^5+17\,A^2\,a^4\,b^6+120\,A^2\,a^3\,b^7-120\,A^2\,a^2\,b^8-72\,A^2\,a\,b^9+72\,A^2\,b^{10}-8\,A\,B\,a^9\,b+16\,A\,B\,a^8\,b^2-40\,A\,B\,a^7\,b^3+64\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5-176\,A\,B\,a^4\,b^6+176\,A\,B\,a^3\,b^7+96\,A\,B\,a^2\,b^8-96\,A\,B\,a\,b^9+4\,A\,C\,a^{10}-8\,A\,C\,a^9\,b+20\,A\,C\,a^8\,b^2-32\,A\,C\,a^7\,b^3+36\,A\,C\,a^6\,b^4+88\,A\,C\,a^5\,b^5-100\,A\,C\,a^4\,b^6-48\,A\,C\,a^3\,b^7+48\,A\,C\,a^2\,b^8+16\,B^2\,a^8\,b^2-32\,B^2\,a^7\,b^3+20\,B^2\,a^6\,b^4+64\,B^2\,a^5\,b^5-64\,B^2\,a^4\,b^6-32\,B^2\,a^3\,b^7+32\,B^2\,a^2\,b^8-16\,B\,C\,a^9\,b+32\,B\,C\,a^8\,b^2-32\,B\,C\,a^7\,b^3-64\,B\,C\,a^6\,b^4+72\,B\,C\,a^5\,b^5+32\,B\,C\,a^4\,b^6-32\,B\,C\,a^3\,b^7+4\,C^2\,a^{10}-8\,C^2\,a^9\,b+12\,C^2\,a^8\,b^2+16\,C^2\,a^7\,b^3-20\,C^2\,a^6\,b^4-8\,C^2\,a^5\,b^5+8\,C^2\,a^4\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\left(2\,A\,a^{15}+4\,C\,a^{15}-12\,A\,a^8\,b^7+6\,A\,a^9\,b^6+28\,A\,a^{10}\,b^5-14\,A\,a^{11}\,b^4-16\,A\,a^{12}\,b^3+6\,A\,a^{13}\,b^2+8\,B\,a^9\,b^6-4\,B\,a^{10}\,b^5-20\,B\,a^{11}\,b^4+12\,B\,a^{12}\,b^3+12\,B\,a^{13}\,b^2-4\,C\,a^{10}\,b^5+12\,C\,a^{12}\,b^3-4\,C\,a^{13}\,b^2-8\,B\,a^{14}\,b-8\,C\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(3\,A\,b^4-2\,C\,a^4-4\,A\,a^2\,b^2+C\,a^2\,b^2-2\,B\,a\,b^3+3\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"(atan(((((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b))/a^4 - (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b)*1i)/a^4 - (((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b))/a^4 + (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b)*1i)/a^4)/((16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 - 32*B^3*a^3*b^8 + 16*B^3*a^4*b^7 + 80*B^3*a^5*b^6 - 24*B^3*a^6*b^5 - 48*B^3*a^7*b^4 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 - 216*A^2*B*a*b^10 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 144*A*B^2*a^2*b^9 - 72*A*B^2*a^3*b^8 - 336*A*B^2*a^4*b^7 + 108*A*B^2*a^5*b^6 + 168*A*B^2*a^6*b^5 - 6*A*B^2*a^7*b^4 + 24*A*B^2*a^8*b^3 + 108*A^2*B*a^2*b^9 + 468*A^2*B*a^3*b^8 - 162*A^2*B*a^4*b^7 - 186*A^2*B*a^5*b^6 + 15*A^2*B*a^6*b^5 - 63*A^2*B*a^7*b^4 + 3*A^2*B*a^8*b^3 - 3*A^2*B*a^9*b^2 + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2 - 24*B*C^2*a^5*b^6 + 20*B*C^2*a^6*b^5 + 68*B*C^2*a^7*b^4 - 36*B*C^2*a^8*b^3 - 44*B*C^2*a^9*b^2 + 48*B^2*C*a^4*b^7 - 32*B^2*C*a^5*b^6 - 128*B^2*C*a^6*b^5 + 52*B^2*C*a^7*b^4 + 80*B^2*C*a^8*b^3 - 144*A*B*C*a^3*b^8 + 96*A*B*C*a^4*b^7 + 360*A*B*C*a^5*b^6 - 152*A*B*C*a^6*b^5 - 188*A*B*C*a^7*b^4 + 4*A*B*C*a^8*b^3 - 28*A*B*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b))/a^4 - (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b))/a^4 + (((((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*tan(c/2 + (d*x)/2)*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/(a^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2)))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b))/a^4 + (8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b))/a^4))*(3*A*b^2 + a^2*(A/2 + C) - 2*B*a*b)*2i)/(a^4*d) - ((tan(c/2 + (d*x)/2)*(A*a^4 + 6*A*b^4 + 2*B*a^4 - 5*A*a^2*b^2 - 2*B*a^2*b^2 + 2*C*a^2*b^2 + 3*A*a*b^3 - 3*A*a^3*b - 4*B*a*b^3 + 2*B*a^3*b))/((a^3*b - a^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(A*a^4 + 6*A*b^4 - 2*B*a^4 - 5*A*a^2*b^2 + 2*B*a^2*b^2 + 2*C*a^2*b^2 - 3*A*a*b^3 + 3*A*a^3*b - 4*B*a*b^3 + 2*B*a^3*b))/((a^3*b - a^4)*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(A*a^4 - 6*A*b^4 + 3*A*a^2*b^2 - 2*C*a^2*b^2 + 4*B*a*b^3 - 2*B*a^3*b))/(a*(a^2*b - a^3)*(a + b)))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) + tan(c/2 + (d*x)/2)^6*(a - b))) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((16*(108*A^3*b^11 - 54*A^3*a*b^10 + 8*C^3*a^10*b - 216*A^3*a^2*b^9 + 81*A^3*a^3*b^8 + 63*A^3*a^4*b^7 - 9*A^3*a^5*b^6 + 41*A^3*a^6*b^5 - 4*A^3*a^7*b^4 + 4*A^3*a^8*b^3 - 32*B^3*a^3*b^8 + 16*B^3*a^4*b^7 + 80*B^3*a^5*b^6 - 24*B^3*a^6*b^5 - 48*B^3*a^7*b^4 + 4*C^3*a^6*b^5 - 4*C^3*a^7*b^4 - 12*C^3*a^8*b^3 + 8*C^3*a^9*b^2 - 216*A^2*B*a*b^10 + 8*A*C^2*a^10*b + 2*A^2*C*a^10*b + 144*A*B^2*a^2*b^9 - 72*A*B^2*a^3*b^8 - 336*A*B^2*a^4*b^7 + 108*A*B^2*a^5*b^6 + 168*A*B^2*a^6*b^5 - 6*A*B^2*a^7*b^4 + 24*A*B^2*a^8*b^3 + 108*A^2*B*a^2*b^9 + 468*A^2*B*a^3*b^8 - 162*A^2*B*a^4*b^7 - 186*A^2*B*a^5*b^6 + 15*A^2*B*a^6*b^5 - 63*A^2*B*a^7*b^4 + 3*A^2*B*a^8*b^3 - 3*A^2*B*a^9*b^2 + 36*A*C^2*a^4*b^7 - 30*A*C^2*a^5*b^6 - 96*A*C^2*a^6*b^5 + 52*A*C^2*a^7*b^4 + 52*A*C^2*a^8*b^3 + 108*A^2*C*a^2*b^9 - 72*A^2*C*a^3*b^8 - 252*A^2*C*a^4*b^7 + 111*A^2*C*a^5*b^6 + 105*A^2*C*a^6*b^5 - 5*A^2*C*a^7*b^4 + 37*A^2*C*a^8*b^3 - 2*A^2*C*a^9*b^2 - 24*B*C^2*a^5*b^6 + 20*B*C^2*a^6*b^5 + 68*B*C^2*a^7*b^4 - 36*B*C^2*a^8*b^3 - 44*B*C^2*a^9*b^2 + 48*B^2*C*a^4*b^7 - 32*B^2*C*a^5*b^6 - 128*B^2*C*a^6*b^5 + 52*B^2*C*a^7*b^4 + 80*B^2*C*a^8*b^3 - 144*A*B*C*a^3*b^8 + 96*A*B*C*a^4*b^7 + 360*A*B*C*a^5*b^6 - 152*A*B*C*a^6*b^5 - 188*A*B*C*a^7*b^4 + 4*A*B*C*a^8*b^3 - 28*A*B*C*a^9*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 + 4*C^2*a^10 - 72*A^2*a*b^9 - 2*A^2*a^9*b - 8*C^2*a^9*b - 120*A^2*a^2*b^8 + 120*A^2*a^3*b^7 + 17*A^2*a^4*b^6 - 26*A^2*a^5*b^5 + 23*A^2*a^6*b^4 - 20*A^2*a^7*b^3 + 11*A^2*a^8*b^2 + 32*B^2*a^2*b^8 - 32*B^2*a^3*b^7 - 64*B^2*a^4*b^6 + 64*B^2*a^5*b^5 + 20*B^2*a^6*b^4 - 32*B^2*a^7*b^3 + 16*B^2*a^8*b^2 + 8*C^2*a^4*b^6 - 8*C^2*a^5*b^5 - 20*C^2*a^6*b^4 + 16*C^2*a^7*b^3 + 12*C^2*a^8*b^2 + 4*A*C*a^10 - 96*A*B*a*b^9 - 8*A*B*a^9*b - 8*A*C*a^9*b - 16*B*C*a^9*b + 96*A*B*a^2*b^8 + 176*A*B*a^3*b^7 - 176*A*B*a^4*b^6 - 40*A*B*a^5*b^5 + 64*A*B*a^6*b^4 - 40*A*B*a^7*b^3 + 16*A*B*a^8*b^2 + 48*A*C*a^2*b^8 - 48*A*C*a^3*b^7 - 100*A*C*a^4*b^6 + 88*A*C*a^5*b^5 + 36*A*C*a^6*b^4 - 32*A*C*a^7*b^3 + 20*A*C*a^8*b^2 - 32*B*C*a^3*b^7 + 32*B*C*a^4*b^6 + 72*B*C*a^5*b^5 - 64*B*C*a^6*b^4 - 32*B*C*a^7*b^3 + 32*B*C*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b*(-(a + b)^3*(a - b)^3)^(1/2)*((8*(2*A*a^15 + 4*C*a^15 - 12*A*a^8*b^7 + 6*A*a^9*b^6 + 28*A*a^10*b^5 - 14*A*a^11*b^4 - 16*A*a^12*b^3 + 6*A*a^13*b^2 + 8*B*a^9*b^6 - 4*B*a^10*b^5 - 20*B*a^11*b^4 + 12*B*a^12*b^3 + 12*B*a^13*b^2 - 4*C*a^10*b^5 + 12*C*a^12*b^3 - 4*C*a^13*b^2 - 8*B*a^14*b - 8*C*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/((a^8*b + a^9 - a^6*b^3 - a^7*b^2)*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^4 - 2*C*a^4 - 4*A*a^2*b^2 + C*a^2*b^2 - 2*B*a*b^3 + 3*B*a^3*b)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
993,1,11677,405,13.529457,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^2),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^5-8\,A\,b^5+B\,a^5+2\,C\,a^5+6\,A\,a^2\,b^3+2\,A\,a^3\,b^2+3\,B\,a^2\,b^3-5\,B\,a^3\,b^2-4\,C\,a^2\,b^3-2\,C\,a^3\,b^2-4\,A\,a\,b^4+6\,B\,a\,b^4-3\,B\,a^4\,b+2\,C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a^5+72\,A\,b^5+3\,B\,a^5-6\,C\,a^5-38\,A\,a^2\,b^3-14\,A\,a^3\,b^2-9\,B\,a^2\,b^3+33\,B\,a^3\,b^2+36\,C\,a^2\,b^3+6\,C\,a^3\,b^2+12\,A\,a\,b^4-16\,A\,a^4\,b-54\,B\,a\,b^4+9\,B\,a^4\,b-18\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^5-72\,A\,b^5-3\,B\,a^5-6\,C\,a^5+38\,A\,a^2\,b^3-14\,A\,a^3\,b^2-9\,B\,a^2\,b^3-33\,B\,a^3\,b^2-36\,C\,a^2\,b^3+6\,C\,a^3\,b^2+12\,A\,a\,b^4+16\,A\,a^4\,b+54\,B\,a\,b^4+9\,B\,a^4\,b+18\,C\,a^4\,b\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,a^5+8\,A\,b^5-B\,a^5+2\,C\,a^5-6\,A\,a^2\,b^3+2\,A\,a^3\,b^2+3\,B\,a^2\,b^3+5\,B\,a^3\,b^2+4\,C\,a^2\,b^3-2\,C\,a^3\,b^2-4\,A\,a\,b^4-6\,B\,a\,b^4-3\,B\,a^4\,b-2\,C\,a^4\,b\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)\,1{}\mathrm{i}}{a^5}}{\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,\left(4\,A\,b^3-\frac{B\,a^3}{2}+a^2\,\left(A\,b+2\,C\,b\right)-3\,B\,a\,b^2\right)}{a^5}-\frac{16\,\left(20\,A^3\,a^8\,b^6-20\,A^3\,a^7\,b^7+124\,A^3\,a^6\,b^8-24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}+192\,A^3\,a^3\,b^{11}-448\,A^3\,a^2\,b^{12}-128\,A^3\,a\,b^{13}+256\,A^3\,b^{14}-36\,A^2\,B\,a^9\,b^5+36\,A^2\,B\,a^8\,b^6-264\,A^2\,B\,a^7\,b^7+54\,A^2\,B\,a^6\,b^8-180\,A^2\,B\,a^5\,b^9-432\,A^2\,B\,a^4\,b^{10}+1056\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-576\,A^2\,B\,a\,b^{13}+12\,A^2\,C\,a^{10}\,b^4-12\,A^2\,C\,a^9\,b^5+156\,A^2\,C\,a^8\,b^6-36\,A^2\,C\,a^7\,b^7+216\,A^2\,C\,a^6\,b^8+288\,A^2\,C\,a^5\,b^9-768\,A^2\,C\,a^4\,b^{10}-192\,A^2\,C\,a^3\,b^{11}+384\,A^2\,C\,a^2\,b^{12}+21\,A\,B^2\,a^{10}\,b^4-21\,A\,B^2\,a^9\,b^5+183\,A\,B^2\,a^8\,b^6-39\,A\,B^2\,a^7\,b^7+192\,A\,B^2\,a^6\,b^8+324\,A\,B^2\,a^5\,b^9-828\,A\,B^2\,a^4\,b^{10}-216\,A\,B^2\,a^3\,b^{11}+432\,A\,B^2\,a^2\,b^{12}-12\,A\,B\,C\,a^{11}\,b^3+12\,A\,B\,C\,a^{10}\,b^4-204\,A\,B\,C\,a^9\,b^5+48\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7-432\,A\,B\,C\,a^6\,b^8+1200\,A\,B\,C\,a^5\,b^9+288\,A\,B\,C\,a^4\,b^{10}-576\,A\,B\,C\,a^3\,b^{11}+48\,A\,C^2\,a^{10}\,b^4-12\,A\,C^2\,a^9\,b^5+192\,A\,C^2\,a^8\,b^6+144\,A\,C^2\,a^7\,b^7-432\,A\,C^2\,a^6\,b^8-96\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}-4\,B^3\,a^{11}\,b^3+4\,B^3\,a^{10}\,b^4-41\,B^3\,a^9\,b^5+9\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7-81\,B^3\,a^6\,b^8+216\,B^3\,a^5\,b^9+54\,B^3\,a^4\,b^{10}-108\,B^3\,a^3\,b^{11}+3\,B^2\,C\,a^{12}\,b^2-3\,B^2\,C\,a^{11}\,b^3+63\,B^2\,C\,a^{10}\,b^4-15\,B^2\,C\,a^9\,b^5+186\,B^2\,C\,a^8\,b^6+162\,B^2\,C\,a^7\,b^7-468\,B^2\,C\,a^6\,b^8-108\,B^2\,C\,a^5\,b^9+216\,B^2\,C\,a^4\,b^{10}-24\,B\,C^2\,a^{11}\,b^3+6\,B\,C^2\,a^{10}\,b^4-168\,B\,C^2\,a^9\,b^5-108\,B\,C^2\,a^8\,b^6+336\,B\,C^2\,a^7\,b^7+72\,B\,C^2\,a^6\,b^8-144\,B\,C^2\,a^5\,b^9+48\,C^3\,a^{10}\,b^4+24\,C^3\,a^9\,b^5-80\,C^3\,a^8\,b^6-16\,C^3\,a^7\,b^7+32\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\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^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}{\frac{16\,\left(20\,A^3\,a^8\,b^6-20\,A^3\,a^7\,b^7+124\,A^3\,a^6\,b^8-24\,A^3\,a^5\,b^9+48\,A^3\,a^4\,b^{10}+192\,A^3\,a^3\,b^{11}-448\,A^3\,a^2\,b^{12}-128\,A^3\,a\,b^{13}+256\,A^3\,b^{14}-36\,A^2\,B\,a^9\,b^5+36\,A^2\,B\,a^8\,b^6-264\,A^2\,B\,a^7\,b^7+54\,A^2\,B\,a^6\,b^8-180\,A^2\,B\,a^5\,b^9-432\,A^2\,B\,a^4\,b^{10}+1056\,A^2\,B\,a^3\,b^{11}+288\,A^2\,B\,a^2\,b^{12}-576\,A^2\,B\,a\,b^{13}+12\,A^2\,C\,a^{10}\,b^4-12\,A^2\,C\,a^9\,b^5+156\,A^2\,C\,a^8\,b^6-36\,A^2\,C\,a^7\,b^7+216\,A^2\,C\,a^6\,b^8+288\,A^2\,C\,a^5\,b^9-768\,A^2\,C\,a^4\,b^{10}-192\,A^2\,C\,a^3\,b^{11}+384\,A^2\,C\,a^2\,b^{12}+21\,A\,B^2\,a^{10}\,b^4-21\,A\,B^2\,a^9\,b^5+183\,A\,B^2\,a^8\,b^6-39\,A\,B^2\,a^7\,b^7+192\,A\,B^2\,a^6\,b^8+324\,A\,B^2\,a^5\,b^9-828\,A\,B^2\,a^4\,b^{10}-216\,A\,B^2\,a^3\,b^{11}+432\,A\,B^2\,a^2\,b^{12}-12\,A\,B\,C\,a^{11}\,b^3+12\,A\,B\,C\,a^{10}\,b^4-204\,A\,B\,C\,a^9\,b^5+48\,A\,B\,C\,a^8\,b^6-408\,A\,B\,C\,a^7\,b^7-432\,A\,B\,C\,a^6\,b^8+1200\,A\,B\,C\,a^5\,b^9+288\,A\,B\,C\,a^4\,b^{10}-576\,A\,B\,C\,a^3\,b^{11}+48\,A\,C^2\,a^{10}\,b^4-12\,A\,C^2\,a^9\,b^5+192\,A\,C^2\,a^8\,b^6+144\,A\,C^2\,a^7\,b^7-432\,A\,C^2\,a^6\,b^8-96\,A\,C^2\,a^5\,b^9+192\,A\,C^2\,a^4\,b^{10}-4\,B^3\,a^{11}\,b^3+4\,B^3\,a^{10}\,b^4-41\,B^3\,a^9\,b^5+9\,B^3\,a^8\,b^6-63\,B^3\,a^7\,b^7-81\,B^3\,a^6\,b^8+216\,B^3\,a^5\,b^9+54\,B^3\,a^4\,b^{10}-108\,B^3\,a^3\,b^{11}+3\,B^2\,C\,a^{12}\,b^2-3\,B^2\,C\,a^{11}\,b^3+63\,B^2\,C\,a^{10}\,b^4-15\,B^2\,C\,a^9\,b^5+186\,B^2\,C\,a^8\,b^6+162\,B^2\,C\,a^7\,b^7-468\,B^2\,C\,a^6\,b^8-108\,B^2\,C\,a^5\,b^9+216\,B^2\,C\,a^4\,b^{10}-24\,B\,C^2\,a^{11}\,b^3+6\,B\,C^2\,a^{10}\,b^4-168\,B\,C^2\,a^9\,b^5-108\,B\,C^2\,a^8\,b^6+336\,B\,C^2\,a^7\,b^7+72\,B\,C^2\,a^6\,b^8-144\,B\,C^2\,a^5\,b^9+48\,C^3\,a^{10}\,b^4+24\,C^3\,a^9\,b^5-80\,C^3\,a^8\,b^6-16\,C^3\,a^7\,b^7+32\,C^3\,a^6\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}+\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3+28\,A^2\,a^8\,b^4-48\,A^2\,a^7\,b^5+28\,A^2\,a^6\,b^6-8\,A^2\,a^5\,b^7+8\,A^2\,a^4\,b^8+192\,A^2\,a^3\,b^9-192\,A^2\,a^2\,b^{10}-128\,A^2\,a\,b^{11}+128\,A^2\,b^{12}-4\,A\,B\,a^{11}\,b+8\,A\,B\,a^{10}\,b^2-36\,A\,B\,a^9\,b^3+64\,A\,B\,a^8\,b^4-52\,A\,B\,a^7\,b^5+40\,A\,B\,a^6\,b^6-28\,A\,B\,a^5\,b^7-304\,A\,B\,a^4\,b^8+304\,A\,B\,a^3\,b^9+192\,A\,B\,a^2\,b^{10}-192\,A\,B\,a\,b^{11}+16\,A\,C\,a^{10}\,b^2-32\,A\,C\,a^9\,b^3+48\,A\,C\,a^8\,b^4-64\,A\,C\,a^7\,b^5+40\,A\,C\,a^6\,b^6+224\,A\,C\,a^5\,b^7-224\,A\,C\,a^4\,b^8-128\,A\,C\,a^3\,b^9+128\,A\,C\,a^2\,b^{10}+B^2\,a^{12}-2\,B^2\,a^{11}\,b+11\,B^2\,a^{10}\,b^2-20\,B^2\,a^9\,b^3+23\,B^2\,a^8\,b^4-26\,B^2\,a^7\,b^5+17\,B^2\,a^6\,b^6+120\,B^2\,a^5\,b^7-120\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+72\,B^2\,a^2\,b^{10}-8\,B\,C\,a^{11}\,b+16\,B\,C\,a^{10}\,b^2-40\,B\,C\,a^9\,b^3+64\,B\,C\,a^8\,b^4-40\,B\,C\,a^7\,b^5-176\,B\,C\,a^6\,b^6+176\,B\,C\,a^5\,b^7+96\,B\,C\,a^4\,b^8-96\,B\,C\,a^3\,b^9+16\,C^2\,a^{10}\,b^2-32\,C^2\,a^9\,b^3+20\,C^2\,a^8\,b^4+64\,C^2\,a^7\,b^5-64\,C^2\,a^6\,b^6-32\,C^2\,a^5\,b^7+32\,C^2\,a^4\,b^8\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,B\,a^{18}+16\,A\,a^{10}\,b^8-8\,A\,a^{11}\,b^7-36\,A\,a^{12}\,b^6+16\,A\,a^{13}\,b^5+20\,A\,a^{14}\,b^4-4\,A\,a^{15}\,b^3-12\,B\,a^{11}\,b^7+6\,B\,a^{12}\,b^6+28\,B\,a^{13}\,b^5-14\,B\,a^{14}\,b^4-16\,B\,a^{15}\,b^3+6\,B\,a^{16}\,b^2+8\,C\,a^{12}\,b^6-4\,C\,a^{13}\,b^5-20\,C\,a^{14}\,b^4+12\,C\,a^{15}\,b^3+12\,C\,a^{16}\,b^2-4\,A\,a^{17}\,b-8\,C\,a^{17}\,b\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{8\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(4\,A\,b^4-3\,C\,a^4-5\,A\,a^2\,b^2+2\,C\,a^2\,b^2-3\,B\,a\,b^3+4\,B\,a^3\,b\right)\,2{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*a^5 - 8*A*b^5 + B*a^5 + 2*C*a^5 + 6*A*a^2*b^3 + 2*A*a^3*b^2 + 3*B*a^2*b^3 - 5*B*a^3*b^2 - 4*C*a^2*b^3 - 2*C*a^3*b^2 - 4*A*a*b^4 + 6*B*a*b^4 - 3*B*a^4*b + 2*C*a^4*b))/(a^4*(a + b)*(a - b)) + (tan(c/2 + (d*x)/2)^3*(2*A*a^5 + 72*A*b^5 + 3*B*a^5 - 6*C*a^5 - 38*A*a^2*b^3 - 14*A*a^3*b^2 - 9*B*a^2*b^3 + 33*B*a^3*b^2 + 36*C*a^2*b^3 + 6*C*a^3*b^2 + 12*A*a*b^4 - 16*A*a^4*b - 54*B*a*b^4 + 9*B*a^4*b - 18*C*a^4*b))/(3*a^4*(a + b)*(a - b)) + (tan(c/2 + (d*x)/2)^5*(2*A*a^5 - 72*A*b^5 - 3*B*a^5 - 6*C*a^5 + 38*A*a^2*b^3 - 14*A*a^3*b^2 - 9*B*a^2*b^3 - 33*B*a^3*b^2 - 36*C*a^2*b^3 + 6*C*a^3*b^2 + 12*A*a*b^4 + 16*A*a^4*b + 54*B*a*b^4 + 9*B*a^4*b + 18*C*a^4*b))/(3*a^4*(a + b)*(a - b)) + (tan(c/2 + (d*x)/2)^7*(2*A*a^5 + 8*A*b^5 - B*a^5 + 2*C*a^5 - 6*A*a^2*b^3 + 2*A*a^3*b^2 + 3*B*a^2*b^3 + 5*B*a^3*b^2 + 4*C*a^2*b^3 - 2*C*a^3*b^2 - 4*A*a*b^4 - 6*B*a*b^4 - 3*B*a^4*b - 2*C*a^4*b))/(a^4*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^8*(a - b) - tan(c/2 + (d*x)/2)^2*(2*a + 4*b) + tan(c/2 + (d*x)/2)^6*(2*a - 4*b) + 6*b*tan(c/2 + (d*x)/2)^4)) + (atan(((((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*tan(c/2 + (d*x)/2)*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2))/a^5 - (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2)*1i)/a^5 - (((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*tan(c/2 + (d*x)/2)*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2))/a^5 + (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2)*1i)/a^5)/((((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*tan(c/2 + (d*x)/2)*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2))/a^5 - (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2))/a^5 - (16*(256*A^3*b^14 - 128*A^3*a*b^13 - 448*A^3*a^2*b^12 + 192*A^3*a^3*b^11 + 48*A^3*a^4*b^10 - 24*A^3*a^5*b^9 + 124*A^3*a^6*b^8 - 20*A^3*a^7*b^7 + 20*A^3*a^8*b^6 - 108*B^3*a^3*b^11 + 54*B^3*a^4*b^10 + 216*B^3*a^5*b^9 - 81*B^3*a^6*b^8 - 63*B^3*a^7*b^7 + 9*B^3*a^8*b^6 - 41*B^3*a^9*b^5 + 4*B^3*a^10*b^4 - 4*B^3*a^11*b^3 + 32*C^3*a^6*b^8 - 16*C^3*a^7*b^7 - 80*C^3*a^8*b^6 + 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 - 576*A^2*B*a*b^13 + 432*A*B^2*a^2*b^12 - 216*A*B^2*a^3*b^11 - 828*A*B^2*a^4*b^10 + 324*A*B^2*a^5*b^9 + 192*A*B^2*a^6*b^8 - 39*A*B^2*a^7*b^7 + 183*A*B^2*a^8*b^6 - 21*A*B^2*a^9*b^5 + 21*A*B^2*a^10*b^4 + 288*A^2*B*a^2*b^12 + 1056*A^2*B*a^3*b^11 - 432*A^2*B*a^4*b^10 - 180*A^2*B*a^5*b^9 + 54*A^2*B*a^6*b^8 - 264*A^2*B*a^7*b^7 + 36*A^2*B*a^8*b^6 - 36*A^2*B*a^9*b^5 + 192*A*C^2*a^4*b^10 - 96*A*C^2*a^5*b^9 - 432*A*C^2*a^6*b^8 + 144*A*C^2*a^7*b^7 + 192*A*C^2*a^8*b^6 - 12*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 + 384*A^2*C*a^2*b^12 - 192*A^2*C*a^3*b^11 - 768*A^2*C*a^4*b^10 + 288*A^2*C*a^5*b^9 + 216*A^2*C*a^6*b^8 - 36*A^2*C*a^7*b^7 + 156*A^2*C*a^8*b^6 - 12*A^2*C*a^9*b^5 + 12*A^2*C*a^10*b^4 - 144*B*C^2*a^5*b^9 + 72*B*C^2*a^6*b^8 + 336*B*C^2*a^7*b^7 - 108*B*C^2*a^8*b^6 - 168*B*C^2*a^9*b^5 + 6*B*C^2*a^10*b^4 - 24*B*C^2*a^11*b^3 + 216*B^2*C*a^4*b^10 - 108*B^2*C*a^5*b^9 - 468*B^2*C*a^6*b^8 + 162*B^2*C*a^7*b^7 + 186*B^2*C*a^8*b^6 - 15*B^2*C*a^9*b^5 + 63*B^2*C*a^10*b^4 - 3*B^2*C*a^11*b^3 + 3*B^2*C*a^12*b^2 - 576*A*B*C*a^3*b^11 + 288*A*B*C*a^4*b^10 + 1200*A*B*C*a^5*b^9 - 432*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 + 48*A*B*C*a^8*b^6 - 204*A*B*C*a^9*b^5 + 12*A*B*C*a^10*b^4 - 12*A*B*C*a^11*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (((((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*tan(c/2 + (d*x)/2)*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2))/a^5 + (8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2))/a^5))*(4*A*b^3 - (B*a^3)/2 + a^2*(A*b + 2*C*b) - 3*B*a*b^2)*2i)/(a^5*d) + (b^2*atan(((b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b)*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))/((16*(256*A^3*b^14 - 128*A^3*a*b^13 - 448*A^3*a^2*b^12 + 192*A^3*a^3*b^11 + 48*A^3*a^4*b^10 - 24*A^3*a^5*b^9 + 124*A^3*a^6*b^8 - 20*A^3*a^7*b^7 + 20*A^3*a^8*b^6 - 108*B^3*a^3*b^11 + 54*B^3*a^4*b^10 + 216*B^3*a^5*b^9 - 81*B^3*a^6*b^8 - 63*B^3*a^7*b^7 + 9*B^3*a^8*b^6 - 41*B^3*a^9*b^5 + 4*B^3*a^10*b^4 - 4*B^3*a^11*b^3 + 32*C^3*a^6*b^8 - 16*C^3*a^7*b^7 - 80*C^3*a^8*b^6 + 24*C^3*a^9*b^5 + 48*C^3*a^10*b^4 - 576*A^2*B*a*b^13 + 432*A*B^2*a^2*b^12 - 216*A*B^2*a^3*b^11 - 828*A*B^2*a^4*b^10 + 324*A*B^2*a^5*b^9 + 192*A*B^2*a^6*b^8 - 39*A*B^2*a^7*b^7 + 183*A*B^2*a^8*b^6 - 21*A*B^2*a^9*b^5 + 21*A*B^2*a^10*b^4 + 288*A^2*B*a^2*b^12 + 1056*A^2*B*a^3*b^11 - 432*A^2*B*a^4*b^10 - 180*A^2*B*a^5*b^9 + 54*A^2*B*a^6*b^8 - 264*A^2*B*a^7*b^7 + 36*A^2*B*a^8*b^6 - 36*A^2*B*a^9*b^5 + 192*A*C^2*a^4*b^10 - 96*A*C^2*a^5*b^9 - 432*A*C^2*a^6*b^8 + 144*A*C^2*a^7*b^7 + 192*A*C^2*a^8*b^6 - 12*A*C^2*a^9*b^5 + 48*A*C^2*a^10*b^4 + 384*A^2*C*a^2*b^12 - 192*A^2*C*a^3*b^11 - 768*A^2*C*a^4*b^10 + 288*A^2*C*a^5*b^9 + 216*A^2*C*a^6*b^8 - 36*A^2*C*a^7*b^7 + 156*A^2*C*a^8*b^6 - 12*A^2*C*a^9*b^5 + 12*A^2*C*a^10*b^4 - 144*B*C^2*a^5*b^9 + 72*B*C^2*a^6*b^8 + 336*B*C^2*a^7*b^7 - 108*B*C^2*a^8*b^6 - 168*B*C^2*a^9*b^5 + 6*B*C^2*a^10*b^4 - 24*B*C^2*a^11*b^3 + 216*B^2*C*a^4*b^10 - 108*B^2*C*a^5*b^9 - 468*B^2*C*a^6*b^8 + 162*B^2*C*a^7*b^7 + 186*B^2*C*a^8*b^6 - 15*B^2*C*a^9*b^5 + 63*B^2*C*a^10*b^4 - 3*B^2*C*a^11*b^3 + 3*B^2*C*a^12*b^2 - 576*A*B*C*a^3*b^11 + 288*A*B*C*a^4*b^10 + 1200*A*B*C*a^5*b^9 - 432*A*B*C*a^6*b^8 - 408*A*B*C*a^7*b^7 + 48*A*B*C*a^8*b^6 - 204*A*B*C*a^9*b^5 + 12*A*B*C*a^10*b^4 - 12*A*B*C*a^11*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^2*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^12 + B^2*a^12 - 128*A^2*a*b^11 - 2*B^2*a^11*b - 192*A^2*a^2*b^10 + 192*A^2*a^3*b^9 + 8*A^2*a^4*b^8 - 8*A^2*a^5*b^7 + 28*A^2*a^6*b^6 - 48*A^2*a^7*b^5 + 28*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 4*A^2*a^10*b^2 + 72*B^2*a^2*b^10 - 72*B^2*a^3*b^9 - 120*B^2*a^4*b^8 + 120*B^2*a^5*b^7 + 17*B^2*a^6*b^6 - 26*B^2*a^7*b^5 + 23*B^2*a^8*b^4 - 20*B^2*a^9*b^3 + 11*B^2*a^10*b^2 + 32*C^2*a^4*b^8 - 32*C^2*a^5*b^7 - 64*C^2*a^6*b^6 + 64*C^2*a^7*b^5 + 20*C^2*a^8*b^4 - 32*C^2*a^9*b^3 + 16*C^2*a^10*b^2 - 192*A*B*a*b^11 - 4*A*B*a^11*b - 8*B*C*a^11*b + 192*A*B*a^2*b^10 + 304*A*B*a^3*b^9 - 304*A*B*a^4*b^8 - 28*A*B*a^5*b^7 + 40*A*B*a^6*b^6 - 52*A*B*a^7*b^5 + 64*A*B*a^8*b^4 - 36*A*B*a^9*b^3 + 8*A*B*a^10*b^2 + 128*A*C*a^2*b^10 - 128*A*C*a^3*b^9 - 224*A*C*a^4*b^8 + 224*A*C*a^5*b^7 + 40*A*C*a^6*b^6 - 64*A*C*a^7*b^5 + 48*A*C*a^8*b^4 - 32*A*C*a^9*b^3 + 16*A*C*a^10*b^2 - 96*B*C*a^3*b^9 + 96*B*C*a^4*b^8 + 176*B*C*a^5*b^7 - 176*B*C*a^6*b^6 - 40*B*C*a^7*b^5 + 64*B*C*a^8*b^4 - 40*B*C*a^9*b^3 + 16*B*C*a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^2*((8*(2*B*a^18 + 16*A*a^10*b^8 - 8*A*a^11*b^7 - 36*A*a^12*b^6 + 16*A*a^13*b^5 + 20*A*a^14*b^4 - 4*A*a^15*b^3 - 12*B*a^11*b^7 + 6*B*a^12*b^6 + 28*B*a^13*b^5 - 14*B*a^14*b^4 - 16*B*a^15*b^3 + 6*B*a^16*b^2 + 8*C*a^12*b^6 - 4*C*a^13*b^5 - 20*C*a^14*b^4 + 12*C*a^15*b^3 + 12*C*a^16*b^2 - 4*A*a^17*b - 8*C*a^17*b))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(4*A*b^4 - 3*C*a^4 - 5*A*a^2*b^2 + 2*C*a^2*b^2 - 3*B*a*b^3 + 4*B*a^3*b)*2i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
994,1,16028,456,17.390604,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,C\,b^7-36\,C\,a^7-2\,B\,b^7-6\,A\,a^2\,b^5+15\,A\,a^3\,b^4+3\,A\,a^4\,b^3-6\,A\,a^5\,b^2+10\,B\,a^2\,b^5+16\,B\,a^3\,b^4-35\,B\,a^4\,b^3-9\,B\,a^5\,b^2+5\,C\,a^2\,b^5-26\,C\,a^3\,b^4-29\,C\,a^4\,b^3+67\,C\,a^5\,b^2-4\,B\,a\,b^6+18\,B\,a^6\,b+4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,b^7+36\,C\,a^7+3\,C\,b^7-6\,A\,a^2\,b^5-15\,A\,a^3\,b^4+3\,A\,a^4\,b^3+6\,A\,a^5\,b^2-10\,B\,a^2\,b^5+16\,B\,a^3\,b^4+35\,B\,a^4\,b^3-9\,B\,a^5\,b^2+5\,C\,a^2\,b^5+26\,C\,a^3\,b^4-29\,C\,a^4\,b^3-67\,C\,a^5\,b^2-4\,B\,a\,b^6-18\,B\,a^6\,b-4\,C\,a\,b^6+18\,C\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(C\,b^6-12\,C\,a^6-2\,B\,b^6+6\,A\,a^2\,b^4+A\,a^3\,b^3-2\,A\,a^4\,b^2+4\,B\,a^2\,b^4-12\,B\,a^3\,b^3-3\,B\,a^4\,b^2-8\,C\,a^2\,b^4-10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+2\,B\,a\,b^5+6\,B\,a^5\,b+5\,C\,a\,b^5+6\,C\,a^5\,b\right)}{\left(a\,b^4-b^5\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^6-12\,C\,a^6+C\,b^6+6\,A\,a^2\,b^4-A\,a^3\,b^3-2\,A\,a^4\,b^2-4\,B\,a^2\,b^4-12\,B\,a^3\,b^3+3\,B\,a^4\,b^2-8\,C\,a^2\,b^4+10\,C\,a^3\,b^3+23\,C\,a^4\,b^2+2\,B\,a\,b^5+6\,B\,a^5\,b-5\,C\,a\,b^5-6\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+4\,b\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,a^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2-3{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6{}\mathrm{i}\,C\,a^2-3{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)\,\left(6{}\mathrm{i}\,C\,a^2-3{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^5}-\frac{\left(\frac{\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6{}\mathrm{i}\,C\,a^2-3{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{b^5\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(6{}\mathrm{i}\,C\,a^2-3{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}\right)\,\left(6{}\mathrm{i}\,C\,a^2-3{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^5}}{-\frac{8\,\left(8\,A^3\,a^9\,b^6-4\,A^3\,a^8\,b^7-36\,A^3\,a^7\,b^8+26\,A^3\,a^6\,b^9+72\,A^3\,a^5\,b^{10}-52\,A^3\,a^4\,b^{11}-68\,A^3\,a^3\,b^{12}+48\,A^3\,a^2\,b^{13}+24\,A^3\,a\,b^{14}-72\,A^2\,B\,a^{10}\,b^5+36\,A^2\,B\,a^9\,b^6+324\,A^2\,B\,a^8\,b^7-210\,A^2\,B\,a^7\,b^8-624\,A^2\,B\,a^6\,b^9+396\,A^2\,B\,a^5\,b^{10}+564\,A^2\,B\,a^4\,b^{11}-312\,A^2\,B\,a^3\,b^{12}-192\,A^2\,B\,a^2\,b^{13}+144\,A^2\,C\,a^{11}\,b^4-72\,A^2\,C\,a^{10}\,b^5-636\,A^2\,C\,a^9\,b^6+408\,A^2\,C\,a^8\,b^7+1188\,A^2\,C\,a^7\,b^8-747\,A^2\,C\,a^6\,b^9-1020\,A^2\,C\,a^5\,b^{10}+552\,A^2\,C\,a^4\,b^{11}+300\,A^2\,C\,a^3\,b^{12}+12\,A^2\,C\,a^2\,b^{13}+24\,A^2\,C\,a\,b^{14}+216\,A\,B^2\,a^{11}\,b^4-108\,A\,B^2\,a^{10}\,b^5-972\,A\,B^2\,a^9\,b^6+558\,A\,B^2\,a^8\,b^7+1800\,A\,B^2\,a^7\,b^8-972\,A\,B^2\,a^6\,b^9-1548\,A\,B^2\,a^5\,b^{10}+648\,A\,B^2\,a^4\,b^{11}+504\,A\,B^2\,a^3\,b^{12}-864\,A\,B\,C\,a^{12}\,b^3+432\,A\,B\,C\,a^{11}\,b^4+3816\,A\,B\,C\,a^{10}\,b^5-2160\,A\,B\,C\,a^9\,b^6-6840\,A\,B\,C\,a^8\,b^7+3642\,A\,B\,C\,a^7\,b^8+5568\,A\,B\,C\,a^6\,b^9-2268\,A\,B\,C\,a^5\,b^{10}-1560\,A\,B\,C\,a^4\,b^{11}-24\,A\,B\,C\,a^3\,b^{12}-120\,A\,B\,C\,a^2\,b^{13}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}-216\,B^3\,a^{12}\,b^3+108\,B^3\,a^{11}\,b^4+972\,B^3\,a^{10}\,b^5-486\,B^3\,a^9\,b^6-1728\,B^3\,a^8\,b^7+756\,B^3\,a^7\,b^8+1404\,B^3\,a^6\,b^9-432\,B^3\,a^5\,b^{10}-432\,B^3\,a^4\,b^{11}+1296\,B^2\,C\,a^{13}\,b^2-648\,B^2\,C\,a^{12}\,b^3-5724\,B^2\,C\,a^{11}\,b^4+2808\,B^2\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5\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}{\frac{8\,\left(8\,A^3\,a^9\,b^6-4\,A^3\,a^8\,b^7-36\,A^3\,a^7\,b^8+26\,A^3\,a^6\,b^9+72\,A^3\,a^5\,b^{10}-52\,A^3\,a^4\,b^{11}-68\,A^3\,a^3\,b^{12}+48\,A^3\,a^2\,b^{13}+24\,A^3\,a\,b^{14}-72\,A^2\,B\,a^{10}\,b^5+36\,A^2\,B\,a^9\,b^6+324\,A^2\,B\,a^8\,b^7-210\,A^2\,B\,a^7\,b^8-624\,A^2\,B\,a^6\,b^9+396\,A^2\,B\,a^5\,b^{10}+564\,A^2\,B\,a^4\,b^{11}-312\,A^2\,B\,a^3\,b^{12}-192\,A^2\,B\,a^2\,b^{13}+144\,A^2\,C\,a^{11}\,b^4-72\,A^2\,C\,a^{10}\,b^5-636\,A^2\,C\,a^9\,b^6+408\,A^2\,C\,a^8\,b^7+1188\,A^2\,C\,a^7\,b^8-747\,A^2\,C\,a^6\,b^9-1020\,A^2\,C\,a^5\,b^{10}+552\,A^2\,C\,a^4\,b^{11}+300\,A^2\,C\,a^3\,b^{12}+12\,A^2\,C\,a^2\,b^{13}+24\,A^2\,C\,a\,b^{14}+216\,A\,B^2\,a^{11}\,b^4-108\,A\,B^2\,a^{10}\,b^5-972\,A\,B^2\,a^9\,b^6+558\,A\,B^2\,a^8\,b^7+1800\,A\,B^2\,a^7\,b^8-972\,A\,B^2\,a^6\,b^9-1548\,A\,B^2\,a^5\,b^{10}+648\,A\,B^2\,a^4\,b^{11}+504\,A\,B^2\,a^3\,b^{12}-864\,A\,B\,C\,a^{12}\,b^3+432\,A\,B\,C\,a^{11}\,b^4+3816\,A\,B\,C\,a^{10}\,b^5-2160\,A\,B\,C\,a^9\,b^6-6840\,A\,B\,C\,a^8\,b^7+3642\,A\,B\,C\,a^7\,b^8+5568\,A\,B\,C\,a^6\,b^9-2268\,A\,B\,C\,a^5\,b^{10}-1560\,A\,B\,C\,a^4\,b^{11}-24\,A\,B\,C\,a^3\,b^{12}-120\,A\,B\,C\,a^2\,b^{13}+864\,A\,C^2\,a^{13}\,b^2-432\,A\,C^2\,a^{12}\,b^3-3744\,A\,C^2\,a^{11}\,b^4+2088\,A\,C^2\,a^{10}\,b^5+6486\,A\,C^2\,a^9\,b^6-3405\,A\,C^2\,a^8\,b^7-4977\,A\,C^2\,a^7\,b^8+1974\,A\,C^2\,a^6\,b^9+1158\,A\,C^2\,a^5\,b^{10}+33\,A\,C^2\,a^4\,b^{11}+207\,A\,C^2\,a^3\,b^{12}-6\,A\,C^2\,a^2\,b^{13}+6\,A\,C^2\,a\,b^{14}-216\,B^3\,a^{12}\,b^3+108\,B^3\,a^{11}\,b^4+972\,B^3\,a^{10}\,b^5-486\,B^3\,a^9\,b^6-1728\,B^3\,a^8\,b^7+756\,B^3\,a^7\,b^8+1404\,B^3\,a^6\,b^9-432\,B^3\,a^5\,b^{10}-432\,B^3\,a^4\,b^{11}+1296\,B^2\,C\,a^{13}\,b^2-648\,B^2\,C\,a^{12}\,b^3-5724\,B^2\,C\,a^{11}\,b^4+2808\,B^2\,C\,a^{10}\,b^5+9828\,B^2\,C\,a^9\,b^6-4203\,B^2\,C\,a^8\,b^7-7524\,B^2\,C\,a^7\,b^8+2268\,B^2\,C\,a^6\,b^9+1980\,B^2\,C\,a^5\,b^{10}+144\,B^2\,C\,a^3\,b^{12}-2592\,B\,C^2\,a^{14}\,b+1296\,B\,C^2\,a^{13}\,b^2+11232\,B\,C^2\,a^{12}\,b^3-5400\,B\,C^2\,a^{11}\,b^4-18594\,B\,C^2\,a^{10}\,b^5+7767\,B\,C^2\,a^9\,b^6+13347\,B\,C^2\,a^8\,b^7-3972\,B\,C^2\,a^7\,b^8-2892\,B\,C^2\,a^6\,b^9+9\,B\,C^2\,a^5\,b^{10}-489\,B\,C^2\,a^4\,b^{11}+12\,B\,C^2\,a^3\,b^{12}-12\,B\,C^2\,a^2\,b^{13}+1728\,C^3\,a^{15}-864\,C^3\,a^{14}\,b-7344\,C^3\,a^{13}\,b^2+3456\,C^3\,a^{12}\,b^3+11700\,C^3\,a^{11}\,b^4-4770\,C^3\,a^{10}\,b^5-7829\,C^3\,a^9\,b^6+2326\,C^3\,a^8\,b^7+1314\,C^3\,a^7\,b^8-11\,C^3\,a^6\,b^9+411\,C^3\,a^5\,b^{10}-20\,C^3\,a^4\,b^{11}+20\,C^3\,a^3\,b^{12}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{10}\,b^4-8\,A^2\,a^9\,b^5-32\,A^2\,a^8\,b^6+32\,A^2\,a^7\,b^7+57\,A^2\,a^6\,b^8-48\,A^2\,a^5\,b^9-52\,A^2\,a^4\,b^{10}+32\,A^2\,a^3\,b^{11}+24\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+4\,A^2\,b^{14}-48\,A\,B\,a^{11}\,b^3+48\,A\,B\,a^{10}\,b^4+192\,A\,B\,a^9\,b^5-192\,A\,B\,a^8\,b^6-318\,A\,B\,a^7\,b^7+288\,A\,B\,a^6\,b^8+252\,A\,B\,a^5\,b^9-192\,A\,B\,a^4\,b^{10}-72\,A\,B\,a^3\,b^{11}+48\,A\,B\,a^2\,b^{12}-24\,A\,B\,a\,b^{13}+96\,A\,C\,a^{12}\,b^2-96\,A\,C\,a^{11}\,b^3-376\,A\,C\,a^{10}\,b^4+376\,A\,C\,a^9\,b^5+598\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7-444\,A\,C\,a^6\,b^8+336\,A\,C\,a^5\,b^9+104\,A\,C\,a^4\,b^{10}-64\,A\,C\,a^3\,b^{11}+36\,A\,C\,a^2\,b^{12}-8\,A\,C\,a\,b^{13}+4\,A\,C\,b^{14}+72\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3-288\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5+441\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7-288\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9+36\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+36\,B^2\,a^2\,b^{12}-288\,B\,C\,a^{13}\,b+288\,B\,C\,a^{12}\,b^2+1128\,B\,C\,a^{11}\,b^3-1128\,B\,C\,a^{10}\,b^4-1650\,B\,C\,a^9\,b^5+1632\,B\,C\,a^8\,b^6+984\,B\,C\,a^7\,b^7-1008\,B\,C\,a^6\,b^8-72\,B\,C\,a^5\,b^9+192\,B\,C\,a^4\,b^{10}-108\,B\,C\,a^3\,b^{11}+24\,B\,C\,a^2\,b^{12}-12\,B\,C\,a\,b^{13}+288\,C^2\,a^{14}-288\,C^2\,a^{13}\,b-1104\,C^2\,a^{12}\,b^2+1104\,C^2\,a^{11}\,b^3+1538\,C^2\,a^{10}\,b^4-1538\,C^2\,a^9\,b^5-827\,C^2\,a^8\,b^6+872\,C^2\,a^7\,b^7+18\,C^2\,a^6\,b^8-108\,C^2\,a^5\,b^9+74\,C^2\,a^4\,b^{10}-40\,C^2\,a^3\,b^{11}+21\,C^2\,a^2\,b^{12}-2\,C^2\,a\,b^{13}+C^2\,b^{14}\right)}{-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\left(\frac{4\,\left(8\,A\,b^{21}+4\,C\,b^{21}-16\,A\,a^2\,b^{19}+68\,A\,a^3\,b^{18}+12\,A\,a^4\,b^{17}-72\,A\,a^5\,b^{16}-8\,A\,a^6\,b^{15}+36\,A\,a^7\,b^{14}+4\,A\,a^8\,b^{13}-8\,A\,a^9\,b^{12}+48\,B\,a^2\,b^{19}+72\,B\,a^3\,b^{18}-156\,B\,a^4\,b^{17}-84\,B\,a^5\,b^{16}+192\,B\,a^6\,b^{15}+48\,B\,a^7\,b^{14}-108\,B\,a^8\,b^{13}-12\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}+28\,C\,a^2\,b^{19}-80\,C\,a^3\,b^{18}-120\,C\,a^4\,b^{17}+276\,C\,a^5\,b^{16}+164\,C\,a^6\,b^{15}-360\,C\,a^7\,b^{14}-100\,C\,a^8\,b^{13}+212\,C\,a^9\,b^{12}+24\,C\,a^{10}\,b^{11}-48\,C\,a^{11}\,b^{10}-24\,A\,a\,b^{20}-24\,B\,a\,b^{20}\right)}{-a^7\,b^{12}-a^6\,b^{13}+3\,a^5\,b^{14}+3\,a^4\,b^{15}-3\,a^3\,b^{16}-3\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+12\,C\,a^6-5\,A\,a^2\,b^4+2\,A\,a^4\,b^2+15\,B\,a^3\,b^3+20\,C\,a^2\,b^4-29\,C\,a^4\,b^2-12\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(3*C*b^7 - 36*C*a^7 - 2*B*b^7 - 6*A*a^2*b^5 + 15*A*a^3*b^4 + 3*A*a^4*b^3 - 6*A*a^5*b^2 + 10*B*a^2*b^5 + 16*B*a^3*b^4 - 35*B*a^4*b^3 - 9*B*a^5*b^2 + 5*C*a^2*b^5 - 26*C*a^3*b^4 - 29*C*a^4*b^3 + 67*C*a^5*b^2 - 4*B*a*b^6 + 18*B*a^6*b + 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^3*(2*B*b^7 + 36*C*a^7 + 3*C*b^7 - 6*A*a^2*b^5 - 15*A*a^3*b^4 + 3*A*a^4*b^3 + 6*A*a^5*b^2 - 10*B*a^2*b^5 + 16*B*a^3*b^4 + 35*B*a^4*b^3 - 9*B*a^5*b^2 + 5*C*a^2*b^5 + 26*C*a^3*b^4 - 29*C*a^4*b^3 - 67*C*a^5*b^2 - 4*B*a*b^6 - 18*B*a^6*b - 4*C*a*b^6 + 18*C*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^7*(C*b^6 - 12*C*a^6 - 2*B*b^6 + 6*A*a^2*b^4 + A*a^3*b^3 - 2*A*a^4*b^2 + 4*B*a^2*b^4 - 12*B*a^3*b^3 - 3*B*a^4*b^2 - 8*C*a^2*b^4 - 10*C*a^3*b^3 + 23*C*a^4*b^2 + 2*B*a*b^5 + 6*B*a^5*b + 5*C*a*b^5 + 6*C*a^5*b))/((a*b^4 - b^5)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*B*b^6 - 12*C*a^6 + C*b^6 + 6*A*a^2*b^4 - A*a^3*b^3 - 2*A*a^4*b^2 - 4*B*a^2*b^4 - 12*B*a^3*b^3 + 3*B*a^4*b^2 - 8*C*a^2*b^4 + 10*C*a^3*b^3 + 23*C*a^4*b^2 + 2*B*a*b^5 + 6*B*a^5*b - 5*C*a*b^5 - 6*C*a^5*b))/((a + b)*(b^6 - 2*a*b^5 + a^2*b^4)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^4*(6*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^2*(4*a*b + 4*a^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 4*a^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (atan(((((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i))/b^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i)*1i)/b^5 - (((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i))/b^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i)*1i)/b^5)/((((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i))/b^5 + (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i))/b^5 - (8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 - 432*B^3*a^4*b^11 - 432*B^3*a^5*b^10 + 1404*B^3*a^6*b^9 + 756*B^3*a^7*b^8 - 1728*B^3*a^8*b^7 - 486*B^3*a^9*b^6 + 972*B^3*a^10*b^5 + 108*B^3*a^11*b^4 - 216*B^3*a^12*b^3 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 2592*B*C^2*a^14*b + 504*A*B^2*a^3*b^12 + 648*A*B^2*a^4*b^11 - 1548*A*B^2*a^5*b^10 - 972*A*B^2*a^6*b^9 + 1800*A*B^2*a^7*b^8 + 558*A*B^2*a^8*b^7 - 972*A*B^2*a^9*b^6 - 108*A*B^2*a^10*b^5 + 216*A*B^2*a^11*b^4 - 192*A^2*B*a^2*b^13 - 312*A^2*B*a^3*b^12 + 564*A^2*B*a^4*b^11 + 396*A^2*B*a^5*b^10 - 624*A^2*B*a^6*b^9 - 210*A^2*B*a^7*b^8 + 324*A^2*B*a^8*b^7 + 36*A^2*B*a^9*b^6 - 72*A^2*B*a^10*b^5 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4 - 12*B*C^2*a^2*b^13 + 12*B*C^2*a^3*b^12 - 489*B*C^2*a^4*b^11 + 9*B*C^2*a^5*b^10 - 2892*B*C^2*a^6*b^9 - 3972*B*C^2*a^7*b^8 + 13347*B*C^2*a^8*b^7 + 7767*B*C^2*a^9*b^6 - 18594*B*C^2*a^10*b^5 - 5400*B*C^2*a^11*b^4 + 11232*B*C^2*a^12*b^3 + 1296*B*C^2*a^13*b^2 + 144*B^2*C*a^3*b^12 + 1980*B^2*C*a^5*b^10 + 2268*B^2*C*a^6*b^9 - 7524*B^2*C*a^7*b^8 - 4203*B^2*C*a^8*b^7 + 9828*B^2*C*a^9*b^6 + 2808*B^2*C*a^10*b^5 - 5724*B^2*C*a^11*b^4 - 648*B^2*C*a^12*b^3 + 1296*B^2*C*a^13*b^2 - 120*A*B*C*a^2*b^13 - 24*A*B*C*a^3*b^12 - 1560*A*B*C*a^4*b^11 - 2268*A*B*C*a^5*b^10 + 5568*A*B*C*a^6*b^9 + 3642*A*B*C*a^7*b^8 - 6840*A*B*C*a^8*b^7 - 2160*A*B*C*a^9*b^6 + 3816*A*B*C*a^10*b^5 + 432*A*B*C*a^11*b^4 - 864*A*B*C*a^12*b^3))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (((((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (8*tan(c/2 + (d*x)/2)*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/(b^5*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i))/b^5 - (8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i))/b^5))*(C*a^2*6i + b^2*(A*1i + (C*1i)/2) - B*a*b*3i)*2i)/(b^5*d) + (a*atan(((a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))/((8*(1728*C^3*a^15 + 24*A^3*a*b^14 - 864*C^3*a^14*b + 48*A^3*a^2*b^13 - 68*A^3*a^3*b^12 - 52*A^3*a^4*b^11 + 72*A^3*a^5*b^10 + 26*A^3*a^6*b^9 - 36*A^3*a^7*b^8 - 4*A^3*a^8*b^7 + 8*A^3*a^9*b^6 - 432*B^3*a^4*b^11 - 432*B^3*a^5*b^10 + 1404*B^3*a^6*b^9 + 756*B^3*a^7*b^8 - 1728*B^3*a^8*b^7 - 486*B^3*a^9*b^6 + 972*B^3*a^10*b^5 + 108*B^3*a^11*b^4 - 216*B^3*a^12*b^3 + 20*C^3*a^3*b^12 - 20*C^3*a^4*b^11 + 411*C^3*a^5*b^10 - 11*C^3*a^6*b^9 + 1314*C^3*a^7*b^8 + 2326*C^3*a^8*b^7 - 7829*C^3*a^9*b^6 - 4770*C^3*a^10*b^5 + 11700*C^3*a^11*b^4 + 3456*C^3*a^12*b^3 - 7344*C^3*a^13*b^2 + 6*A*C^2*a*b^14 + 24*A^2*C*a*b^14 - 2592*B*C^2*a^14*b + 504*A*B^2*a^3*b^12 + 648*A*B^2*a^4*b^11 - 1548*A*B^2*a^5*b^10 - 972*A*B^2*a^6*b^9 + 1800*A*B^2*a^7*b^8 + 558*A*B^2*a^8*b^7 - 972*A*B^2*a^9*b^6 - 108*A*B^2*a^10*b^5 + 216*A*B^2*a^11*b^4 - 192*A^2*B*a^2*b^13 - 312*A^2*B*a^3*b^12 + 564*A^2*B*a^4*b^11 + 396*A^2*B*a^5*b^10 - 624*A^2*B*a^6*b^9 - 210*A^2*B*a^7*b^8 + 324*A^2*B*a^8*b^7 + 36*A^2*B*a^9*b^6 - 72*A^2*B*a^10*b^5 - 6*A*C^2*a^2*b^13 + 207*A*C^2*a^3*b^12 + 33*A*C^2*a^4*b^11 + 1158*A*C^2*a^5*b^10 + 1974*A*C^2*a^6*b^9 - 4977*A*C^2*a^7*b^8 - 3405*A*C^2*a^8*b^7 + 6486*A*C^2*a^9*b^6 + 2088*A*C^2*a^10*b^5 - 3744*A*C^2*a^11*b^4 - 432*A*C^2*a^12*b^3 + 864*A*C^2*a^13*b^2 + 12*A^2*C*a^2*b^13 + 300*A^2*C*a^3*b^12 + 552*A^2*C*a^4*b^11 - 1020*A^2*C*a^5*b^10 - 747*A^2*C*a^6*b^9 + 1188*A^2*C*a^7*b^8 + 408*A^2*C*a^8*b^7 - 636*A^2*C*a^9*b^6 - 72*A^2*C*a^10*b^5 + 144*A^2*C*a^11*b^4 - 12*B*C^2*a^2*b^13 + 12*B*C^2*a^3*b^12 - 489*B*C^2*a^4*b^11 + 9*B*C^2*a^5*b^10 - 2892*B*C^2*a^6*b^9 - 3972*B*C^2*a^7*b^8 + 13347*B*C^2*a^8*b^7 + 7767*B*C^2*a^9*b^6 - 18594*B*C^2*a^10*b^5 - 5400*B*C^2*a^11*b^4 + 11232*B*C^2*a^12*b^3 + 1296*B*C^2*a^13*b^2 + 144*B^2*C*a^3*b^12 + 1980*B^2*C*a^5*b^10 + 2268*B^2*C*a^6*b^9 - 7524*B^2*C*a^7*b^8 - 4203*B^2*C*a^8*b^7 + 9828*B^2*C*a^9*b^6 + 2808*B^2*C*a^10*b^5 - 5724*B^2*C*a^11*b^4 - 648*B^2*C*a^12*b^3 + 1296*B^2*C*a^13*b^2 - 120*A*B*C*a^2*b^13 - 24*A*B*C*a^3*b^12 - 1560*A*B*C*a^4*b^11 - 2268*A*B*C*a^5*b^10 + 5568*A*B*C*a^6*b^9 + 3642*A*B*C*a^7*b^8 - 6840*A*B*C*a^8*b^7 - 2160*A*B*C*a^9*b^6 + 3816*A*B*C*a^10*b^5 + 432*A*B*C*a^11*b^4 - 864*A*B*C*a^12*b^3))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) + (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 288*C^2*a^14 + C^2*b^14 - 8*A^2*a*b^13 - 2*C^2*a*b^13 - 288*C^2*a^13*b + 24*A^2*a^2*b^12 + 32*A^2*a^3*b^11 - 52*A^2*a^4*b^10 - 48*A^2*a^5*b^9 + 57*A^2*a^6*b^8 + 32*A^2*a^7*b^7 - 32*A^2*a^8*b^6 - 8*A^2*a^9*b^5 + 8*A^2*a^10*b^4 + 36*B^2*a^2*b^12 - 72*B^2*a^3*b^11 + 36*B^2*a^4*b^10 + 288*B^2*a^5*b^9 - 288*B^2*a^6*b^8 - 432*B^2*a^7*b^7 + 441*B^2*a^8*b^6 + 288*B^2*a^9*b^5 - 288*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 72*B^2*a^12*b^2 + 21*C^2*a^2*b^12 - 40*C^2*a^3*b^11 + 74*C^2*a^4*b^10 - 108*C^2*a^5*b^9 + 18*C^2*a^6*b^8 + 872*C^2*a^7*b^7 - 827*C^2*a^8*b^6 - 1538*C^2*a^9*b^5 + 1538*C^2*a^10*b^4 + 1104*C^2*a^11*b^3 - 1104*C^2*a^12*b^2 + 4*A*C*b^14 - 24*A*B*a*b^13 - 8*A*C*a*b^13 - 12*B*C*a*b^13 - 288*B*C*a^13*b + 48*A*B*a^2*b^12 - 72*A*B*a^3*b^11 - 192*A*B*a^4*b^10 + 252*A*B*a^5*b^9 + 288*A*B*a^6*b^8 - 318*A*B*a^7*b^7 - 192*A*B*a^8*b^6 + 192*A*B*a^9*b^5 + 48*A*B*a^10*b^4 - 48*A*B*a^11*b^3 + 36*A*C*a^2*b^12 - 64*A*C*a^3*b^11 + 104*A*C*a^4*b^10 + 336*A*C*a^5*b^9 - 444*A*C*a^6*b^8 - 544*A*C*a^7*b^7 + 598*A*C*a^8*b^6 + 376*A*C*a^9*b^5 - 376*A*C*a^10*b^4 - 96*A*C*a^11*b^3 + 96*A*C*a^12*b^2 + 24*B*C*a^2*b^12 - 108*B*C*a^3*b^11 + 192*B*C*a^4*b^10 - 72*B*C*a^5*b^9 - 1008*B*C*a^6*b^8 + 984*B*C*a^7*b^7 + 1632*B*C*a^8*b^6 - 1650*B*C*a^9*b^5 - 1128*B*C*a^10*b^4 + 1128*B*C*a^11*b^3 + 288*B*C*a^12*b^2))/(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8) - (a*((4*(8*A*b^21 + 4*C*b^21 - 16*A*a^2*b^19 + 68*A*a^3*b^18 + 12*A*a^4*b^17 - 72*A*a^5*b^16 - 8*A*a^6*b^15 + 36*A*a^7*b^14 + 4*A*a^8*b^13 - 8*A*a^9*b^12 + 48*B*a^2*b^19 + 72*B*a^3*b^18 - 156*B*a^4*b^17 - 84*B*a^5*b^16 + 192*B*a^6*b^15 + 48*B*a^7*b^14 - 108*B*a^8*b^13 - 12*B*a^9*b^12 + 24*B*a^10*b^11 + 28*C*a^2*b^19 - 80*C*a^3*b^18 - 120*C*a^4*b^17 + 276*C*a^5*b^16 + 164*C*a^6*b^15 - 360*C*a^7*b^14 - 100*C*a^8*b^13 + 212*C*a^9*b^12 + 24*C*a^10*b^11 - 48*C*a^11*b^10 - 24*A*a*b^20 - 24*B*a*b^20))/(a*b^18 + b^19 - 3*a^2*b^17 - 3*a^3*b^16 + 3*a^4*b^15 + 3*a^5*b^14 - a^6*b^13 - a^7*b^12) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 12*C*a^6 - 5*A*a^2*b^4 + 2*A*a^4*b^2 + 15*B*a^3*b^3 + 20*C*a^2*b^4 - 29*C*a^4*b^2 - 12*B*a*b^5 - 6*B*a^5*b)*1i)/(d*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))","B"
995,1,6721,314,7.973536,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,C\,b^5-6\,C\,a^5+A\,a^2\,b^3-6\,B\,a^2\,b^3-B\,a^3\,b^2-4\,C\,a^2\,b^3+12\,C\,a^3\,b^2+4\,A\,a\,b^4+2\,B\,a^4\,b-2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,C\,a^5+2\,C\,b^5+A\,a^2\,b^3+6\,B\,a^2\,b^3-B\,a^3\,b^2-4\,C\,a^2\,b^3-12\,C\,a^3\,b^2-4\,A\,a\,b^4-2\,B\,a^4\,b+2\,C\,a\,b^4+3\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,b^6-6\,C\,a^6+3\,A\,a^2\,b^4-5\,B\,a^3\,b^3-6\,C\,a^2\,b^4+13\,C\,a^4\,b^2+2\,B\,a^5\,b\right)}{b\,\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+2\,a\,b-b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^2+2\,a\,b+b^2\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b-3\,C\,a\right)\,1{}\mathrm{i}}{b^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(B\,b\,1{}\mathrm{i}-C\,a\,3{}\mathrm{i}\right)}{b^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{16\,\left(-A^2\,B\,a^4\,b^8-4\,A^2\,B\,a^2\,b^{10}-4\,A^2\,B\,b^{12}+3\,A^2\,C\,a^5\,b^7+12\,A^2\,C\,a^3\,b^9+12\,A^2\,C\,a\,b^{11}+2\,A\,B^2\,a^7\,b^5+2\,A\,B^2\,a^6\,b^6-2\,A\,B^2\,a^5\,b^7-2\,A\,B^2\,a^3\,b^9-6\,A\,B^2\,a^2\,b^{10}+20\,A\,B^2\,a\,b^{11}+4\,A\,B^2\,b^{12}-12\,A\,B\,C\,a^8\,b^4-12\,A\,B\,C\,a^7\,b^5+12\,A\,B\,C\,a^6\,b^6+24\,A\,B\,C\,a^4\,b^8+36\,A\,B\,C\,a^3\,b^9-96\,A\,B\,C\,a^2\,b^{10}-24\,A\,B\,C\,a\,b^{11}+18\,A\,C^2\,a^9\,b^3+18\,A\,C^2\,a^8\,b^4-18\,A\,C^2\,a^7\,b^5-54\,A\,C^2\,a^5\,b^7-54\,A\,C^2\,a^4\,b^8+108\,A\,C^2\,a^3\,b^9+36\,A\,C^2\,a^2\,b^{10}-4\,B^3\,a^9\,b^3+2\,B^3\,a^8\,b^4+18\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6-36\,B^3\,a^5\,b^7+26\,B^3\,a^4\,b^8+34\,B^3\,a^3\,b^9-24\,B^3\,a^2\,b^{10}-12\,B^3\,a\,b^{11}+36\,B^2\,C\,a^{10}\,b^2-18\,B^2\,C\,a^9\,b^3-162\,B^2\,C\,a^8\,b^4+105\,B^2\,C\,a^7\,b^5+312\,B^2\,C\,a^6\,b^6-198\,B^2\,C\,a^5\,b^7-282\,B^2\,C\,a^4\,b^8+156\,B^2\,C\,a^3\,b^9+96\,B^2\,C\,a^2\,b^{10}-108\,B\,C^2\,a^{11}\,b+54\,B\,C^2\,a^{10}\,b^2+486\,B\,C^2\,a^9\,b^3-279\,B\,C^2\,a^8\,b^4-900\,B\,C^2\,a^7\,b^5+486\,B\,C^2\,a^6\,b^6+774\,B\,C^2\,a^5\,b^7-324\,B\,C^2\,a^4\,b^8-252\,B\,C^2\,a^3\,b^9+108\,C^3\,a^{12}-54\,C^3\,a^{11}\,b-486\,C^3\,a^{10}\,b^2+243\,C^3\,a^9\,b^3+864\,C^3\,a^8\,b^4-378\,C^3\,a^7\,b^5-702\,C^3\,a^6\,b^6+216\,C^3\,a^5\,b^7+216\,C^3\,a^4\,b^8\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^8+4\,A^2\,a^2\,b^{10}+4\,A^2\,b^{12}-4\,A\,B\,a^7\,b^5+2\,A\,B\,a^5\,b^7+8\,A\,B\,a^3\,b^9-24\,A\,B\,a\,b^{11}+12\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6-36\,A\,C\,a^4\,b^8+48\,A\,C\,a^2\,b^{10}+8\,B^2\,a^{10}\,b^2-8\,B^2\,a^9\,b^3-32\,B^2\,a^8\,b^4+32\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6-48\,B^2\,a^5\,b^7-52\,B^2\,a^4\,b^8+32\,B^2\,a^3\,b^9+24\,B^2\,a^2\,b^{10}-8\,B^2\,a\,b^{11}+4\,B^2\,b^{12}-48\,B\,C\,a^{11}\,b+48\,B\,C\,a^{10}\,b^2+192\,B\,C\,a^9\,b^3-192\,B\,C\,a^8\,b^4-318\,B\,C\,a^7\,b^5+288\,B\,C\,a^6\,b^6+252\,B\,C\,a^5\,b^7-192\,B\,C\,a^4\,b^8-72\,B\,C\,a^3\,b^9+48\,B\,C\,a^2\,b^{10}-24\,B\,C\,a\,b^{11}+72\,C^2\,a^{12}-72\,C^2\,a^{11}\,b-288\,C^2\,a^{10}\,b^2+288\,C^2\,a^9\,b^3+441\,C^2\,a^8\,b^4-432\,C^2\,a^7\,b^5-288\,C^2\,a^6\,b^6+288\,C^2\,a^5\,b^7+36\,C^2\,a^4\,b^8-72\,C^2\,a^3\,b^9+36\,C^2\,a^2\,b^{10}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,A\,b^{18}+4\,B\,b^{18}-6\,A\,a^2\,b^{16}+6\,A\,a^3\,b^{15}+2\,A\,a^6\,b^{12}-2\,A\,a^7\,b^{11}-8\,B\,a^2\,b^{16}+34\,B\,a^3\,b^{15}+6\,B\,a^4\,b^{14}-36\,B\,a^5\,b^{13}-4\,B\,a^6\,b^{12}+18\,B\,a^7\,b^{11}+2\,B\,a^8\,b^{10}-4\,B\,a^9\,b^9+24\,C\,a^2\,b^{16}+36\,C\,a^3\,b^{15}-78\,C\,a^4\,b^{14}-42\,C\,a^5\,b^{13}+96\,C\,a^6\,b^{12}+24\,C\,a^7\,b^{11}-54\,C\,a^8\,b^{10}-6\,C\,a^9\,b^9+12\,C\,a^{10}\,b^8-4\,A\,a\,b^{17}-12\,B\,a\,b^{17}-12\,C\,a\,b^{17}\right)}{-a^7\,b^9-a^6\,b^{10}+3\,a^5\,b^{11}+3\,a^4\,b^{12}-3\,a^3\,b^{13}-3\,a^2\,b^{14}+a\,b^{15}+b^{16}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^6+6\,C\,a^6+A\,a^2\,b^4+5\,B\,a^3\,b^3+12\,C\,a^2\,b^4-15\,C\,a^4\,b^2-6\,B\,a\,b^5-2\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1i)*(B*b - 3*C*a)*1i)/(b^4*d) - ((tan(c/2 + (d*x)/2)^5*(2*C*b^5 - 6*C*a^5 + A*a^2*b^3 - 6*B*a^2*b^3 - B*a^3*b^2 - 4*C*a^2*b^3 + 12*C*a^3*b^2 + 4*A*a*b^4 + 2*B*a^4*b - 2*C*a*b^4 + 3*C*a^4*b))/((a*b^3 - b^4)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(6*C*a^5 + 2*C*b^5 + A*a^2*b^3 + 6*B*a^2*b^3 - B*a^3*b^2 - 4*C*a^2*b^3 - 12*C*a^3*b^2 - 4*A*a*b^4 - 2*B*a^4*b + 2*C*a*b^4 + 3*C*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) + (2*tan(c/2 + (d*x)/2)^3*(2*C*b^6 - 6*C*a^6 + 3*A*a^2*b^4 - 5*B*a^3*b^3 - 6*C*a^2*b^4 + 13*C*a^4*b^2 + 2*B*a^5*b))/(b*(a*b^2 - b^3)*(a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) - (log(tan(c/2 + (d*x)/2) - 1i)*(B*b*1i - C*a*3i))/(b^4*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*1i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((16*(108*C^3*a^12 + 4*A*B^2*b^12 - 4*A^2*B*b^12 - 12*B^3*a*b^11 - 54*C^3*a^11*b - 24*B^3*a^2*b^10 + 34*B^3*a^3*b^9 + 26*B^3*a^4*b^8 - 36*B^3*a^5*b^7 - 13*B^3*a^6*b^6 + 18*B^3*a^7*b^5 + 2*B^3*a^8*b^4 - 4*B^3*a^9*b^3 + 216*C^3*a^4*b^8 + 216*C^3*a^5*b^7 - 702*C^3*a^6*b^6 - 378*C^3*a^7*b^5 + 864*C^3*a^8*b^4 + 243*C^3*a^9*b^3 - 486*C^3*a^10*b^2 + 20*A*B^2*a*b^11 + 12*A^2*C*a*b^11 - 108*B*C^2*a^11*b - 6*A*B^2*a^2*b^10 - 2*A*B^2*a^3*b^9 - 2*A*B^2*a^5*b^7 + 2*A*B^2*a^6*b^6 + 2*A*B^2*a^7*b^5 - 4*A^2*B*a^2*b^10 - A^2*B*a^4*b^8 + 36*A*C^2*a^2*b^10 + 108*A*C^2*a^3*b^9 - 54*A*C^2*a^4*b^8 - 54*A*C^2*a^5*b^7 - 18*A*C^2*a^7*b^5 + 18*A*C^2*a^8*b^4 + 18*A*C^2*a^9*b^3 + 12*A^2*C*a^3*b^9 + 3*A^2*C*a^5*b^7 - 252*B*C^2*a^3*b^9 - 324*B*C^2*a^4*b^8 + 774*B*C^2*a^5*b^7 + 486*B*C^2*a^6*b^6 - 900*B*C^2*a^7*b^5 - 279*B*C^2*a^8*b^4 + 486*B*C^2*a^9*b^3 + 54*B*C^2*a^10*b^2 + 96*B^2*C*a^2*b^10 + 156*B^2*C*a^3*b^9 - 282*B^2*C*a^4*b^8 - 198*B^2*C*a^5*b^7 + 312*B^2*C*a^6*b^6 + 105*B^2*C*a^7*b^5 - 162*B^2*C*a^8*b^4 - 18*B^2*C*a^9*b^3 + 36*B^2*C*a^10*b^2 - 24*A*B*C*a*b^11 - 96*A*B*C*a^2*b^10 + 36*A*B*C*a^3*b^9 + 24*A*B*C*a^4*b^8 + 12*A*B*C*a^6*b^6 - 12*A*B*C*a^7*b^5 - 12*A*B*C*a^8*b^4))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 4*B^2*b^12 + 72*C^2*a^12 - 8*B^2*a*b^11 - 72*C^2*a^11*b + 4*A^2*a^2*b^10 + A^2*a^4*b^8 + 24*B^2*a^2*b^10 + 32*B^2*a^3*b^9 - 52*B^2*a^4*b^8 - 48*B^2*a^5*b^7 + 57*B^2*a^6*b^6 + 32*B^2*a^7*b^5 - 32*B^2*a^8*b^4 - 8*B^2*a^9*b^3 + 8*B^2*a^10*b^2 + 36*C^2*a^2*b^10 - 72*C^2*a^3*b^9 + 36*C^2*a^4*b^8 + 288*C^2*a^5*b^7 - 288*C^2*a^6*b^6 - 432*C^2*a^7*b^5 + 441*C^2*a^8*b^4 + 288*C^2*a^9*b^3 - 288*C^2*a^10*b^2 - 24*A*B*a*b^11 - 24*B*C*a*b^11 - 48*B*C*a^11*b + 8*A*B*a^3*b^9 + 2*A*B*a^5*b^7 - 4*A*B*a^7*b^5 + 48*A*C*a^2*b^10 - 36*A*C*a^4*b^8 - 6*A*C*a^6*b^6 + 12*A*C*a^8*b^4 + 48*B*C*a^2*b^10 - 72*B*C*a^3*b^9 - 192*B*C*a^4*b^8 + 252*B*C*a^5*b^7 + 288*B*C*a^6*b^6 - 318*B*C*a^7*b^5 - 192*B*C*a^8*b^4 + 192*B*C*a^9*b^3 + 48*B*C*a^10*b^2))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*A*b^18 + 4*B*b^18 - 6*A*a^2*b^16 + 6*A*a^3*b^15 + 2*A*a^6*b^12 - 2*A*a^7*b^11 - 8*B*a^2*b^16 + 34*B*a^3*b^15 + 6*B*a^4*b^14 - 36*B*a^5*b^13 - 4*B*a^6*b^12 + 18*B*a^7*b^11 + 2*B*a^8*b^10 - 4*B*a^9*b^9 + 24*C*a^2*b^16 + 36*C*a^3*b^15 - 78*C*a^4*b^14 - 42*C*a^5*b^13 + 96*C*a^6*b^12 + 24*C*a^7*b^11 - 54*C*a^8*b^10 - 6*C*a^9*b^9 + 12*C*a^10*b^8 - 4*A*a*b^17 - 12*B*a*b^17 - 12*C*a*b^17))/(a*b^15 + b^16 - 3*a^2*b^14 - 3*a^3*b^13 + 3*a^4*b^12 + 3*a^5*b^11 - a^6*b^10 - a^7*b^9) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^6 + 6*C*a^6 + A*a^2*b^4 + 5*B*a^3*b^3 + 12*C*a^2*b^4 - 15*C*a^4*b^2 - 6*B*a*b^5 - 2*B*a^5*b)*1i)/(d*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))","B"
996,1,8146,233,12.092066,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2-B\,a^2\,b^2+6\,C\,a^2\,b^2+A\,a\,b^3-4\,B\,a\,b^3+C\,a^3\,b\right)}{\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4+2\,A\,a^2\,b^2+B\,a^2\,b^2+6\,C\,a^2\,b^2-A\,a\,b^3-4\,B\,a\,b^3-C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^2\,b^2-2\,a\,b^3+b^4\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{2\,C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)}{b^3}}{\frac{16\,\left(9\,A^2\,C\,a^2\,b^7-6\,A\,B\,C\,a^3\,b^6-12\,A\,B\,C\,a\,b^8+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{C\,\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)\,8{}\mathrm{i}}{b^3\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^3}\right)\,1{}\mathrm{i}}{b^3}}\right)}{b^3\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}{\frac{16\,\left(9\,A^2\,C\,a^2\,b^7-6\,A\,B\,C\,a^3\,b^6-12\,A\,B\,C\,a\,b^8+6\,A\,C^2\,a^6\,b^3+6\,A\,C^2\,a^5\,b^4-18\,A\,C^2\,a^4\,b^5-12\,A\,C^2\,a^3\,b^6+30\,A\,C^2\,a^2\,b^7+6\,A\,C^2\,a\,b^8+B^2\,C\,a^4\,b^5+4\,B^2\,C\,a^2\,b^7+4\,B^2\,C\,b^9-2\,B\,C^2\,a^7\,b^2-2\,B\,C^2\,a^6\,b^3+2\,B\,C^2\,a^5\,b^4+2\,B\,C^2\,a^3\,b^6+6\,B\,C^2\,a^2\,b^7-20\,B\,C^2\,a\,b^8-4\,B\,C^2\,b^9+4\,C^3\,a^9-2\,C^3\,a^8\,b-18\,C^3\,a^7\,b^2+13\,C^3\,a^6\,b^3+36\,C^3\,a^5\,b^4-26\,C^3\,a^4\,b^5-34\,C^3\,a^3\,b^6+24\,C^3\,a^2\,b^7+12\,C^3\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^2\,b^8-6\,A\,B\,a^3\,b^7-12\,A\,B\,a\,b^9+12\,A\,C\,a^6\,b^4-30\,A\,C\,a^4\,b^6+36\,A\,C\,a^2\,b^8+B^2\,a^4\,b^6+4\,B^2\,a^2\,b^8+4\,B^2\,b^{10}-4\,B\,C\,a^7\,b^3+2\,B\,C\,a^5\,b^5+8\,B\,C\,a^3\,b^7-24\,B\,C\,a\,b^9+8\,C^2\,a^{10}-8\,C^2\,a^9\,b-32\,C^2\,a^8\,b^2+32\,C^2\,a^7\,b^3+57\,C^2\,a^6\,b^4-48\,C^2\,a^5\,b^5-52\,C^2\,a^4\,b^6+32\,C^2\,a^3\,b^7+24\,C^2\,a^2\,b^8-8\,C^2\,a\,b^9+4\,C^2\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{\left(\frac{8\,\left(4\,B\,b^{15}+4\,C\,b^{15}+6\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-12\,A\,a^4\,b^{11}-6\,A\,a^5\,b^{10}+6\,A\,a^6\,b^9-6\,B\,a^2\,b^{13}+6\,B\,a^3\,b^{12}+2\,B\,a^6\,b^9-2\,B\,a^7\,b^8-8\,C\,a^2\,b^{13}+34\,C\,a^3\,b^{12}+6\,C\,a^4\,b^{11}-36\,C\,a^5\,b^{10}-4\,C\,a^6\,b^9+18\,C\,a^7\,b^8+2\,C\,a^8\,b^7-4\,C\,a^9\,b^6-6\,A\,a\,b^{14}-4\,B\,a\,b^{14}-12\,C\,a\,b^{14}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,B\,b^5-2\,C\,a^5+B\,a^2\,b^3+5\,C\,a^3\,b^2-3\,A\,a\,b^4-6\,C\,a\,b^4\right)\,1{}\mathrm{i}}{d\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 - B*a^2*b^2 + 6*C*a^2*b^2 + A*a*b^3 - 4*B*a*b^3 + C*a^3*b))/((a*b^2 - b^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 + 2*A*a^2*b^2 + B*a^2*b^2 + 6*C*a^2*b^2 - A*a*b^3 - 4*B*a*b^3 - C*a^3*b))/((a + b)*(b^4 - 2*a*b^3 + a^2*b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (2*C*atan(((C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3))/b^3 + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3))/b^3)/((16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 - 20*B*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5 - 12*A*B*C*a*b^8 - 6*A*B*C*a^3*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3)*1i)/b^3 + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (C*((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (C*tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3)*1i)/b^3)))/(b^3*d) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))/((16*(4*C^3*a^9 - 4*B*C^2*b^9 + 4*B^2*C*b^9 + 12*C^3*a*b^8 - 2*C^3*a^8*b + 24*C^3*a^2*b^7 - 34*C^3*a^3*b^6 - 26*C^3*a^4*b^5 + 36*C^3*a^5*b^4 + 13*C^3*a^6*b^3 - 18*C^3*a^7*b^2 + 6*A*C^2*a*b^8 - 20*B*C^2*a*b^8 + 30*A*C^2*a^2*b^7 - 12*A*C^2*a^3*b^6 - 18*A*C^2*a^4*b^5 + 6*A*C^2*a^5*b^4 + 6*A*C^2*a^6*b^3 + 9*A^2*C*a^2*b^7 + 6*B*C^2*a^2*b^7 + 2*B*C^2*a^3*b^6 + 2*B*C^2*a^5*b^4 - 2*B*C^2*a^6*b^3 - 2*B*C^2*a^7*b^2 + 4*B^2*C*a^2*b^7 + B^2*C*a^4*b^5 - 12*A*B*C*a*b^8 - 6*A*B*C*a^3*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^10 + 8*C^2*a^10 + 4*C^2*b^10 - 8*C^2*a*b^9 - 8*C^2*a^9*b + 9*A^2*a^2*b^8 + 4*B^2*a^2*b^8 + B^2*a^4*b^6 + 24*C^2*a^2*b^8 + 32*C^2*a^3*b^7 - 52*C^2*a^4*b^6 - 48*C^2*a^5*b^5 + 57*C^2*a^6*b^4 + 32*C^2*a^7*b^3 - 32*C^2*a^8*b^2 - 12*A*B*a*b^9 - 24*B*C*a*b^9 - 6*A*B*a^3*b^7 + 36*A*C*a^2*b^8 - 30*A*C*a^4*b^6 + 12*A*C*a^6*b^4 + 8*B*C*a^3*b^7 + 2*B*C*a^5*b^5 - 4*B*C*a^7*b^3))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (((8*(4*B*b^15 + 4*C*b^15 + 6*A*a^2*b^13 + 12*A*a^3*b^12 - 12*A*a^4*b^11 - 6*A*a^5*b^10 + 6*A*a^6*b^9 - 6*B*a^2*b^13 + 6*B*a^3*b^12 + 2*B*a^6*b^9 - 2*B*a^7*b^8 - 8*C*a^2*b^13 + 34*C*a^3*b^12 + 6*C*a^4*b^11 - 36*C*a^5*b^10 - 4*C*a^6*b^9 + 18*C*a^7*b^8 + 2*C*a^8*b^7 - 4*C*a^9*b^6 - 6*A*a*b^14 - 4*B*a*b^14 - 12*C*a*b^14))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*B*b^5 - 2*C*a^5 + B*a^2*b^3 + 5*C*a^3*b^2 - 3*A*a*b^4 - 6*C*a*b^4)*1i)/(d*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))","B"
997,1,281,202,4.966945,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,A\,a^2+A\,b^2+C\,a^2+2\,C\,b^2-3\,B\,a\,b\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^2-2\,B\,a^2-2\,B\,b^2+C\,a^2+4\,A\,a\,b-B\,a\,b+4\,C\,a\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^2+2\,B\,a^2+2\,B\,b^2+C\,a^2-4\,A\,a\,b-B\,a\,b-4\,C\,a\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"(atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*A*a^2 + A*b^2 + C*a^2 + 2*C*b^2 - 3*B*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((tan(c/2 + (d*x)/2)^3*(A*b^2 - 2*B*a^2 - 2*B*b^2 + C*a^2 + 4*A*a*b - B*a*b + 4*C*a*b))/((a + b)^2*(a - b)) - (tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 + C*a^2 - 4*A*a*b - B*a*b - 4*C*a*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
998,1,8151,238,12.288555,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,a^4-2\,A\,b^4+6\,A\,a^2\,b^2-B\,a^2\,b^2+2\,C\,a^2\,b^2+A\,a\,b^3-4\,B\,a^3\,b+C\,a^3\,b\right)}{\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^4-2\,C\,a^4-6\,A\,a^2\,b^2-B\,a^2\,b^2-2\,C\,a^2\,b^2+A\,a\,b^3+4\,B\,a^3\,b+C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}\right)\,1{}\mathrm{i}}{a^3}}{\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9-4\,A^2\,B\,a^9-20\,A^2\,B\,a^8\,b+6\,A^2\,B\,a^7\,b^2+2\,A^2\,B\,a^6\,b^3+2\,A^2\,B\,a^4\,b^5-2\,A^2\,B\,a^3\,b^6-2\,A^2\,B\,a^2\,b^7+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^2\,a^5\,b^4-12\,A\,B\,C\,a^8\,b-6\,A\,B\,C\,a^6\,b^3+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}\right)}{a^3}-\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)}{a^3}\right)}{a^3}}\right)\,2{}\mathrm{i}}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}{\frac{16\,\left(12\,A^3\,a^8\,b+24\,A^3\,a^7\,b^2-34\,A^3\,a^6\,b^3-26\,A^3\,a^5\,b^4+36\,A^3\,a^4\,b^5+13\,A^3\,a^3\,b^6-18\,A^3\,a^2\,b^7-2\,A^3\,a\,b^8+4\,A^3\,b^9-4\,A^2\,B\,a^9-20\,A^2\,B\,a^8\,b+6\,A^2\,B\,a^7\,b^2+2\,A^2\,B\,a^6\,b^3+2\,A^2\,B\,a^4\,b^5-2\,A^2\,B\,a^3\,b^6-2\,A^2\,B\,a^2\,b^7+6\,A^2\,C\,a^8\,b+30\,A^2\,C\,a^7\,b^2-12\,A^2\,C\,a^6\,b^3-18\,A^2\,C\,a^5\,b^4+6\,A^2\,C\,a^4\,b^5+6\,A^2\,C\,a^3\,b^6+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^2\,a^5\,b^4-12\,A\,B\,C\,a^8\,b-6\,A\,B\,C\,a^6\,b^3+9\,A\,C^2\,a^7\,b^2\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{10}-8\,A^2\,a^9\,b+24\,A^2\,a^8\,b^2+32\,A^2\,a^7\,b^3-52\,A^2\,a^6\,b^4-48\,A^2\,a^5\,b^5+57\,A^2\,a^4\,b^6+32\,A^2\,a^3\,b^7-32\,A^2\,a^2\,b^8-8\,A^2\,a\,b^9+8\,A^2\,b^{10}-24\,A\,B\,a^9\,b+8\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5-4\,A\,B\,a^3\,b^7+36\,A\,C\,a^8\,b^2-30\,A\,C\,a^6\,b^4+12\,A\,C\,a^4\,b^6+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^2\,a^6\,b^4-12\,B\,C\,a^9\,b-6\,B\,C\,a^7\,b^3+9\,C^2\,a^8\,b^2\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{\left(\frac{8\,\left(4\,A\,a^{15}+4\,B\,a^{15}-4\,A\,a^6\,b^9+2\,A\,a^7\,b^8+18\,A\,a^8\,b^7-4\,A\,a^9\,b^6-36\,A\,a^{10}\,b^5+6\,A\,a^{11}\,b^4+34\,A\,a^{12}\,b^3-8\,A\,a^{13}\,b^2-2\,B\,a^8\,b^7+2\,B\,a^9\,b^6+6\,B\,a^{12}\,b^3-6\,B\,a^{13}\,b^2+6\,C\,a^9\,b^6-6\,C\,a^{10}\,b^5-12\,C\,a^{11}\,b^4+12\,C\,a^{12}\,b^3+6\,C\,a^{13}\,b^2-12\,A\,a^{14}\,b-4\,B\,a^{14}\,b-6\,C\,a^{14}\,b\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,A\,b^5-2\,B\,a^5-5\,A\,a^2\,b^3-B\,a^3\,b^2+6\,A\,a^4\,b+3\,C\,a^4\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^3*(2*C*a^4 - 2*A*b^4 + 6*A*a^2*b^2 - B*a^2*b^2 + 2*C*a^2*b^2 + A*a*b^3 - 4*B*a^3*b + C*a^3*b))/((a^2*b - a^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*A*b^4 - 2*C*a^4 - 6*A*a^2*b^2 - B*a^2*b^2 - 2*C*a^2*b^2 + A*a*b^3 + 4*B*a^3*b + C*a^3*b))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (A*atan(((A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3)*1i)/a^3 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3)*1i)/a^3)/((16*(4*A^3*b^9 + 4*A*B^2*a^9 - 4*A^2*B*a^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 - 20*A^2*B*a^8*b + 6*A^2*C*a^8*b + A*B^2*a^5*b^4 + 4*A*B^2*a^7*b^2 - 2*A^2*B*a^2*b^7 - 2*A^2*B*a^3*b^6 + 2*A^2*B*a^4*b^5 + 2*A^2*B*a^6*b^3 + 6*A^2*B*a^7*b^2 + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2 - 12*A*B*C*a^8*b - 6*A*B*C*a^6*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3))/a^3 - (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (A*((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))))/a^3))/a^3))*2i)/(a^3*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))/((16*(4*A^3*b^9 + 4*A*B^2*a^9 - 4*A^2*B*a^9 - 2*A^3*a*b^8 + 12*A^3*a^8*b - 18*A^3*a^2*b^7 + 13*A^3*a^3*b^6 + 36*A^3*a^4*b^5 - 26*A^3*a^5*b^4 - 34*A^3*a^6*b^3 + 24*A^3*a^7*b^2 - 20*A^2*B*a^8*b + 6*A^2*C*a^8*b + A*B^2*a^5*b^4 + 4*A*B^2*a^7*b^2 - 2*A^2*B*a^2*b^7 - 2*A^2*B*a^3*b^6 + 2*A^2*B*a^4*b^5 + 2*A^2*B*a^6*b^3 + 6*A^2*B*a^7*b^2 + 9*A*C^2*a^7*b^2 + 6*A^2*C*a^3*b^6 + 6*A^2*C*a^4*b^5 - 18*A^2*C*a^5*b^4 - 12*A^2*C*a^6*b^3 + 30*A^2*C*a^7*b^2 - 12*A*B*C*a^8*b - 6*A*B*C*a^6*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^10 + 8*A^2*b^10 + 4*B^2*a^10 - 8*A^2*a*b^9 - 8*A^2*a^9*b - 32*A^2*a^2*b^8 + 32*A^2*a^3*b^7 + 57*A^2*a^4*b^6 - 48*A^2*a^5*b^5 - 52*A^2*a^6*b^4 + 32*A^2*a^7*b^3 + 24*A^2*a^8*b^2 + B^2*a^6*b^4 + 4*B^2*a^8*b^2 + 9*C^2*a^8*b^2 - 24*A*B*a^9*b - 12*B*C*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*a^7*b^3 + 12*A*C*a^4*b^6 - 30*A*C*a^6*b^4 + 36*A*C*a^8*b^2 - 6*B*C*a^7*b^3))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (((8*(4*A*a^15 + 4*B*a^15 - 4*A*a^6*b^9 + 2*A*a^7*b^8 + 18*A*a^8*b^7 - 4*A*a^9*b^6 - 36*A*a^10*b^5 + 6*A*a^11*b^4 + 34*A*a^12*b^3 - 8*A*a^13*b^2 - 2*B*a^8*b^7 + 2*B*a^9*b^6 + 6*B*a^12*b^3 - 6*B*a^13*b^2 + 6*C*a^9*b^6 - 6*C*a^10*b^5 - 12*C*a^11*b^4 + 12*C*a^12*b^3 + 6*C*a^13*b^2 - 12*A*a^14*b - 4*B*a^14*b - 6*C*a^14*b))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*A*b^5 - 2*B*a^5 - 5*A*a^2*b^3 - B*a^3*b^2 + 6*A*a^4*b + 3*C*a^4*b)*1i)/(d*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))","B"
999,1,11417,339,13.864427,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^5-6\,A\,b^5+12\,A\,a^2\,b^3-4\,A\,a^3\,b^2-B\,a^2\,b^3-6\,B\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4-2\,A\,a^4\,b+2\,B\,a\,b^4+4\,C\,a^4\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^5+6\,A\,b^5-12\,A\,a^2\,b^3-4\,A\,a^3\,b^2-B\,a^2\,b^3+6\,B\,a^3\,b^2+C\,a^3\,b^2+3\,A\,a\,b^4+2\,A\,a^4\,b-2\,B\,a\,b^4-4\,C\,a^4\,b\right)}{\left(a+b\right)\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,a^6-6\,A\,b^6+13\,A\,a^2\,b^4-6\,A\,a^4\,b^2-5\,B\,a^3\,b^3+3\,C\,a^4\,b^2+2\,B\,a\,b^5\right)}{a\,\left(a^2\,b-a^3\right)\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^2+2\,a\,b+3\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+2\,a\,b-3\,b^2\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A\,b-B\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A\,b-B\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}\right)\,1{}\mathrm{i}}{a^4}}{\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A\,b-B\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}\right)}{a^4}-\frac{16\,\left(216\,A^3\,a^8\,b^4+216\,A^3\,a^7\,b^5-702\,A^3\,a^6\,b^6-378\,A^3\,a^5\,b^7+864\,A^3\,a^4\,b^8+243\,A^3\,a^3\,b^9-486\,A^3\,a^2\,b^{10}-54\,A^3\,a\,b^{11}+108\,A^3\,b^{12}-252\,A^2\,B\,a^9\,b^3-324\,A^2\,B\,a^8\,b^4+774\,A^2\,B\,a^7\,b^5+486\,A^2\,B\,a^6\,b^6-900\,A^2\,B\,a^5\,b^7-279\,A^2\,B\,a^4\,b^8+486\,A^2\,B\,a^3\,b^9+54\,A^2\,B\,a^2\,b^{10}-108\,A^2\,B\,a\,b^{11}+36\,A^2\,C\,a^{10}\,b^2+108\,A^2\,C\,a^9\,b^3-54\,A^2\,C\,a^8\,b^4-54\,A^2\,C\,a^7\,b^5-18\,A^2\,C\,a^5\,b^7+18\,A^2\,C\,a^4\,b^8+18\,A^2\,C\,a^3\,b^9+96\,A\,B^2\,a^{10}\,b^2+156\,A\,B^2\,a^9\,b^3-282\,A\,B^2\,a^8\,b^4-198\,A\,B^2\,a^7\,b^5+312\,A\,B^2\,a^6\,b^6+105\,A\,B^2\,a^5\,b^7-162\,A\,B^2\,a^4\,b^8-18\,A\,B^2\,a^3\,b^9+36\,A\,B^2\,a^2\,b^{10}-24\,A\,B\,C\,a^{11}\,b-96\,A\,B\,C\,a^{10}\,b^2+36\,A\,B\,C\,a^9\,b^3+24\,A\,B\,C\,a^8\,b^4+12\,A\,B\,C\,a^6\,b^6-12\,A\,B\,C\,a^5\,b^7-12\,A\,B\,C\,a^4\,b^8+12\,A\,C^2\,a^{11}\,b+12\,A\,C^2\,a^9\,b^3+3\,A\,C^2\,a^7\,b^5-12\,B^3\,a^{11}\,b-24\,B^3\,a^{10}\,b^2+34\,B^3\,a^9\,b^3+26\,B^3\,a^8\,b^4-36\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6+18\,B^3\,a^5\,b^7+2\,B^3\,a^4\,b^8-4\,B^3\,a^3\,b^9+4\,B^2\,C\,a^{12}+20\,B^2\,C\,a^{11}\,b-6\,B^2\,C\,a^{10}\,b^2-2\,B^2\,C\,a^9\,b^3-2\,B^2\,C\,a^7\,b^5+2\,B^2\,C\,a^6\,b^6+2\,B^2\,C\,a^5\,b^7-4\,B\,C^2\,a^{12}-4\,B\,C^2\,a^{10}\,b^2-B\,C^2\,a^8\,b^4\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{\left(3\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A\,b-B\,a\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}\right)}{a^4}}\right)\,\left(3\,A\,b-B\,a\right)\,2{}\mathrm{i}}{a^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{16\,\left(216\,A^3\,a^8\,b^4+216\,A^3\,a^7\,b^5-702\,A^3\,a^6\,b^6-378\,A^3\,a^5\,b^7+864\,A^3\,a^4\,b^8+243\,A^3\,a^3\,b^9-486\,A^3\,a^2\,b^{10}-54\,A^3\,a\,b^{11}+108\,A^3\,b^{12}-252\,A^2\,B\,a^9\,b^3-324\,A^2\,B\,a^8\,b^4+774\,A^2\,B\,a^7\,b^5+486\,A^2\,B\,a^6\,b^6-900\,A^2\,B\,a^5\,b^7-279\,A^2\,B\,a^4\,b^8+486\,A^2\,B\,a^3\,b^9+54\,A^2\,B\,a^2\,b^{10}-108\,A^2\,B\,a\,b^{11}+36\,A^2\,C\,a^{10}\,b^2+108\,A^2\,C\,a^9\,b^3-54\,A^2\,C\,a^8\,b^4-54\,A^2\,C\,a^7\,b^5-18\,A^2\,C\,a^5\,b^7+18\,A^2\,C\,a^4\,b^8+18\,A^2\,C\,a^3\,b^9+96\,A\,B^2\,a^{10}\,b^2+156\,A\,B^2\,a^9\,b^3-282\,A\,B^2\,a^8\,b^4-198\,A\,B^2\,a^7\,b^5+312\,A\,B^2\,a^6\,b^6+105\,A\,B^2\,a^5\,b^7-162\,A\,B^2\,a^4\,b^8-18\,A\,B^2\,a^3\,b^9+36\,A\,B^2\,a^2\,b^{10}-24\,A\,B\,C\,a^{11}\,b-96\,A\,B\,C\,a^{10}\,b^2+36\,A\,B\,C\,a^9\,b^3+24\,A\,B\,C\,a^8\,b^4+12\,A\,B\,C\,a^6\,b^6-12\,A\,B\,C\,a^5\,b^7-12\,A\,B\,C\,a^4\,b^8+12\,A\,C^2\,a^{11}\,b+12\,A\,C^2\,a^9\,b^3+3\,A\,C^2\,a^7\,b^5-12\,B^3\,a^{11}\,b-24\,B^3\,a^{10}\,b^2+34\,B^3\,a^9\,b^3+26\,B^3\,a^8\,b^4-36\,B^3\,a^7\,b^5-13\,B^3\,a^6\,b^6+18\,B^3\,a^5\,b^7+2\,B^3\,a^4\,b^8-4\,B^3\,a^3\,b^9+4\,B^2\,C\,a^{12}+20\,B^2\,C\,a^{11}\,b-6\,B^2\,C\,a^{10}\,b^2-2\,B^2\,C\,a^9\,b^3-2\,B^2\,C\,a^7\,b^5+2\,B^2\,C\,a^6\,b^6+2\,B^2\,C\,a^5\,b^7-4\,B\,C^2\,a^{12}-4\,B\,C^2\,a^{10}\,b^2-B\,C^2\,a^8\,b^4\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,A^2\,a^{10}\,b^2-72\,A^2\,a^9\,b^3+36\,A^2\,a^8\,b^4+288\,A^2\,a^7\,b^5-288\,A^2\,a^6\,b^6-432\,A^2\,a^5\,b^7+441\,A^2\,a^4\,b^8+288\,A^2\,a^3\,b^9-288\,A^2\,a^2\,b^{10}-72\,A^2\,a\,b^{11}+72\,A^2\,b^{12}-24\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2-72\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4+252\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6-318\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8+192\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-48\,A\,B\,a\,b^{11}+48\,A\,C\,a^{10}\,b^2-36\,A\,C\,a^8\,b^4-6\,A\,C\,a^6\,b^6+12\,A\,C\,a^4\,b^8+4\,B^2\,a^{12}-8\,B^2\,a^{11}\,b+24\,B^2\,a^{10}\,b^2+32\,B^2\,a^9\,b^3-52\,B^2\,a^8\,b^4-48\,B^2\,a^7\,b^5+57\,B^2\,a^6\,b^6+32\,B^2\,a^5\,b^7-32\,B^2\,a^4\,b^8-8\,B^2\,a^3\,b^9+8\,B^2\,a^2\,b^{10}-24\,B\,C\,a^{11}\,b+8\,B\,C\,a^9\,b^3+2\,B\,C\,a^7\,b^5-4\,B\,C\,a^5\,b^7+4\,C^2\,a^{12}+4\,C^2\,a^{10}\,b^2+C^2\,a^8\,b^4\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\left(4\,B\,a^{18}+4\,C\,a^{18}+12\,A\,a^8\,b^{10}-6\,A\,a^9\,b^9-54\,A\,a^{10}\,b^8+24\,A\,a^{11}\,b^7+96\,A\,a^{12}\,b^6-42\,A\,a^{13}\,b^5-78\,A\,a^{14}\,b^4+36\,A\,a^{15}\,b^3+24\,A\,a^{16}\,b^2-4\,B\,a^9\,b^9+2\,B\,a^{10}\,b^8+18\,B\,a^{11}\,b^7-4\,B\,a^{12}\,b^6-36\,B\,a^{13}\,b^5+6\,B\,a^{14}\,b^4+34\,B\,a^{15}\,b^3-8\,B\,a^{16}\,b^2-2\,C\,a^{11}\,b^7+2\,C\,a^{12}\,b^6+6\,C\,a^{15}\,b^3-6\,C\,a^{16}\,b^2-12\,A\,a^{17}\,b-12\,B\,a^{17}\,b-4\,C\,a^{17}\,b\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,A\,b^6+2\,C\,a^6-15\,A\,a^2\,b^4+12\,A\,a^4\,b^2+5\,B\,a^3\,b^3+C\,a^4\,b^2-2\,B\,a\,b^5-6\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}","Not used",1,"(atan((((3*A*b - B*a)*(((3*A*b - B*a)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (8*tan(c/2 + (d*x)/2)*(3*A*b - B*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4 - (8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))*1i)/a^4 - ((3*A*b - B*a)*(((3*A*b - B*a)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (8*tan(c/2 + (d*x)/2)*(3*A*b - B*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4 + (8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))*1i)/a^4)/(((3*A*b - B*a)*(((3*A*b - B*a)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (8*tan(c/2 + (d*x)/2)*(3*A*b - B*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4 - (8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))/a^4 - (16*(108*A^3*b^12 - 4*B*C^2*a^12 + 4*B^2*C*a^12 - 54*A^3*a*b^11 - 12*B^3*a^11*b - 486*A^3*a^2*b^10 + 243*A^3*a^3*b^9 + 864*A^3*a^4*b^8 - 378*A^3*a^5*b^7 - 702*A^3*a^6*b^6 + 216*A^3*a^7*b^5 + 216*A^3*a^8*b^4 - 4*B^3*a^3*b^9 + 2*B^3*a^4*b^8 + 18*B^3*a^5*b^7 - 13*B^3*a^6*b^6 - 36*B^3*a^7*b^5 + 26*B^3*a^8*b^4 + 34*B^3*a^9*b^3 - 24*B^3*a^10*b^2 - 108*A^2*B*a*b^11 + 12*A*C^2*a^11*b + 20*B^2*C*a^11*b + 36*A*B^2*a^2*b^10 - 18*A*B^2*a^3*b^9 - 162*A*B^2*a^4*b^8 + 105*A*B^2*a^5*b^7 + 312*A*B^2*a^6*b^6 - 198*A*B^2*a^7*b^5 - 282*A*B^2*a^8*b^4 + 156*A*B^2*a^9*b^3 + 96*A*B^2*a^10*b^2 + 54*A^2*B*a^2*b^10 + 486*A^2*B*a^3*b^9 - 279*A^2*B*a^4*b^8 - 900*A^2*B*a^5*b^7 + 486*A^2*B*a^6*b^6 + 774*A^2*B*a^7*b^5 - 324*A^2*B*a^8*b^4 - 252*A^2*B*a^9*b^3 + 3*A*C^2*a^7*b^5 + 12*A*C^2*a^9*b^3 + 18*A^2*C*a^3*b^9 + 18*A^2*C*a^4*b^8 - 18*A^2*C*a^5*b^7 - 54*A^2*C*a^7*b^5 - 54*A^2*C*a^8*b^4 + 108*A^2*C*a^9*b^3 + 36*A^2*C*a^10*b^2 - B*C^2*a^8*b^4 - 4*B*C^2*a^10*b^2 + 2*B^2*C*a^5*b^7 + 2*B^2*C*a^6*b^6 - 2*B^2*C*a^7*b^5 - 2*B^2*C*a^9*b^3 - 6*B^2*C*a^10*b^2 - 24*A*B*C*a^11*b - 12*A*B*C*a^4*b^8 - 12*A*B*C*a^5*b^7 + 12*A*B*C*a^6*b^6 + 24*A*B*C*a^8*b^4 + 36*A*B*C*a^9*b^3 - 96*A*B*C*a^10*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + ((3*A*b - B*a)*(((3*A*b - B*a)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (8*tan(c/2 + (d*x)/2)*(3*A*b - B*a)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4 + (8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))/a^4))*(3*A*b - B*a)*2i)/(a^4*d) - ((tan(c/2 + (d*x)/2)^5*(2*A*a^5 - 6*A*b^5 + 12*A*a^2*b^3 - 4*A*a^3*b^2 - B*a^2*b^3 - 6*B*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 - 2*A*a^4*b + 2*B*a*b^4 + 4*C*a^4*b))/((a^3*b - a^4)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*A*a^5 + 6*A*b^5 - 12*A*a^2*b^3 - 4*A*a^3*b^2 - B*a^2*b^3 + 6*B*a^3*b^2 + C*a^3*b^2 + 3*A*a*b^4 + 2*A*a^4*b - 2*B*a*b^4 - 4*C*a^4*b))/((a + b)*(a^5 - 2*a^4*b + a^3*b^2)) + (2*tan(c/2 + (d*x)/2)^3*(2*A*a^6 - 6*A*b^6 + 13*A*a^2*b^4 - 6*A*a^4*b^2 - 5*B*a^3*b^3 + 3*C*a^4*b^2 + 2*B*a*b^5))/(a*(a^2*b - a^3)*(a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) + (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*1i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((16*(108*A^3*b^12 - 4*B*C^2*a^12 + 4*B^2*C*a^12 - 54*A^3*a*b^11 - 12*B^3*a^11*b - 486*A^3*a^2*b^10 + 243*A^3*a^3*b^9 + 864*A^3*a^4*b^8 - 378*A^3*a^5*b^7 - 702*A^3*a^6*b^6 + 216*A^3*a^7*b^5 + 216*A^3*a^8*b^4 - 4*B^3*a^3*b^9 + 2*B^3*a^4*b^8 + 18*B^3*a^5*b^7 - 13*B^3*a^6*b^6 - 36*B^3*a^7*b^5 + 26*B^3*a^8*b^4 + 34*B^3*a^9*b^3 - 24*B^3*a^10*b^2 - 108*A^2*B*a*b^11 + 12*A*C^2*a^11*b + 20*B^2*C*a^11*b + 36*A*B^2*a^2*b^10 - 18*A*B^2*a^3*b^9 - 162*A*B^2*a^4*b^8 + 105*A*B^2*a^5*b^7 + 312*A*B^2*a^6*b^6 - 198*A*B^2*a^7*b^5 - 282*A*B^2*a^8*b^4 + 156*A*B^2*a^9*b^3 + 96*A*B^2*a^10*b^2 + 54*A^2*B*a^2*b^10 + 486*A^2*B*a^3*b^9 - 279*A^2*B*a^4*b^8 - 900*A^2*B*a^5*b^7 + 486*A^2*B*a^6*b^6 + 774*A^2*B*a^7*b^5 - 324*A^2*B*a^8*b^4 - 252*A^2*B*a^9*b^3 + 3*A*C^2*a^7*b^5 + 12*A*C^2*a^9*b^3 + 18*A^2*C*a^3*b^9 + 18*A^2*C*a^4*b^8 - 18*A^2*C*a^5*b^7 - 54*A^2*C*a^7*b^5 - 54*A^2*C*a^8*b^4 + 108*A^2*C*a^9*b^3 + 36*A^2*C*a^10*b^2 - B*C^2*a^8*b^4 - 4*B*C^2*a^10*b^2 + 2*B^2*C*a^5*b^7 + 2*B^2*C*a^6*b^6 - 2*B^2*C*a^7*b^5 - 2*B^2*C*a^9*b^3 - 6*B^2*C*a^10*b^2 - 24*A*B*C*a^11*b - 12*A*B*C*a^4*b^8 - 12*A*B*C*a^5*b^7 + 12*A*B*C*a^6*b^6 + 24*A*B*C*a^8*b^4 + 36*A*B*C*a^9*b^3 - 96*A*B*C*a^10*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^2*a^12 + 4*C^2*a^12 - 72*A^2*a*b^11 - 8*B^2*a^11*b - 288*A^2*a^2*b^10 + 288*A^2*a^3*b^9 + 441*A^2*a^4*b^8 - 432*A^2*a^5*b^7 - 288*A^2*a^6*b^6 + 288*A^2*a^7*b^5 + 36*A^2*a^8*b^4 - 72*A^2*a^9*b^3 + 36*A^2*a^10*b^2 + 8*B^2*a^2*b^10 - 8*B^2*a^3*b^9 - 32*B^2*a^4*b^8 + 32*B^2*a^5*b^7 + 57*B^2*a^6*b^6 - 48*B^2*a^7*b^5 - 52*B^2*a^8*b^4 + 32*B^2*a^9*b^3 + 24*B^2*a^10*b^2 + C^2*a^8*b^4 + 4*C^2*a^10*b^2 - 48*A*B*a*b^11 - 24*A*B*a^11*b - 24*B*C*a^11*b + 48*A*B*a^2*b^10 + 192*A*B*a^3*b^9 - 192*A*B*a^4*b^8 - 318*A*B*a^5*b^7 + 288*A*B*a^6*b^6 + 252*A*B*a^7*b^5 - 192*A*B*a^8*b^4 - 72*A*B*a^9*b^3 + 48*A*B*a^10*b^2 + 12*A*C*a^4*b^8 - 6*A*C*a^6*b^6 - 36*A*C*a^8*b^4 + 48*A*C*a^10*b^2 - 4*B*C*a^5*b^7 + 2*B*C*a^7*b^5 + 8*B*C*a^9*b^3))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*(4*B*a^18 + 4*C*a^18 + 12*A*a^8*b^10 - 6*A*a^9*b^9 - 54*A*a^10*b^8 + 24*A*a^11*b^7 + 96*A*a^12*b^6 - 42*A*a^13*b^5 - 78*A*a^14*b^4 + 36*A*a^15*b^3 + 24*A*a^16*b^2 - 4*B*a^9*b^9 + 2*B*a^10*b^8 + 18*B*a^11*b^7 - 4*B*a^12*b^6 - 36*B*a^13*b^5 + 6*B*a^14*b^4 + 34*B*a^15*b^3 - 8*B*a^16*b^2 - 2*C*a^11*b^7 + 2*C*a^12*b^6 + 6*C*a^15*b^3 - 6*C*a^16*b^2 - 12*A*a^17*b - 12*B*a^17*b - 4*C*a^17*b))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*A*b^6 + 2*C*a^6 - 15*A*a^2*b^4 + 12*A*a^4*b^2 + 5*B*a^3*b^3 + C*a^4*b^2 - 2*B*a*b^5 - 6*B*a^5*b)*1i)/(d*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))","B"
1000,1,15951,462,17.219147,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^7+36\,A\,b^7+2\,B\,a^7-67\,A\,a^2\,b^5-29\,A\,a^3\,b^4+26\,A\,a^4\,b^3+5\,A\,a^5\,b^2-9\,B\,a^2\,b^5+35\,B\,a^3\,b^4+16\,B\,a^4\,b^3-10\,B\,a^5\,b^2+6\,C\,a^2\,b^5+3\,C\,a^3\,b^4-15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6-4\,A\,a^6\,b-18\,B\,a\,b^6-4\,B\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A\,a^7-36\,A\,b^7-2\,B\,a^7+67\,A\,a^2\,b^5-29\,A\,a^3\,b^4-26\,A\,a^4\,b^3+5\,A\,a^5\,b^2-9\,B\,a^2\,b^5-35\,B\,a^3\,b^4+16\,B\,a^4\,b^3+10\,B\,a^5\,b^2-6\,C\,a^2\,b^5+3\,C\,a^3\,b^4+15\,C\,a^4\,b^3-6\,C\,a^5\,b^2+18\,A\,a\,b^6+4\,A\,a^6\,b+18\,B\,a\,b^6-4\,B\,a^6\,b\right)}{{\left(a+b\right)}^2\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A\,a^6-12\,A\,b^6-2\,B\,a^6+23\,A\,a^2\,b^4-10\,A\,a^3\,b^3-8\,A\,a^4\,b^2-3\,B\,a^2\,b^4-12\,B\,a^3\,b^3+4\,B\,a^4\,b^2-2\,C\,a^2\,b^4+C\,a^3\,b^3+6\,C\,a^4\,b^2+6\,A\,a\,b^5+5\,A\,a^5\,b+6\,B\,a\,b^5+2\,B\,a^5\,b\right)}{\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^6-12\,A\,b^6+2\,B\,a^6+23\,A\,a^2\,b^4+10\,A\,a^3\,b^3-8\,A\,a^4\,b^2+3\,B\,a^2\,b^4-12\,B\,a^3\,b^3-4\,B\,a^4\,b^2-2\,C\,a^2\,b^4-C\,a^3\,b^3+6\,C\,a^4\,b^2-6\,A\,a\,b^5-5\,A\,a^5\,b+6\,B\,a\,b^5+2\,B\,a^5\,b\right)}{\left(a+b\right)\,\left(a^6-2\,a^5\,b+a^4\,b^2\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-6\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,b^2+4\,a\,b\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)\,1{}\mathrm{i}}{a^5}}{\frac{8\,\left(20\,A^3\,a^{12}\,b^3-20\,A^3\,a^{11}\,b^4+411\,A^3\,a^{10}\,b^5-11\,A^3\,a^9\,b^6+1314\,A^3\,a^8\,b^7+2326\,A^3\,a^7\,b^8-7829\,A^3\,a^6\,b^9-4770\,A^3\,a^5\,b^{10}+11700\,A^3\,a^4\,b^{11}+3456\,A^3\,a^3\,b^{12}-7344\,A^3\,a^2\,b^{13}-864\,A^3\,a\,b^{14}+1728\,A^3\,b^{15}-12\,A^2\,B\,a^{13}\,b^2+12\,A^2\,B\,a^{12}\,b^3-489\,A^2\,B\,a^{11}\,b^4+9\,A^2\,B\,a^{10}\,b^5-2892\,A^2\,B\,a^9\,b^6-3972\,A^2\,B\,a^8\,b^7+13347\,A^2\,B\,a^7\,b^8+7767\,A^2\,B\,a^6\,b^9-18594\,A^2\,B\,a^5\,b^{10}-5400\,A^2\,B\,a^4\,b^{11}+11232\,A^2\,B\,a^3\,b^{12}+1296\,A^2\,B\,a^2\,b^{13}-2592\,A^2\,B\,a\,b^{14}+6\,A^2\,C\,a^{14}\,b-6\,A^2\,C\,a^{13}\,b^2+207\,A^2\,C\,a^{12}\,b^3+33\,A^2\,C\,a^{11}\,b^4+1158\,A^2\,C\,a^{10}\,b^5+1974\,A^2\,C\,a^9\,b^6-4977\,A^2\,C\,a^8\,b^7-3405\,A^2\,C\,a^7\,b^8+6486\,A^2\,C\,a^6\,b^9+2088\,A^2\,C\,a^5\,b^{10}-3744\,A^2\,C\,a^4\,b^{11}-432\,A^2\,C\,a^3\,b^{12}+864\,A^2\,C\,a^2\,b^{13}+144\,A\,B^2\,a^{12}\,b^3+1980\,A\,B^2\,a^{10}\,b^5+2268\,A\,B^2\,a^9\,b^6-7524\,A\,B^2\,a^8\,b^7-4203\,A\,B^2\,a^7\,b^8+9828\,A\,B^2\,a^6\,b^9+2808\,A\,B^2\,a^5\,b^{10}-5724\,A\,B^2\,a^4\,b^{11}-648\,A\,B^2\,a^3\,b^{12}+1296\,A\,B^2\,a^2\,b^{13}-120\,A\,B\,C\,a^{13}\,b^2-24\,A\,B\,C\,a^{12}\,b^3-1560\,A\,B\,C\,a^{11}\,b^4-2268\,A\,B\,C\,a^{10}\,b^5+5568\,A\,B\,C\,a^9\,b^6+3642\,A\,B\,C\,a^8\,b^7-6840\,A\,B\,C\,a^7\,b^8-2160\,A\,B\,C\,a^6\,b^9+3816\,A\,B\,C\,a^5\,b^{10}+432\,A\,B\,C\,a^4\,b^{11}-864\,A\,B\,C\,a^3\,b^{12}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}-432\,B^3\,a^{11}\,b^4-432\,B^3\,a^{10}\,b^5+1404\,B^3\,a^9\,b^6+756\,B^3\,a^8\,b^7-1728\,B^3\,a^7\,b^8-486\,B^3\,a^6\,b^9+972\,B^3\,a^5\,b^{10}+108\,B^3\,a^4\,b^{11}-216\,B^3\,a^3\,b^{12}+504\,B^2\,C\,a^{12}\,b^3+648\,B^2\,C\,a^{11}\,b^4-1548\,B^2\,C\,a^{10}\,b^5-972\,B^2\,C\,a^9\,b^6+1800\,B^2\,C\,a^8\,b^7+558\,B^2\,C\,a^7\,b^8-972\,B^2\,C\,a^6\,b^9-108\,B^2\,C\,a^5\,b^{10}+216\,B^2\,C\,a^4\,b^{11}-192\,B\,C^2\,a^{13}\,b^2-312\,B\,C^2\,a^{12}\,b^3+564\,B\,C^2\,a^{11}\,b^4+396\,B\,C^2\,a^{10}\,b^5-624\,B\,C^2\,a^9\,b^6-210\,B\,C^2\,a^8\,b^7+324\,B\,C^2\,a^7\,b^8+36\,B\,C^2\,a^6\,b^9-72\,B\,C^2\,a^5\,b^{10}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)}{a^5}+\frac{\left(\frac{\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{a^5\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)}{a^5}}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-3\,B\,a\,b+6\,A\,b^2\right)\,2{}\mathrm{i}}{a^5\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{b\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\righ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5\,b^{10}-5724\,A\,B^2\,a^4\,b^{11}-648\,A\,B^2\,a^3\,b^{12}+1296\,A\,B^2\,a^2\,b^{13}-120\,A\,B\,C\,a^{13}\,b^2-24\,A\,B\,C\,a^{12}\,b^3-1560\,A\,B\,C\,a^{11}\,b^4-2268\,A\,B\,C\,a^{10}\,b^5+5568\,A\,B\,C\,a^9\,b^6+3642\,A\,B\,C\,a^8\,b^7-6840\,A\,B\,C\,a^7\,b^8-2160\,A\,B\,C\,a^6\,b^9+3816\,A\,B\,C\,a^5\,b^{10}+432\,A\,B\,C\,a^4\,b^{11}-864\,A\,B\,C\,a^3\,b^{12}+24\,A\,C^2\,a^{14}\,b+12\,A\,C^2\,a^{13}\,b^2+300\,A\,C^2\,a^{12}\,b^3+552\,A\,C^2\,a^{11}\,b^4-1020\,A\,C^2\,a^{10}\,b^5-747\,A\,C^2\,a^9\,b^6+1188\,A\,C^2\,a^8\,b^7+408\,A\,C^2\,a^7\,b^8-636\,A\,C^2\,a^6\,b^9-72\,A\,C^2\,a^5\,b^{10}+144\,A\,C^2\,a^4\,b^{11}-432\,B^3\,a^{11}\,b^4-432\,B^3\,a^{10}\,b^5+1404\,B^3\,a^9\,b^6+756\,B^3\,a^8\,b^7-1728\,B^3\,a^7\,b^8-486\,B^3\,a^6\,b^9+972\,B^3\,a^5\,b^{10}+108\,B^3\,a^4\,b^{11}-216\,B^3\,a^3\,b^{12}+504\,B^2\,C\,a^{12}\,b^3+648\,B^2\,C\,a^{11}\,b^4-1548\,B^2\,C\,a^{10}\,b^5-972\,B^2\,C\,a^9\,b^6+1800\,B^2\,C\,a^8\,b^7+558\,B^2\,C\,a^7\,b^8-972\,B^2\,C\,a^6\,b^9-108\,B^2\,C\,a^5\,b^{10}+216\,B^2\,C\,a^4\,b^{11}-192\,B\,C^2\,a^{13}\,b^2-312\,B\,C^2\,a^{12}\,b^3+564\,B\,C^2\,a^{11}\,b^4+396\,B\,C^2\,a^{10}\,b^5-624\,B\,C^2\,a^9\,b^6-210\,B\,C^2\,a^8\,b^7+324\,B\,C^2\,a^7\,b^8+36\,B\,C^2\,a^6\,b^9-72\,B\,C^2\,a^5\,b^{10}+24\,C^3\,a^{14}\,b+48\,C^3\,a^{13}\,b^2-68\,C^3\,a^{12}\,b^3-52\,C^3\,a^{11}\,b^4+72\,C^3\,a^{10}\,b^5+26\,C^3\,a^9\,b^6-36\,C^3\,a^8\,b^7-4\,C^3\,a^7\,b^8+8\,C^3\,a^6\,b^9\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}-\frac{b\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{14}-2\,A^2\,a^{13}\,b+21\,A^2\,a^{12}\,b^2-40\,A^2\,a^{11}\,b^3+74\,A^2\,a^{10}\,b^4-108\,A^2\,a^9\,b^5+18\,A^2\,a^8\,b^6+872\,A^2\,a^7\,b^7-827\,A^2\,a^6\,b^8-1538\,A^2\,a^5\,b^9+1538\,A^2\,a^4\,b^{10}+1104\,A^2\,a^3\,b^{11}-1104\,A^2\,a^2\,b^{12}-288\,A^2\,a\,b^{13}+288\,A^2\,b^{14}-12\,A\,B\,a^{13}\,b+24\,A\,B\,a^{12}\,b^2-108\,A\,B\,a^{11}\,b^3+192\,A\,B\,a^{10}\,b^4-72\,A\,B\,a^9\,b^5-1008\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7+1632\,A\,B\,a^6\,b^8-1650\,A\,B\,a^5\,b^9-1128\,A\,B\,a^4\,b^{10}+1128\,A\,B\,a^3\,b^{11}+288\,A\,B\,a^2\,b^{12}-288\,A\,B\,a\,b^{13}+4\,A\,C\,a^{14}-8\,A\,C\,a^{13}\,b+36\,A\,C\,a^{12}\,b^2-64\,A\,C\,a^{11}\,b^3+104\,A\,C\,a^{10}\,b^4+336\,A\,C\,a^9\,b^5-444\,A\,C\,a^8\,b^6-544\,A\,C\,a^7\,b^7+598\,A\,C\,a^6\,b^8+376\,A\,C\,a^5\,b^9-376\,A\,C\,a^4\,b^{10}-96\,A\,C\,a^3\,b^{11}+96\,A\,C\,a^2\,b^{12}+36\,B^2\,a^{12}\,b^2-72\,B^2\,a^{11}\,b^3+36\,B^2\,a^{10}\,b^4+288\,B^2\,a^9\,b^5-288\,B^2\,a^8\,b^6-432\,B^2\,a^7\,b^7+441\,B^2\,a^6\,b^8+288\,B^2\,a^5\,b^9-288\,B^2\,a^4\,b^{10}-72\,B^2\,a^3\,b^{11}+72\,B^2\,a^2\,b^{12}-24\,B\,C\,a^{13}\,b+48\,B\,C\,a^{12}\,b^2-72\,B\,C\,a^{11}\,b^3-192\,B\,C\,a^{10}\,b^4+252\,B\,C\,a^9\,b^5+288\,B\,C\,a^8\,b^6-318\,B\,C\,a^7\,b^7-192\,B\,C\,a^6\,b^8+192\,B\,C\,a^5\,b^9+48\,B\,C\,a^4\,b^{10}-48\,B\,C\,a^3\,b^{11}+4\,C^2\,a^{14}-8\,C^2\,a^{13}\,b+24\,C^2\,a^{12}\,b^2+32\,C^2\,a^{11}\,b^3-52\,C^2\,a^{10}\,b^4-48\,C^2\,a^9\,b^5+57\,C^2\,a^8\,b^6+32\,C^2\,a^7\,b^7-32\,C^2\,a^6\,b^8-8\,C^2\,a^5\,b^9+8\,C^2\,a^4\,b^{10}\right)}{a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7}+\frac{b\,\left(\frac{4\,\left(4\,A\,a^{21}+8\,C\,a^{21}-48\,A\,a^{10}\,b^{11}+24\,A\,a^{11}\,b^{10}+212\,A\,a^{12}\,b^9-100\,A\,a^{13}\,b^8-360\,A\,a^{14}\,b^7+164\,A\,a^{15}\,b^6+276\,A\,a^{16}\,b^5-120\,A\,a^{17}\,b^4-80\,A\,a^{18}\,b^3+28\,A\,a^{19}\,b^2+24\,B\,a^{11}\,b^{10}-12\,B\,a^{12}\,b^9-108\,B\,a^{13}\,b^8+48\,B\,a^{14}\,b^7+192\,B\,a^{15}\,b^6-84\,B\,a^{16}\,b^5-156\,B\,a^{17}\,b^4+72\,B\,a^{18}\,b^3+48\,B\,a^{19}\,b^2-8\,C\,a^{12}\,b^9+4\,C\,a^{13}\,b^8+36\,C\,a^{14}\,b^7-8\,C\,a^{15}\,b^6-72\,C\,a^{16}\,b^5+12\,C\,a^{17}\,b^4+68\,C\,a^{18}\,b^3-16\,C\,a^{19}\,b^2-24\,B\,a^{20}\,b-24\,C\,a^{20}\,b\right)}{a^{19}+a^{18}\,b-3\,a^{17}\,b^2-3\,a^{16}\,b^3+3\,a^{15}\,b^4+3\,a^{14}\,b^5-a^{13}\,b^6-a^{12}\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,A\,b^6+6\,C\,a^6-29\,A\,a^2\,b^4+20\,A\,a^4\,b^2+15\,B\,a^3\,b^3+2\,C\,a^2\,b^4-5\,C\,a^4\,b^2-6\,B\,a\,b^5-12\,B\,a^5\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(3*A*a^7 + 36*A*b^7 + 2*B*a^7 - 67*A*a^2*b^5 - 29*A*a^3*b^4 + 26*A*a^4*b^3 + 5*A*a^5*b^2 - 9*B*a^2*b^5 + 35*B*a^3*b^4 + 16*B*a^4*b^3 - 10*B*a^5*b^2 + 6*C*a^2*b^5 + 3*C*a^3*b^4 - 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 - 4*A*a^6*b - 18*B*a*b^6 - 4*B*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) + (tan(c/2 + (d*x)/2)^5*(3*A*a^7 - 36*A*b^7 - 2*B*a^7 + 67*A*a^2*b^5 - 29*A*a^3*b^4 - 26*A*a^4*b^3 + 5*A*a^5*b^2 - 9*B*a^2*b^5 - 35*B*a^3*b^4 + 16*B*a^4*b^3 + 10*B*a^5*b^2 - 6*C*a^2*b^5 + 3*C*a^3*b^4 + 15*C*a^4*b^3 - 6*C*a^5*b^2 + 18*A*a*b^6 + 4*A*a^6*b + 18*B*a*b^6 - 4*B*a^6*b))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) - (tan(c/2 + (d*x)/2)^7*(A*a^6 - 12*A*b^6 - 2*B*a^6 + 23*A*a^2*b^4 - 10*A*a^3*b^3 - 8*A*a^4*b^2 - 3*B*a^2*b^4 - 12*B*a^3*b^3 + 4*B*a^4*b^2 - 2*C*a^2*b^4 + C*a^3*b^3 + 6*C*a^4*b^2 + 6*A*a*b^5 + 5*A*a^5*b + 6*B*a*b^5 + 2*B*a^5*b))/((a^4*b - a^5)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(A*a^6 - 12*A*b^6 + 2*B*a^6 + 23*A*a^2*b^4 + 10*A*a^3*b^3 - 8*A*a^4*b^2 + 3*B*a^2*b^4 - 12*B*a^3*b^3 - 4*B*a^4*b^2 - 2*C*a^2*b^4 - C*a^3*b^3 + 6*C*a^4*b^2 - 6*A*a*b^5 - 5*A*a^5*b + 6*B*a*b^5 + 2*B*a^5*b))/((a + b)*(a^6 - 2*a^5*b + a^4*b^2)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^4*(2*a^2 - 6*b^2) - tan(c/2 + (d*x)/2)^2*(4*a*b + 4*b^2) + tan(c/2 + (d*x)/2)^6*(4*a*b - 4*b^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan(((((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b))/a^5 - (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b)*1i)/a^5 - (((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b))/a^5 + (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b)*1i)/a^5)/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 - 216*B^3*a^3*b^12 + 108*B^3*a^4*b^11 + 972*B^3*a^5*b^10 - 486*B^3*a^6*b^9 - 1728*B^3*a^7*b^8 + 756*B^3*a^8*b^7 + 1404*B^3*a^9*b^6 - 432*B^3*a^10*b^5 - 432*B^3*a^11*b^4 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 - 2592*A^2*B*a*b^14 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 1296*A*B^2*a^2*b^13 - 648*A*B^2*a^3*b^12 - 5724*A*B^2*a^4*b^11 + 2808*A*B^2*a^5*b^10 + 9828*A*B^2*a^6*b^9 - 4203*A*B^2*a^7*b^8 - 7524*A*B^2*a^8*b^7 + 2268*A*B^2*a^9*b^6 + 1980*A*B^2*a^10*b^5 + 144*A*B^2*a^12*b^3 + 1296*A^2*B*a^2*b^13 + 11232*A^2*B*a^3*b^12 - 5400*A^2*B*a^4*b^11 - 18594*A^2*B*a^5*b^10 + 7767*A^2*B*a^6*b^9 + 13347*A^2*B*a^7*b^8 - 3972*A^2*B*a^8*b^7 - 2892*A^2*B*a^9*b^6 + 9*A^2*B*a^10*b^5 - 489*A^2*B*a^11*b^4 + 12*A^2*B*a^12*b^3 - 12*A^2*B*a^13*b^2 + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2 - 72*B*C^2*a^5*b^10 + 36*B*C^2*a^6*b^9 + 324*B*C^2*a^7*b^8 - 210*B*C^2*a^8*b^7 - 624*B*C^2*a^9*b^6 + 396*B*C^2*a^10*b^5 + 564*B*C^2*a^11*b^4 - 312*B*C^2*a^12*b^3 - 192*B*C^2*a^13*b^2 + 216*B^2*C*a^4*b^11 - 108*B^2*C*a^5*b^10 - 972*B^2*C*a^6*b^9 + 558*B^2*C*a^7*b^8 + 1800*B^2*C*a^8*b^7 - 972*B^2*C*a^9*b^6 - 1548*B^2*C*a^10*b^5 + 648*B^2*C*a^11*b^4 + 504*B^2*C*a^12*b^3 - 864*A*B*C*a^3*b^12 + 432*A*B*C*a^4*b^11 + 3816*A*B*C*a^5*b^10 - 2160*A*B*C*a^6*b^9 - 6840*A*B*C*a^7*b^8 + 3642*A*B*C*a^8*b^7 + 5568*A*B*C*a^9*b^6 - 2268*A*B*C*a^10*b^5 - 1560*A*B*C*a^11*b^4 - 24*A*B*C*a^12*b^3 - 120*A*B*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b))/a^5 - (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b))/a^5 + (((((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (8*tan(c/2 + (d*x)/2)*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^5*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b))/a^5 + (8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b))/a^5))*(6*A*b^2 + a^2*(A/2 + C) - 3*B*a*b)*2i)/(a^5*d) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 + 24*C^3*a^14*b - 7344*A^3*a^2*b^13 + 3456*A^3*a^3*b^12 + 11700*A^3*a^4*b^11 - 4770*A^3*a^5*b^10 - 7829*A^3*a^6*b^9 + 2326*A^3*a^7*b^8 + 1314*A^3*a^8*b^7 - 11*A^3*a^9*b^6 + 411*A^3*a^10*b^5 - 20*A^3*a^11*b^4 + 20*A^3*a^12*b^3 - 216*B^3*a^3*b^12 + 108*B^3*a^4*b^11 + 972*B^3*a^5*b^10 - 486*B^3*a^6*b^9 - 1728*B^3*a^7*b^8 + 756*B^3*a^8*b^7 + 1404*B^3*a^9*b^6 - 432*B^3*a^10*b^5 - 432*B^3*a^11*b^4 + 8*C^3*a^6*b^9 - 4*C^3*a^7*b^8 - 36*C^3*a^8*b^7 + 26*C^3*a^9*b^6 + 72*C^3*a^10*b^5 - 52*C^3*a^11*b^4 - 68*C^3*a^12*b^3 + 48*C^3*a^13*b^2 - 2592*A^2*B*a*b^14 + 24*A*C^2*a^14*b + 6*A^2*C*a^14*b + 1296*A*B^2*a^2*b^13 - 648*A*B^2*a^3*b^12 - 5724*A*B^2*a^4*b^11 + 2808*A*B^2*a^5*b^10 + 9828*A*B^2*a^6*b^9 - 4203*A*B^2*a^7*b^8 - 7524*A*B^2*a^8*b^7 + 2268*A*B^2*a^9*b^6 + 1980*A*B^2*a^10*b^5 + 144*A*B^2*a^12*b^3 + 1296*A^2*B*a^2*b^13 + 11232*A^2*B*a^3*b^12 - 5400*A^2*B*a^4*b^11 - 18594*A^2*B*a^5*b^10 + 7767*A^2*B*a^6*b^9 + 13347*A^2*B*a^7*b^8 - 3972*A^2*B*a^8*b^7 - 2892*A^2*B*a^9*b^6 + 9*A^2*B*a^10*b^5 - 489*A^2*B*a^11*b^4 + 12*A^2*B*a^12*b^3 - 12*A^2*B*a^13*b^2 + 144*A*C^2*a^4*b^11 - 72*A*C^2*a^5*b^10 - 636*A*C^2*a^6*b^9 + 408*A*C^2*a^7*b^8 + 1188*A*C^2*a^8*b^7 - 747*A*C^2*a^9*b^6 - 1020*A*C^2*a^10*b^5 + 552*A*C^2*a^11*b^4 + 300*A*C^2*a^12*b^3 + 12*A*C^2*a^13*b^2 + 864*A^2*C*a^2*b^13 - 432*A^2*C*a^3*b^12 - 3744*A^2*C*a^4*b^11 + 2088*A^2*C*a^5*b^10 + 6486*A^2*C*a^6*b^9 - 3405*A^2*C*a^7*b^8 - 4977*A^2*C*a^8*b^7 + 1974*A^2*C*a^9*b^6 + 1158*A^2*C*a^10*b^5 + 33*A^2*C*a^11*b^4 + 207*A^2*C*a^12*b^3 - 6*A^2*C*a^13*b^2 - 72*B*C^2*a^5*b^10 + 36*B*C^2*a^6*b^9 + 324*B*C^2*a^7*b^8 - 210*B*C^2*a^8*b^7 - 624*B*C^2*a^9*b^6 + 396*B*C^2*a^10*b^5 + 564*B*C^2*a^11*b^4 - 312*B*C^2*a^12*b^3 - 192*B*C^2*a^13*b^2 + 216*B^2*C*a^4*b^11 - 108*B^2*C*a^5*b^10 - 972*B^2*C*a^6*b^9 + 558*B^2*C*a^7*b^8 + 1800*B^2*C*a^8*b^7 - 972*B^2*C*a^9*b^6 - 1548*B^2*C*a^10*b^5 + 648*B^2*C*a^11*b^4 + 504*B^2*C*a^12*b^3 - 864*A*B*C*a^3*b^12 + 432*A*B*C*a^4*b^11 + 3816*A*B*C*a^5*b^10 - 2160*A*B*C*a^6*b^9 - 6840*A*B*C*a^7*b^8 + 3642*A*B*C*a^8*b^7 + 5568*A*B*C*a^9*b^6 - 2268*A*B*C*a^10*b^5 - 1560*A*B*C*a^11*b^4 - 24*A*B*C*a^12*b^3 - 120*A*B*C*a^13*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) - (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 + 4*C^2*a^14 - 288*A^2*a*b^13 - 2*A^2*a^13*b - 8*C^2*a^13*b - 1104*A^2*a^2*b^12 + 1104*A^2*a^3*b^11 + 1538*A^2*a^4*b^10 - 1538*A^2*a^5*b^9 - 827*A^2*a^6*b^8 + 872*A^2*a^7*b^7 + 18*A^2*a^8*b^6 - 108*A^2*a^9*b^5 + 74*A^2*a^10*b^4 - 40*A^2*a^11*b^3 + 21*A^2*a^12*b^2 + 72*B^2*a^2*b^12 - 72*B^2*a^3*b^11 - 288*B^2*a^4*b^10 + 288*B^2*a^5*b^9 + 441*B^2*a^6*b^8 - 432*B^2*a^7*b^7 - 288*B^2*a^8*b^6 + 288*B^2*a^9*b^5 + 36*B^2*a^10*b^4 - 72*B^2*a^11*b^3 + 36*B^2*a^12*b^2 + 8*C^2*a^4*b^10 - 8*C^2*a^5*b^9 - 32*C^2*a^6*b^8 + 32*C^2*a^7*b^7 + 57*C^2*a^8*b^6 - 48*C^2*a^9*b^5 - 52*C^2*a^10*b^4 + 32*C^2*a^11*b^3 + 24*C^2*a^12*b^2 + 4*A*C*a^14 - 288*A*B*a*b^13 - 12*A*B*a^13*b - 8*A*C*a^13*b - 24*B*C*a^13*b + 288*A*B*a^2*b^12 + 1128*A*B*a^3*b^11 - 1128*A*B*a^4*b^10 - 1650*A*B*a^5*b^9 + 1632*A*B*a^6*b^8 + 984*A*B*a^7*b^7 - 1008*A*B*a^8*b^6 - 72*A*B*a^9*b^5 + 192*A*B*a^10*b^4 - 108*A*B*a^11*b^3 + 24*A*B*a^12*b^2 + 96*A*C*a^2*b^12 - 96*A*C*a^3*b^11 - 376*A*C*a^4*b^10 + 376*A*C*a^5*b^9 + 598*A*C*a^6*b^8 - 544*A*C*a^7*b^7 - 444*A*C*a^8*b^6 + 336*A*C*a^9*b^5 + 104*A*C*a^10*b^4 - 64*A*C*a^11*b^3 + 36*A*C*a^12*b^2 - 48*B*C*a^3*b^11 + 48*B*C*a^4*b^10 + 192*B*C*a^5*b^9 - 192*B*C*a^6*b^8 - 318*B*C*a^7*b^7 + 288*B*C*a^8*b^6 + 252*B*C*a^9*b^5 - 192*B*C*a^10*b^4 - 72*B*C*a^11*b^3 + 48*B*C*a^12*b^2))/(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2) + (b*((4*(4*A*a^21 + 8*C*a^21 - 48*A*a^10*b^11 + 24*A*a^11*b^10 + 212*A*a^12*b^9 - 100*A*a^13*b^8 - 360*A*a^14*b^7 + 164*A*a^15*b^6 + 276*A*a^16*b^5 - 120*A*a^17*b^4 - 80*A*a^18*b^3 + 28*A*a^19*b^2 + 24*B*a^11*b^10 - 12*B*a^12*b^9 - 108*B*a^13*b^8 + 48*B*a^14*b^7 + 192*B*a^15*b^6 - 84*B*a^16*b^5 - 156*B*a^17*b^4 + 72*B*a^18*b^3 + 48*B*a^19*b^2 - 8*C*a^12*b^9 + 4*C*a^13*b^8 + 36*C*a^14*b^7 - 8*C*a^15*b^6 - 72*C*a^16*b^5 + 12*C*a^17*b^4 + 68*C*a^18*b^3 - 16*C*a^19*b^2 - 24*B*a^20*b - 24*C*a^20*b))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^6 + 6*C*a^6 - 29*A*a^2*b^4 + 20*A*a^4*b^2 + 15*B*a^3*b^3 + 2*C*a^2*b^4 - 5*C*a^4*b^2 - 6*B*a*b^5 - 12*B*a^5*b)*1i)/(d*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))","B"
1001,1,21924,649,22.211030,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^8+20\,C\,a^8+C\,b^8+12\,A\,a^2\,b^6-4\,A\,a^3\,b^5-6\,A\,a^4\,b^4+A\,a^5\,b^3+2\,A\,a^6\,b^2-6\,B\,a^2\,b^6-26\,B\,a^3\,b^5+11\,B\,a^4\,b^4+24\,B\,a^5\,b^3-4\,B\,a^6\,b^2-11\,C\,a^2\,b^6+21\,C\,a^3\,b^5+57\,C\,a^4\,b^4-27\,C\,a^5\,b^3-59\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b-7\,C\,a\,b^7+10\,C\,a^7\,b\right)}{b^5\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(20\,C\,a^8-2\,B\,b^8+C\,b^8+12\,A\,a^2\,b^6+4\,A\,a^3\,b^5-6\,A\,a^4\,b^4-A\,a^5\,b^3+2\,A\,a^6\,b^2+6\,B\,a^2\,b^6-26\,B\,a^3\,b^5-11\,B\,a^4\,b^4+24\,B\,a^5\,b^3+4\,B\,a^6\,b^2-11\,C\,a^2\,b^6-21\,C\,a^3\,b^5+57\,C\,a^4\,b^4+27\,C\,a^5\,b^3-59\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b+7\,C\,a\,b^7-10\,C\,a^7\,b\right)}{b^5\,{\left(a+b\right)}^3\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,B\,b^9-120\,C\,a^9+6\,C\,b^9-60\,A\,a^3\,b^6+8\,A\,a^4\,b^5+37\,A\,a^5\,b^4-3\,A\,a^6\,b^3-12\,A\,a^7\,b^2-30\,B\,a^2\,b^7+18\,B\,a^3\,b^6+159\,B\,a^4\,b^5-29\,B\,a^5\,b^4-148\,B\,a^6\,b^3+12\,B\,a^7\,b^2+3\,C\,a^2\,b^7+111\,C\,a^3\,b^6-45\,C\,a^4\,b^5-369\,C\,a^5\,b^4+71\,C\,a^6\,b^3+364\,C\,a^7\,b^2-6\,B\,a\,b^8+48\,B\,a^8\,b-21\,C\,a\,b^8-30\,C\,a^8\,b\right)}{3\,b^5\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(120\,C\,a^9-6\,B\,b^9+6\,C\,b^9+60\,A\,a^3\,b^6+8\,A\,a^4\,b^5-37\,A\,a^5\,b^4-3\,A\,a^6\,b^3+12\,A\,a^7\,b^2+30\,B\,a^2\,b^7+18\,B\,a^3\,b^6-159\,B\,a^4\,b^5-29\,B\,a^5\,b^4+148\,B\,a^6\,b^3+12\,B\,a^7\,b^2+3\,C\,a^2\,b^7-111\,C\,a^3\,b^6-45\,C\,a^4\,b^5+369\,C\,a^5\,b^4+71\,C\,a^6\,b^3-364\,C\,a^7\,b^2-6\,B\,a\,b^8-48\,B\,a^8\,b+21\,C\,a\,b^8-30\,C\,a^8\,b\right)}{3\,b^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(180\,C\,a^{10}+9\,C\,b^{10}-36\,A\,a^2\,b^8+110\,A\,a^4\,b^6-62\,A\,a^6\,b^4+18\,A\,a^8\,b^2+132\,B\,a^3\,b^7-320\,B\,a^5\,b^5+248\,B\,a^7\,b^3+36\,C\,a^2\,b^8-324\,C\,a^4\,b^6+740\,C\,a^6\,b^4-611\,C\,a^8\,b^2-18\,B\,a\,b^9-72\,B\,a^9\,b\right)}{3\,b^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^3+9\,a^2\,b+3\,a\,b^2-b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-10\,a^3-6\,a^2\,b+6\,a\,b^2+2\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-10\,a^3+6\,a^2\,b+6\,a\,b^2-2\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^3-9\,a^2\,b+3\,a\,b^2+b^3\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^4-8\,A^2\,a^{13}\,b^5-48\,A^2\,a^{12}\,b^6+48\,A^2\,a^{11}\,b^7+117\,A^2\,a^{10}\,b^8-120\,A^2\,a^9\,b^9-164\,A^2\,a^8\,b^{10}+160\,A^2\,a^7\,b^{11}+156\,A^2\,a^6\,b^{12}-120\,A^2\,a^5\,b^{13}-92\,A^2\,a^4\,b^{14}+48\,A^2\,a^3\,b^{15}+44\,A^2\,a^2\,b^{16}-8\,A^2\,a\,b^{17}+4\,A^2\,b^{18}-64\,A\,B\,a^{15}\,b^3+64\,A\,B\,a^{14}\,b^4+384\,A\,B\,a^{13}\,b^5-384\,A\,B\,a^{12}\,b^6-948\,A\,B\,a^{11}\,b^7+960\,A\,B\,a^{10}\,b^8+1306\,A\,B\,a^9\,b^9-1280\,A\,B\,a^8\,b^{10}-1128\,A\,B\,a^7\,b^{11}+960\,A\,B\,a^6\,b^{12}+592\,A\,B\,a^5\,b^{13}-384\,A\,B\,a^4\,b^{14}-160\,A\,B\,a^3\,b^{15}+64\,A\,B\,a^2\,b^{16}-32\,A\,B\,a\,b^{17}+160\,A\,C\,a^{16}\,b^2-160\,A\,C\,a^{15}\,b^3-952\,A\,C\,a^{14}\,b^4+952\,A\,C\,a^{13}\,b^5+2322\,A\,C\,a^{12}\,b^6-2352\,A\,C\,a^{11}\,b^7-3124\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9+2588\,A\,C\,a^8\,b^{10}-2240\,A\,C\,a^7\,b^{11}-1284\,A\,C\,a^6\,b^{12}+840\,A\,C\,a^5\,b^{13}+276\,A\,C\,a^4\,b^{14}-112\,A\,C\,a^3\,b^{15}+60\,A\,C\,a^2\,b^{16}-8\,A\,C\,a\,b^{17}+4\,A\,C\,b^{18}+128\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3-768\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5+1920\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7-2600\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9+2025\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}-824\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}+80\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+64\,B^2\,a^2\,b^{16}-640\,B\,C\,a^{17}\,b+640\,B\,C\,a^{16}\,b^2+3808\,B\,C\,a^{15}\,b^3-3808\,B\,C\,a^{14}\,b^4-9408\,B\,C\,a^{13}\,b^5+9408\,B\,C\,a^{12}\,b^6+12430\,B\,C\,a^{11}\,b^7-12320\,B\,C\,a^{10}\,b^8-9200\,B\,C\,a^9\,b^9+8960\,B\,C\,a^8\,b^{10}+3360\,B\,C\,a^7\,b^{11}-3360\,B\,C\,a^6\,b^{12}-144\,B\,C\,a^5\,b^{13}+448\,B\,C\,a^4\,b^{14}-240\,B\,C\,a^3\,b^{15}+32\,B\,C\,a^2\,b^{16}-16\,B\,C\,a\,b^{17}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}+\frac{\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+80\,B\,a^2\,b^{25}+144\,B\,a^3\,b^{24}-380\,B\,a^4\,b^{23}-292\,B\,a^5\,b^{22}+772\,B\,a^6\,b^{21}+348\,B\,a^7\,b^{20}-868\,B\,a^8\,b^{19}-252\,B\,a^9\,b^{18}+572\,B\,a^{10}\,b^{17}+100\,B\,a^{11}\,b^{16}-208\,B\,a^{12}\,b^{15}-16\,B\,a^{13}\,b^{14}+32\,B\,a^{14}\,b^{13}+52\,C\,a^2\,b^{25}-160\,C\,a^3\,b^{24}-316\,C\,a^4\,b^{23}+816\,C\,a^5\,b^{22}+724\,C\,a^6\,b^{21}-1764\,C\,a^7\,b^{20}-896\,C\,a^8\,b^{19}+2076\,C\,a^9\,b^{18}+640\,C\,a^{10}\,b^{17}-1404\,C\,a^{11}\,b^{16}-248\,C\,a^{12}\,b^{15}+516\,C\,a^{13}\,b^{14}+40\,C\,a^{14}\,b^{13}-80\,C\,a^{15}\,b^{12}-32\,A\,a\,b^{26}-32\,B\,a\,b^{26}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,\left(-8\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}+48\,a^{12}\,b^{14}-48\,a^{11}\,b^{15}-120\,a^{10}\,b^{16}+120\,a^9\,b^{17}+160\,a^8\,b^{18}-160\,a^7\,b^{19}-120\,a^6\,b^{20}+120\,a^5\,b^{21}+48\,a^4\,b^{22}-48\,a^3\,b^{23}-8\,a^2\,b^{24}+8\,a\,b^{25}\right)}{b^6\,\left(-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}\right)}\right)\,\left(10{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)}{b^6}\right)\,\left(10{}\mathrm{i}\,C\,a^2-4{}\mathrm{i}\,B\,a\,b+\left(A\,1{}\mathrm{i}+\frac{C\,1{}\mathrm{i}}{2}\right)\,b^2\right)\,1{}\mathrm{i}}{b^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^4-8\,A^2\,a^{13}\,b^5-48\,A^2\,a^{12}\,b^6+48\,A^2\,a^{11}\,b^7+117\,A^2\,a^{10}\,b^8-120\,A^2\,a^9\,b^9-164\,A^2\,a^8\,b^{10}+160\,A^2\,a^7\,b^{11}+156\,A^2\,a^6\,b^{12}-120\,A^2\,a^5\,b^{13}-92\,A^2\,a^4\,b^{14}+48\,A^2\,a^3\,b^{15}+44\,A^2\,a^2\,b^{16}-8\,A^2\,a\,b^{17}+4\,A^2\,b^{18}-64\,A\,B\,a^{15}\,b^3+64\,A\,B\,a^{14}\,b^4+384\,A\,B\,a^{13}\,b^5-384\,A\,B\,a^{12}\,b^6-948\,A\,B\,a^{11}\,b^7+960\,A\,B\,a^{10}\,b^8+1306\,A\,B\,a^9\,b^9-1280\,A\,B\,a^8\,b^{10}-1128\,A\,B\,a^7\,b^{11}+960\,A\,B\,a^6\,b^{12}+592\,A\,B\,a^5\,b^{13}-384\,A\,B\,a^4\,b^{14}-160\,A\,B\,a^3\,b^{15}+64\,A\,B\,a^2\,b^{16}-32\,A\,B\,a\,b^{17}+160\,A\,C\,a^{16}\,b^2-160\,A\,C\,a^{15}\,b^3-952\,A\,C\,a^{14}\,b^4+952\,A\,C\,a^{13}\,b^5+2322\,A\,C\,a^{12}\,b^6-2352\,A\,C\,a^{11}\,b^7-3124\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9+2588\,A\,C\,a^8\,b^{10}-2240\,A\,C\,a^7\,b^{11}-1284\,A\,C\,a^6\,b^{12}+840\,A\,C\,a^5\,b^{13}+276\,A\,C\,a^4\,b^{14}-112\,A\,C\,a^3\,b^{15}+60\,A\,C\,a^2\,b^{16}-8\,A\,C\,a\,b^{17}+4\,A\,C\,b^{18}+128\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3-768\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5+1920\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7-2600\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9+2025\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}-824\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}+80\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+64\,B^2\,a^2\,b^{16}-640\,B\,C\,a^{17}\,b+640\,B\,C\,a^{16}\,b^2+3808\,B\,C\,a^{15}\,b^3-3808\,B\,C\,a^{14}\,b^4-9408\,B\,C\,a^{13}\,b^5+9408\,B\,C\,a^{12}\,b^6+12430\,B\,C\,a^{11}\,b^7-12320\,B\,C\,a^{10}\,b^8-9200\,B\,C\,a^9\,b^9+8960\,B\,C\,a^8\,b^{10}+3360\,B\,C\,a^7\,b^{11}-3360\,B\,C\,a^6\,b^{12}-144\,B\,C\,a^5\,b^{13}+448\,B\,C\,a^4\,b^{14}-240\,B\,C\,a^3\,b^{15}+32\,B\,C\,a^2\,b^{16}-16\,B\,C\,a\,b^{17}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}-\frac{\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+80\,B\,a^2\,b^{25}+144\,B\,a^3\,b^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\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5+1920\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7-2600\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9+2025\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}-824\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}+80\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+64\,B^2\,a^2\,b^{16}-640\,B\,C\,a^{17}\,b+640\,B\,C\,a^{16}\,b^2+3808\,B\,C\,a^{15}\,b^3-3808\,B\,C\,a^{14}\,b^4-9408\,B\,C\,a^{13}\,b^5+9408\,B\,C\,a^{12}\,b^6+12430\,B\,C\,a^{11}\,b^7-12320\,B\,C\,a^{10}\,b^8-9200\,B\,C\,a^9\,b^9+8960\,B\,C\,a^8\,b^{10}+3360\,B\,C\,a^7\,b^{11}-3360\,B\,C\,a^6\,b^{12}-144\,B\,C\,a^5\,b^{13}+448\,B\,C\,a^4\,b^{14}-240\,B\,C\,a^3\,b^{15}+32\,B\,C\,a^2\,b^{16}-16\,B\,C\,a\,b^{17}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}+\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+80\,B\,a^2\,b^{25}+144\,B\,a^3\,b^{24}-380\,B\,a^4\,b^{23}-292\,B\,a^5\,b^{22}+772\,B\,a^6\,b^{21}+348\,B\,a^7\,b^{20}-868\,B\,a^8\,b^{19}-252\,B\,a^9\,b^{18}+572\,B\,a^{10}\,b^{17}+100\,B\,a^{11}\,b^{16}-208\,B\,a^{12}\,b^{15}-16\,B\,a^{13}\,b^{14}+32\,B\,a^{14}\,b^{13}+52\,C\,a^2\,b^{25}-160\,C\,a^3\,b^{24}-316\,C\,a^4\,b^{23}+816\,C\,a^5\,b^{22}+724\,C\,a^6\,b^{21}-1764\,C\,a^7\,b^{20}-896\,C\,a^8\,b^{19}+2076\,C\,a^9\,b^{18}+640\,C\,a^{10}\,b^{17}-1404\,C\,a^{11}\,b^{16}-248\,C\,a^{12}\,b^{15}+516\,C\,a^{13}\,b^{14}+40\,C\,a^{14}\,b^{13}-80\,C\,a^{15}\,b^{12}-32\,A\,a\,b^{26}-32\,B\,a\,b^{26}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+35\,B\,a^3\,b^5-28\,B\,a^5\,b^3+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2-20\,B\,a\,b^7+8\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}+48\,a^{12}\,b^{14}-48\,a^{11}\,b^{15}-120\,a^{10}\,b^{16}+120\,a^9\,b^{17}+160\,a^8\,b^{18}-160\,a^7\,b^{19}-120\,a^6\,b^{20}+120\,a^5\,b^{21}+48\,a^4\,b^{22}-48\,a^3\,b^{23}-8\,a^2\,b^{24}+8\,a\,b^{25}\right)}{\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)\,\left(-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}\right)}\right)\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+35\,B\,a^3\,b^5-28\,B\,a^5\,b^3+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2-20\,B\,a\,b^7+8\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}\right)\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+35\,B\,a^3\,b^5-28\,B\,a^5\,b^3+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2-20\,B\,a\,b^7+8\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}+\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^4-8\,A^2\,a^{13}\,b^5-48\,A^2\,a^{12}\,b^6+48\,A^2\,a^{11}\,b^7+117\,A^2\,a^{10}\,b^8-120\,A^2\,a^9\,b^9-164\,A^2\,a^8\,b^{10}+160\,A^2\,a^7\,b^{11}+156\,A^2\,a^6\,b^{12}-120\,A^2\,a^5\,b^{13}-92\,A^2\,a^4\,b^{14}+48\,A^2\,a^3\,b^{15}+44\,A^2\,a^2\,b^{16}-8\,A^2\,a\,b^{17}+4\,A^2\,b^{18}-64\,A\,B\,a^{15}\,b^3+64\,A\,B\,a^{14}\,b^4+384\,A\,B\,a^{13}\,b^5-384\,A\,B\,a^{12}\,b^6-948\,A\,B\,a^{11}\,b^7+960\,A\,B\,a^{10}\,b^8+1306\,A\,B\,a^9\,b^9-1280\,A\,B\,a^8\,b^{10}-1128\,A\,B\,a^7\,b^{11}+960\,A\,B\,a^6\,b^{12}+592\,A\,B\,a^5\,b^{13}-384\,A\,B\,a^4\,b^{14}-160\,A\,B\,a^3\,b^{15}+64\,A\,B\,a^2\,b^{16}-32\,A\,B\,a\,b^{17}+160\,A\,C\,a^{16}\,b^2-160\,A\,C\,a^{15}\,b^3-952\,A\,C\,a^{14}\,b^4+952\,A\,C\,a^{13}\,b^5+2322\,A\,C\,a^{12}\,b^6-2352\,A\,C\,a^{11}\,b^7-3124\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9+2588\,A\,C\,a^8\,b^{10}-2240\,A\,C\,a^7\,b^{11}-1284\,A\,C\,a^6\,b^{12}+840\,A\,C\,a^5\,b^{13}+276\,A\,C\,a^4\,b^{14}-112\,A\,C\,a^3\,b^{15}+60\,A\,C\,a^2\,b^{16}-8\,A\,C\,a\,b^{17}+4\,A\,C\,b^{18}+128\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3-768\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5+1920\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7-2600\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9+2025\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}-824\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}+80\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+64\,B^2\,a^2\,b^{16}-640\,B\,C\,a^{17}\,b+640\,B\,C\,a^{16}\,b^2+3808\,B\,C\,a^{15}\,b^3-3808\,B\,C\,a^{14}\,b^4-9408\,B\,C\,a^{13}\,b^5+9408\,B\,C\,a^{12}\,b^6+12430\,B\,C\,a^{11}\,b^7-12320\,B\,C\,a^{10}\,b^8-9200\,B\,C\,a^9\,b^9+8960\,B\,C\,a^8\,b^{10}+3360\,B\,C\,a^7\,b^{11}-3360\,B\,C\,a^6\,b^{12}-144\,B\,C\,a^5\,b^{13}+448\,B\,C\,a^4\,b^{14}-240\,B\,C\,a^3\,b^{15}+32\,B\,C\,a^2\,b^{16}-16\,B\,C\,a\,b^{17}+800\,C^2\,a^{18}-800\,C^2\,a^{17}\,b-4720\,C^2\,a^{16}\,b^2+4720\,C^2\,a^{15}\,b^3+11522\,C^2\,a^{14}\,b^4-11522\,C^2\,a^{13}\,b^5-14837\,C^2\,a^{12}\,b^6+14812\,C^2\,a^{11}\,b^7+10385\,C^2\,a^{10}\,b^8-10430\,C^2\,a^9\,b^9-3325\,C^2\,a^8\,b^{10}+3640\,C^2\,a^7\,b^{11}-45\,C^2\,a^6\,b^{12}-350\,C^2\,a^5\,b^{13}+209\,C^2\,a^4\,b^{14}-68\,C^2\,a^3\,b^{15}+35\,C^2\,a^2\,b^{16}-2\,C^2\,a\,b^{17}+C^2\,b^{18}\right)}{-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}}-\frac{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(8\,A\,b^{27}+4\,C\,b^{27}-24\,A\,a^2\,b^{25}+128\,A\,a^3\,b^{24}+40\,A\,a^4\,b^{23}-220\,A\,a^5\,b^{22}-60\,A\,a^6\,b^{21}+220\,A\,a^7\,b^{20}+60\,A\,a^8\,b^{19}-140\,A\,a^9\,b^{18}-28\,A\,a^{10}\,b^{17}+52\,A\,a^{11}\,b^{16}+4\,A\,a^{12}\,b^{15}-8\,A\,a^{13}\,b^{14}+80\,B\,a^2\,b^{25}+144\,B\,a^3\,b^{24}-380\,B\,a^4\,b^{23}-292\,B\,a^5\,b^{22}+772\,B\,a^6\,b^{21}+348\,B\,a^7\,b^{20}-868\,B\,a^8\,b^{19}-252\,B\,a^9\,b^{18}+572\,B\,a^{10}\,b^{17}+100\,B\,a^{11}\,b^{16}-208\,B\,a^{12}\,b^{15}-16\,B\,a^{13}\,b^{14}+32\,B\,a^{14}\,b^{13}+52\,C\,a^2\,b^{25}-160\,C\,a^3\,b^{24}-316\,C\,a^4\,b^{23}+816\,C\,a^5\,b^{22}+724\,C\,a^6\,b^{21}-1764\,C\,a^7\,b^{20}-896\,C\,a^8\,b^{19}+2076\,C\,a^9\,b^{18}+640\,C\,a^{10}\,b^{17}-1404\,C\,a^{11}\,b^{16}-248\,C\,a^{12}\,b^{15}+516\,C\,a^{13}\,b^{14}+40\,C\,a^{14}\,b^{13}-80\,C\,a^{15}\,b^{12}-32\,A\,a\,b^{26}-32\,B\,a\,b^{26}\right)}{-a^{11}\,b^{15}-a^{10}\,b^{16}+5\,a^9\,b^{17}+5\,a^8\,b^{18}-10\,a^7\,b^{19}-10\,a^6\,b^{20}+10\,a^5\,b^{21}+10\,a^4\,b^{22}-5\,a^3\,b^{23}-5\,a^2\,b^{24}+a\,b^{25}+b^{26}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+35\,B\,a^3\,b^5-28\,B\,a^5\,b^3+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2-20\,B\,a\,b^7+8\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}+48\,a^{12}\,b^{14}-48\,a^{11}\,b^{15}-120\,a^{10}\,b^{16}+120\,a^9\,b^{17}+160\,a^8\,b^{18}-160\,a^7\,b^{19}-120\,a^6\,b^{20}+120\,a^5\,b^{21}+48\,a^4\,b^{22}-48\,a^3\,b^{23}-8\,a^2\,b^{24}+8\,a\,b^{25}\right)}{\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)\,\left(-a^{11}\,b^{10}-a^{10}\,b^{11}+5\,a^9\,b^{12}+5\,a^8\,b^{13}-10\,a^7\,b^{14}-10\,a^6\,b^{15}+10\,a^5\,b^{16}+10\,a^4\,b^{17}-5\,a^3\,b^{18}-5\,a^2\,b^{19}+a\,b^{20}+b^{21}\right)}\right)\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+35\,B\,a^3\,b^5-28\,B\,a^5\,b^3+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2-20\,B\,a\,b^7+8\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}\right)\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+35\,B\,a^3\,b^5-28\,B\,a^5\,b^3+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2-20\,B\,a\,b^7+8\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,A\,b^8-20\,C\,a^8-8\,A\,a^2\,b^6+7\,A\,a^4\,b^4-2\,A\,a^6\,b^2+35\,B\,a^3\,b^5-28\,B\,a^5\,b^3+40\,C\,a^2\,b^6-84\,C\,a^4\,b^4+69\,C\,a^6\,b^2-20\,B\,a\,b^7+8\,B\,a^7\,b\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^6+7\,a^{12}\,b^8-21\,a^{10}\,b^{10}+35\,a^8\,b^{12}-35\,a^6\,b^{14}+21\,a^4\,b^{16}-7\,a^2\,b^{18}+b^{20}\right)}","Not used",1,"(atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) + (((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i))/b^6)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i)*1i)/b^6 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) - (((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i))/b^6)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i)*1i)/b^6)/((8*(8000*C^3*a^19 + 32*A^3*a*b^18 - 4000*C^3*a^18*b + 96*A^3*a^2*b^17 - 128*A^3*a^3*b^16 - 128*A^3*a^4*b^15 + 220*A^3*a^5*b^14 + 132*A^3*a^6*b^13 - 220*A^3*a^7*b^12 - 68*A^3*a^8*b^11 + 140*A^3*a^9*b^10 + 22*A^3*a^10*b^9 - 52*A^3*a^11*b^8 - 4*A^3*a^12*b^7 + 8*A^3*a^13*b^6 - 1280*B^3*a^4*b^15 - 1920*B^3*a^5*b^14 + 6080*B^3*a^6*b^13 + 5120*B^3*a^7*b^12 - 12352*B^3*a^8*b^11 - 6408*B^3*a^9*b^10 + 13888*B^3*a^10*b^9 + 4352*B^3*a^11*b^8 - 9152*B^3*a^12*b^7 - 1600*B^3*a^13*b^6 + 3328*B^3*a^14*b^5 + 256*B^3*a^15*b^4 - 512*B^3*a^16*b^3 + 40*C^3*a^3*b^16 - 40*C^3*a^4*b^15 + 1396*C^3*a^5*b^14 + 204*C^3*a^6*b^13 + 8281*C^3*a^7*b^12 + 16999*C^3*a^8*b^11 - 64479*C^3*a^9*b^10 - 57345*C^3*a^10*b^9 + 155991*C^3*a^11*b^8 + 82337*C^3*a^12*b^7 - 193689*C^3*a^13*b^6 - 62030*C^3*a^14*b^5 + 135260*C^3*a^15*b^4 + 24400*C^3*a^16*b^3 - 50800*C^3*a^17*b^2 + 8*A*C^2*a*b^18 + 32*A^2*C*a*b^18 - 9600*B*C^2*a^18*b + 1152*A*B^2*a^3*b^16 + 2208*A*B^2*a^4*b^15 - 5088*A*B^2*a^5*b^14 - 4752*A*B^2*a^6*b^13 + 9696*A*B^2*a^7*b^12 + 5298*A*B^2*a^8*b^11 - 10464*A*B^2*a^9*b^10 - 3264*A*B^2*a^10*b^9 + 6816*A*B^2*a^11*b^8 + 1152*A*B^2*a^12*b^7 - 2496*A*B^2*a^13*b^6 - 192*A*B^2*a^14*b^5 + 384*A*B^2*a^15*b^4 - 336*A^2*B*a^2*b^17 - 816*A^2*B*a^3*b^16 + 1404*A^2*B*a^4*b^15 + 1380*A^2*B*a^5*b^14 - 2532*A^2*B*a^6*b^13 - 1452*A^2*B*a^7*b^12 + 2628*A^2*B*a^8*b^11 + 816*A^2*B*a^9*b^10 - 1692*A^2*B*a^10*b^9 - 276*A^2*B*a^11*b^8 + 624*A^2*B*a^12*b^7 + 48*A^2*B*a^13*b^6 - 96*A^2*B*a^14*b^5 - 8*A*C^2*a^2*b^17 + 448*A*C^2*a^3*b^16 + 192*A*C^2*a^4*b^15 + 4359*A*C^2*a^5*b^14 + 9657*A*C^2*a^6*b^13 - 25211*A*C^2*a^7*b^12 - 24901*A*C^2*a^8*b^11 + 53039*A*C^2*a^9*b^10 + 29513*A*C^2*a^10*b^9 - 60729*A*C^2*a^11*b^8 - 19233*A*C^2*a^12*b^7 + 41046*A*C^2*a^13*b^6 + 7080*A*C^2*a^14*b^5 - 15360*A*C^2*a^15*b^4 - 1200*A*C^2*a^16*b^3 + 2400*A*C^2*a^17*b^2 + 32*A^2*C*a^2*b^17 + 672*A^2*C*a^3*b^16 + 1760*A^2*C*a^4*b^15 - 3156*A^2*C*a^5*b^14 - 3196*A^2*C*a^6*b^13 + 5944*A^2*C*a^7*b^12 + 3448*A^2*C*a^8*b^11 - 6336*A^2*C*a^9*b^10 - 1983*A^2*C*a^10*b^9 + 4152*A^2*C*a^11*b^8 + 684*A^2*C*a^12*b^7 - 1548*A^2*C*a^13*b^6 - 120*A^2*C*a^14*b^5 + 240*A^2*C*a^15*b^4 - 20*B*C^2*a^2*b^17 + 20*B*C^2*a^3*b^16 - 1345*B*C^2*a^4*b^15 - 255*B*C^2*a^5*b^14 - 13929*B*C^2*a^6*b^13 - 24711*B*C^2*a^7*b^12 + 88721*B*C^2*a^8*b^11 + 77359*B*C^2*a^9*b^10 - 201479*B*C^2*a^10*b^9 - 105755*B*C^2*a^11*b^8 + 241596*B*C^2*a^12*b^7 + 76812*B*C^2*a^13*b^6 - 165384*B*C^2*a^14*b^5 - 29520*B*C^2*a^15*b^4 + 61440*B*C^2*a^16*b^3 + 4800*B*C^2*a^17*b^2 + 320*B^2*C*a^3*b^16 + 80*B^2*C*a^4*b^15 + 7440*B^2*C*a^5*b^14 + 11960*B^2*C*a^6*b^13 - 40368*B^2*C*a^7*b^12 - 34567*B^2*C*a^8*b^11 + 86512*B^2*C*a^9*b^10 + 45148*B^2*C*a^10*b^9 - 100368*B^2*C*a^11*b^8 - 31680*B^2*C*a^12*b^7 + 67392*B^2*C*a^13*b^6 + 11904*B^2*C*a^14*b^5 - 24768*B^2*C*a^15*b^4 - 1920*B^2*C*a^16*b^3 + 3840*B^2*C*a^17*b^2 - 208*A*B*C*a^2*b^17 - 112*A*B*C*a^3*b^16 - 4548*A*B*C*a^4*b^15 - 9292*A*B*C*a^5*b^14 + 22716*A*B*C*a^6*b^13 + 21788*A*B*C*a^7*b^12 - 45404*A*B*C*a^8*b^11 - 25034*A*B*C*a^9*b^10 + 50436*A*B*C*a^10*b^9 + 15852*A*B*C*a^11*b^8 - 33456*A*B*C*a^12*b^7 - 5712*A*B*C*a^13*b^6 + 12384*A*B*C*a^14*b^5 + 960*A*B*C*a^15*b^4 - 1920*A*B*C*a^16*b^3))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) + (((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i))/b^6)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i))/b^6 + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) - (((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (8*tan(c/2 + (d*x)/2)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/(b^6*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i))/b^6)*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i))/b^6))*(C*a^2*10i + b^2*(A*1i + (C*1i)/2) - B*a*b*4i)*2i)/(b^6*d) - ((tan(c/2 + (d*x)/2)*(2*B*b^8 + 20*C*a^8 + C*b^8 + 12*A*a^2*b^6 - 4*A*a^3*b^5 - 6*A*a^4*b^4 + A*a^5*b^3 + 2*A*a^6*b^2 - 6*B*a^2*b^6 - 26*B*a^3*b^5 + 11*B*a^4*b^4 + 24*B*a^5*b^3 - 4*B*a^6*b^2 - 11*C*a^2*b^6 + 21*C*a^3*b^5 + 57*C*a^4*b^4 - 27*C*a^5*b^3 - 59*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b - 7*C*a*b^7 + 10*C*a^7*b))/(b^5*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^9*(20*C*a^8 - 2*B*b^8 + C*b^8 + 12*A*a^2*b^6 + 4*A*a^3*b^5 - 6*A*a^4*b^4 - A*a^5*b^3 + 2*A*a^6*b^2 + 6*B*a^2*b^6 - 26*B*a^3*b^5 - 11*B*a^4*b^4 + 24*B*a^5*b^3 + 4*B*a^6*b^2 - 11*C*a^2*b^6 - 21*C*a^3*b^5 + 57*C*a^4*b^4 + 27*C*a^5*b^3 - 59*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b + 7*C*a*b^7 - 10*C*a^7*b))/(b^5*(a + b)^3*(a - b)) - (2*tan(c/2 + (d*x)/2)^3*(6*B*b^9 - 120*C*a^9 + 6*C*b^9 - 60*A*a^3*b^6 + 8*A*a^4*b^5 + 37*A*a^5*b^4 - 3*A*a^6*b^3 - 12*A*a^7*b^2 - 30*B*a^2*b^7 + 18*B*a^3*b^6 + 159*B*a^4*b^5 - 29*B*a^5*b^4 - 148*B*a^6*b^3 + 12*B*a^7*b^2 + 3*C*a^2*b^7 + 111*C*a^3*b^6 - 45*C*a^4*b^5 - 369*C*a^5*b^4 + 71*C*a^6*b^3 + 364*C*a^7*b^2 - 6*B*a*b^8 + 48*B*a^8*b - 21*C*a*b^8 - 30*C*a^8*b))/(3*b^5*(a + b)^2*(a - b)^3) + (2*tan(c/2 + (d*x)/2)^7*(120*C*a^9 - 6*B*b^9 + 6*C*b^9 + 60*A*a^3*b^6 + 8*A*a^4*b^5 - 37*A*a^5*b^4 - 3*A*a^6*b^3 + 12*A*a^7*b^2 + 30*B*a^2*b^7 + 18*B*a^3*b^6 - 159*B*a^4*b^5 - 29*B*a^5*b^4 + 148*B*a^6*b^3 + 12*B*a^7*b^2 + 3*C*a^2*b^7 - 111*C*a^3*b^6 - 45*C*a^4*b^5 + 369*C*a^5*b^4 + 71*C*a^6*b^3 - 364*C*a^7*b^2 - 6*B*a*b^8 - 48*B*a^8*b + 21*C*a*b^8 - 30*C*a^8*b))/(3*b^5*(a + b)^3*(a - b)^2) + (2*tan(c/2 + (d*x)/2)^5*(180*C*a^10 + 9*C*b^10 - 36*A*a^2*b^8 + 110*A*a^4*b^6 - 62*A*a^6*b^4 + 18*A*a^8*b^2 + 132*B*a^3*b^7 - 320*B*a^5*b^5 + 248*B*a^7*b^3 + 36*C*a^2*b^8 - 324*C*a^4*b^6 + 740*C*a^6*b^4 - 611*C*a^8*b^2 - 18*B*a*b^9 - 72*B*a^9*b))/(3*b^5*(a + b)^3*(a - b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 + 9*a^2*b + 5*a^3 - b^3) - tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^2*b - 10*a^3 + 2*b^3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 6*a^2*b - 10*a^3 - 2*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^10*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 9*a^2*b + 5*a^3 + b^3))) + (a*atan(((a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b)*1i)/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b)*1i)/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))/((8*(8000*C^3*a^19 + 32*A^3*a*b^18 - 4000*C^3*a^18*b + 96*A^3*a^2*b^17 - 128*A^3*a^3*b^16 - 128*A^3*a^4*b^15 + 220*A^3*a^5*b^14 + 132*A^3*a^6*b^13 - 220*A^3*a^7*b^12 - 68*A^3*a^8*b^11 + 140*A^3*a^9*b^10 + 22*A^3*a^10*b^9 - 52*A^3*a^11*b^8 - 4*A^3*a^12*b^7 + 8*A^3*a^13*b^6 - 1280*B^3*a^4*b^15 - 1920*B^3*a^5*b^14 + 6080*B^3*a^6*b^13 + 5120*B^3*a^7*b^12 - 12352*B^3*a^8*b^11 - 6408*B^3*a^9*b^10 + 13888*B^3*a^10*b^9 + 4352*B^3*a^11*b^8 - 9152*B^3*a^12*b^7 - 1600*B^3*a^13*b^6 + 3328*B^3*a^14*b^5 + 256*B^3*a^15*b^4 - 512*B^3*a^16*b^3 + 40*C^3*a^3*b^16 - 40*C^3*a^4*b^15 + 1396*C^3*a^5*b^14 + 204*C^3*a^6*b^13 + 8281*C^3*a^7*b^12 + 16999*C^3*a^8*b^11 - 64479*C^3*a^9*b^10 - 57345*C^3*a^10*b^9 + 155991*C^3*a^11*b^8 + 82337*C^3*a^12*b^7 - 193689*C^3*a^13*b^6 - 62030*C^3*a^14*b^5 + 135260*C^3*a^15*b^4 + 24400*C^3*a^16*b^3 - 50800*C^3*a^17*b^2 + 8*A*C^2*a*b^18 + 32*A^2*C*a*b^18 - 9600*B*C^2*a^18*b + 1152*A*B^2*a^3*b^16 + 2208*A*B^2*a^4*b^15 - 5088*A*B^2*a^5*b^14 - 4752*A*B^2*a^6*b^13 + 9696*A*B^2*a^7*b^12 + 5298*A*B^2*a^8*b^11 - 10464*A*B^2*a^9*b^10 - 3264*A*B^2*a^10*b^9 + 6816*A*B^2*a^11*b^8 + 1152*A*B^2*a^12*b^7 - 2496*A*B^2*a^13*b^6 - 192*A*B^2*a^14*b^5 + 384*A*B^2*a^15*b^4 - 336*A^2*B*a^2*b^17 - 816*A^2*B*a^3*b^16 + 1404*A^2*B*a^4*b^15 + 1380*A^2*B*a^5*b^14 - 2532*A^2*B*a^6*b^13 - 1452*A^2*B*a^7*b^12 + 2628*A^2*B*a^8*b^11 + 816*A^2*B*a^9*b^10 - 1692*A^2*B*a^10*b^9 - 276*A^2*B*a^11*b^8 + 624*A^2*B*a^12*b^7 + 48*A^2*B*a^13*b^6 - 96*A^2*B*a^14*b^5 - 8*A*C^2*a^2*b^17 + 448*A*C^2*a^3*b^16 + 192*A*C^2*a^4*b^15 + 4359*A*C^2*a^5*b^14 + 9657*A*C^2*a^6*b^13 - 25211*A*C^2*a^7*b^12 - 24901*A*C^2*a^8*b^11 + 53039*A*C^2*a^9*b^10 + 29513*A*C^2*a^10*b^9 - 60729*A*C^2*a^11*b^8 - 19233*A*C^2*a^12*b^7 + 41046*A*C^2*a^13*b^6 + 7080*A*C^2*a^14*b^5 - 15360*A*C^2*a^15*b^4 - 1200*A*C^2*a^16*b^3 + 2400*A*C^2*a^17*b^2 + 32*A^2*C*a^2*b^17 + 672*A^2*C*a^3*b^16 + 1760*A^2*C*a^4*b^15 - 3156*A^2*C*a^5*b^14 - 3196*A^2*C*a^6*b^13 + 5944*A^2*C*a^7*b^12 + 3448*A^2*C*a^8*b^11 - 6336*A^2*C*a^9*b^10 - 1983*A^2*C*a^10*b^9 + 4152*A^2*C*a^11*b^8 + 684*A^2*C*a^12*b^7 - 1548*A^2*C*a^13*b^6 - 120*A^2*C*a^14*b^5 + 240*A^2*C*a^15*b^4 - 20*B*C^2*a^2*b^17 + 20*B*C^2*a^3*b^16 - 1345*B*C^2*a^4*b^15 - 255*B*C^2*a^5*b^14 - 13929*B*C^2*a^6*b^13 - 24711*B*C^2*a^7*b^12 + 88721*B*C^2*a^8*b^11 + 77359*B*C^2*a^9*b^10 - 201479*B*C^2*a^10*b^9 - 105755*B*C^2*a^11*b^8 + 241596*B*C^2*a^12*b^7 + 76812*B*C^2*a^13*b^6 - 165384*B*C^2*a^14*b^5 - 29520*B*C^2*a^15*b^4 + 61440*B*C^2*a^16*b^3 + 4800*B*C^2*a^17*b^2 + 320*B^2*C*a^3*b^16 + 80*B^2*C*a^4*b^15 + 7440*B^2*C*a^5*b^14 + 11960*B^2*C*a^6*b^13 - 40368*B^2*C*a^7*b^12 - 34567*B^2*C*a^8*b^11 + 86512*B^2*C*a^9*b^10 + 45148*B^2*C*a^10*b^9 - 100368*B^2*C*a^11*b^8 - 31680*B^2*C*a^12*b^7 + 67392*B^2*C*a^13*b^6 + 11904*B^2*C*a^14*b^5 - 24768*B^2*C*a^15*b^4 - 1920*B^2*C*a^16*b^3 + 3840*B^2*C*a^17*b^2 - 208*A*B*C*a^2*b^17 - 112*A*B*C*a^3*b^16 - 4548*A*B*C*a^4*b^15 - 9292*A*B*C*a^5*b^14 + 22716*A*B*C*a^6*b^13 + 21788*A*B*C*a^7*b^12 - 45404*A*B*C*a^8*b^11 - 25034*A*B*C*a^9*b^10 + 50436*A*B*C*a^10*b^9 + 15852*A*B*C*a^11*b^8 - 33456*A*B*C*a^12*b^7 - 5712*A*B*C*a^13*b^6 + 12384*A*B*C*a^14*b^5 + 960*A*B*C*a^15*b^4 - 1920*A*B*C*a^16*b^3))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^18 + 800*C^2*a^18 + C^2*b^18 - 8*A^2*a*b^17 - 2*C^2*a*b^17 - 800*C^2*a^17*b + 44*A^2*a^2*b^16 + 48*A^2*a^3*b^15 - 92*A^2*a^4*b^14 - 120*A^2*a^5*b^13 + 156*A^2*a^6*b^12 + 160*A^2*a^7*b^11 - 164*A^2*a^8*b^10 - 120*A^2*a^9*b^9 + 117*A^2*a^10*b^8 + 48*A^2*a^11*b^7 - 48*A^2*a^12*b^6 - 8*A^2*a^13*b^5 + 8*A^2*a^14*b^4 + 64*B^2*a^2*b^16 - 128*B^2*a^3*b^15 + 80*B^2*a^4*b^14 + 768*B^2*a^5*b^13 - 824*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 + 2025*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 - 2600*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 + 1920*B^2*a^12*b^6 + 768*B^2*a^13*b^5 - 768*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 128*B^2*a^16*b^2 + 35*C^2*a^2*b^16 - 68*C^2*a^3*b^15 + 209*C^2*a^4*b^14 - 350*C^2*a^5*b^13 - 45*C^2*a^6*b^12 + 3640*C^2*a^7*b^11 - 3325*C^2*a^8*b^10 - 10430*C^2*a^9*b^9 + 10385*C^2*a^10*b^8 + 14812*C^2*a^11*b^7 - 14837*C^2*a^12*b^6 - 11522*C^2*a^13*b^5 + 11522*C^2*a^14*b^4 + 4720*C^2*a^15*b^3 - 4720*C^2*a^16*b^2 + 4*A*C*b^18 - 32*A*B*a*b^17 - 8*A*C*a*b^17 - 16*B*C*a*b^17 - 640*B*C*a^17*b + 64*A*B*a^2*b^16 - 160*A*B*a^3*b^15 - 384*A*B*a^4*b^14 + 592*A*B*a^5*b^13 + 960*A*B*a^6*b^12 - 1128*A*B*a^7*b^11 - 1280*A*B*a^8*b^10 + 1306*A*B*a^9*b^9 + 960*A*B*a^10*b^8 - 948*A*B*a^11*b^7 - 384*A*B*a^12*b^6 + 384*A*B*a^13*b^5 + 64*A*B*a^14*b^4 - 64*A*B*a^15*b^3 + 60*A*C*a^2*b^16 - 112*A*C*a^3*b^15 + 276*A*C*a^4*b^14 + 840*A*C*a^5*b^13 - 1284*A*C*a^6*b^12 - 2240*A*C*a^7*b^11 + 2588*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 - 3124*A*C*a^10*b^8 - 2352*A*C*a^11*b^7 + 2322*A*C*a^12*b^6 + 952*A*C*a^13*b^5 - 952*A*C*a^14*b^4 - 160*A*C*a^15*b^3 + 160*A*C*a^16*b^2 + 32*B*C*a^2*b^16 - 240*B*C*a^3*b^15 + 448*B*C*a^4*b^14 - 144*B*C*a^5*b^13 - 3360*B*C*a^6*b^12 + 3360*B*C*a^7*b^11 + 8960*B*C*a^8*b^10 - 9200*B*C*a^9*b^9 - 12320*B*C*a^10*b^8 + 12430*B*C*a^11*b^7 + 9408*B*C*a^12*b^6 - 9408*B*C*a^13*b^5 - 3808*B*C*a^14*b^4 + 3808*B*C*a^15*b^3 + 640*B*C*a^16*b^2))/(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(8*A*b^27 + 4*C*b^27 - 24*A*a^2*b^25 + 128*A*a^3*b^24 + 40*A*a^4*b^23 - 220*A*a^5*b^22 - 60*A*a^6*b^21 + 220*A*a^7*b^20 + 60*A*a^8*b^19 - 140*A*a^9*b^18 - 28*A*a^10*b^17 + 52*A*a^11*b^16 + 4*A*a^12*b^15 - 8*A*a^13*b^14 + 80*B*a^2*b^25 + 144*B*a^3*b^24 - 380*B*a^4*b^23 - 292*B*a^5*b^22 + 772*B*a^6*b^21 + 348*B*a^7*b^20 - 868*B*a^8*b^19 - 252*B*a^9*b^18 + 572*B*a^10*b^17 + 100*B*a^11*b^16 - 208*B*a^12*b^15 - 16*B*a^13*b^14 + 32*B*a^14*b^13 + 52*C*a^2*b^25 - 160*C*a^3*b^24 - 316*C*a^4*b^23 + 816*C*a^5*b^22 + 724*C*a^6*b^21 - 1764*C*a^7*b^20 - 896*C*a^8*b^19 + 2076*C*a^9*b^18 + 640*C*a^10*b^17 - 1404*C*a^11*b^16 - 248*C*a^12*b^15 + 516*C*a^13*b^14 + 40*C*a^14*b^13 - 80*C*a^15*b^12 - 32*A*a*b^26 - 32*B*a*b^26))/(a*b^25 + b^26 - 5*a^2*b^24 - 5*a^3*b^23 + 10*a^4*b^22 + 10*a^5*b^21 - 10*a^6*b^20 - 10*a^7*b^19 + 5*a^8*b^18 + 5*a^9*b^17 - a^10*b^16 - a^11*b^15) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b)*(8*a*b^25 - 8*a^2*b^24 - 48*a^3*b^23 + 48*a^4*b^22 + 120*a^5*b^21 - 120*a^6*b^20 - 160*a^7*b^19 + 160*a^8*b^18 + 120*a^9*b^17 - 120*a^10*b^16 - 48*a^11*b^15 + 48*a^12*b^14 + 8*a^13*b^13 - 8*a^14*b^12))/((b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)*(a*b^20 + b^21 - 5*a^2*b^19 - 5*a^3*b^18 + 10*a^4*b^17 + 10*a^5*b^16 - 10*a^6*b^15 - 10*a^7*b^14 + 5*a^8*b^13 + 5*a^9*b^12 - a^10*b^11 - a^11*b^10)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6)))*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b))/(2*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6))))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^8 - 20*C*a^8 - 8*A*a^2*b^6 + 7*A*a^4*b^4 - 2*A*a^6*b^2 + 35*B*a^3*b^5 - 28*B*a^5*b^3 + 40*C*a^2*b^6 - 84*C*a^4*b^4 + 69*C*a^6*b^2 - 20*B*a*b^7 + 8*B*a^7*b)*1i)/(d*(b^20 - 7*a^2*b^18 + 21*a^4*b^16 - 35*a^6*b^14 + 35*a^8*b^12 - 21*a^10*b^10 + 7*a^12*b^8 - a^14*b^6))","B"
1002,1,9423,461,9.894738,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(8\,C\,a^7+2\,C\,b^7+3\,A\,a^2\,b^5+2\,A\,a^3\,b^4-12\,B\,a^2\,b^5-4\,B\,a^3\,b^4+6\,B\,a^4\,b^3+B\,a^5\,b^2-6\,C\,a^2\,b^5+26\,C\,a^3\,b^4+11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,B\,a^6\,b-2\,C\,a\,b^6-4\,C\,a^6\,b\right)}{b^4\,{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,C\,a^7-2\,C\,b^7-3\,A\,a^2\,b^5+2\,A\,a^3\,b^4-12\,B\,a^2\,b^5+4\,B\,a^3\,b^4+6\,B\,a^4\,b^3-B\,a^5\,b^2+6\,C\,a^2\,b^5+26\,C\,a^3\,b^4-11\,C\,a^4\,b^3-24\,C\,a^5\,b^2+6\,A\,a\,b^6-2\,B\,a^6\,b-2\,C\,a\,b^6+4\,C\,a^6\,b\right)}{b^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6-7\,A\,a^3\,b^5+10\,A\,a^4\,b^4+36\,B\,a^2\,b^6-96\,B\,a^3\,b^5-14\,B\,a^4\,b^4+59\,B\,a^5\,b^3+3\,B\,a^6\,b^2-72\,C\,a^2\,b^6-60\,C\,a^3\,b^5+273\,C\,a^4\,b^4+47\,C\,a^5\,b^3-236\,C\,a^6\,b^2-18\,A\,a\,b^7-18\,B\,a^7\,b-12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(72\,C\,a^8+18\,C\,b^8+45\,A\,a^2\,b^6+7\,A\,a^3\,b^5+10\,A\,a^4\,b^4-36\,B\,a^2\,b^6-96\,B\,a^3\,b^5+14\,B\,a^4\,b^4+59\,B\,a^5\,b^3-3\,B\,a^6\,b^2-72\,C\,a^2\,b^6+60\,C\,a^3\,b^5+273\,C\,a^4\,b^4-47\,C\,a^5\,b^3-236\,C\,a^6\,b^2+18\,A\,a\,b^7-18\,B\,a^7\,b+12\,C\,a^7\,b\right)}{3\,b^4\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a\,b^2-6\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3+6\,a^2\,b-2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3-6\,a^2\,b+2\,b^3\right)+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(B\,b-4\,C\,a\right)\,1{}\mathrm{i}}{b^5\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(B\,b\,1{}\mathrm{i}-C\,a\,4{}\mathrm{i}\right)}{b^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}{\frac{16\,\left(-9\,A^2\,B\,a^4\,b^{12}-12\,A^2\,B\,a^2\,b^{14}-4\,A^2\,B\,b^{16}+36\,A^2\,C\,a^5\,b^{11}+48\,A^2\,C\,a^3\,b^{13}+16\,A^2\,C\,a\,b^{15}-6\,A\,B^2\,a^9\,b^7-6\,A\,B^2\,a^8\,b^8+20\,A\,B^2\,a^7\,b^9+14\,A\,B^2\,a^6\,b^{10}-14\,A\,B^2\,a^5\,b^{11}-6\,A\,B^2\,a^4\,b^{12}+22\,A\,B^2\,a^3\,b^{13}-6\,A\,B^2\,a^2\,b^{14}+28\,A\,B^2\,a\,b^{15}+4\,A\,B^2\,b^{16}+48\,A\,B\,C\,a^{10}\,b^6+48\,A\,B\,C\,a^9\,b^7-160\,A\,B\,C\,a^8\,b^8-112\,A\,B\,C\,a^7\,b^9+130\,A\,B\,C\,a^6\,b^{10}+48\,A\,B\,C\,a^5\,b^{11}-92\,A\,B\,C\,a^4\,b^{12}+48\,A\,B\,C\,a^3\,b^{13}-176\,A\,B\,C\,a^2\,b^{14}-32\,A\,B\,C\,a\,b^{15}-96\,A\,C^2\,a^{11}\,b^5-96\,A\,C^2\,a^{10}\,b^6+320\,A\,C^2\,a^9\,b^7+224\,A\,C^2\,a^8\,b^8-296\,A\,C^2\,a^7\,b^9-96\,A\,C^2\,a^6\,b^{10}+16\,A\,C^2\,a^5\,b^{11}-96\,A\,C^2\,a^4\,b^{12}+256\,A\,C^2\,a^3\,b^{13}+64\,A\,C^2\,a^2\,b^{14}-4\,B^3\,a^{13}\,b^3+2\,B^3\,a^{12}\,b^4+26\,B^3\,a^{11}\,b^5-11\,B^3\,a^{10}\,b^6-70\,B^3\,a^9\,b^7+34\,B^3\,a^8\,b^8+110\,B^3\,a^7\,b^9-66\,B^3\,a^6\,b^{10}-110\,B^3\,a^5\,b^{11}+64\,B^3\,a^4\,b^{12}+64\,B^3\,a^3\,b^{13}-48\,B^3\,a^2\,b^{14}-16\,B^3\,a\,b^{15}+48\,B^2\,C\,a^{14}\,b^2-24\,B^2\,C\,a^{13}\,b^3-312\,B^2\,C\,a^{12}\,b^4+138\,B^2\,C\,a^{11}\,b^5+846\,B^2\,C\,a^{10}\,b^6-408\,B^2\,C\,a^9\,b^7-1314\,B^2\,C\,a^8\,b^8+726\,B^2\,C\,a^7\,b^9+1266\,B^2\,C\,a^6\,b^{10}-690\,B^2\,C\,a^5\,b^{11}-702\,B^2\,C\,a^4\,b^{12}+408\,B^2\,C\,a^3\,b^{13}+168\,B^2\,C\,a^2\,b^{14}-192\,B\,C^2\,a^{15}\,b+96\,B\,C^2\,a^{14}\,b^2+1248\,B\,C^2\,a^{13}\,b^3-576\,B\,C^2\,a^{12}\,b^4-3408\,B\,C^2\,a^{11}\,b^5+1632\,B\,C^2\,a^{10}\,b^6+5232\,B\,C^2\,a^9\,b^7-2649\,B\,C^2\,a^8\,b^8-4848\,B\,C^2\,a^7\,b^9+2376\,B\,C^2\,a^6\,b^{10}+2544\,B\,C^2\,a^5\,b^{11}-1104\,B\,C^2\,a^4\,b^{12}-576\,B\,C^2\,a^3\,b^{13}+256\,C^3\,a^{16}-128\,C^3\,a^{15}\,b-1664\,C^3\,a^{14}\,b^2+800\,C^3\,a^{13}\,b^3+4576\,C^3\,a^{12}\,b^4-2176\,C^3\,a^{11}\,b^5-6944\,C^3\,a^{10}\,b^6+3204\,C^3\,a^9\,b^7+6176\,C^3\,a^8\,b^8-2560\,C^3\,a^7\,b^9-3040\,C^3\,a^6\,b^{10}+960\,C^3\,a^5\,b^{11}+640\,C^3\,a^4\,b^{12}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}+\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{12}+12\,A^2\,a^2\,b^{14}+4\,A^2\,b^{16}+12\,A\,B\,a^9\,b^7-34\,A\,B\,a^7\,b^9+20\,A\,B\,a^5\,b^{11}-16\,A\,B\,a^3\,b^{13}-32\,A\,B\,a\,b^{15}-48\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-98\,A\,C\,a^6\,b^{10}-20\,A\,C\,a^4\,b^{12}+80\,A\,C\,a^2\,b^{14}+8\,B^2\,a^{14}\,b^2-8\,B^2\,a^{13}\,b^3-48\,B^2\,a^{12}\,b^4+48\,B^2\,a^{11}\,b^5+117\,B^2\,a^{10}\,b^6-120\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8+160\,B^2\,a^7\,b^9+156\,B^2\,a^6\,b^{10}-120\,B^2\,a^5\,b^{11}-92\,B^2\,a^4\,b^{12}+48\,B^2\,a^3\,b^{13}+44\,B^2\,a^2\,b^{14}-8\,B^2\,a\,b^{15}+4\,B^2\,b^{16}-64\,B\,C\,a^{15}\,b+64\,B\,C\,a^{14}\,b^2+384\,B\,C\,a^{13}\,b^3-384\,B\,C\,a^{12}\,b^4-948\,B\,C\,a^{11}\,b^5+960\,B\,C\,a^{10}\,b^6+1306\,B\,C\,a^9\,b^7-1280\,B\,C\,a^8\,b^8-1128\,B\,C\,a^7\,b^9+960\,B\,C\,a^6\,b^{10}+592\,B\,C\,a^5\,b^{11}-384\,B\,C\,a^4\,b^{12}-160\,B\,C\,a^3\,b^{13}+64\,B\,C\,a^2\,b^{14}-32\,B\,C\,a\,b^{15}+128\,C^2\,a^{16}-128\,C^2\,a^{15}\,b-768\,C^2\,a^{14}\,b^2+768\,C^2\,a^{13}\,b^3+1920\,C^2\,a^{12}\,b^4-1920\,C^2\,a^{11}\,b^5-2600\,C^2\,a^{10}\,b^6+2560\,C^2\,a^9\,b^7+2025\,C^2\,a^8\,b^8-1920\,C^2\,a^7\,b^9-824\,C^2\,a^6\,b^{10}+768\,C^2\,a^5\,b^{11}+80\,C^2\,a^4\,b^{12}-128\,C^2\,a^3\,b^{13}+64\,C^2\,a^2\,b^{14}\right)}{-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}}-\frac{\left(\frac{8\,\left(4\,A\,b^{24}+4\,B\,b^{24}-6\,A\,a^2\,b^{22}+6\,A\,a^3\,b^{21}-6\,A\,a^4\,b^{20}+6\,A\,a^5\,b^{19}+14\,A\,a^6\,b^{18}-14\,A\,a^7\,b^{17}-6\,A\,a^8\,b^{16}+6\,A\,a^9\,b^{15}-12\,B\,a^2\,b^{22}+64\,B\,a^3\,b^{21}+20\,B\,a^4\,b^{20}-110\,B\,a^5\,b^{19}-30\,B\,a^6\,b^{18}+110\,B\,a^7\,b^{17}+30\,B\,a^8\,b^{16}-70\,B\,a^9\,b^{15}-14\,B\,a^{10}\,b^{14}+26\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}-4\,B\,a^{13}\,b^{11}+40\,C\,a^2\,b^{22}+72\,C\,a^3\,b^{21}-190\,C\,a^4\,b^{20}-146\,C\,a^5\,b^{19}+386\,C\,a^6\,b^{18}+174\,C\,a^7\,b^{17}-434\,C\,a^8\,b^{16}-126\,C\,a^9\,b^{15}+286\,C\,a^{10}\,b^{14}+50\,C\,a^{11}\,b^{13}-104\,C\,a^{12}\,b^{12}-8\,C\,a^{13}\,b^{11}+16\,C\,a^{14}\,b^{10}-4\,A\,a\,b^{23}-16\,B\,a\,b^{23}-16\,C\,a\,b^{23}\right)}{-a^{11}\,b^{12}-a^{10}\,b^{13}+5\,a^9\,b^{14}+5\,a^8\,b^{15}-10\,a^7\,b^{16}-10\,a^6\,b^{17}+10\,a^5\,b^{18}+10\,a^4\,b^{19}-5\,a^3\,b^{20}-5\,a^2\,b^{21}+a\,b^{22}+b^{23}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^8-8\,C\,a^8+3\,A\,a^2\,b^6+8\,B\,a^3\,b^5-7\,B\,a^5\,b^3+20\,C\,a^2\,b^6-35\,C\,a^4\,b^4+28\,C\,a^6\,b^2-8\,B\,a\,b^7+2\,B\,a^7\,b\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^7*(8*C*a^7 + 2*C*b^7 + 3*A*a^2*b^5 + 2*A*a^3*b^4 - 12*B*a^2*b^5 - 4*B*a^3*b^4 + 6*B*a^4*b^3 + B*a^5*b^2 - 6*C*a^2*b^5 + 26*C*a^3*b^4 + 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*B*a^6*b - 2*C*a*b^6 - 4*C*a^6*b))/(b^4*(a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(8*C*a^7 - 2*C*b^7 - 3*A*a^2*b^5 + 2*A*a^3*b^4 - 12*B*a^2*b^5 + 4*B*a^3*b^4 + 6*B*a^4*b^3 - B*a^5*b^2 + 6*C*a^2*b^5 + 26*C*a^3*b^4 - 11*C*a^4*b^3 - 24*C*a^5*b^2 + 6*A*a*b^6 - 2*B*a^6*b - 2*C*a*b^6 + 4*C*a^6*b))/(b^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^3*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 - 7*A*a^3*b^5 + 10*A*a^4*b^4 + 36*B*a^2*b^6 - 96*B*a^3*b^5 - 14*B*a^4*b^4 + 59*B*a^5*b^3 + 3*B*a^6*b^2 - 72*C*a^2*b^6 - 60*C*a^3*b^5 + 273*C*a^4*b^4 + 47*C*a^5*b^3 - 236*C*a^6*b^2 - 18*A*a*b^7 - 18*B*a^7*b - 12*C*a^7*b))/(3*b^4*(a + b)^2*(a - b)^3) + (tan(c/2 + (d*x)/2)^5*(72*C*a^8 + 18*C*b^8 + 45*A*a^2*b^6 + 7*A*a^3*b^5 + 10*A*a^4*b^4 - 36*B*a^2*b^6 - 96*B*a^3*b^5 + 14*B*a^4*b^4 + 59*B*a^5*b^3 - 3*B*a^6*b^2 - 72*C*a^2*b^6 + 60*C*a^3*b^5 + 273*C*a^4*b^4 - 47*C*a^5*b^3 - 236*C*a^6*b^2 + 18*A*a*b^7 - 18*B*a^7*b + 12*C*a^7*b))/(3*b^4*(a + b)^3*(a - b)^2))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^3) + tan(c/2 + (d*x)/2)^2*(6*a^2*b + 4*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)^6*(4*a^3 - 6*a^2*b + 2*b^3) + a^3 + b^3 + tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (log(tan(c/2 + (d*x)/2) + 1i)*(B*b - 4*C*a)*1i)/(b^5*d) - (log(tan(c/2 + (d*x)/2) - 1i)*(B*b*1i - C*a*4i))/(b^5*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))/((16*(256*C^3*a^16 + 4*A*B^2*b^16 - 4*A^2*B*b^16 - 16*B^3*a*b^15 - 128*C^3*a^15*b - 48*B^3*a^2*b^14 + 64*B^3*a^3*b^13 + 64*B^3*a^4*b^12 - 110*B^3*a^5*b^11 - 66*B^3*a^6*b^10 + 110*B^3*a^7*b^9 + 34*B^3*a^8*b^8 - 70*B^3*a^9*b^7 - 11*B^3*a^10*b^6 + 26*B^3*a^11*b^5 + 2*B^3*a^12*b^4 - 4*B^3*a^13*b^3 + 640*C^3*a^4*b^12 + 960*C^3*a^5*b^11 - 3040*C^3*a^6*b^10 - 2560*C^3*a^7*b^9 + 6176*C^3*a^8*b^8 + 3204*C^3*a^9*b^7 - 6944*C^3*a^10*b^6 - 2176*C^3*a^11*b^5 + 4576*C^3*a^12*b^4 + 800*C^3*a^13*b^3 - 1664*C^3*a^14*b^2 + 28*A*B^2*a*b^15 + 16*A^2*C*a*b^15 - 192*B*C^2*a^15*b - 6*A*B^2*a^2*b^14 + 22*A*B^2*a^3*b^13 - 6*A*B^2*a^4*b^12 - 14*A*B^2*a^5*b^11 + 14*A*B^2*a^6*b^10 + 20*A*B^2*a^7*b^9 - 6*A*B^2*a^8*b^8 - 6*A*B^2*a^9*b^7 - 12*A^2*B*a^2*b^14 - 9*A^2*B*a^4*b^12 + 64*A*C^2*a^2*b^14 + 256*A*C^2*a^3*b^13 - 96*A*C^2*a^4*b^12 + 16*A*C^2*a^5*b^11 - 96*A*C^2*a^6*b^10 - 296*A*C^2*a^7*b^9 + 224*A*C^2*a^8*b^8 + 320*A*C^2*a^9*b^7 - 96*A*C^2*a^10*b^6 - 96*A*C^2*a^11*b^5 + 48*A^2*C*a^3*b^13 + 36*A^2*C*a^5*b^11 - 576*B*C^2*a^3*b^13 - 1104*B*C^2*a^4*b^12 + 2544*B*C^2*a^5*b^11 + 2376*B*C^2*a^6*b^10 - 4848*B*C^2*a^7*b^9 - 2649*B*C^2*a^8*b^8 + 5232*B*C^2*a^9*b^7 + 1632*B*C^2*a^10*b^6 - 3408*B*C^2*a^11*b^5 - 576*B*C^2*a^12*b^4 + 1248*B*C^2*a^13*b^3 + 96*B*C^2*a^14*b^2 + 168*B^2*C*a^2*b^14 + 408*B^2*C*a^3*b^13 - 702*B^2*C*a^4*b^12 - 690*B^2*C*a^5*b^11 + 1266*B^2*C*a^6*b^10 + 726*B^2*C*a^7*b^9 - 1314*B^2*C*a^8*b^8 - 408*B^2*C*a^9*b^7 + 846*B^2*C*a^10*b^6 + 138*B^2*C*a^11*b^5 - 312*B^2*C*a^12*b^4 - 24*B^2*C*a^13*b^3 + 48*B^2*C*a^14*b^2 - 32*A*B*C*a*b^15 - 176*A*B*C*a^2*b^14 + 48*A*B*C*a^3*b^13 - 92*A*B*C*a^4*b^12 + 48*A*B*C*a^5*b^11 + 130*A*B*C*a^6*b^10 - 112*A*B*C*a^7*b^9 - 160*A*B*C*a^8*b^8 + 48*A*B*C*a^9*b^7 + 48*A*B*C*a^10*b^6))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) + (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 4*B^2*b^16 + 128*C^2*a^16 - 8*B^2*a*b^15 - 128*C^2*a^15*b + 12*A^2*a^2*b^14 + 9*A^2*a^4*b^12 + 44*B^2*a^2*b^14 + 48*B^2*a^3*b^13 - 92*B^2*a^4*b^12 - 120*B^2*a^5*b^11 + 156*B^2*a^6*b^10 + 160*B^2*a^7*b^9 - 164*B^2*a^8*b^8 - 120*B^2*a^9*b^7 + 117*B^2*a^10*b^6 + 48*B^2*a^11*b^5 - 48*B^2*a^12*b^4 - 8*B^2*a^13*b^3 + 8*B^2*a^14*b^2 + 64*C^2*a^2*b^14 - 128*C^2*a^3*b^13 + 80*C^2*a^4*b^12 + 768*C^2*a^5*b^11 - 824*C^2*a^6*b^10 - 1920*C^2*a^7*b^9 + 2025*C^2*a^8*b^8 + 2560*C^2*a^9*b^7 - 2600*C^2*a^10*b^6 - 1920*C^2*a^11*b^5 + 1920*C^2*a^12*b^4 + 768*C^2*a^13*b^3 - 768*C^2*a^14*b^2 - 32*A*B*a*b^15 - 32*B*C*a*b^15 - 64*B*C*a^15*b - 16*A*B*a^3*b^13 + 20*A*B*a^5*b^11 - 34*A*B*a^7*b^9 + 12*A*B*a^9*b^7 + 80*A*C*a^2*b^14 - 20*A*C*a^4*b^12 - 98*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 48*A*C*a^10*b^6 + 64*B*C*a^2*b^14 - 160*B*C*a^3*b^13 - 384*B*C*a^4*b^12 + 592*B*C*a^5*b^11 + 960*B*C*a^6*b^10 - 1128*B*C*a^7*b^9 - 1280*B*C*a^8*b^8 + 1306*B*C*a^9*b^7 + 960*B*C*a^10*b^6 - 948*B*C*a^11*b^5 - 384*B*C*a^12*b^4 + 384*B*C*a^13*b^3 + 64*B*C*a^14*b^2))/(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8) - (((8*(4*A*b^24 + 4*B*b^24 - 6*A*a^2*b^22 + 6*A*a^3*b^21 - 6*A*a^4*b^20 + 6*A*a^5*b^19 + 14*A*a^6*b^18 - 14*A*a^7*b^17 - 6*A*a^8*b^16 + 6*A*a^9*b^15 - 12*B*a^2*b^22 + 64*B*a^3*b^21 + 20*B*a^4*b^20 - 110*B*a^5*b^19 - 30*B*a^6*b^18 + 110*B*a^7*b^17 + 30*B*a^8*b^16 - 70*B*a^9*b^15 - 14*B*a^10*b^14 + 26*B*a^11*b^13 + 2*B*a^12*b^12 - 4*B*a^13*b^11 + 40*C*a^2*b^22 + 72*C*a^3*b^21 - 190*C*a^4*b^20 - 146*C*a^5*b^19 + 386*C*a^6*b^18 + 174*C*a^7*b^17 - 434*C*a^8*b^16 - 126*C*a^9*b^15 + 286*C*a^10*b^14 + 50*C*a^11*b^13 - 104*C*a^12*b^12 - 8*C*a^13*b^11 + 16*C*a^14*b^10 - 4*A*a*b^23 - 16*B*a*b^23 - 16*C*a*b^23))/(a*b^22 + b^23 - 5*a^2*b^21 - 5*a^3*b^20 + 10*a^4*b^19 + 10*a^5*b^18 - 10*a^6*b^17 - 10*a^7*b^16 + 5*a^8*b^15 + 5*a^9*b^14 - a^10*b^13 - a^11*b^12) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^8 - 8*C*a^8 + 3*A*a^2*b^6 + 8*B*a^3*b^5 - 7*B*a^5*b^3 + 20*C*a^2*b^6 - 35*C*a^4*b^4 + 28*C*a^6*b^2 - 8*B*a*b^7 + 2*B*a^7*b)*1i)/(d*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))","B"
1003,1,11947,349,14.669227,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4-A\,a^3\,b^3+3\,B\,a^2\,b^4-2\,B\,a^3\,b^3+12\,C\,a^2\,b^4-4\,C\,a^3\,b^3-6\,C\,a^4\,b^2-2\,A\,a\,b^5-6\,B\,a\,b^5+C\,a^5\,b\right)}{\left(a+b\right)\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6+7\,A\,a^2\,b^4-B\,a^3\,b^3+18\,C\,a^2\,b^4-11\,C\,a^4\,b^2-9\,B\,a\,b^5\right)}{3\,{\left(a+b\right)}^2\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6+6\,A\,a^2\,b^4+A\,a^3\,b^3-3\,B\,a^2\,b^4-2\,B\,a^3\,b^3+12\,C\,a^2\,b^4+4\,C\,a^3\,b^3-6\,C\,a^4\,b^2+2\,A\,a\,b^5-6\,B\,a\,b^5-C\,a^5\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^3}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{2\,C\,\mathrm{atan}\left(\frac{\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{C\,\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)}{b^4}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-6\,A\,B\,C\,a^5\,b^8-28\,A\,B\,C\,a^3\,b^{10}-16\,A\,B\,C\,a\,b^{12}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+9\,B^2\,C\,a^4\,b^9+12\,B^2\,C\,a^2\,b^{11}+4\,B^2\,C\,b^{13}+6\,B\,C^2\,a^9\,b^4+6\,B\,C^2\,a^8\,b^5-20\,B\,C^2\,a^7\,b^6-14\,B\,C^2\,a^6\,b^7+14\,B\,C^2\,a^5\,b^8+6\,B\,C^2\,a^4\,b^9-22\,B\,C^2\,a^3\,b^{10}+6\,B\,C^2\,a^2\,b^{11}-28\,B\,C^2\,a\,b^{12}-4\,B\,C^2\,b^{13}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{C\,\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{C\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{C\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a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}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}{\frac{16\,\left(A^2\,C\,a^6\,b^7+8\,A^2\,C\,a^4\,b^9+16\,A^2\,C\,a^2\,b^{11}-6\,A\,B\,C\,a^5\,b^8-28\,A\,B\,C\,a^3\,b^{10}-16\,A\,B\,C\,a\,b^{12}-2\,A\,C^2\,a^{10}\,b^3-2\,A\,C^2\,a^9\,b^4-2\,A\,C^2\,a^7\,b^6+22\,A\,C^2\,a^6\,b^7+18\,A\,C^2\,a^5\,b^8-26\,A\,C^2\,a^4\,b^9-22\,A\,C^2\,a^3\,b^{10}+56\,A\,C^2\,a^2\,b^{11}+8\,A\,C^2\,a\,b^{12}+9\,B^2\,C\,a^4\,b^9+12\,B^2\,C\,a^2\,b^{11}+4\,B^2\,C\,b^{13}+6\,B\,C^2\,a^9\,b^4+6\,B\,C^2\,a^8\,b^5-20\,B\,C^2\,a^7\,b^6-14\,B\,C^2\,a^6\,b^7+14\,B\,C^2\,a^5\,b^8+6\,B\,C^2\,a^4\,b^9-22\,B\,C^2\,a^3\,b^{10}+6\,B\,C^2\,a^2\,b^{11}-28\,B\,C^2\,a\,b^{12}-4\,B\,C^2\,b^{13}+4\,C^3\,a^{13}-2\,C^3\,a^{12}\,b-26\,C^3\,a^{11}\,b^2+11\,C^3\,a^{10}\,b^3+70\,C^3\,a^9\,b^4-34\,C^3\,a^8\,b^5-110\,C^3\,a^7\,b^6+66\,C^3\,a^6\,b^7+110\,C^3\,a^5\,b^8-64\,C^3\,a^4\,b^9-64\,C^3\,a^3\,b^{10}+48\,C^3\,a^2\,b^{11}+16\,C^3\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^6\,b^8+8\,A^2\,a^4\,b^{10}+16\,A^2\,a^2\,b^{12}-6\,A\,B\,a^5\,b^9-28\,A\,B\,a^3\,b^{11}-16\,A\,B\,a\,b^{13}-4\,A\,C\,a^{10}\,b^4-2\,A\,C\,a^8\,b^6+40\,A\,C\,a^6\,b^8-48\,A\,C\,a^4\,b^{10}+64\,A\,C\,a^2\,b^{12}+9\,B^2\,a^4\,b^{10}+12\,B^2\,a^2\,b^{12}+4\,B^2\,b^{14}+12\,B\,C\,a^9\,b^5-34\,B\,C\,a^7\,b^7+20\,B\,C\,a^5\,b^9-16\,B\,C\,a^3\,b^{11}-32\,B\,C\,a\,b^{13}+8\,C^2\,a^{14}-8\,C^2\,a^{13}\,b-48\,C^2\,a^{12}\,b^2+48\,C^2\,a^{11}\,b^3+117\,C^2\,a^{10}\,b^4-120\,C^2\,a^9\,b^5-164\,C^2\,a^8\,b^6+160\,C^2\,a^7\,b^7+156\,C^2\,a^6\,b^8-120\,C^2\,a^5\,b^9-92\,C^2\,a^4\,b^{10}+48\,C^2\,a^3\,b^{11}+44\,C^2\,a^2\,b^{12}-8\,C^2\,a\,b^{13}+4\,C^2\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{\left(\frac{8\,\left(4\,B\,b^{21}+4\,C\,b^{21}+8\,A\,a^2\,b^{19}+22\,A\,a^3\,b^{18}-22\,A\,a^4\,b^{17}-18\,A\,a^5\,b^{16}+18\,A\,a^6\,b^{15}+2\,A\,a^7\,b^{14}-2\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}-2\,A\,a^{10}\,b^{11}-6\,B\,a^2\,b^{19}+6\,B\,a^3\,b^{18}-6\,B\,a^4\,b^{17}+6\,B\,a^5\,b^{16}+14\,B\,a^6\,b^{15}-14\,B\,a^7\,b^{14}-6\,B\,a^8\,b^{13}+6\,B\,a^9\,b^{12}-12\,C\,a^2\,b^{19}+64\,C\,a^3\,b^{18}+20\,C\,a^4\,b^{17}-110\,C\,a^5\,b^{16}-30\,C\,a^6\,b^{15}+110\,C\,a^7\,b^{14}+30\,C\,a^8\,b^{13}-70\,C\,a^9\,b^{12}-14\,C\,a^{10}\,b^{11}+26\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-4\,C\,a^{13}\,b^8-8\,A\,a\,b^{20}-4\,B\,a\,b^{20}-16\,C\,a\,b^{20}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,B\,b^7+2\,C\,a^7-A\,a^3\,b^4+3\,B\,a^2\,b^5+8\,C\,a^3\,b^4-7\,C\,a^5\,b^2-4\,A\,a\,b^6-8\,C\,a\,b^6\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}","Not used",1,"(2*C*atan(((C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4))/b^4 + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4))/b^4)/((16*(4*C^3*a^13 - 4*B*C^2*b^13 + 4*B^2*C*b^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 - 28*B*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7 + 6*B*C^2*a^2*b^11 - 22*B*C^2*a^3*b^10 + 6*B*C^2*a^4*b^9 + 14*B*C^2*a^5*b^8 - 14*B*C^2*a^6*b^7 - 20*B*C^2*a^7*b^6 + 6*B*C^2*a^8*b^5 + 6*B*C^2*a^9*b^4 + 12*B^2*C*a^2*b^11 + 9*B^2*C*a^4*b^9 - 16*A*B*C*a*b^12 - 28*A*B*C*a^3*b^10 - 6*A*B*C*a^5*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4)*1i)/b^4 + (C*((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (C*((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (C*tan(c/2 + (d*x)/2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8)*8i)/(b^4*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*1i)/b^4)*1i)/b^4)))/(b^4*d) - ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 - A*a^3*b^3 + 3*B*a^2*b^4 - 2*B*a^3*b^3 + 12*C*a^2*b^4 - 4*C*a^3*b^3 - 6*C*a^4*b^2 - 2*A*a*b^5 - 6*B*a*b^5 + C*a^5*b))/((a + b)*(3*a*b^5 - b^6 - 3*a^2*b^4 + a^3*b^3)) + (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 + 7*A*a^2*b^4 - B*a^3*b^3 + 18*C*a^2*b^4 - 11*C*a^4*b^2 - 9*B*a*b^5))/(3*(a + b)^2*(b^5 - 2*a*b^4 + a^2*b^3)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 + 6*A*a^2*b^4 + A*a^3*b^3 - 3*B*a^2*b^4 - 2*B*a^3*b^3 + 12*C*a^2*b^4 + 4*C*a^3*b^3 - 6*C*a^4*b^2 + 2*A*a*b^5 - 6*B*a*b^5 - C*a^5*b))/((a*b^3 - b^4)*(a + b)^3))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))/((16*(4*C^3*a^13 - 4*B*C^2*b^13 + 4*B^2*C*b^13 + 16*C^3*a*b^12 - 2*C^3*a^12*b + 48*C^3*a^2*b^11 - 64*C^3*a^3*b^10 - 64*C^3*a^4*b^9 + 110*C^3*a^5*b^8 + 66*C^3*a^6*b^7 - 110*C^3*a^7*b^6 - 34*C^3*a^8*b^5 + 70*C^3*a^9*b^4 + 11*C^3*a^10*b^3 - 26*C^3*a^11*b^2 + 8*A*C^2*a*b^12 - 28*B*C^2*a*b^12 + 56*A*C^2*a^2*b^11 - 22*A*C^2*a^3*b^10 - 26*A*C^2*a^4*b^9 + 18*A*C^2*a^5*b^8 + 22*A*C^2*a^6*b^7 - 2*A*C^2*a^7*b^6 - 2*A*C^2*a^9*b^4 - 2*A*C^2*a^10*b^3 + 16*A^2*C*a^2*b^11 + 8*A^2*C*a^4*b^9 + A^2*C*a^6*b^7 + 6*B*C^2*a^2*b^11 - 22*B*C^2*a^3*b^10 + 6*B*C^2*a^4*b^9 + 14*B*C^2*a^5*b^8 - 14*B*C^2*a^6*b^7 - 20*B*C^2*a^7*b^6 + 6*B*C^2*a^8*b^5 + 6*B*C^2*a^9*b^4 + 12*B^2*C*a^2*b^11 + 9*B^2*C*a^4*b^9 - 16*A*B*C*a*b^12 - 28*A*B*C*a^3*b^10 - 6*A*B*C*a^5*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (((8*tan(c/2 + (d*x)/2)*(4*B^2*b^14 + 8*C^2*a^14 + 4*C^2*b^14 - 8*C^2*a*b^13 - 8*C^2*a^13*b + 16*A^2*a^2*b^12 + 8*A^2*a^4*b^10 + A^2*a^6*b^8 + 12*B^2*a^2*b^12 + 9*B^2*a^4*b^10 + 44*C^2*a^2*b^12 + 48*C^2*a^3*b^11 - 92*C^2*a^4*b^10 - 120*C^2*a^5*b^9 + 156*C^2*a^6*b^8 + 160*C^2*a^7*b^7 - 164*C^2*a^8*b^6 - 120*C^2*a^9*b^5 + 117*C^2*a^10*b^4 + 48*C^2*a^11*b^3 - 48*C^2*a^12*b^2 - 16*A*B*a*b^13 - 32*B*C*a*b^13 - 28*A*B*a^3*b^11 - 6*A*B*a^5*b^9 + 64*A*C*a^2*b^12 - 48*A*C*a^4*b^10 + 40*A*C*a^6*b^8 - 2*A*C*a^8*b^6 - 4*A*C*a^10*b^4 - 16*B*C*a^3*b^11 + 20*B*C*a^5*b^9 - 34*B*C*a^7*b^7 + 12*B*C*a^9*b^5))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (((8*(4*B*b^21 + 4*C*b^21 + 8*A*a^2*b^19 + 22*A*a^3*b^18 - 22*A*a^4*b^17 - 18*A*a^5*b^16 + 18*A*a^6*b^15 + 2*A*a^7*b^14 - 2*A*a^8*b^13 + 2*A*a^9*b^12 - 2*A*a^10*b^11 - 6*B*a^2*b^19 + 6*B*a^3*b^18 - 6*B*a^4*b^17 + 6*B*a^5*b^16 + 14*B*a^6*b^15 - 14*B*a^7*b^14 - 6*B*a^8*b^13 + 6*B*a^9*b^12 - 12*C*a^2*b^19 + 64*C*a^3*b^18 + 20*C*a^4*b^17 - 110*C*a^5*b^16 - 30*C*a^6*b^15 + 110*C*a^7*b^14 + 30*C*a^8*b^13 - 70*C*a^9*b^12 - 14*C*a^10*b^11 + 26*C*a^11*b^10 + 2*C*a^12*b^9 - 4*C*a^13*b^8 - 8*A*a*b^20 - 4*B*a*b^20 - 16*C*a*b^20))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*B*b^7 + 2*C*a^7 - A*a^3*b^4 + 3*B*a^2*b^5 + 8*C*a^3*b^4 - 7*C*a^5*b^2 - 4*A*a*b^6 - 8*C*a*b^6)*1i)/(d*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))","B"
1004,1,516,314,4.838756,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^4,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^3-A\,b^3+B\,a^3-2\,B\,b^3+2\,C\,a^3+6\,A\,a\,b^2-2\,A\,a^2\,b+2\,B\,a\,b^2-6\,B\,a^2\,b+6\,C\,a\,b^2-3\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,a^3-3\,B\,b^3+C\,a^3+7\,A\,a\,b^2-7\,B\,a^2\,b+9\,C\,a\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,a^3+A\,b^3-B\,a^3-2\,B\,b^3+2\,C\,a^3+6\,A\,a\,b^2+2\,A\,a^2\,b-2\,B\,a\,b^2-6\,B\,a^2\,b+6\,C\,a\,b^2+3\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(A\,b^3-B\,a^3+2\,C\,b^3+4\,A\,a^2\,b-4\,B\,a\,b^2+3\,C\,a^2\,b\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*a^3 - A*b^3 + B*a^3 - 2*B*b^3 + 2*C*a^3 + 6*A*a*b^2 - 2*A*a^2*b + 2*B*a*b^2 - 6*B*a^2*b + 6*C*a*b^2 - 3*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)) + (4*tan(c/2 + (d*x)/2)^3*(3*A*a^3 - 3*B*b^3 + C*a^3 + 7*A*a*b^2 - 7*B*a^2*b + 9*C*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*a^3 + A*b^3 - B*a^3 - 2*B*b^3 + 2*C*a^3 + 6*A*a*b^2 + 2*A*a^2*b - 2*B*a*b^2 - 6*B*a^2*b + 6*C*a*b^2 + 3*C*a^2*b))/((a + b)^3*(a - b)))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(a + b)^(1/2)*(a - b)^(7/2)))*(A*b^3 - B*a^3 + 2*C*b^3 + 4*A*a^2*b - 4*B*a*b^2 + 3*C*a^2*b))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
1005,1,516,299,4.780967,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^4,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(2\,A\,a^3-B\,b^3+C\,a^3+3\,A\,a\,b^2-4\,B\,a^2\,b+4\,C\,a\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^3-2\,B\,a^3+B\,b^3-C\,a^3+2\,C\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2+2\,B\,a^2\,b-2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,b^3-3\,B\,a^3+3\,C\,b^3+9\,A\,a^2\,b-7\,B\,a\,b^2+7\,C\,a^2\,b\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^3-2\,B\,a^3-B\,b^3+C\,a^3+2\,C\,b^3+3\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2-2\,B\,a^2\,b+2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}","Not used",1,"(atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(a + b)^(1/2)*(a - b)^(7/2)))*(2*A*a^3 - B*b^3 + C*a^3 + 3*A*a*b^2 - 4*B*a^2*b + 4*C*a*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((tan(c/2 + (d*x)/2)*(2*A*b^3 - 2*B*a^3 + B*b^3 - C*a^3 + 2*C*b^3 - 3*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 + 2*B*a^2*b - 2*C*a*b^2 + 6*C*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)) + (4*tan(c/2 + (d*x)/2)^3*(A*b^3 - 3*B*a^3 + 3*C*b^3 + 9*A*a^2*b - 7*B*a*b^2 + 7*C*a^2*b))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^3 - 2*B*a^3 - B*b^3 + C*a^3 + 2*C*b^3 + 3*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 - 2*B*a^2*b + 2*C*a*b^2 + 6*C*a^2*b))/((a + b)^3*(a - b)))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))","B"
1006,1,11939,345,14.973774,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^4),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4-4\,A\,a^3\,b^3+12\,A\,a^4\,b^2-2\,B\,a^3\,b^3+3\,B\,a^4\,b^2-C\,a^3\,b^3+6\,C\,a^4\,b^2+A\,a\,b^5-6\,B\,a^5\,b-2\,C\,a^5\,b\right)}{\left(a+b\right)\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A\,b^6+3\,C\,a^6-11\,A\,a^2\,b^4+18\,A\,a^4\,b^2-B\,a^3\,b^3+7\,C\,a^4\,b^2-9\,B\,a^5\,b\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,A\,b^6+2\,C\,a^6-6\,A\,a^2\,b^4+4\,A\,a^3\,b^3+12\,A\,a^4\,b^2-2\,B\,a^3\,b^3-3\,B\,a^4\,b^2+C\,a^3\,b^3+6\,C\,a^4\,b^2-A\,a\,b^5-6\,B\,a^5\,b+2\,C\,a^5\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^3}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}-4\,A^2\,B\,a^{13}-28\,A^2\,B\,a^{12}\,b+6\,A^2\,B\,a^{11}\,b^2-22\,A^2\,B\,a^{10}\,b^3+6\,A^2\,B\,a^9\,b^4+14\,A^2\,B\,a^8\,b^5-14\,A^2\,B\,a^7\,b^6-20\,A^2\,B\,a^6\,b^7+6\,A^2\,B\,a^5\,b^8+6\,A^2\,B\,a^4\,b^9+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4-16\,A\,B\,C\,a^{12}\,b-28\,A\,B\,C\,a^{10}\,b^3-6\,A\,B\,C\,a^8\,b^5+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)}{a^4}-\frac{A\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{A\,\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{8\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)}{a^4}\right)}{a^4}}\right)\,2{}\mathrm{i}}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}{\frac{16\,\left(16\,A^3\,a^{12}\,b+48\,A^3\,a^{11}\,b^2-64\,A^3\,a^{10}\,b^3-64\,A^3\,a^9\,b^4+110\,A^3\,a^8\,b^5+66\,A^3\,a^7\,b^6-110\,A^3\,a^6\,b^7-34\,A^3\,a^5\,b^8+70\,A^3\,a^4\,b^9+11\,A^3\,a^3\,b^{10}-26\,A^3\,a^2\,b^{11}-2\,A^3\,a\,b^{12}+4\,A^3\,b^{13}-4\,A^2\,B\,a^{13}-28\,A^2\,B\,a^{12}\,b+6\,A^2\,B\,a^{11}\,b^2-22\,A^2\,B\,a^{10}\,b^3+6\,A^2\,B\,a^9\,b^4+14\,A^2\,B\,a^8\,b^5-14\,A^2\,B\,a^7\,b^6-20\,A^2\,B\,a^6\,b^7+6\,A^2\,B\,a^5\,b^8+6\,A^2\,B\,a^4\,b^9+8\,A^2\,C\,a^{12}\,b+56\,A^2\,C\,a^{11}\,b^2-22\,A^2\,C\,a^{10}\,b^3-26\,A^2\,C\,a^9\,b^4+18\,A^2\,C\,a^8\,b^5+22\,A^2\,C\,a^7\,b^6-2\,A^2\,C\,a^6\,b^7-2\,A^2\,C\,a^4\,b^9-2\,A^2\,C\,a^3\,b^{10}+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4-16\,A\,B\,C\,a^{12}\,b-28\,A\,B\,C\,a^{10}\,b^3-6\,A\,B\,C\,a^8\,b^5+16\,A\,C^2\,a^{11}\,b^2+8\,A\,C^2\,a^9\,b^4+A\,C^2\,a^7\,b^6\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A^2\,a^{14}-8\,A^2\,a^{13}\,b+44\,A^2\,a^{12}\,b^2+48\,A^2\,a^{11}\,b^3-92\,A^2\,a^{10}\,b^4-120\,A^2\,a^9\,b^5+156\,A^2\,a^8\,b^6+160\,A^2\,a^7\,b^7-164\,A^2\,a^6\,b^8-120\,A^2\,a^5\,b^9+117\,A^2\,a^4\,b^{10}+48\,A^2\,a^3\,b^{11}-48\,A^2\,a^2\,b^{12}-8\,A^2\,a\,b^{13}+8\,A^2\,b^{14}-32\,A\,B\,a^{13}\,b-16\,A\,B\,a^{11}\,b^3+20\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+12\,A\,B\,a^5\,b^9+64\,A\,C\,a^{12}\,b^2-48\,A\,C\,a^{10}\,b^4+40\,A\,C\,a^8\,b^6-2\,A\,C\,a^6\,b^8-4\,A\,C\,a^4\,b^{10}+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4-16\,B\,C\,a^{13}\,b-28\,B\,C\,a^{11}\,b^3-6\,B\,C\,a^9\,b^5+16\,C^2\,a^{12}\,b^2+8\,C^2\,a^{10}\,b^4+C^2\,a^8\,b^6\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{\left(\frac{8\,\left(4\,A\,a^{21}+4\,B\,a^{21}-4\,A\,a^8\,b^{13}+2\,A\,a^9\,b^{12}+26\,A\,a^{10}\,b^{11}-14\,A\,a^{11}\,b^{10}-70\,A\,a^{12}\,b^9+30\,A\,a^{13}\,b^8+110\,A\,a^{14}\,b^7-30\,A\,a^{15}\,b^6-110\,A\,a^{16}\,b^5+20\,A\,a^{17}\,b^4+64\,A\,a^{18}\,b^3-12\,A\,a^{19}\,b^2+6\,B\,a^{12}\,b^9-6\,B\,a^{13}\,b^8-14\,B\,a^{14}\,b^7+14\,B\,a^{15}\,b^6+6\,B\,a^{16}\,b^5-6\,B\,a^{17}\,b^4+6\,B\,a^{18}\,b^3-6\,B\,a^{19}\,b^2-2\,C\,a^{11}\,b^{10}+2\,C\,a^{12}\,b^9-2\,C\,a^{13}\,b^8+2\,C\,a^{14}\,b^7+18\,C\,a^{15}\,b^6-18\,C\,a^{16}\,b^5-22\,C\,a^{17}\,b^4+22\,C\,a^{18}\,b^3+8\,C\,a^{19}\,b^2-16\,A\,a^{20}\,b-4\,B\,a^{20}\,b-8\,C\,a^{20}\,b\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,\left(8\,a^{21}\,b-8\,a^{20}\,b^2-48\,a^{19}\,b^3+48\,a^{18}\,b^4+120\,a^{17}\,b^5-120\,a^{16}\,b^6-160\,a^{15}\,b^7+160\,a^{14}\,b^8+120\,a^{13}\,b^9-120\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}+48\,a^{10}\,b^{12}+8\,a^9\,b^{13}-8\,a^8\,b^{14}\right)}{\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,A\,b^7+2\,B\,a^7-7\,A\,a^2\,b^5+8\,A\,a^4\,b^3+3\,B\,a^5\,b^2-C\,a^4\,b^3-8\,A\,a^6\,b-4\,C\,a^6\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 - 4*A*a^3*b^3 + 12*A*a^4*b^2 - 2*B*a^3*b^3 + 3*B*a^4*b^2 - C*a^3*b^3 + 6*C*a^4*b^2 + A*a*b^5 - 6*B*a^5*b - 2*C*a^5*b))/((a + b)*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) - (4*tan(c/2 + (d*x)/2)^3*(3*A*b^6 + 3*C*a^6 - 11*A*a^2*b^4 + 18*A*a^4*b^2 - B*a^3*b^3 + 7*C*a^4*b^2 - 9*B*a^5*b))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*b^2)) + (tan(c/2 + (d*x)/2)^5*(2*A*b^6 + 2*C*a^6 - 6*A*a^2*b^4 + 4*A*a^3*b^3 + 12*A*a^4*b^2 - 2*B*a^3*b^3 - 3*B*a^4*b^2 + C*a^3*b^3 + 6*C*a^4*b^2 - A*a*b^5 - 6*B*a^5*b + 2*C*a^5*b))/((a^3*b - a^4)*(a + b)^3))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (A*atan(((A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4)*1i)/a^4 + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4)*1i)/a^4)/((16*(4*A^3*b^13 + 4*A*B^2*a^13 - 4*A^2*B*a^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 - 28*A^2*B*a^12*b + 8*A^2*C*a^12*b + 9*A*B^2*a^9*b^4 + 12*A*B^2*a^11*b^2 + 6*A^2*B*a^4*b^9 + 6*A^2*B*a^5*b^8 - 20*A^2*B*a^6*b^7 - 14*A^2*B*a^7*b^6 + 14*A^2*B*a^8*b^5 + 6*A^2*B*a^9*b^4 - 22*A^2*B*a^10*b^3 + 6*A^2*B*a^11*b^2 + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2 - 16*A*B*C*a^12*b - 6*A*B*C*a^8*b^5 - 28*A*B*C*a^10*b^3))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4))/a^4 - (A*((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (A*((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (8*A*tan(c/2 + (d*x)/2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/(a^4*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))))/a^4))/a^4))*2i)/(a^4*d) - (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))/((16*(4*A^3*b^13 + 4*A*B^2*a^13 - 4*A^2*B*a^13 - 2*A^3*a*b^12 + 16*A^3*a^12*b - 26*A^3*a^2*b^11 + 11*A^3*a^3*b^10 + 70*A^3*a^4*b^9 - 34*A^3*a^5*b^8 - 110*A^3*a^6*b^7 + 66*A^3*a^7*b^6 + 110*A^3*a^8*b^5 - 64*A^3*a^9*b^4 - 64*A^3*a^10*b^3 + 48*A^3*a^11*b^2 - 28*A^2*B*a^12*b + 8*A^2*C*a^12*b + 9*A*B^2*a^9*b^4 + 12*A*B^2*a^11*b^2 + 6*A^2*B*a^4*b^9 + 6*A^2*B*a^5*b^8 - 20*A^2*B*a^6*b^7 - 14*A^2*B*a^7*b^6 + 14*A^2*B*a^8*b^5 + 6*A^2*B*a^9*b^4 - 22*A^2*B*a^10*b^3 + 6*A^2*B*a^11*b^2 + A*C^2*a^7*b^6 + 8*A*C^2*a^9*b^4 + 16*A*C^2*a^11*b^2 - 2*A^2*C*a^3*b^10 - 2*A^2*C*a^4*b^9 - 2*A^2*C*a^6*b^7 + 22*A^2*C*a^7*b^6 + 18*A^2*C*a^8*b^5 - 26*A^2*C*a^9*b^4 - 22*A^2*C*a^10*b^3 + 56*A^2*C*a^11*b^2 - 16*A*B*C*a^12*b - 6*A*B*C*a^8*b^5 - 28*A*B*C*a^10*b^3))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (((8*tan(c/2 + (d*x)/2)*(4*A^2*a^14 + 8*A^2*b^14 + 4*B^2*a^14 - 8*A^2*a*b^13 - 8*A^2*a^13*b - 48*A^2*a^2*b^12 + 48*A^2*a^3*b^11 + 117*A^2*a^4*b^10 - 120*A^2*a^5*b^9 - 164*A^2*a^6*b^8 + 160*A^2*a^7*b^7 + 156*A^2*a^8*b^6 - 120*A^2*a^9*b^5 - 92*A^2*a^10*b^4 + 48*A^2*a^11*b^3 + 44*A^2*a^12*b^2 + 9*B^2*a^10*b^4 + 12*B^2*a^12*b^2 + C^2*a^8*b^6 + 8*C^2*a^10*b^4 + 16*C^2*a^12*b^2 - 32*A*B*a^13*b - 16*B*C*a^13*b + 12*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 20*A*B*a^9*b^5 - 16*A*B*a^11*b^3 - 4*A*C*a^4*b^10 - 2*A*C*a^6*b^8 + 40*A*C*a^8*b^6 - 48*A*C*a^10*b^4 + 64*A*C*a^12*b^2 - 6*B*C*a^9*b^5 - 28*B*C*a^11*b^3))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (((8*(4*A*a^21 + 4*B*a^21 - 4*A*a^8*b^13 + 2*A*a^9*b^12 + 26*A*a^10*b^11 - 14*A*a^11*b^10 - 70*A*a^12*b^9 + 30*A*a^13*b^8 + 110*A*a^14*b^7 - 30*A*a^15*b^6 - 110*A*a^16*b^5 + 20*A*a^17*b^4 + 64*A*a^18*b^3 - 12*A*a^19*b^2 + 6*B*a^12*b^9 - 6*B*a^13*b^8 - 14*B*a^14*b^7 + 14*B*a^15*b^6 + 6*B*a^16*b^5 - 6*B*a^17*b^4 + 6*B*a^18*b^3 - 6*B*a^19*b^2 - 2*C*a^11*b^10 + 2*C*a^12*b^9 - 2*C*a^13*b^8 + 2*C*a^14*b^7 + 18*C*a^15*b^6 - 18*C*a^16*b^5 - 22*C*a^17*b^4 + 22*C*a^18*b^3 + 8*C*a^19*b^2 - 16*A*a^20*b - 4*B*a^20*b - 8*C*a^20*b))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*A*b^7 + 2*B*a^7 - 7*A*a^2*b^5 + 8*A*a^4*b^3 + 3*B*a^5*b^2 - C*a^4*b^3 - 8*A*a^6*b - 4*C*a^6*b)*1i)/(d*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))","B"
1007,1,15980,480,15.873842,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^4),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,A\,a^7+8\,A\,b^7-24\,A\,a^2\,b^5+11\,A\,a^3\,b^4+26\,A\,a^4\,b^3-6\,A\,a^5\,b^2+B\,a^2\,b^5+6\,B\,a^3\,b^4-4\,B\,a^4\,b^3-12\,B\,a^5\,b^2+2\,C\,a^4\,b^3+3\,C\,a^5\,b^2-4\,A\,a\,b^6-2\,A\,a^6\,b-2\,B\,a\,b^6+6\,C\,a^6\,b\right)}{a^4\,{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,a^7-8\,A\,b^7+24\,A\,a^2\,b^5+11\,A\,a^3\,b^4-26\,A\,a^4\,b^3-6\,A\,a^5\,b^2+B\,a^2\,b^5-6\,B\,a^3\,b^4-4\,B\,a^4\,b^3+12\,B\,a^5\,b^2-2\,C\,a^4\,b^3+3\,C\,a^5\,b^2-4\,A\,a\,b^6+2\,A\,a^6\,b+2\,B\,a\,b^6-6\,C\,a^6\,b\right)}{a^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6+47\,A\,a^3\,b^5+273\,A\,a^4\,b^4-60\,A\,a^5\,b^3-72\,A\,a^6\,b^2+3\,B\,a^2\,b^6+59\,B\,a^3\,b^5-14\,B\,a^4\,b^4-96\,B\,a^5\,b^3+36\,B\,a^6\,b^2+10\,C\,a^4\,b^4-7\,C\,a^5\,b^3+45\,C\,a^6\,b^2-12\,A\,a\,b^7-18\,B\,a\,b^7-18\,C\,a^7\,b\right)}{3\,a^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(18\,A\,a^8+72\,A\,b^8-236\,A\,a^2\,b^6-47\,A\,a^3\,b^5+273\,A\,a^4\,b^4+60\,A\,a^5\,b^3-72\,A\,a^6\,b^2-3\,B\,a^2\,b^6+59\,B\,a^3\,b^5+14\,B\,a^4\,b^4-96\,B\,a^5\,b^3-36\,B\,a^6\,b^2+10\,C\,a^4\,b^4+7\,C\,a^5\,b^3+45\,C\,a^6\,b^2+12\,A\,a\,b^7-18\,B\,a\,b^7+18\,C\,a^7\,b\right)}{3\,a^4\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2\,b-6\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^3+6\,a\,b^2+4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^3-6\,a\,b^2+4\,b^3\right)+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b-B\,a\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b-B\,a\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}\right)\,1{}\mathrm{i}}{a^5}}{\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A\,b-B\,a\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,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^2\,C\,a^7\,b^9-96\,A^2\,C\,a^6\,b^{10}-96\,A^2\,C\,a^5\,b^{11}+168\,A\,B^2\,a^{14}\,b^2+408\,A\,B^2\,a^{13}\,b^3-702\,A\,B^2\,a^{12}\,b^4-690\,A\,B^2\,a^{11}\,b^5+1266\,A\,B^2\,a^{10}\,b^6+726\,A\,B^2\,a^9\,b^7-1314\,A\,B^2\,a^8\,b^8-408\,A\,B^2\,a^7\,b^9+846\,A\,B^2\,a^6\,b^{10}+138\,A\,B^2\,a^5\,b^{11}-312\,A\,B^2\,a^4\,b^{12}-24\,A\,B^2\,a^3\,b^{13}+48\,A\,B^2\,a^2\,b^{14}-32\,A\,B\,C\,a^{15}\,b-176\,A\,B\,C\,a^{14}\,b^2+48\,A\,B\,C\,a^{13}\,b^3-92\,A\,B\,C\,a^{12}\,b^4+48\,A\,B\,C\,a^{11}\,b^5+130\,A\,B\,C\,a^{10}\,b^6-112\,A\,B\,C\,a^9\,b^7-160\,A\,B\,C\,a^8\,b^8+48\,A\,B\,C\,a^7\,b^9+48\,A\,B\,C\,a^6\,b^{10}+16\,A\,C^2\,a^{15}\,b+48\,A\,C^2\,a^{13}\,b^3+36\,A\,C^2\,a^{11}\,b^5-16\,B^3\,a^{15}\,b-48\,B^3\,a^{14}\,b^2+64\,B^3\,a^{13}\,b^3+64\,B^3\,a^{12}\,b^4-110\,B^3\,a^{11}\,b^5-66\,B^3\,a^{10}\,b^6+110\,B^3\,a^9\,b^7+34\,B^3\,a^8\,b^8-70\,B^3\,a^7\,b^9-11\,B^3\,a^6\,b^{10}+26\,B^3\,a^5\,b^{11}+2\,B^3\,a^4\,b^{12}-4\,B^3\,a^3\,b^{13}+4\,B^2\,C\,a^{16}+28\,B^2\,C\,a^{15}\,b-6\,B^2\,C\,a^{14}\,b^2+22\,B^2\,C\,a^{13}\,b^3-6\,B^2\,C\,a^{12}\,b^4-14\,B^2\,C\,a^{11}\,b^5+14\,B^2\,C\,a^{10}\,b^6+20\,B^2\,C\,a^9\,b^7-6\,B^2\,C\,a^8\,b^8-6\,B^2\,C\,a^7\,b^9-4\,B\,C^2\,a^{16}-12\,B\,C^2\,a^{14}\,b^2-9\,B\,C^2\,a^{12}\,b^4\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}-\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,A^2\,a^{14}\,b^2-128\,A^2\,a^{13}\,b^3+80\,A^2\,a^{12}\,b^4+768\,A^2\,a^{11}\,b^5-824\,A^2\,a^{10}\,b^6-1920\,A^2\,a^9\,b^7+2025\,A^2\,a^8\,b^8+2560\,A^2\,a^7\,b^9-2600\,A^2\,a^6\,b^{10}-1920\,A^2\,a^5\,b^{11}+1920\,A^2\,a^4\,b^{12}+768\,A^2\,a^3\,b^{13}-768\,A^2\,a^2\,b^{14}-128\,A^2\,a\,b^{15}+128\,A^2\,b^{16}-32\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2-160\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4+592\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6-1128\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8+1306\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}-948\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}+384\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-64\,A\,B\,a\,b^{15}+80\,A\,C\,a^{14}\,b^2-20\,A\,C\,a^{12}\,b^4-98\,A\,C\,a^{10}\,b^6+136\,A\,C\,a^8\,b^8-48\,A\,C\,a^6\,b^{10}+4\,B^2\,a^{16}-8\,B^2\,a^{15}\,b+44\,B^2\,a^{14}\,b^2+48\,B^2\,a^{13}\,b^3-92\,B^2\,a^{12}\,b^4-120\,B^2\,a^{11}\,b^5+156\,B^2\,a^{10}\,b^6+160\,B^2\,a^9\,b^7-164\,B^2\,a^8\,b^8-120\,B^2\,a^7\,b^9+117\,B^2\,a^6\,b^{10}+48\,B^2\,a^5\,b^{11}-48\,B^2\,a^4\,b^{12}-8\,B^2\,a^3\,b^{13}+8\,B^2\,a^2\,b^{14}-32\,B\,C\,a^{15}\,b-16\,B\,C\,a^{13}\,b^3+20\,B\,C\,a^{11}\,b^5-34\,B\,C\,a^9\,b^7+12\,B\,C\,a^7\,b^9+4\,C^2\,a^{16}+12\,C^2\,a^{14}\,b^2+9\,C^2\,a^{12}\,b^4\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{\left(\frac{8\,\left(4\,B\,a^{24}+4\,C\,a^{24}+16\,A\,a^{10}\,b^{14}-8\,A\,a^{11}\,b^{13}-104\,A\,a^{12}\,b^{12}+50\,A\,a^{13}\,b^{11}+286\,A\,a^{14}\,b^{10}-126\,A\,a^{15}\,b^9-434\,A\,a^{16}\,b^8+174\,A\,a^{17}\,b^7+386\,A\,a^{18}\,b^6-146\,A\,a^{19}\,b^5-190\,A\,a^{20}\,b^4+72\,A\,a^{21}\,b^3+40\,A\,a^{22}\,b^2-4\,B\,a^{11}\,b^{13}+2\,B\,a^{12}\,b^{12}+26\,B\,a^{13}\,b^{11}-14\,B\,a^{14}\,b^{10}-70\,B\,a^{15}\,b^9+30\,B\,a^{16}\,b^8+110\,B\,a^{17}\,b^7-30\,B\,a^{18}\,b^6-110\,B\,a^{19}\,b^5+20\,B\,a^{20}\,b^4+64\,B\,a^{21}\,b^3-12\,B\,a^{22}\,b^2+6\,C\,a^{15}\,b^9-6\,C\,a^{16}\,b^8-14\,C\,a^{17}\,b^7+14\,C\,a^{18}\,b^6+6\,C\,a^{19}\,b^5-6\,C\,a^{20}\,b^4+6\,C\,a^{21}\,b^3-6\,C\,a^{22}\,b^2-16\,A\,a^{23}\,b-16\,B\,a^{23}\,b-4\,C\,a^{23}\,b\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,C\,a^8-8\,A\,b^8+28\,A\,a^2\,b^6-35\,A\,a^4\,b^4+20\,A\,a^6\,b^2-7\,B\,a^3\,b^5+8\,B\,a^5\,b^3+3\,C\,a^6\,b^2+2\,B\,a\,b^7-8\,B\,a^7\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^7*(2*A*a^7 + 8*A*b^7 - 24*A*a^2*b^5 + 11*A*a^3*b^4 + 26*A*a^4*b^3 - 6*A*a^5*b^2 + B*a^2*b^5 + 6*B*a^3*b^4 - 4*B*a^4*b^3 - 12*B*a^5*b^2 + 2*C*a^4*b^3 + 3*C*a^5*b^2 - 4*A*a*b^6 - 2*A*a^6*b - 2*B*a*b^6 + 6*C*a^6*b))/(a^4*(a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(2*A*a^7 - 8*A*b^7 + 24*A*a^2*b^5 + 11*A*a^3*b^4 - 26*A*a^4*b^3 - 6*A*a^5*b^2 + B*a^2*b^5 - 6*B*a^3*b^4 - 4*B*a^4*b^3 + 12*B*a^5*b^2 - 2*C*a^4*b^3 + 3*C*a^5*b^2 - 4*A*a*b^6 + 2*A*a^6*b + 2*B*a*b^6 - 6*C*a^6*b))/(a^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^3*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 + 47*A*a^3*b^5 + 273*A*a^4*b^4 - 60*A*a^5*b^3 - 72*A*a^6*b^2 + 3*B*a^2*b^6 + 59*B*a^3*b^5 - 14*B*a^4*b^4 - 96*B*a^5*b^3 + 36*B*a^6*b^2 + 10*C*a^4*b^4 - 7*C*a^5*b^3 + 45*C*a^6*b^2 - 12*A*a*b^7 - 18*B*a*b^7 - 18*C*a^7*b))/(3*a^4*(a + b)^2*(a - b)^3) + (tan(c/2 + (d*x)/2)^5*(18*A*a^8 + 72*A*b^8 - 236*A*a^2*b^6 - 47*A*a^3*b^5 + 273*A*a^4*b^4 + 60*A*a^5*b^3 - 72*A*a^6*b^2 - 3*B*a^2*b^6 + 59*B*a^3*b^5 + 14*B*a^4*b^4 - 96*B*a^5*b^3 - 36*B*a^6*b^2 + 10*C*a^4*b^4 + 7*C*a^5*b^3 + 45*C*a^6*b^2 + 12*A*a*b^7 - 18*B*a*b^7 + 18*C*a^7*b))/(3*a^4*(a + b)^3*(a - b)^2))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a^2*b - 6*b^3) - tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 2*a^3 + 4*b^3) - tan(c/2 + (d*x)/2)^6*(2*a^3 - 6*a*b^2 + 4*b^3) + a^3 + b^3 - tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (atan((((4*A*b - B*a)*(((4*A*b - B*a)*((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (8*tan(c/2 + (d*x)/2)*(4*A*b - B*a)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5 - (8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))*1i)/a^5 - ((4*A*b - B*a)*(((4*A*b - B*a)*((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (8*tan(c/2 + (d*x)/2)*(4*A*b - B*a)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5 + (8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))*1i)/a^5)/(((4*A*b - B*a)*(((4*A*b - B*a)*((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (8*tan(c/2 + (d*x)/2)*(4*A*b - B*a)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5 - (8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))/a^5 - (16*(256*A^3*b^16 - 4*B*C^2*a^16 + 4*B^2*C*a^16 - 128*A^3*a*b^15 - 16*B^3*a^15*b - 1664*A^3*a^2*b^14 + 800*A^3*a^3*b^13 + 4576*A^3*a^4*b^12 - 2176*A^3*a^5*b^11 - 6944*A^3*a^6*b^10 + 3204*A^3*a^7*b^9 + 6176*A^3*a^8*b^8 - 2560*A^3*a^9*b^7 - 3040*A^3*a^10*b^6 + 960*A^3*a^11*b^5 + 640*A^3*a^12*b^4 - 4*B^3*a^3*b^13 + 2*B^3*a^4*b^12 + 26*B^3*a^5*b^11 - 11*B^3*a^6*b^10 - 70*B^3*a^7*b^9 + 34*B^3*a^8*b^8 + 110*B^3*a^9*b^7 - 66*B^3*a^10*b^6 - 110*B^3*a^11*b^5 + 64*B^3*a^12*b^4 + 64*B^3*a^13*b^3 - 48*B^3*a^14*b^2 - 192*A^2*B*a*b^15 + 16*A*C^2*a^15*b + 28*B^2*C*a^15*b + 48*A*B^2*a^2*b^14 - 24*A*B^2*a^3*b^13 - 312*A*B^2*a^4*b^12 + 138*A*B^2*a^5*b^11 + 846*A*B^2*a^6*b^10 - 408*A*B^2*a^7*b^9 - 1314*A*B^2*a^8*b^8 + 726*A*B^2*a^9*b^7 + 1266*A*B^2*a^10*b^6 - 690*A*B^2*a^11*b^5 - 702*A*B^2*a^12*b^4 + 408*A*B^2*a^13*b^3 + 168*A*B^2*a^14*b^2 + 96*A^2*B*a^2*b^14 + 1248*A^2*B*a^3*b^13 - 576*A^2*B*a^4*b^12 - 3408*A^2*B*a^5*b^11 + 1632*A^2*B*a^6*b^10 + 5232*A^2*B*a^7*b^9 - 2649*A^2*B*a^8*b^8 - 4848*A^2*B*a^9*b^7 + 2376*A^2*B*a^10*b^6 + 2544*A^2*B*a^11*b^5 - 1104*A^2*B*a^12*b^4 - 576*A^2*B*a^13*b^3 + 36*A*C^2*a^11*b^5 + 48*A*C^2*a^13*b^3 - 96*A^2*C*a^5*b^11 - 96*A^2*C*a^6*b^10 + 320*A^2*C*a^7*b^9 + 224*A^2*C*a^8*b^8 - 296*A^2*C*a^9*b^7 - 96*A^2*C*a^10*b^6 + 16*A^2*C*a^11*b^5 - 96*A^2*C*a^12*b^4 + 256*A^2*C*a^13*b^3 + 64*A^2*C*a^14*b^2 - 9*B*C^2*a^12*b^4 - 12*B*C^2*a^14*b^2 - 6*B^2*C*a^7*b^9 - 6*B^2*C*a^8*b^8 + 20*B^2*C*a^9*b^7 + 14*B^2*C*a^10*b^6 - 14*B^2*C*a^11*b^5 - 6*B^2*C*a^12*b^4 + 22*B^2*C*a^13*b^3 - 6*B^2*C*a^14*b^2 - 32*A*B*C*a^15*b + 48*A*B*C*a^6*b^10 + 48*A*B*C*a^7*b^9 - 160*A*B*C*a^8*b^8 - 112*A*B*C*a^9*b^7 + 130*A*B*C*a^10*b^6 + 48*A*B*C*a^11*b^5 - 92*A*B*C*a^12*b^4 + 48*A*B*C*a^13*b^3 - 176*A*B*C*a^14*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + ((4*A*b - B*a)*(((4*A*b - B*a)*((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (8*tan(c/2 + (d*x)/2)*(4*A*b - B*a)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5 + (8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))/a^5))*(4*A*b - B*a)*2i)/(a^5*d) + (atan(((((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))/((16*(256*A^3*b^16 - 4*B*C^2*a^16 + 4*B^2*C*a^16 - 128*A^3*a*b^15 - 16*B^3*a^15*b - 1664*A^3*a^2*b^14 + 800*A^3*a^3*b^13 + 4576*A^3*a^4*b^12 - 2176*A^3*a^5*b^11 - 6944*A^3*a^6*b^10 + 3204*A^3*a^7*b^9 + 6176*A^3*a^8*b^8 - 2560*A^3*a^9*b^7 - 3040*A^3*a^10*b^6 + 960*A^3*a^11*b^5 + 640*A^3*a^12*b^4 - 4*B^3*a^3*b^13 + 2*B^3*a^4*b^12 + 26*B^3*a^5*b^11 - 11*B^3*a^6*b^10 - 70*B^3*a^7*b^9 + 34*B^3*a^8*b^8 + 110*B^3*a^9*b^7 - 66*B^3*a^10*b^6 - 110*B^3*a^11*b^5 + 64*B^3*a^12*b^4 + 64*B^3*a^13*b^3 - 48*B^3*a^14*b^2 - 192*A^2*B*a*b^15 + 16*A*C^2*a^15*b + 28*B^2*C*a^15*b + 48*A*B^2*a^2*b^14 - 24*A*B^2*a^3*b^13 - 312*A*B^2*a^4*b^12 + 138*A*B^2*a^5*b^11 + 846*A*B^2*a^6*b^10 - 408*A*B^2*a^7*b^9 - 1314*A*B^2*a^8*b^8 + 726*A*B^2*a^9*b^7 + 1266*A*B^2*a^10*b^6 - 690*A*B^2*a^11*b^5 - 702*A*B^2*a^12*b^4 + 408*A*B^2*a^13*b^3 + 168*A*B^2*a^14*b^2 + 96*A^2*B*a^2*b^14 + 1248*A^2*B*a^3*b^13 - 576*A^2*B*a^4*b^12 - 3408*A^2*B*a^5*b^11 + 1632*A^2*B*a^6*b^10 + 5232*A^2*B*a^7*b^9 - 2649*A^2*B*a^8*b^8 - 4848*A^2*B*a^9*b^7 + 2376*A^2*B*a^10*b^6 + 2544*A^2*B*a^11*b^5 - 1104*A^2*B*a^12*b^4 - 576*A^2*B*a^13*b^3 + 36*A*C^2*a^11*b^5 + 48*A*C^2*a^13*b^3 - 96*A^2*C*a^5*b^11 - 96*A^2*C*a^6*b^10 + 320*A^2*C*a^7*b^9 + 224*A^2*C*a^8*b^8 - 296*A^2*C*a^9*b^7 - 96*A^2*C*a^10*b^6 + 16*A^2*C*a^11*b^5 - 96*A^2*C*a^12*b^4 + 256*A^2*C*a^13*b^3 + 64*A^2*C*a^14*b^2 - 9*B*C^2*a^12*b^4 - 12*B*C^2*a^14*b^2 - 6*B^2*C*a^7*b^9 - 6*B^2*C*a^8*b^8 + 20*B^2*C*a^9*b^7 + 14*B^2*C*a^10*b^6 - 14*B^2*C*a^11*b^5 - 6*B^2*C*a^12*b^4 + 22*B^2*C*a^13*b^3 - 6*B^2*C*a^14*b^2 - 32*A*B*C*a^15*b + 48*A*B*C*a^6*b^10 + 48*A*B*C*a^7*b^9 - 160*A*B*C*a^8*b^8 - 112*A*B*C*a^9*b^7 + 130*A*B*C*a^10*b^6 + 48*A*B*C*a^11*b^5 - 92*A*B*C*a^12*b^4 + 48*A*B*C*a^13*b^3 - 176*A*B*C*a^14*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) - (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) - (((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^2*a^16 + 4*C^2*a^16 - 128*A^2*a*b^15 - 8*B^2*a^15*b - 768*A^2*a^2*b^14 + 768*A^2*a^3*b^13 + 1920*A^2*a^4*b^12 - 1920*A^2*a^5*b^11 - 2600*A^2*a^6*b^10 + 2560*A^2*a^7*b^9 + 2025*A^2*a^8*b^8 - 1920*A^2*a^9*b^7 - 824*A^2*a^10*b^6 + 768*A^2*a^11*b^5 + 80*A^2*a^12*b^4 - 128*A^2*a^13*b^3 + 64*A^2*a^14*b^2 + 8*B^2*a^2*b^14 - 8*B^2*a^3*b^13 - 48*B^2*a^4*b^12 + 48*B^2*a^5*b^11 + 117*B^2*a^6*b^10 - 120*B^2*a^7*b^9 - 164*B^2*a^8*b^8 + 160*B^2*a^9*b^7 + 156*B^2*a^10*b^6 - 120*B^2*a^11*b^5 - 92*B^2*a^12*b^4 + 48*B^2*a^13*b^3 + 44*B^2*a^14*b^2 + 9*C^2*a^12*b^4 + 12*C^2*a^14*b^2 - 64*A*B*a*b^15 - 32*A*B*a^15*b - 32*B*C*a^15*b + 64*A*B*a^2*b^14 + 384*A*B*a^3*b^13 - 384*A*B*a^4*b^12 - 948*A*B*a^5*b^11 + 960*A*B*a^6*b^10 + 1306*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 - 1128*A*B*a^9*b^7 + 960*A*B*a^10*b^6 + 592*A*B*a^11*b^5 - 384*A*B*a^12*b^4 - 160*A*B*a^13*b^3 + 64*A*B*a^14*b^2 - 48*A*C*a^6*b^10 + 136*A*C*a^8*b^8 - 98*A*C*a^10*b^6 - 20*A*C*a^12*b^4 + 80*A*C*a^14*b^2 + 12*B*C*a^7*b^9 - 34*B*C*a^9*b^7 + 20*B*C*a^11*b^5 - 16*B*C*a^13*b^3))/(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2) + (((8*(4*B*a^24 + 4*C*a^24 + 16*A*a^10*b^14 - 8*A*a^11*b^13 - 104*A*a^12*b^12 + 50*A*a^13*b^11 + 286*A*a^14*b^10 - 126*A*a^15*b^9 - 434*A*a^16*b^8 + 174*A*a^17*b^7 + 386*A*a^18*b^6 - 146*A*a^19*b^5 - 190*A*a^20*b^4 + 72*A*a^21*b^3 + 40*A*a^22*b^2 - 4*B*a^11*b^13 + 2*B*a^12*b^12 + 26*B*a^13*b^11 - 14*B*a^14*b^10 - 70*B*a^15*b^9 + 30*B*a^16*b^8 + 110*B*a^17*b^7 - 30*B*a^18*b^6 - 110*B*a^19*b^5 + 20*B*a^20*b^4 + 64*B*a^21*b^3 - 12*B*a^22*b^2 + 6*C*a^15*b^9 - 6*C*a^16*b^8 - 14*C*a^17*b^7 + 14*C*a^18*b^6 + 6*C*a^19*b^5 - 6*C*a^20*b^4 + 6*C*a^21*b^3 - 6*C*a^22*b^2 - 16*A*a^23*b - 16*B*a^23*b - 4*C*a^23*b))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*C*a^8 - 8*A*b^8 + 28*A*a^2*b^6 - 35*A*a^4*b^4 + 20*A*a^6*b^2 - 7*B*a^3*b^5 + 8*B*a^5*b^3 + 3*C*a^6*b^2 + 2*B*a*b^7 - 8*B*a^7*b)*1i)/(d*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))","B"
1008,1,21844,657,22.185942,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^4),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(A\,a^8+20\,A\,b^8-2\,B\,a^8-59\,A\,a^2\,b^6+27\,A\,a^3\,b^5+57\,A\,a^4\,b^4-21\,A\,a^5\,b^3-11\,A\,a^6\,b^2+4\,B\,a^2\,b^6+24\,B\,a^3\,b^5-11\,B\,a^4\,b^4-26\,B\,a^5\,b^3+6\,B\,a^6\,b^2+2\,C\,a^2\,b^6-C\,a^3\,b^5-6\,C\,a^4\,b^4+4\,C\,a^5\,b^3+12\,C\,a^6\,b^2-10\,A\,a\,b^7+7\,A\,a^7\,b-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{a^5\,{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,A\,a^9-120\,A\,b^9+6\,B\,a^9+364\,A\,a^2\,b^7+71\,A\,a^3\,b^6-369\,A\,a^4\,b^5-45\,A\,a^5\,b^4+111\,A\,a^6\,b^3+3\,A\,a^7\,b^2+12\,B\,a^2\,b^7-148\,B\,a^3\,b^6-29\,B\,a^4\,b^5+159\,B\,a^5\,b^4+18\,B\,a^6\,b^3-30\,B\,a^7\,b^2-12\,C\,a^2\,b^7-3\,C\,a^3\,b^6+37\,C\,a^4\,b^5+8\,C\,a^5\,b^4-60\,C\,a^6\,b^3-30\,A\,a\,b^8-21\,A\,a^8\,b+48\,B\,a\,b^8-6\,B\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,A\,a^9+120\,A\,b^9-6\,B\,a^9-364\,A\,a^2\,b^7+71\,A\,a^3\,b^6+369\,A\,a^4\,b^5-45\,A\,a^5\,b^4-111\,A\,a^6\,b^3+3\,A\,a^7\,b^2+12\,B\,a^2\,b^7+148\,B\,a^3\,b^6-29\,B\,a^4\,b^5-159\,B\,a^5\,b^4+18\,B\,a^6\,b^3+30\,B\,a^7\,b^2+12\,C\,a^2\,b^7-3\,C\,a^3\,b^6-37\,C\,a^4\,b^5+8\,C\,a^5\,b^4+60\,C\,a^6\,b^3-30\,A\,a\,b^8+21\,A\,a^8\,b-48\,B\,a\,b^8-6\,B\,a^8\,b\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,A\,a^{10}+180\,A\,b^{10}-611\,A\,a^2\,b^8+740\,A\,a^4\,b^6-324\,A\,a^6\,b^4+36\,A\,a^8\,b^2+248\,B\,a^3\,b^7-320\,B\,a^5\,b^5+132\,B\,a^7\,b^3+18\,C\,a^2\,b^8-62\,C\,a^4\,b^6+110\,C\,a^6\,b^4-36\,C\,a^8\,b^2-72\,B\,a\,b^9-18\,B\,a^9\,b\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^8+20\,A\,b^8+2\,B\,a^8-59\,A\,a^2\,b^6-27\,A\,a^3\,b^5+57\,A\,a^4\,b^4+21\,A\,a^5\,b^3-11\,A\,a^6\,b^2-4\,B\,a^2\,b^6+24\,B\,a^3\,b^5+11\,B\,a^4\,b^4-26\,B\,a^5\,b^3-6\,B\,a^6\,b^2+2\,C\,a^2\,b^6+C\,a^3\,b^5-6\,C\,a^4\,b^4-4\,C\,a^5\,b^3+12\,C\,a^6\,b^2+10\,A\,a\,b^7-7\,A\,a^7\,b-8\,B\,a\,b^7+2\,B\,a^7\,b\right)}{a^5\,\left(a+b\right)\,{\left(a-b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^3-6\,a^2\,b+6\,a\,b^2+10\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^3+3\,a^2\,b+9\,a\,b^2+5\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-2\,a^3+6\,a^2\,b+6\,a\,b^2-10\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3+3\,a^2\,b-9\,a\,b^2+5\,b^3\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}-16\,A\,B\,a^{17}\,b+32\,A\,B\,a^{16}\,b^2-240\,A\,B\,a^{15}\,b^3+448\,A\,B\,a^{14}\,b^4-144\,A\,B\,a^{13}\,b^5-3360\,A\,B\,a^{12}\,b^6+3360\,A\,B\,a^{11}\,b^7+8960\,A\,B\,a^{10}\,b^8-9200\,A\,B\,a^9\,b^9-12320\,A\,B\,a^8\,b^{10}+12430\,A\,B\,a^7\,b^{11}+9408\,A\,B\,a^6\,b^{12}-9408\,A\,B\,a^5\,b^{13}-3808\,A\,B\,a^4\,b^{14}+3808\,A\,B\,a^3\,b^{15}+640\,A\,B\,a^2\,b^{16}-640\,A\,B\,a\,b^{17}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+64\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3+80\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5-824\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7+2025\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9-2600\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}+1920\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}-768\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+128\,B^2\,a^2\,b^{16}-32\,B\,C\,a^{17}\,b+64\,B\,C\,a^{16}\,b^2-160\,B\,C\,a^{15}\,b^3-384\,B\,C\,a^{14}\,b^4+592\,B\,C\,a^{13}\,b^5+960\,B\,C\,a^{12}\,b^6-1128\,B\,C\,a^{11}\,b^7-1280\,B\,C\,a^{10}\,b^8+1306\,B\,C\,a^9\,b^9+960\,B\,C\,a^8\,b^{10}-948\,B\,C\,a^7\,b^{11}-384\,B\,C\,a^6\,b^{12}+384\,B\,C\,a^5\,b^{13}+64\,B\,C\,a^4\,b^{14}-64\,B\,C\,a^3\,b^{15}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2+32\,B\,a^{13}\,b^{14}-16\,B\,a^{14}\,b^{13}-208\,B\,a^{15}\,b^{12}+100\,B\,a^{16}\,b^{11}+572\,B\,a^{17}\,b^{10}-252\,B\,a^{18}\,b^9-868\,B\,a^{19}\,b^8+348\,B\,a^{20}\,b^7+772\,B\,a^{21}\,b^6-292\,B\,a^{22}\,b^5-380\,B\,a^{23}\,b^4+144\,B\,a^{24}\,b^3+80\,B\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,B\,a^{26}\,b-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-4\,B\,a\,b+10\,A\,b^2\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-4\,B\,a\,b+10\,A\,b^2\right)}{a^6}\right)\,\left(\left(\frac{A}{2}+C\right)\,a^2-4\,B\,a\,b+10\,A\,b^2\right)\,1{}\mathrm{i}}{a^6}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}-16\,A\,B\,a^{17}\,b+32\,A\,B\,a^{16}\,b^2-240\,A\,B\,a^{15}\,b^3+448\,A\,B\,a^{14}\,b^4-144\,A\,B\,a^{13}\,b^5-3360\,A\,B\,a^{12}\,b^6+3360\,A\,B\,a^{11}\,b^7+8960\,A\,B\,a^{10}\,b^8-9200\,A\,B\,a^9\,b^9-12320\,A\,B\,a^8\,b^{10}+12430\,A\,B\,a^7\,b^{11}+9408\,A\,B\,a^6\,b^{12}-9408\,A\,B\,a^5\,b^{13}-3808\,A\,B\,a^4\,b^{14}+3808\,A\,B\,a^3\,b^{15}+640\,A\,B\,a^2\,b^{16}-640\,A\,B\,a\,b^{17}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+64\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3+80\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5-824\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7+2025\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9-2600\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}+1920\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}-768\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+128\,B^2\,a^2\,b^{16}-32\,B\,C\,a^{17}\,b+64\,B\,C\,a^{16}\,b^2-160\,B\,C\,a^{15}\,b^3-384\,B\,C\,a^{14}\,b^4+592\,B\,C\,a^{13}\,b^5+960\,B\,C\,a^{12}\,b^6-1128\,B\,C\,a^{11}\,b^7-1280\,B\,C\,a^{10}\,b^8+1306\,B\,C\,a^9\,b^9+960\,B\,C\,a^8\,b^{10}-948\,B\,C\,a^7\,b^{11}-384\,B\,C\,a^6\,b^{12}+384\,B\,C\,a^5\,b^{13}+64\,B\,C\,a^4\,b^{14}-64\,B\,C\,a^3\,b^{15}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2+32\,B\,a^{13}\,b^{14}-16\,B\,a^{14}\,b^{13}-208\,B\,a^{15}\,b^{12}+100\,B\,a^{16}\,b^{11}+572\,B\,a^{17}\,b^{10}-252\,B\,a^{18}\,b^9-868\,B\,a^{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,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2+32\,B\,a^{13}\,b^{14}-16\,B\,a^{14}\,b^{13}-208\,B\,a^{15}\,b^{12}+100\,B\,a^{16}\,b^{11}+572\,B\,a^{17}\,b^{10}-252\,B\,a^{18}\,b^9-868\,B\,a^{19}\,b^8+348\,B\,a^{20}\,b^7+772\,B\,a^{21}\,b^6-292\,B\,a^{22}\,b^5-380\,B\,a^{23}\,b^4+144\,B\,a^{24}\,b^3+80\,B\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,B\,a^{26}\,b-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^{18}-2\,A^2\,a^{17}\,b+35\,A^2\,a^{16}\,b^2-68\,A^2\,a^{15}\,b^3+209\,A^2\,a^{14}\,b^4-350\,A^2\,a^{13}\,b^5-45\,A^2\,a^{12}\,b^6+3640\,A^2\,a^{11}\,b^7-3325\,A^2\,a^{10}\,b^8-10430\,A^2\,a^9\,b^9+10385\,A^2\,a^8\,b^{10}+14812\,A^2\,a^7\,b^{11}-14837\,A^2\,a^6\,b^{12}-11522\,A^2\,a^5\,b^{13}+11522\,A^2\,a^4\,b^{14}+4720\,A^2\,a^3\,b^{15}-4720\,A^2\,a^2\,b^{16}-800\,A^2\,a\,b^{17}+800\,A^2\,b^{18}-16\,A\,B\,a^{17}\,b+32\,A\,B\,a^{16}\,b^2-240\,A\,B\,a^{15}\,b^3+448\,A\,B\,a^{14}\,b^4-144\,A\,B\,a^{13}\,b^5-3360\,A\,B\,a^{12}\,b^6+3360\,A\,B\,a^{11}\,b^7+8960\,A\,B\,a^{10}\,b^8-9200\,A\,B\,a^9\,b^9-12320\,A\,B\,a^8\,b^{10}+12430\,A\,B\,a^7\,b^{11}+9408\,A\,B\,a^6\,b^{12}-9408\,A\,B\,a^5\,b^{13}-3808\,A\,B\,a^4\,b^{14}+3808\,A\,B\,a^3\,b^{15}+640\,A\,B\,a^2\,b^{16}-640\,A\,B\,a\,b^{17}+4\,A\,C\,a^{18}-8\,A\,C\,a^{17}\,b+60\,A\,C\,a^{16}\,b^2-112\,A\,C\,a^{15}\,b^3+276\,A\,C\,a^{14}\,b^4+840\,A\,C\,a^{13}\,b^5-1284\,A\,C\,a^{12}\,b^6-2240\,A\,C\,a^{11}\,b^7+2588\,A\,C\,a^{10}\,b^8+3080\,A\,C\,a^9\,b^9-3124\,A\,C\,a^8\,b^{10}-2352\,A\,C\,a^7\,b^{11}+2322\,A\,C\,a^6\,b^{12}+952\,A\,C\,a^5\,b^{13}-952\,A\,C\,a^4\,b^{14}-160\,A\,C\,a^3\,b^{15}+160\,A\,C\,a^2\,b^{16}+64\,B^2\,a^{16}\,b^2-128\,B^2\,a^{15}\,b^3+80\,B^2\,a^{14}\,b^4+768\,B^2\,a^{13}\,b^5-824\,B^2\,a^{12}\,b^6-1920\,B^2\,a^{11}\,b^7+2025\,B^2\,a^{10}\,b^8+2560\,B^2\,a^9\,b^9-2600\,B^2\,a^8\,b^{10}-1920\,B^2\,a^7\,b^{11}+1920\,B^2\,a^6\,b^{12}+768\,B^2\,a^5\,b^{13}-768\,B^2\,a^4\,b^{14}-128\,B^2\,a^3\,b^{15}+128\,B^2\,a^2\,b^{16}-32\,B\,C\,a^{17}\,b+64\,B\,C\,a^{16}\,b^2-160\,B\,C\,a^{15}\,b^3-384\,B\,C\,a^{14}\,b^4+592\,B\,C\,a^{13}\,b^5+960\,B\,C\,a^{12}\,b^6-1128\,B\,C\,a^{11}\,b^7-1280\,B\,C\,a^{10}\,b^8+1306\,B\,C\,a^9\,b^9+960\,B\,C\,a^8\,b^{10}-948\,B\,C\,a^7\,b^{11}-384\,B\,C\,a^6\,b^{12}+384\,B\,C\,a^5\,b^{13}+64\,B\,C\,a^4\,b^{14}-64\,B\,C\,a^3\,b^{15}+4\,C^2\,a^{18}-8\,C^2\,a^{17}\,b+44\,C^2\,a^{16}\,b^2+48\,C^2\,a^{15}\,b^3-92\,C^2\,a^{14}\,b^4-120\,C^2\,a^{13}\,b^5+156\,C^2\,a^{12}\,b^6+160\,C^2\,a^{11}\,b^7-164\,C^2\,a^{10}\,b^8-120\,C^2\,a^9\,b^9+117\,C^2\,a^8\,b^{10}+48\,C^2\,a^7\,b^{11}-48\,C^2\,a^6\,b^{12}-8\,C^2\,a^5\,b^{13}+8\,C^2\,a^4\,b^{14}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,a^{27}+8\,C\,a^{27}-80\,A\,a^{12}\,b^{15}+40\,A\,a^{13}\,b^{14}+516\,A\,a^{14}\,b^{13}-248\,A\,a^{15}\,b^{12}-1404\,A\,a^{16}\,b^{11}+640\,A\,a^{17}\,b^{10}+2076\,A\,a^{18}\,b^9-896\,A\,a^{19}\,b^8-1764\,A\,a^{20}\,b^7+724\,A\,a^{21}\,b^6+816\,A\,a^{22}\,b^5-316\,A\,a^{23}\,b^4-160\,A\,a^{24}\,b^3+52\,A\,a^{25}\,b^2+32\,B\,a^{13}\,b^{14}-16\,B\,a^{14}\,b^{13}-208\,B\,a^{15}\,b^{12}+100\,B\,a^{16}\,b^{11}+572\,B\,a^{17}\,b^{10}-252\,B\,a^{18}\,b^9-868\,B\,a^{19}\,b^8+348\,B\,a^{20}\,b^7+772\,B\,a^{21}\,b^6-292\,B\,a^{22}\,b^5-380\,B\,a^{23}\,b^4+144\,B\,a^{24}\,b^3+80\,B\,a^{25}\,b^2-8\,C\,a^{14}\,b^{13}+4\,C\,a^{15}\,b^{12}+52\,C\,a^{16}\,b^{11}-28\,C\,a^{17}\,b^{10}-140\,C\,a^{18}\,b^9+60\,C\,a^{19}\,b^8+220\,C\,a^{20}\,b^7-60\,C\,a^{21}\,b^6-220\,C\,a^{22}\,b^5+40\,C\,a^{23}\,b^4+128\,C\,a^{24}\,b^3-24\,C\,a^{25}\,b^2-32\,B\,a^{26}\,b-32\,C\,a^{26}\,b\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,A\,b^8-8\,C\,a^8-69\,A\,a^2\,b^6+84\,A\,a^4\,b^4-40\,A\,a^6\,b^2+28\,B\,a^3\,b^5-35\,B\,a^5\,b^3+2\,C\,a^2\,b^6-7\,C\,a^4\,b^4+8\,C\,a^6\,b^2-8\,B\,a\,b^7+20\,B\,a^7\,b\right)\,1{}\mathrm{i}}{d\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^9*(A*a^8 + 20*A*b^8 - 2*B*a^8 - 59*A*a^2*b^6 + 27*A*a^3*b^5 + 57*A*a^4*b^4 - 21*A*a^5*b^3 - 11*A*a^6*b^2 + 4*B*a^2*b^6 + 24*B*a^3*b^5 - 11*B*a^4*b^4 - 26*B*a^5*b^3 + 6*B*a^6*b^2 + 2*C*a^2*b^6 - C*a^3*b^5 - 6*C*a^4*b^4 + 4*C*a^5*b^3 + 12*C*a^6*b^2 - 10*A*a*b^7 + 7*A*a^7*b - 8*B*a*b^7 + 2*B*a^7*b))/(a^5*(a + b)^3*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(6*A*a^9 - 120*A*b^9 + 6*B*a^9 + 364*A*a^2*b^7 + 71*A*a^3*b^6 - 369*A*a^4*b^5 - 45*A*a^5*b^4 + 111*A*a^6*b^3 + 3*A*a^7*b^2 + 12*B*a^2*b^7 - 148*B*a^3*b^6 - 29*B*a^4*b^5 + 159*B*a^5*b^4 + 18*B*a^6*b^3 - 30*B*a^7*b^2 - 12*C*a^2*b^7 - 3*C*a^3*b^6 + 37*C*a^4*b^5 + 8*C*a^5*b^4 - 60*C*a^6*b^3 - 30*A*a*b^8 - 21*A*a^8*b + 48*B*a*b^8 - 6*B*a^8*b))/(3*a^5*(a + b)^2*(a - b)^3) + (2*tan(c/2 + (d*x)/2)^7*(6*A*a^9 + 120*A*b^9 - 6*B*a^9 - 364*A*a^2*b^7 + 71*A*a^3*b^6 + 369*A*a^4*b^5 - 45*A*a^5*b^4 - 111*A*a^6*b^3 + 3*A*a^7*b^2 + 12*B*a^2*b^7 + 148*B*a^3*b^6 - 29*B*a^4*b^5 - 159*B*a^5*b^4 + 18*B*a^6*b^3 + 30*B*a^7*b^2 + 12*C*a^2*b^7 - 3*C*a^3*b^6 - 37*C*a^4*b^5 + 8*C*a^5*b^4 + 60*C*a^6*b^3 - 30*A*a*b^8 + 21*A*a^8*b - 48*B*a*b^8 - 6*B*a^8*b))/(3*a^5*(a + b)^3*(a - b)^2) + (2*tan(c/2 + (d*x)/2)^5*(9*A*a^10 + 180*A*b^10 - 611*A*a^2*b^8 + 740*A*a^4*b^6 - 324*A*a^6*b^4 + 36*A*a^8*b^2 + 248*B*a^3*b^7 - 320*B*a^5*b^5 + 132*B*a^7*b^3 + 18*C*a^2*b^8 - 62*C*a^4*b^6 + 110*C*a^6*b^4 - 36*C*a^8*b^2 - 72*B*a*b^9 - 18*B*a^9*b))/(3*a^5*(a + b)^3*(a - b)^3) + (tan(c/2 + (d*x)/2)*(A*a^8 + 20*A*b^8 + 2*B*a^8 - 59*A*a^2*b^6 - 27*A*a^3*b^5 + 57*A*a^4*b^4 + 21*A*a^5*b^3 - 11*A*a^6*b^2 - 4*B*a^2*b^6 + 24*B*a^3*b^5 + 11*B*a^4*b^4 - 26*B*a^5*b^3 - 6*B*a^6*b^2 + 2*C*a^2*b^6 + C*a^3*b^5 - 6*C*a^4*b^4 - 4*C*a^5*b^3 + 12*C*a^6*b^2 + 10*A*a*b^7 - 7*A*a^7*b - 8*B*a*b^7 + 2*B*a^7*b))/(a^5*(a + b)*(a - b)^3))/(d*(tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^2*b - 2*a^3 + 10*b^3) - tan(c/2 + (d*x)/2)^2*(9*a*b^2 + 3*a^2*b - a^3 + 5*b^3) + tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 6*a^2*b - 2*a^3 - 10*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^10*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + tan(c/2 + (d*x)/2)^8*(3*a^2*b - 9*a*b^2 + a^3 + 5*b^3))) - (atan(((((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b))/a^6)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b)*1i)/a^6 + (((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b))/a^6)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b)*1i)/a^6)/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 - 512*B^3*a^3*b^16 + 256*B^3*a^4*b^15 + 3328*B^3*a^5*b^14 - 1600*B^3*a^6*b^13 - 9152*B^3*a^7*b^12 + 4352*B^3*a^8*b^11 + 13888*B^3*a^9*b^10 - 6408*B^3*a^10*b^9 - 12352*B^3*a^11*b^8 + 5120*B^3*a^12*b^7 + 6080*B^3*a^13*b^6 - 1920*B^3*a^14*b^5 - 1280*B^3*a^15*b^4 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 - 9600*A^2*B*a*b^18 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 3840*A*B^2*a^2*b^17 - 1920*A*B^2*a^3*b^16 - 24768*A*B^2*a^4*b^15 + 11904*A*B^2*a^5*b^14 + 67392*A*B^2*a^6*b^13 - 31680*A*B^2*a^7*b^12 - 100368*A*B^2*a^8*b^11 + 45148*A*B^2*a^9*b^10 + 86512*A*B^2*a^10*b^9 - 34567*A*B^2*a^11*b^8 - 40368*A*B^2*a^12*b^7 + 11960*A*B^2*a^13*b^6 + 7440*A*B^2*a^14*b^5 + 80*A*B^2*a^15*b^4 + 320*A*B^2*a^16*b^3 + 4800*A^2*B*a^2*b^17 + 61440*A^2*B*a^3*b^16 - 29520*A^2*B*a^4*b^15 - 165384*A^2*B*a^5*b^14 + 76812*A^2*B*a^6*b^13 + 241596*A^2*B*a^7*b^12 - 105755*A^2*B*a^8*b^11 - 201479*A^2*B*a^9*b^10 + 77359*A^2*B*a^10*b^9 + 88721*A^2*B*a^11*b^8 - 24711*A^2*B*a^12*b^7 - 13929*A^2*B*a^13*b^6 - 255*A^2*B*a^14*b^5 - 1345*A^2*B*a^15*b^4 + 20*A^2*B*a^16*b^3 - 20*A^2*B*a^17*b^2 + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2 - 96*B*C^2*a^5*b^14 + 48*B*C^2*a^6*b^13 + 624*B*C^2*a^7*b^12 - 276*B*C^2*a^8*b^11 - 1692*B*C^2*a^9*b^10 + 816*B*C^2*a^10*b^9 + 2628*B*C^2*a^11*b^8 - 1452*B*C^2*a^12*b^7 - 2532*B*C^2*a^13*b^6 + 1380*B*C^2*a^14*b^5 + 1404*B*C^2*a^15*b^4 - 816*B*C^2*a^16*b^3 - 336*B*C^2*a^17*b^2 + 384*B^2*C*a^4*b^15 - 192*B^2*C*a^5*b^14 - 2496*B^2*C*a^6*b^13 + 1152*B^2*C*a^7*b^12 + 6816*B^2*C*a^8*b^11 - 3264*B^2*C*a^9*b^10 - 10464*B^2*C*a^10*b^9 + 5298*B^2*C*a^11*b^8 + 9696*B^2*C*a^12*b^7 - 4752*B^2*C*a^13*b^6 - 5088*B^2*C*a^14*b^5 + 2208*B^2*C*a^15*b^4 + 1152*B^2*C*a^16*b^3 - 1920*A*B*C*a^3*b^16 + 960*A*B*C*a^4*b^15 + 12384*A*B*C*a^5*b^14 - 5712*A*B*C*a^6*b^13 - 33456*A*B*C*a^7*b^12 + 15852*A*B*C*a^8*b^11 + 50436*A*B*C*a^9*b^10 - 25034*A*B*C*a^10*b^9 - 45404*A*B*C*a^11*b^8 + 21788*A*B*C*a^12*b^7 + 22716*A*B*C*a^13*b^6 - 9292*A*B*C*a^14*b^5 - 4548*A*B*C*a^15*b^4 - 112*A*B*C*a^16*b^3 - 208*A*B*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b))/a^6)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b))/a^6 - (((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (8*tan(c/2 + (d*x)/2)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b))/a^6)*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b))/a^6))*(10*A*b^2 + a^2*(A/2 + C) - 4*B*a*b)*2i)/(a^6*d) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 + 32*C^3*a^18*b - 50800*A^3*a^2*b^17 + 24400*A^3*a^3*b^16 + 135260*A^3*a^4*b^15 - 62030*A^3*a^5*b^14 - 193689*A^3*a^6*b^13 + 82337*A^3*a^7*b^12 + 155991*A^3*a^8*b^11 - 57345*A^3*a^9*b^10 - 64479*A^3*a^10*b^9 + 16999*A^3*a^11*b^8 + 8281*A^3*a^12*b^7 + 204*A^3*a^13*b^6 + 1396*A^3*a^14*b^5 - 40*A^3*a^15*b^4 + 40*A^3*a^16*b^3 - 512*B^3*a^3*b^16 + 256*B^3*a^4*b^15 + 3328*B^3*a^5*b^14 - 1600*B^3*a^6*b^13 - 9152*B^3*a^7*b^12 + 4352*B^3*a^8*b^11 + 13888*B^3*a^9*b^10 - 6408*B^3*a^10*b^9 - 12352*B^3*a^11*b^8 + 5120*B^3*a^12*b^7 + 6080*B^3*a^13*b^6 - 1920*B^3*a^14*b^5 - 1280*B^3*a^15*b^4 + 8*C^3*a^6*b^13 - 4*C^3*a^7*b^12 - 52*C^3*a^8*b^11 + 22*C^3*a^9*b^10 + 140*C^3*a^10*b^9 - 68*C^3*a^11*b^8 - 220*C^3*a^12*b^7 + 132*C^3*a^13*b^6 + 220*C^3*a^14*b^5 - 128*C^3*a^15*b^4 - 128*C^3*a^16*b^3 + 96*C^3*a^17*b^2 - 9600*A^2*B*a*b^18 + 32*A*C^2*a^18*b + 8*A^2*C*a^18*b + 3840*A*B^2*a^2*b^17 - 1920*A*B^2*a^3*b^16 - 24768*A*B^2*a^4*b^15 + 11904*A*B^2*a^5*b^14 + 67392*A*B^2*a^6*b^13 - 31680*A*B^2*a^7*b^12 - 100368*A*B^2*a^8*b^11 + 45148*A*B^2*a^9*b^10 + 86512*A*B^2*a^10*b^9 - 34567*A*B^2*a^11*b^8 - 40368*A*B^2*a^12*b^7 + 11960*A*B^2*a^13*b^6 + 7440*A*B^2*a^14*b^5 + 80*A*B^2*a^15*b^4 + 320*A*B^2*a^16*b^3 + 4800*A^2*B*a^2*b^17 + 61440*A^2*B*a^3*b^16 - 29520*A^2*B*a^4*b^15 - 165384*A^2*B*a^5*b^14 + 76812*A^2*B*a^6*b^13 + 241596*A^2*B*a^7*b^12 - 105755*A^2*B*a^8*b^11 - 201479*A^2*B*a^9*b^10 + 77359*A^2*B*a^10*b^9 + 88721*A^2*B*a^11*b^8 - 24711*A^2*B*a^12*b^7 - 13929*A^2*B*a^13*b^6 - 255*A^2*B*a^14*b^5 - 1345*A^2*B*a^15*b^4 + 20*A^2*B*a^16*b^3 - 20*A^2*B*a^17*b^2 + 240*A*C^2*a^4*b^15 - 120*A*C^2*a^5*b^14 - 1548*A*C^2*a^6*b^13 + 684*A*C^2*a^7*b^12 + 4152*A*C^2*a^8*b^11 - 1983*A*C^2*a^9*b^10 - 6336*A*C^2*a^10*b^9 + 3448*A*C^2*a^11*b^8 + 5944*A*C^2*a^12*b^7 - 3196*A*C^2*a^13*b^6 - 3156*A*C^2*a^14*b^5 + 1760*A*C^2*a^15*b^4 + 672*A*C^2*a^16*b^3 + 32*A*C^2*a^17*b^2 + 2400*A^2*C*a^2*b^17 - 1200*A^2*C*a^3*b^16 - 15360*A^2*C*a^4*b^15 + 7080*A^2*C*a^5*b^14 + 41046*A^2*C*a^6*b^13 - 19233*A^2*C*a^7*b^12 - 60729*A^2*C*a^8*b^11 + 29513*A^2*C*a^9*b^10 + 53039*A^2*C*a^10*b^9 - 24901*A^2*C*a^11*b^8 - 25211*A^2*C*a^12*b^7 + 9657*A^2*C*a^13*b^6 + 4359*A^2*C*a^14*b^5 + 192*A^2*C*a^15*b^4 + 448*A^2*C*a^16*b^3 - 8*A^2*C*a^17*b^2 - 96*B*C^2*a^5*b^14 + 48*B*C^2*a^6*b^13 + 624*B*C^2*a^7*b^12 - 276*B*C^2*a^8*b^11 - 1692*B*C^2*a^9*b^10 + 816*B*C^2*a^10*b^9 + 2628*B*C^2*a^11*b^8 - 1452*B*C^2*a^12*b^7 - 2532*B*C^2*a^13*b^6 + 1380*B*C^2*a^14*b^5 + 1404*B*C^2*a^15*b^4 - 816*B*C^2*a^16*b^3 - 336*B*C^2*a^17*b^2 + 384*B^2*C*a^4*b^15 - 192*B^2*C*a^5*b^14 - 2496*B^2*C*a^6*b^13 + 1152*B^2*C*a^7*b^12 + 6816*B^2*C*a^8*b^11 - 3264*B^2*C*a^9*b^10 - 10464*B^2*C*a^10*b^9 + 5298*B^2*C*a^11*b^8 + 9696*B^2*C*a^12*b^7 - 4752*B^2*C*a^13*b^6 - 5088*B^2*C*a^14*b^5 + 2208*B^2*C*a^15*b^4 + 1152*B^2*C*a^16*b^3 - 1920*A*B*C*a^3*b^16 + 960*A*B*C*a^4*b^15 + 12384*A*B*C*a^5*b^14 - 5712*A*B*C*a^6*b^13 - 33456*A*B*C*a^7*b^12 + 15852*A*B*C*a^8*b^11 + 50436*A*B*C*a^9*b^10 - 25034*A*B*C*a^10*b^9 - 45404*A*B*C*a^11*b^8 + 21788*A*B*C*a^12*b^7 + 22716*A*B*C*a^13*b^6 - 9292*A*B*C*a^14*b^5 - 4548*A*B*C*a^15*b^4 - 112*A*B*C*a^16*b^3 - 208*A*B*C*a^17*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(A^2*a^18 + 800*A^2*b^18 + 4*C^2*a^18 - 800*A^2*a*b^17 - 2*A^2*a^17*b - 8*C^2*a^17*b - 4720*A^2*a^2*b^16 + 4720*A^2*a^3*b^15 + 11522*A^2*a^4*b^14 - 11522*A^2*a^5*b^13 - 14837*A^2*a^6*b^12 + 14812*A^2*a^7*b^11 + 10385*A^2*a^8*b^10 - 10430*A^2*a^9*b^9 - 3325*A^2*a^10*b^8 + 3640*A^2*a^11*b^7 - 45*A^2*a^12*b^6 - 350*A^2*a^13*b^5 + 209*A^2*a^14*b^4 - 68*A^2*a^15*b^3 + 35*A^2*a^16*b^2 + 128*B^2*a^2*b^16 - 128*B^2*a^3*b^15 - 768*B^2*a^4*b^14 + 768*B^2*a^5*b^13 + 1920*B^2*a^6*b^12 - 1920*B^2*a^7*b^11 - 2600*B^2*a^8*b^10 + 2560*B^2*a^9*b^9 + 2025*B^2*a^10*b^8 - 1920*B^2*a^11*b^7 - 824*B^2*a^12*b^6 + 768*B^2*a^13*b^5 + 80*B^2*a^14*b^4 - 128*B^2*a^15*b^3 + 64*B^2*a^16*b^2 + 8*C^2*a^4*b^14 - 8*C^2*a^5*b^13 - 48*C^2*a^6*b^12 + 48*C^2*a^7*b^11 + 117*C^2*a^8*b^10 - 120*C^2*a^9*b^9 - 164*C^2*a^10*b^8 + 160*C^2*a^11*b^7 + 156*C^2*a^12*b^6 - 120*C^2*a^13*b^5 - 92*C^2*a^14*b^4 + 48*C^2*a^15*b^3 + 44*C^2*a^16*b^2 + 4*A*C*a^18 - 640*A*B*a*b^17 - 16*A*B*a^17*b - 8*A*C*a^17*b - 32*B*C*a^17*b + 640*A*B*a^2*b^16 + 3808*A*B*a^3*b^15 - 3808*A*B*a^4*b^14 - 9408*A*B*a^5*b^13 + 9408*A*B*a^6*b^12 + 12430*A*B*a^7*b^11 - 12320*A*B*a^8*b^10 - 9200*A*B*a^9*b^9 + 8960*A*B*a^10*b^8 + 3360*A*B*a^11*b^7 - 3360*A*B*a^12*b^6 - 144*A*B*a^13*b^5 + 448*A*B*a^14*b^4 - 240*A*B*a^15*b^3 + 32*A*B*a^16*b^2 + 160*A*C*a^2*b^16 - 160*A*C*a^3*b^15 - 952*A*C*a^4*b^14 + 952*A*C*a^5*b^13 + 2322*A*C*a^6*b^12 - 2352*A*C*a^7*b^11 - 3124*A*C*a^8*b^10 + 3080*A*C*a^9*b^9 + 2588*A*C*a^10*b^8 - 2240*A*C*a^11*b^7 - 1284*A*C*a^12*b^6 + 840*A*C*a^13*b^5 + 276*A*C*a^14*b^4 - 112*A*C*a^15*b^3 + 60*A*C*a^16*b^2 - 64*B*C*a^3*b^15 + 64*B*C*a^4*b^14 + 384*B*C*a^5*b^13 - 384*B*C*a^6*b^12 - 948*B*C*a^7*b^11 + 960*B*C*a^8*b^10 + 1306*B*C*a^9*b^9 - 1280*B*C*a^10*b^8 - 1128*B*C*a^11*b^7 + 960*B*C*a^12*b^6 + 592*B*C*a^13*b^5 - 384*B*C*a^14*b^4 - 160*B*C*a^15*b^3 + 64*B*C*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*a^27 + 8*C*a^27 - 80*A*a^12*b^15 + 40*A*a^13*b^14 + 516*A*a^14*b^13 - 248*A*a^15*b^12 - 1404*A*a^16*b^11 + 640*A*a^17*b^10 + 2076*A*a^18*b^9 - 896*A*a^19*b^8 - 1764*A*a^20*b^7 + 724*A*a^21*b^6 + 816*A*a^22*b^5 - 316*A*a^23*b^4 - 160*A*a^24*b^3 + 52*A*a^25*b^2 + 32*B*a^13*b^14 - 16*B*a^14*b^13 - 208*B*a^15*b^12 + 100*B*a^16*b^11 + 572*B*a^17*b^10 - 252*B*a^18*b^9 - 868*B*a^19*b^8 + 348*B*a^20*b^7 + 772*B*a^21*b^6 - 292*B*a^22*b^5 - 380*B*a^23*b^4 + 144*B*a^24*b^3 + 80*B*a^25*b^2 - 8*C*a^14*b^13 + 4*C*a^15*b^12 + 52*C*a^16*b^11 - 28*C*a^17*b^10 - 140*C*a^18*b^9 + 60*C*a^19*b^8 + 220*C*a^20*b^7 - 60*C*a^21*b^6 - 220*C*a^22*b^5 + 40*C*a^23*b^4 + 128*C*a^24*b^3 - 24*C*a^25*b^2 - 32*B*a^26*b - 32*C*a^26*b))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^8 - 8*C*a^8 - 69*A*a^2*b^6 + 84*A*a^4*b^4 - 40*A*a^6*b^2 + 28*B*a^3*b^5 - 35*B*a^5*b^3 + 2*C*a^2*b^6 - 7*C*a^4*b^4 + 8*C*a^6*b^2 - 8*B*a*b^7 + 20*B*a^7*b)*1i)/(d*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))","B"
1009,1,25,23,1.872729,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x)),x)","\frac{C\,b\,\sin\left(c+d\,x\right)+d\,x\,\left(B\,b-C\,a\right)}{d}","Not used",1,"(C*b*sin(c + d*x) + d*x*(B*b - C*a))/d","B"
1010,1,248,61,2.496429,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^2,x)","\frac{2\,C\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^2-4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B\,C\,a\,b+3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,a^2+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,C^2\,b^2}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B^2\,b^2-4\,B\,C\,a\,b+3\,C^2\,a^2+C^2\,b^2\right)}\right)}{d}-\frac{2\,B\,b\,\mathrm{atanh}\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}\right)}{d\,\sqrt{b^2-a^2}}+\frac{4\,C\,a\,\mathrm{atanh}\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}\right)}{d\,\sqrt{b^2-a^2}}","Not used",1,"(2*C*atan((B^2*b^2*sin(c/2 + (d*x)/2) + 3*C^2*a^2*sin(c/2 + (d*x)/2) + C^2*b^2*sin(c/2 + (d*x)/2) - 4*B*C*a*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(B^2*b^2 + 3*C^2*a^2 + C^2*b^2 - 4*B*C*a*b))))/d - (2*B*b*atanh((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))))/(d*(b^2 - a^2)^(1/2)) + (4*C*a*atanh((a*sin(c/2 + (d*x)/2) - b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))))/(d*(b^2 - a^2)^(1/2))","B"
1011,1,124,110,2.182539,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^3,x)","-\frac{2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a+b}\,\sqrt{a-b}}\right)\,\left(C\,a^2-B\,a\,b+C\,b^2\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^2-2\,C\,a\,b\right)}{d\,\left(a+b\right)\,\left(a-b\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"- (2*atan((tan(c/2 + (d*x)/2)*(2*a - 2*b))/(2*(a + b)^(1/2)*(a - b)^(1/2)))*(C*a^2 + C*b^2 - B*a*b))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (2*tan(c/2 + (d*x)/2)*(B*b^2 - 2*C*a*b))/(d*(a + b)*(a - b)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
1012,1,268,175,5.010685,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,C\,b^3-B\,b^3-4\,B\,a\,b^2+2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(B\,b^3+2\,C\,b^3-4\,B\,a\,b^2-2\,C\,a\,b^2+6\,C\,a^2\,b\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(-2\,C\,a^3+2\,B\,a^2\,b-4\,C\,a\,b^2+B\,b^3\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(2*C*b^3 - B*b^3 - 4*B*a*b^2 + 2*C*a*b^2 + 6*C*a^2*b))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(B*b^3 + 2*C*b^3 - 4*B*a*b^2 - 2*C*a*b^2 + 6*C*a^2*b))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(B*b^3 - 2*C*a^3 + 2*B*a^2*b - 4*C*a*b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
1013,1,462,249,5.411795,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^5,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,b^4+C\,b^4+6\,B\,a^2\,b^2+5\,C\,a^2\,b^2-3\,B\,a\,b^3-8\,C\,a\,b^3-8\,C\,a^3\,b\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(C\,b^4-2\,B\,b^4-6\,B\,a^2\,b^2+5\,C\,a^2\,b^2-3\,B\,a\,b^3+8\,C\,a\,b^3+8\,C\,a^3\,b\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-12\,C\,a^3\,b+9\,B\,a^2\,b^2-8\,C\,a\,b^3+B\,b^4\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(2\,C\,a^4-2\,B\,a^3\,b+7\,C\,a^2\,b^2-3\,B\,a\,b^3+C\,b^4\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(2*B*b^4 + C*b^4 + 6*B*a^2*b^2 + 5*C*a^2*b^2 - 3*B*a*b^3 - 8*C*a*b^3 - 8*C*a^3*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)) - (tan(c/2 + (d*x)/2)^5*(C*b^4 - 2*B*b^4 - 6*B*a^2*b^2 + 5*C*a^2*b^2 - 3*B*a*b^3 + 8*C*a*b^3 + 8*C*a^3*b))/((a + b)^3*(a - b)) + (4*tan(c/2 + (d*x)/2)^3*(B*b^4 + 9*B*a^2*b^2 - 8*C*a*b^3 - 12*C*a^3*b))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(a + b)^(1/2)*(a - b)^(7/2)))*(2*C*a^4 + C*b^4 + 7*C*a^2*b^2 - 3*B*a*b^3 - 2*B*a^3*b))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
1014,0,-1,416,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1015,0,-1,321,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1016,0,-1,237,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1017,0,-1,240,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x), x)","F"
1018,0,-1,217,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
1019,0,-1,299,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
1020,0,-1,399,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4, x)","F"
1021,0,-1,518,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1022,0,-1,408,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1023,0,-1,315,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1024,0,-1,306,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x), x)","F"
1025,0,-1,286,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
1026,0,-1,307,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
1027,0,-1,399,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4, x)","F"
1028,0,-1,503,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5, x)","F"
1029,0,-1,629,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1030,0,-1,510,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1031,0,-1,402,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1032,0,-1,383,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x), x)","F"
1033,0,-1,357,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^2, x)","F"
1034,0,-1,372,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^3, x)","F"
1035,0,-1,407,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^4, x)","F"
1036,0,-1,502,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^5, x)","F"
1037,0,-1,624,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6,x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^6, x)","F"
1038,0,-1,285,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(3/2)*(C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x)),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(-C\,a^2+B\,a\,b+C\,b^2\,{\cos\left(c+d\,x\right)}^2+B\,b^2\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)*(C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x)), x)","F"
1039,0,-1,221,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)*(C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x)),x)","\int \sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(-C\,a^2+B\,a\,b+C\,b^2\,{\cos\left(c+d\,x\right)}^2+B\,b^2\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((a + b*cos(c + d*x))^(1/2)*(C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x)), x)","F"
1040,0,-1,344,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1041,0,-1,258,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1042,1,252,188,2.240729,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}+\frac{2\,C\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{3\,b\,d}+\frac{2\,B\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)-a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{b\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}+\frac{2\,C\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}\,\left(\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(2\,a^2+b^2\right)-2\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)\right)}{3\,b^2\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2)) + (2*C*sin(c + d*x)*(a + b*cos(c + d*x))^(1/2))/(3*b*d) + (2*B*(ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b) - a*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b)))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(b*d*(a + b*cos(c + d*x))^(1/2)) + (2*C*((a + b*cos(c + d*x))/(a + b))^(1/2)*(ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*(2*a^2 + b^2) - 2*a*ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b)))/(3*b^2*d*(a + b*cos(c + d*x))^(1/2))","B"
1043,0,-1,189,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\cos\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1044,0,-1,220,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)), x)","F"
1045,0,-1,303,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)), x)","F"
1046,0,-1,405,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^4*(a + b*cos(c + d*x))^(1/2)), x)","F"
1047,0,-1,426,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1048,0,-1,280,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1049,0,-1,219,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(3/2), x)","F"
1050,0,-1,271,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1051,0,-1,313,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)), x)","F"
1052,0,-1,416,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)), x)","F"
1053,0,-1,622,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1054,0,-1,453,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1055,0,-1,359,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1056,0,-1,333,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(5/2), x)","F"
1057,0,-1,401,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\cos\left(c+d\,x\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)), x)","F"
1058,0,-1,461,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^2\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)), x)","F"
1059,0,-1,572,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^3\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2)), x)","F"
1060,0,-1,449,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(7/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(a + b*cos(c + d*x))^(7/2), x)","F"
1061,1,303,167,2.583032,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,C\,b\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{3\,d}+\frac{2\,C\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}\,\left(\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(2\,a^2+b^2\right)-2\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)\right)}{3\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}-\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}+\frac{2\,B\,b\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)-a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}+\frac{2\,B\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*C*b*sin(c + d*x)*(a + b*cos(c + d*x))^(1/2))/(3*d) + (2*C*((a + b*cos(c + d*x))/(a + b))^(1/2)*(ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*(2*a^2 + b^2) - 2*a*ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b)))/(3*d*(a + b*cos(c + d*x))^(1/2)) - (2*C*a^2*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2)) + (2*B*b*(ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b) - a*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b)))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2)) + (2*B*a*b*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2))","B"
1062,0,-1,124,0.000000,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{-C\,a^2+B\,a\,b+C\,b^2\,{\cos\left(c+d\,x\right)}^2+B\,b^2\,\cos\left(c+d\,x\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^(3/2), x)","F"
1063,0,-1,180,0.000000,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{-C\,a^2+B\,a\,b+C\,b^2\,{\cos\left(c+d\,x\right)}^2+B\,b^2\,\cos\left(c+d\,x\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^(5/2), x)","F"
1064,0,-1,271,0.000000,"\text{Not used}","int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^(7/2),x)","\int \frac{-C\,a^2+B\,a\,b+C\,b^2\,{\cos\left(c+d\,x\right)}^2+B\,b^2\,\cos\left(c+d\,x\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((C*b^2*cos(c + d*x)^2 - C*a^2 + B*a*b + B*b^2*cos(c + d*x))/(a + b*cos(c + d*x))^(7/2), x)","F"
1065,1,254,190,2.982548,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,A\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*A*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
1066,1,216,154,2.791578,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,B\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,B\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*B*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*B*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1067,1,162,116,2.634162,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{2\,B\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,C\,a\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,C\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*C*a*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticE(c/2 + (d*x)/2, 2))/d - (2*C*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1068,1,146,107,2.933408,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{2\,C\,b\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*C*b*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1069,1,184,111,3.767506,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\frac{2\,B\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1070,1,217,152,4.461746,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{6\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*a*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*C*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1071,1,223,190,5.106973,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{30\,A\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,C\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+42\,B\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,A\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,C\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+10\,B\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(30*A*a*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*C*a*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 42*B*a*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*A*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*C*b*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 10*B*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
1072,1,401,305,3.413420,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,A\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}-\frac{2\,B\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,A\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) - (2*B*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*A*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (4*A*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
1073,1,366,251,3.313017,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,B\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
1074,1,303,203,3.232558,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{A\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,a^2\,\left(\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,A\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}-\frac{2\,B\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(A*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*a^2*(cos(c + d*x)^(1/2)*sin(c + d*x) + ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*A*a*b*ellipticE(c/2 + (d*x)/2, 2))/d - (2*B*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1075,1,260,189,3.584416,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{B\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,A\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(B*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*A*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*B*a*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1076,1,268,180,3.975378,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\frac{C\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(C*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*C*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*B*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1077,1,310,200,5.002957,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{6\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,A\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,A\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(6*A*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*A*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*A*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*B*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*C*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1078,1,343,248,5.452466,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{30\,A\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,A\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,A\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,B\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+20\,B\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(30*A*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*A*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 84*A*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*B*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*B*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 20*B*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1079,1,851,302,5.995823,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{28\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{12\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{36\,A\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,A\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{36\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{45\,C\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{72\,B\,a\,b\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{18\,B\,a\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{4\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{3\,B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{7\,B\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{8\,A\,a\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{6\,A\,a\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{14\,C\,a\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{21\,d}+\frac{8\,\left(\frac{B\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,A\,a\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,A\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,A\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{18\,B\,a\,b\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}\right)}{135\,d}","Not used",1,"(2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((28*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (12*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^2*sin(c + d*x))/(cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + (36*A*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*A*b^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (36*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (45*C*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (72*B*a*b*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (18*B*a*b*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((4*B*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (3*B*a^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (7*B*b^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (8*A*a*b*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (6*A*a*b*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (14*C*a*b*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2))))/(21*d) + (8*((B*a^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*A*a*b*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)))*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((7*A*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (5*A*a^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*A*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*C*a^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (18*B*a*b*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2))))/(135*d)","B"
1080,1,514,361,3.798393,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,\left(A\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{B\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^3*ellipticE(c/2 + (d*x)/2, 2) + A*a^2*b*ellipticF(c/2 + (d*x)/2, 2) + A*a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (B*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (6*A*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*a*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a^2*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a*b^2*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2))","B"
1081,1,452,296,3.488802,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{2\,\left(B\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,A\,a\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a^2\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^3*ellipticE(c/2 + (d*x)/2, 2) + B*a^2*b*ellipticF(c/2 + (d*x)/2, 2) + B*a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*A*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (3*A*a*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*B*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a^2*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*a*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2))","B"
1082,1,398,279,3.400311,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{2\,\left(C\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{A\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,A\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,B\,a\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,C\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^3*ellipticE(c/2 + (d*x)/2, 2) + C*a^2*b*ellipticF(c/2 + (d*x)/2, 2) + C*a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (A*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*A*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*A*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (6*B*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (3*B*a*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*B*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (6*C*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1083,1,379,271,4.072083,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\frac{2\,\left(A\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{B\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,C\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,B\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{3\,C\,a\,b^2\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,A\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*b^3*ellipticE(c/2 + (d*x)/2, 2) + 3*A*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + (B*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*C*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*B*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*B*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (3*C*a*b^2*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (6*A*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1084,1,414,273,5.384083,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{2\,\left(B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,B\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{C\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,A\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,C\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,A\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,A\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*b^3*ellipticE(c/2 + (d*x)/2, 2) + 3*B*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + (C*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*A*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*C*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*C*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (6*A*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*A*a^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1085,1,442,294,7.091630,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{2\,\left(C\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,C\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{\frac{2\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,A\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+\frac{6\,A\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,B\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,B\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*b^3*ellipticE(c/2 + (d*x)/2, 2) + 3*C*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + ((2*A*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*A*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 2*A*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + (6*A*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5)/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*B*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*B*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a^2*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1086,1,463,357,7.493766,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{70\,A\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{9}{4},\frac{1}{2};\ -\frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)+210\,A\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+378\,A\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+270\,A\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{315\,d\,{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{\frac{2\,B\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,B\,b^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+2\,B\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+\frac{6\,B\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}+\frac{2\,C\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{6\,C\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(70*A*a^3*sin(c + d*x)*hypergeom([-9/4, 1/2], -5/4, cos(c + d*x)^2) + 210*A*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 378*A*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 270*A*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(315*d*cos(c + d*x)^(9/2)*(1 - cos(c + d*x)^2)^(1/2)) + ((2*B*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*B*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + 2*B*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + (6*B*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5)/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (2*C*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^3*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (6*C*a*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1087,1,903,477,4.388097,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{B\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{136\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{23}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{11\,C\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{9\,C\,a^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{42\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{21945\,d}-\frac{2\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{15}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{165\,C\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{52\,C\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{36\,C\,a^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{77\,C\,b^4\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{630\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{168\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{15/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{1155\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{13\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{9\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{117\,d}+\frac{2\,A\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a^3\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{160\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{21}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{663\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{12\,A\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,B\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(B*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (136*hypergeom([1/2, 15/4], 23/4, cos(c + d*x)^2)*((11*C*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (9*C*a^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (42*C*a^2*b^2*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2)))/(21945*d) - (2*hypergeom([1/2, 15/4], 19/4, cos(c + d*x)^2)*((165*C*a^4*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (52*C*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (36*C*a^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (77*C*b^4*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (630*C*a^2*b^2*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (168*C*a^2*b^2*cos(c + d*x)^(15/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2)))/(1155*d) - (8*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2)*((13*C*a^3*b*cos(c + d*x)^(9/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) + (9*C*a*b^3*cos(c + d*x)^(13/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (4*C*a^3*b*cos(c + d*x)^(13/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2)))/(117*d) + (2*A*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (4*A*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (8*A*a*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a^3*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (160*C*a^3*b*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 21/4, cos(c + d*x)^2))/(663*d*(sin(c + d*x)^2)^(1/2)) - (12*A*a^2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*B*a^2*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2))","B"
1088,1,600,404,3.955995,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\frac{2\,\left(A\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,A\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,A\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,A\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{C\,a^4\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{2\,B\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}-\frac{2\,A\,b^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,A\,a\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a^3\,b\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{12\,B\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(A*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*A*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + 2*A*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*A*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (C*a^4*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (2*B*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d - (2*A*b^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2)) - (8*A*a*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a^3*b*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a*b^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (12*B*a^2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*C*a^2*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2))","B"
1089,1,547,379,3.966235,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\frac{2\,\left(B\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,B\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,B\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,B\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{2\,C\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,A\,a\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{4\,C\,a^3\,b\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,A\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,A\,b^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,B\,a\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{12\,C\,a^2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*B*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + 2*B*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*B*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (2*C*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*A*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*A*a*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (4*C*a^3*b*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*A*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*A*b^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*B*b^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (8*B*a*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (8*C*a*b^3*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (12*C*a^2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1090,1,516,373,4.294415,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\frac{2\,\left(C\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,C\,a^3\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,C\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,C\,a^2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}+\frac{2\,\left(A\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,A\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+A\,b^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,A\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{8\,B\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,B\,a\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,B\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,B\,b^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,C\,a\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*C*a^3*b*ellipticE(c/2 + (d*x)/2, 2) + 2*C*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2) + 2*C*a^2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/d + (2*(A*b^4*ellipticF(c/2 + (d*x)/2, 2) + 12*A*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + A*b^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*A*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (8*B*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*B*a*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*B*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*B*b^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) + (8*A*a^3*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (8*C*a*b^3*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
1091,1,524,386,6.011141,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\frac{2\,\left(B\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,B\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,b^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,B\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,b^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,A\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,C\,a^3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,C\,a\,b^3\,\left(\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3}+\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3}\right)}{d}+\frac{12\,C\,a^2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,C\,b^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(B*b^4*ellipticF(c/2 + (d*x)/2, 2) + 12*B*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + B*b^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*B*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*b^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*A*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (8*C*a^3*b*ellipticF(c/2 + (d*x)/2, 2))/d + (4*C*a*b^3*((2*cos(c + d*x)^(1/2)*sin(c + d*x))/3 + (2*ellipticF(c/2 + (d*x)/2, 2))/3))/d + (12*C*a^2*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*C*b^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) + (8*A*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a^3*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (12*A*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1092,1,559,383,8.002614,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\frac{2\,\left(C\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+12\,C\,a\,b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+C\,b^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)+18\,C\,a^2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{3\,d}+\frac{2\,A\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,b^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,B\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(C*b^4*ellipticF(c/2 + (d*x)/2, 2) + 12*C*a*b^3*ellipticE(c/2 + (d*x)/2, 2) + C*b^4*cos(c + d*x)^(1/2)*sin(c + d*x) + 18*C*a^2*b^2*ellipticF(c/2 + (d*x)/2, 2)))/(3*d) + (2*A*b^4*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*b^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*B*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*A*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*A*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*A*a^3*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^3*b*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a^2*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (12*B*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1093,1,866,401,10.081318,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{3\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{21\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,A\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{28\,A\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{45\,A\,b^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{216\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,B\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,b^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,C\,a\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{32\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,B\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(8*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((7*A*a*b^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (3*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((7*A*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (5*A*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (54*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((28*A*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (12*A*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*A*a^4*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2)) + (45*A*b^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (216*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (54*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (2*B*b^4*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*b^4*ellipticE(c/2 + (d*x)/2, 2))/d + (8*C*a*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (2*C*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (32*A*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*B*a^3*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a^2*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (12*C*a^2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
1094,1,1161,475,10.597845,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(13/2),x)","\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{9\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,B\,a\,b^3\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,B\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{3\,B\,a^3\,b\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{21\,d}+\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{9\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{7\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{66\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{231\,d}-\frac{8\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{7\,B\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{135\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{36\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{20\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{21\,A\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{11/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{77\,A\,b^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{264\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{198\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{231\,d}+\frac{2\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)\,\left(\frac{28\,B\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{12\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{5\,B\,a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{45\,B\,b^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{216\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{54\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)}{45\,d}+\frac{2\,C\,b^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,C\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{32\,A\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{32\,B\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{5}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{21\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,C\,a^3\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,C\,a^2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(8*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2)*((9*A*a*b^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (4*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*A*a^3*b*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (8*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((7*B*a*b^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*B*a^3*b*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (3*B*a^3*b*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))))/(21*d) + (8*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2)*((9*A*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (7*A*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (66*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))))/(231*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((7*B*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (5*B*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (54*B*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))))/(135*d) + (2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((36*A*a^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (20*A*a^4*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) + (21*A*a^4*sin(c + d*x))/(cos(c + d*x)^(11/2)*(sin(c + d*x)^2)^(1/2)) + (77*A*b^4*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (264*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (198*A*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))))/(231*d) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((28*B*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (12*B*a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (5*B*a^4*sin(c + d*x))/(cos(c + d*x)^(9/2)*(sin(c + d*x)^2)^(1/2)) + (45*B*b^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (216*B*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (54*B*a^2*b^2*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))))/(45*d) + (2*C*b^4*ellipticF(c/2 + (d*x)/2, 2))/d + (2*C*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2)) - (32*A*a^3*b*sin(c + d*x)*hypergeom([-5/4, 1/2], 3/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (32*B*a^3*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 5/4, cos(c + d*x)^2))/(21*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (8*C*a^3*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (4*C*a^2*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
1095,0,-1,285,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1096,0,-1,210,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1097,0,-1,147,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1098,0,-1,97,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))), x)","F"
1099,0,-1,118,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))), x)","F"
1100,0,-1,158,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))), x)","F"
1101,0,-1,234,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))), x)","F"
1102,0,-1,318,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{9/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))), x)","F"
1103,0,-1,445,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
1104,0,-1,343,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
1105,0,-1,251,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
1106,0,-1,243,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
1107,0,-1,306,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
1108,0,-1,392,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
1109,0,-1,654,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
1110,0,-1,536,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
1111,0,-1,423,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
1112,0,-1,418,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
1113,0,-1,413,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
1114,0,-1,502,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
1115,0,-1,609,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
1116,0,-1,586,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1117,0,-1,483,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1118,0,-1,449,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1119,0,-1,407,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
1120,0,-1,360,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2), x)","F"
1121,0,-1,447,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2), x)","F"
1122,0,-1,704,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1123,0,-1,587,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1124,0,-1,535,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1125,0,-1,528,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
1126,0,-1,490,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2), x)","F"
1127,0,-1,450,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2), x)","F"
1128,0,-1,550,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2), x)","F"
1129,0,-1,834,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1130,0,-1,700,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(1/2), x)","F"
1131,0,-1,647,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(3/2), x)","F"
1132,0,-1,622,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(5/2), x)","F"
1133,0,-1,643,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(7/2), x)","F"
1134,0,-1,580,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(9/2), x)","F"
1135,0,-1,552,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/cos(c + d*x)^(11/2), x)","F"
1136,0,-1,593,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1137,0,-1,485,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1138,0,-1,401,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1139,0,-1,347,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1140,0,-1,293,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1141,0,-1,372,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1142,0,-1,466,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{9/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(9/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1143,0,-1,473,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(B\,b\,{\cos\left(c+d\,x\right)}^2+\left(A\,b+B\,a\right)\,\cos\left(c+d\,x\right)+A\,a\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1144,0,-1,256,0.000000,"\text{Not used}","int((a + a*cos(c + d*x) + 2*b*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{2\,b\,{\cos\left(c+d\,x\right)}^2+a\,\cos\left(c+d\,x\right)+a}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*cos(c + d*x) + 2*b*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1145,0,-1,660,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1146,0,-1,535,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1147,0,-1,436,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1148,0,-1,322,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1149,0,-1,424,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1150,0,-1,545,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1151,0,-1,723,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1152,0,-1,589,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1153,0,-1,457,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
1154,0,-1,495,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
1155,0,-1,620,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
1156,0,-1,367,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1157,0,-1,235,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\cos\left(c+d\,x\right)}^m\,\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1158,0,-1,372,0.000000,"\text{Not used}","int((cos(c + d*x)^m*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^m\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)^m*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1159,0,-1,564,0.000000,"\text{Not used}","int((cos(c + d*x)^m*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^m\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^m*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
1160,0,-1,205,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x)), x)","F"
1161,0,-1,172,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x)), x)","F"
1162,0,-1,135,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x)), x)","F"
1163,0,-1,135,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x)), x)","F"
1164,0,-1,141,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+a\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x)), x)","F"
1165,0,-1,174,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\left(a+a\,\cos\left(c+d\,x\right)\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(1/2), x)","F"
1166,0,-1,205,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\left(a+a\,\cos\left(c+d\,x\right)\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(3/2), x)","F"
1167,0,-1,270,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^2, x)","F"
1168,0,-1,237,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^2, x)","F"
1169,0,-1,196,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2, x)","F"
1170,0,-1,196,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2, x)","F"
1171,0,-1,200,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2, x)","F"
1172,0,-1,204,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2, x)","F"
1173,0,-1,237,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2), x)","F"
1174,0,-1,270,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2), x)","F"
1175,0,-1,319,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^3, x)","F"
1176,0,-1,286,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^3, x)","F"
1177,0,-1,253,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3, x)","F"
1178,0,-1,253,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3, x)","F"
1179,0,-1,251,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3, x)","F"
1180,0,-1,257,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3, x)","F"
1181,0,-1,253,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3, x)","F"
1182,0,-1,286,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2), x)","F"
1183,0,-1,319,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2), x)","F"
1184,0,-1,232,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x)), x)","F"
1185,0,-1,190,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x)), x)","F"
1186,0,-1,153,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x)), x)","F"
1187,0,-1,123,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x)), x)","F"
1188,0,-1,162,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))), x)","F"
1189,0,-1,199,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))), x)","F"
1190,0,-1,232,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))), x)","F"
1191,0,-1,229,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^2, x)","F"
1192,0,-1,195,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^2, x)","F"
1193,0,-1,165,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^2, x)","F"
1194,0,-1,166,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
1195,0,-1,201,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
1196,0,-1,236,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
1197,0,-1,282,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^3, x)","F"
1198,0,-1,259,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^3, x)","F"
1199,0,-1,224,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^3, x)","F"
1200,0,-1,220,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
1201,0,-1,218,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
1202,0,-1,249,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
1203,0,-1,290,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3), x)","F"
1204,1,581,213,7.304817,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^(1/2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(256\,A+336\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(256\,A+336\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(1152\,A+1512\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(1152\,A+1512\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2016\,A+2016\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2016\,A+2016\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}+\frac{C\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(256*A + 336*C)*1i)/(315*d) - (exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(256*A + 336*C)*1i)/(315*d) + (exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1152*A + 1512*C)*1i)/(315*d) - (exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1152*A + 1512*C)*1i)/(315*d) + (exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2016*A + 2016*C)*1i)/(315*d) - (exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2016*A + 2016*C)*1i)/(315*d) - (C*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d) + (C*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d)))/(exp(c*1i + d*x*1i) + 4*exp(c*2i + d*x*2i) + 4*exp(c*3i + d*x*3i) + 6*exp(c*4i + d*x*4i) + 6*exp(c*5i + d*x*5i) + 4*exp(c*6i + d*x*6i) + 4*exp(c*7i + d*x*7i) + exp(c*8i + d*x*8i) + exp(c*9i + d*x*9i) + 1)","B"
1205,1,441,168,6.107253,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(1/2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(\frac{32\,A}{35}+\frac{4\,C}{3}\right)\,1{}\mathrm{i}}{d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(96\,A+140\,C\right)\,1{}\mathrm{i}}{105\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(336\,A+280\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(336\,A+280\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,4{}\mathrm{i}}{3\,d}+\frac{C\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,4{}\mathrm{i}}{3\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((32*A)/35 + (4*C)/3)*1i)/d - (exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(96*A + 140*C)*1i)/(105*d) + (exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(336*A + 280*C)*1i)/(105*d) - (exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(336*A + 280*C)*1i)/(105*d) - (C*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*4i)/(3*d) + (C*exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*4i)/(3*d)))/(exp(c*1i + d*x*1i) + 3*exp(c*2i + d*x*2i) + 3*exp(c*3i + d*x*3i) + 3*exp(c*4i + d*x*4i) + 3*exp(c*5i + d*x*5i) + exp(c*6i + d*x*6i) + exp(c*7i + d*x*7i) + 1)","B"
1206,1,172,123,2.487098,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(28\,A\,\sin\left(c+d\,x\right)+30\,C\,\sin\left(c+d\,x\right)+16\,A\,\sin\left(2\,c+2\,d\,x\right)+36\,A\,\sin\left(3\,c+3\,d\,x\right)+8\,A\,\sin\left(4\,c+4\,d\,x\right)+8\,A\,\sin\left(5\,c+5\,d\,x\right)+45\,C\,\sin\left(3\,c+3\,d\,x\right)+15\,C\,\sin\left(5\,c+5\,d\,x\right)\right)}{15\,d\,\left(10\,\cos\left(c+d\,x\right)+8\,\cos\left(2\,c+2\,d\,x\right)+5\,\cos\left(3\,c+3\,d\,x\right)+2\,\cos\left(4\,c+4\,d\,x\right)+\cos\left(5\,c+5\,d\,x\right)+6\right)}","Not used",1,"(2*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(28*A*sin(c + d*x) + 30*C*sin(c + d*x) + 16*A*sin(2*c + 2*d*x) + 36*A*sin(3*c + 3*d*x) + 8*A*sin(4*c + 4*d*x) + 8*A*sin(5*c + 5*d*x) + 45*C*sin(3*c + 3*d*x) + 15*C*sin(5*c + 5*d*x)))/(15*d*(10*cos(c + d*x) + 8*cos(2*c + 2*d*x) + 5*cos(3*c + 3*d*x) + 2*cos(4*c + 4*d*x) + cos(5*c + 5*d*x) + 6))","B"
1207,0,-1,136,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
1208,0,-1,137,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
1209,0,-1,144,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
1210,0,-1,189,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2), x)","F"
1211,0,-1,234,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2), x)","F"
1212,1,387,266,6.886896,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^(3/2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-\frac{16\,C\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,d}-\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A+23\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{15\,d}+\frac{48\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(28\,A+27\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{35\,d}+\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(112\,A+143\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{105\,d}+\frac{32\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(112\,A+143\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{1155\,d}\right)}{20\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+20\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+10\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+10\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((48*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((3*c)/2 + (3*d*x)/2)*(28*A + 27*C)*(a + a*cos(c + d*x))^(1/2))/(35*d) - (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin(c/2 + (d*x)/2)*(12*A + 23*C)*(a + a*cos(c + d*x))^(1/2))/(15*d) - (16*C*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((5*c)/2 + (5*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/(3*d) + (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((7*c)/2 + (7*d*x)/2)*(112*A + 143*C)*(a + a*cos(c + d*x))^(1/2))/(105*d) + (32*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((11*c)/2 + (11*d*x)/2)*(112*A + 143*C)*(a + a*cos(c + d*x))^(1/2))/(1155*d)))/(20*exp((c*11i)/2 + (d*x*11i)/2)*cos(c/2 + (d*x)/2) + 20*exp((c*11i)/2 + (d*x*11i)/2)*cos((3*c)/2 + (3*d*x)/2) + 10*exp((c*11i)/2 + (d*x*11i)/2)*cos((5*c)/2 + (5*d*x)/2) + 10*exp((c*11i)/2 + (d*x*11i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*exp((c*11i)/2 + (d*x*11i)/2)*cos((9*c)/2 + (9*d*x)/2) + 2*exp((c*11i)/2 + (d*x*11i)/2)*cos((11*c)/2 + (11*d*x)/2))","B"
1213,1,320,219,6.536910,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^(3/2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-\frac{8\,C\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,A+13\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{5\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(68\,A+77\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{35\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(136\,A+189\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{315\,d}\right)}{12\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+8\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2)*(12*A + 13*C)*(a + a*cos(c + d*x))^(1/2))/(5*d) - (8*C*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/d + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2)*(68*A + 77*C)*(a + a*cos(c + d*x))^(1/2))/(35*d) + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2)*(136*A + 189*C)*(a + a*cos(c + d*x))^(1/2))/(315*d)))/(12*exp((c*9i)/2 + (d*x*9i)/2)*cos(c/2 + (d*x)/2) + 8*exp((c*9i)/2 + (d*x*9i)/2)*cos((3*c)/2 + (3*d*x)/2) + 8*exp((c*9i)/2 + (d*x*9i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*exp((c*9i)/2 + (d*x*9i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*exp((c*9i)/2 + (d*x*9i)/2)*cos((9*c)/2 + (9*d*x)/2))","B"
1214,1,299,172,6.684539,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(3/2),x)","-\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{4\,C\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{d}-\frac{52\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(4\,A+5\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{15\,d}+\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,A+11\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,d}-\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(104\,A+175\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{105\,d}\right)}{6\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}","Not used",1,"-((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((4*C*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((5*c)/2 + (5*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/d - (52*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((3*c)/2 + (3*d*x)/2)*(4*A + 5*C)*(a + a*cos(c + d*x))^(1/2))/(15*d) + (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin(c/2 + (d*x)/2)*(4*A + 11*C)*(a + a*cos(c + d*x))^(1/2))/(3*d) - (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((7*c)/2 + (7*d*x)/2)*(104*A + 175*C)*(a + a*cos(c + d*x))^(1/2))/(105*d)))/(6*exp((c*7i)/2 + (d*x*7i)/2)*cos(c/2 + (d*x)/2) + 6*exp((c*7i)/2 + (d*x*7i)/2)*cos((3*c)/2 + (3*d*x)/2) + 2*exp((c*7i)/2 + (d*x*7i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*exp((c*7i)/2 + (d*x*7i)/2)*cos((7*c)/2 + (7*d*x)/2))","B"
1215,0,-1,183,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
1216,0,-1,181,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
1217,0,-1,195,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
1218,0,-1,191,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
1219,0,-1,238,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2), x)","F"
1220,0,-1,285,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2), x)","F"
1221,1,897,313,8.024302,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(15/2)*(a + a*cos(c + d*x))^(5/2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(6\,A+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(6\,A+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(348\,A+379\,C\right)\,16{}\mathrm{i}}{105\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(348\,A+379\,C\right)\,16{}\mathrm{i}}{105\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(523\,A+554\,C\right)\,32{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(523\,A+554\,C\right)\,32{}\mathrm{i}}{315\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+20\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+20\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}+{\mathrm{e}}^{c\,12{}\mathrm{i}+d\,x\,12{}\mathrm{i}}+{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 10439*C)*16i)/(45045*d) - (C*a^2*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d) + (C*a^2*exp(c*10i + d*x*10i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d) - (a^2*exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(6*A + 23*C)*16i)/(15*d) + (a^2*exp(c*8i + d*x*8i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(6*A + 23*C)*16i)/(15*d) + (a^2*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(348*A + 379*C)*16i)/(105*d) - (a^2*exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(348*A + 379*C)*16i)/(105*d) + (a^2*exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(523*A + 554*C)*32i)/(315*d) - (a^2*exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(523*A + 554*C)*32i)/(315*d) + (a^2*exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 10439*C)*8i)/(3465*d) - (a^2*exp(c*11i + d*x*11i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 10439*C)*8i)/(3465*d) - (a^2*exp(c*13i + d*x*13i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 10439*C)*16i)/(45045*d)))/(exp(c*1i + d*x*1i) + 6*exp(c*2i + d*x*2i) + 6*exp(c*3i + d*x*3i) + 15*exp(c*4i + d*x*4i) + 15*exp(c*5i + d*x*5i) + 20*exp(c*6i + d*x*6i) + 20*exp(c*7i + d*x*7i) + 15*exp(c*8i + d*x*8i) + 15*exp(c*9i + d*x*9i) + 6*exp(c*10i + d*x*10i) + 6*exp(c*11i + d*x*11i) + exp(c*12i + d*x*12i) + exp(c*13i + d*x*13i) + 1)","B"
1222,1,751,266,6.677968,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^(5/2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(568\,A+759\,C\right)\,4{}\mathrm{i}}{693\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,20{}\mathrm{i}}{3\,d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,20{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(3\,A+5\,C\right)\,16{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(3\,A+5\,C\right)\,16{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(32\,A+33\,C\right)\,8{}\mathrm{i}}{7\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(32\,A+33\,C\right)\,8{}\mathrm{i}}{7\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(71\,A+87\,C\right)\,16{}\mathrm{i}}{63\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(71\,A+87\,C\right)\,16{}\mathrm{i}}{63\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(568\,A+759\,C\right)\,4{}\mathrm{i}}{693\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}+{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(568*A + 759*C)*4i)/(693*d) - (C*a^2*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*20i)/(3*d) + (C*a^2*exp(c*8i + d*x*8i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*20i)/(3*d) - (a^2*exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(3*A + 5*C)*16i)/(3*d) + (a^2*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(3*A + 5*C)*16i)/(3*d) + (a^2*exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(32*A + 33*C)*8i)/(7*d) - (a^2*exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(32*A + 33*C)*8i)/(7*d) + (a^2*exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(71*A + 87*C)*16i)/(63*d) - (a^2*exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(71*A + 87*C)*16i)/(63*d) - (a^2*exp(c*11i + d*x*11i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(568*A + 759*C)*4i)/(693*d)))/(exp(c*1i + d*x*1i) + 5*exp(c*2i + d*x*2i) + 5*exp(c*3i + d*x*3i) + 10*exp(c*4i + d*x*4i) + 10*exp(c*5i + d*x*5i) + 10*exp(c*6i + d*x*6i) + 10*exp(c*7i + d*x*7i) + 5*exp(c*8i + d*x*8i) + 5*exp(c*9i + d*x*9i) + exp(c*10i + d*x*10i) + exp(c*11i + d*x*11i) + 1)","B"
1223,1,721,219,6.847334,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^(5/2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(584\,A+903\,C\right)\,2{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(A+5\,C\right)\,8{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(A+5\,C\right)\,8{}\mathrm{i}}{3\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,2{}\mathrm{i}}{d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,2{}\mathrm{i}}{d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8\,A+11\,C\right)\,12{}\mathrm{i}}{5\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8\,A+11\,C\right)\,12{}\mathrm{i}}{5\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(73\,A+91\,C\right)\,8{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(73\,A+91\,C\right)\,8{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(584\,A+903\,C\right)\,2{}\mathrm{i}}{315\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(584*A + 903*C)*2i)/(315*d) - (a^2*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(A + 5*C)*8i)/(3*d) + (a^2*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(A + 5*C)*8i)/(3*d) - (C*a^2*exp(c*1i + d*x*1i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*2i)/d + (C*a^2*exp(c*8i + d*x*8i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*2i)/d + (a^2*exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8*A + 11*C)*12i)/(5*d) - (a^2*exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8*A + 11*C)*12i)/(5*d) + (a^2*exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(73*A + 91*C)*8i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(73*A + 91*C)*8i)/(35*d) - (a^2*exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(584*A + 903*C)*2i)/(315*d)))/(exp(c*1i + d*x*1i) + 4*exp(c*2i + d*x*2i) + 4*exp(c*3i + d*x*3i) + 6*exp(c*4i + d*x*4i) + 6*exp(c*5i + d*x*5i) + 4*exp(c*6i + d*x*6i) + 4*exp(c*7i + d*x*7i) + exp(c*8i + d*x*8i) + exp(c*9i + d*x*9i) + 1)","B"
1224,0,-1,230,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
1225,0,-1,230,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
1226,0,-1,238,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
1227,0,-1,242,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
1228,0,-1,238,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
1229,0,-1,285,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2), x)","F"
1230,0,-1,332,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2), x)","F"
1231,0,-1,289,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1232,0,-1,244,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1233,0,-1,201,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1234,0,-1,156,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1235,0,-1,175,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1236,0,-1,173,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1237,0,-1,223,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
1238,0,-1,266,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
1239,0,-1,315,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1240,0,-1,268,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1241,0,-1,221,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1242,0,-1,172,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1243,0,-1,185,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1244,0,-1,228,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
1245,0,-1,285,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
1246,0,-1,315,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1247,0,-1,266,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1248,0,-1,219,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1249,0,-1,174,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1250,0,-1,232,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
1251,0,-1,277,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
1252,0,-1,334,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
1253,0,-1,151,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1254,0,-1,123,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1255,0,-1,97,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1256,0,-1,75,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1257,0,-1,101,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1258,0,-1,127,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(1/2), x)","F"
1259,0,-1,151,0.000000,"\text{Not used}","int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(3/2), x)","F"
1260,0,-1,163,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1261,0,-1,127,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1262,0,-1,101,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1263,0,-1,105,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1264,0,-1,133,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(1/2), x)","F"
1265,0,-1,163,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/(1/cos(c + d*x))^(3/2), x)","F"
1266,0,-1,217,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1267,0,-1,179,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1268,0,-1,140,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1269,0,-1,141,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1270,0,-1,147,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+a\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1271,0,-1,184,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(a+a\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1272,0,-1,217,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(a+a\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1273,0,-1,291,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1274,0,-1,255,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1275,0,-1,214,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1276,0,-1,212,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1277,0,-1,212,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1278,0,-1,219,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1279,0,-1,255,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1280,0,-1,291,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1281,0,-1,343,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1282,0,-1,307,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1283,0,-1,271,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1284,0,-1,270,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1285,0,-1,267,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1286,0,-1,269,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1287,0,-1,271,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1288,0,-1,307,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1289,0,-1,343,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1290,0,-1,250,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
1291,0,-1,205,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
1292,0,-1,165,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
1293,0,-1,130,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x)), x)","F"
1294,0,-1,174,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))), x)","F"
1295,0,-1,214,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))), x)","F"
1296,0,-1,250,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))), x)","F"
1297,0,-1,251,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
1298,0,-1,215,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
1299,0,-1,173,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^2, x)","F"
1300,0,-1,179,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
1301,0,-1,220,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
1302,0,-1,254,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
1303,0,-1,310,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
1304,0,-1,277,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
1305,0,-1,233,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^3, x)","F"
1306,0,-1,231,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
1307,0,-1,235,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
1308,0,-1,272,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
1309,0,-1,313,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3), x)","F"
1310,1,599,226,7.431166,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(256\,A+288\,B+336\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{C\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}+\frac{C\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(256\,A+288\,B+336\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(1152\,A+1296\,B+1512\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(1152\,A+1296\,B+1512\,C\right)\,1{}\mathrm{i}}{315\,d}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2016\,A+1008\,B+2016\,C\right)\,1{}\mathrm{i}}{315\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2016\,A+1008\,B+2016\,C\right)\,1{}\mathrm{i}}{315\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(256*A + 288*B + 336*C)*1i)/(315*d) - (C*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d) + (C*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d) - (exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(256*A + 288*B + 336*C)*1i)/(315*d) + (exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1152*A + 1296*B + 1512*C)*1i)/(315*d) - (exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1152*A + 1296*B + 1512*C)*1i)/(315*d) + (exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2016*A + 1008*B + 2016*C)*1i)/(315*d) - (exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2016*A + 1008*B + 2016*C)*1i)/(315*d)))/(exp(c*1i + d*x*1i) + 4*exp(c*2i + d*x*2i) + 4*exp(c*3i + d*x*3i) + 6*exp(c*4i + d*x*4i) + 6*exp(c*5i + d*x*5i) + 4*exp(c*6i + d*x*6i) + 4*exp(c*7i + d*x*7i) + exp(c*8i + d*x*8i) + exp(c*9i + d*x*9i) + 1)","B"
1311,1,465,178,6.504971,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(96\,A+112\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(280\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}+\frac{{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(280\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(96\,A+112\,B+140\,C\right)\,1{}\mathrm{i}}{105\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(336\,A+392\,B+280\,C\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(336\,A+392\,B+280\,C\right)\,1{}\mathrm{i}}{105\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+3\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(((a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(96*A + 112*B + 140*C)*1i)/(105*d) - (exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(280*B + 140*C)*1i)/(105*d) + (exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(280*B + 140*C)*1i)/(105*d) - (exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(96*A + 112*B + 140*C)*1i)/(105*d) + (exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(336*A + 392*B + 280*C)*1i)/(105*d) - (exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(336*A + 392*B + 280*C)*1i)/(105*d)))/(exp(c*1i + d*x*1i) + 3*exp(c*2i + d*x*2i) + 3*exp(c*3i + d*x*3i) + 3*exp(c*4i + d*x*4i) + 3*exp(c*5i + d*x*5i) + exp(c*6i + d*x*6i) + exp(c*7i + d*x*7i) + 1)","B"
1312,1,229,130,2.946177,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{2\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(28\,A\,\sin\left(c+d\,x\right)+20\,B\,\sin\left(c+d\,x\right)+30\,C\,\sin\left(c+d\,x\right)+16\,A\,\sin\left(2\,c+2\,d\,x\right)+36\,A\,\sin\left(3\,c+3\,d\,x\right)+8\,A\,\sin\left(4\,c+4\,d\,x\right)+8\,A\,\sin\left(5\,c+5\,d\,x\right)+20\,B\,\sin\left(2\,c+2\,d\,x\right)+30\,B\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(4\,c+4\,d\,x\right)+10\,B\,\sin\left(5\,c+5\,d\,x\right)+45\,C\,\sin\left(3\,c+3\,d\,x\right)+15\,C\,\sin\left(5\,c+5\,d\,x\right)\right)}{15\,d\,\left(10\,\cos\left(c+d\,x\right)+8\,\cos\left(2\,c+2\,d\,x\right)+5\,\cos\left(3\,c+3\,d\,x\right)+2\,\cos\left(4\,c+4\,d\,x\right)+\cos\left(5\,c+5\,d\,x\right)+6\right)}","Not used",1,"(2*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(28*A*sin(c + d*x) + 20*B*sin(c + d*x) + 30*C*sin(c + d*x) + 16*A*sin(2*c + 2*d*x) + 36*A*sin(3*c + 3*d*x) + 8*A*sin(4*c + 4*d*x) + 8*A*sin(5*c + 5*d*x) + 20*B*sin(2*c + 2*d*x) + 30*B*sin(3*c + 3*d*x) + 10*B*sin(4*c + 4*d*x) + 10*B*sin(5*c + 5*d*x) + 45*C*sin(3*c + 3*d*x) + 15*C*sin(5*c + 5*d*x)))/(15*d*(10*cos(c + d*x) + 8*cos(2*c + 2*d*x) + 5*cos(3*c + 3*d*x) + 2*cos(4*c + 4*d*x) + cos(5*c + 5*d*x) + 6))","B"
1313,0,-1,140,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1314,0,-1,141,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1315,0,-1,151,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1316,0,-1,199,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1317,0,-1,247,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1318,1,399,284,7.561927,"\text{Not used}","int((1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(-\frac{16\,C\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,d}-\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(12\,A+18\,B+23\,C\right)}{15\,d}+\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(84\,A+76\,B+81\,C\right)}{35\,d}+\frac{16\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(336\,A+374\,B+429\,C\right)}{315\,d}+\frac{32\,a\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(336\,A+374\,B+429\,C\right)}{3465\,d}\right)}{20\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+20\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+10\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+10\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,11{}\mathrm{i}}{2}+\frac{d\,x\,11{}\mathrm{i}}{2}}\,\cos\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(84*A + 76*B + 81*C))/(35*d) - (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(12*A + 18*B + 23*C))/(15*d) - (16*C*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((5*c)/2 + (5*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/(3*d) + (16*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((7*c)/2 + (7*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(336*A + 374*B + 429*C))/(315*d) + (32*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((11*c)/2 + (11*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(336*A + 374*B + 429*C))/(3465*d)))/(20*exp((c*11i)/2 + (d*x*11i)/2)*cos(c/2 + (d*x)/2) + 20*exp((c*11i)/2 + (d*x*11i)/2)*cos((3*c)/2 + (3*d*x)/2) + 10*exp((c*11i)/2 + (d*x*11i)/2)*cos((5*c)/2 + (5*d*x)/2) + 10*exp((c*11i)/2 + (d*x*11i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*exp((c*11i)/2 + (d*x*11i)/2)*cos((9*c)/2 + (9*d*x)/2) + 2*exp((c*11i)/2 + (d*x*11i)/2)*cos((11*c)/2 + (11*d*x)/2))","B"
1319,1,335,232,7.001433,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(12\,A+12\,B+13\,C\right)}{5\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(68\,A+78\,B+77\,C\right)}{35\,d}+\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(136\,A+156\,B+189\,C\right)}{315\,d}-\frac{8\,a\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(2\,B+3\,C\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,d}\right)}{12\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+8\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(12*A + 12*B + 13*C))/(5*d) + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(68*A + 78*B + 77*C))/(35*d) + (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(136*A + 156*B + 189*C))/(315*d) - (8*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((3*c)/2 + (3*d*x)/2)*(2*B + 3*C)*(a + a*cos(c + d*x))^(1/2))/(3*d)))/(12*exp((c*9i)/2 + (d*x*9i)/2)*cos(c/2 + (d*x)/2) + 8*exp((c*9i)/2 + (d*x*9i)/2)*cos((3*c)/2 + (3*d*x)/2) + 8*exp((c*9i)/2 + (d*x*9i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*exp((c*9i)/2 + (d*x*9i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*exp((c*9i)/2 + (d*x*9i)/2)*cos((9*c)/2 + (9*d*x)/2))","B"
1320,1,308,184,7.079101,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","-\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{4\,C\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{d}+\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(4\,A+6\,B+11\,C\right)}{3\,d}-\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(52\,A+48\,B+65\,C\right)}{15\,d}-\frac{4\,a\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(104\,A+126\,B+175\,C\right)}{105\,d}\right)}{6\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,{\mathrm{e}}^{\frac{c\,7{}\mathrm{i}}{2}+\frac{d\,x\,7{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}","Not used",1,"-((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((4*C*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((5*c)/2 + (5*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/d + (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(4*A + 6*B + 11*C))/(3*d) - (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(52*A + 48*B + 65*C))/(15*d) - (4*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((7*c)/2 + (7*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(104*A + 126*B + 175*C))/(105*d)))/(6*exp((c*7i)/2 + (d*x*7i)/2)*cos(c/2 + (d*x)/2) + 6*exp((c*7i)/2 + (d*x*7i)/2)*cos((3*c)/2 + (3*d*x)/2) + 2*exp((c*7i)/2 + (d*x*7i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*exp((c*7i)/2 + (d*x*7i)/2)*cos((7*c)/2 + (7*d*x)/2))","B"
1321,0,-1,192,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1322,0,-1,191,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1323,0,-1,201,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1324,0,-1,201,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1325,0,-1,253,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1326,0,-1,303,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1327,1,927,334,8.439331,"\text{Not used}","int((1/cos(c + d*x))^(15/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+9230\,B+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,8{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(6\,A+15\,B+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(6\,A+15\,B+23\,C\right)\,16{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(348\,A+345\,B+379\,C\right)\,16{}\mathrm{i}}{105\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(348\,A+345\,B+379\,C\right)\,16{}\mathrm{i}}{105\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(1046\,A+1075\,B+1108\,C\right)\,16{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(1046\,A+1075\,B+1108\,C\right)\,16{}\mathrm{i}}{315\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+9230\,B+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+9230\,B+10439\,C\right)\,8{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(8368\,A+9230\,B+10439\,C\right)\,16{}\mathrm{i}}{45045\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+20\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+20\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+15\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}+{\mathrm{e}}^{c\,12{}\mathrm{i}+d\,x\,12{}\mathrm{i}}+{\mathrm{e}}^{c\,13{}\mathrm{i}+d\,x\,13{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 9230*B + 10439*C)*16i)/(45045*d) - (C*a^2*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d) + (C*a^2*exp(c*10i + d*x*10i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*8i)/(3*d) - (a^2*exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(6*A + 15*B + 23*C)*16i)/(15*d) + (a^2*exp(c*8i + d*x*8i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(6*A + 15*B + 23*C)*16i)/(15*d) + (a^2*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(348*A + 345*B + 379*C)*16i)/(105*d) - (a^2*exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(348*A + 345*B + 379*C)*16i)/(105*d) + (a^2*exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1046*A + 1075*B + 1108*C)*16i)/(315*d) - (a^2*exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(1046*A + 1075*B + 1108*C)*16i)/(315*d) + (a^2*exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 9230*B + 10439*C)*8i)/(3465*d) - (a^2*exp(c*11i + d*x*11i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 9230*B + 10439*C)*8i)/(3465*d) - (a^2*exp(c*13i + d*x*13i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(8368*A + 9230*B + 10439*C)*16i)/(45045*d)))/(exp(c*1i + d*x*1i) + 6*exp(c*2i + d*x*2i) + 6*exp(c*3i + d*x*3i) + 15*exp(c*4i + d*x*4i) + 15*exp(c*5i + d*x*5i) + 20*exp(c*6i + d*x*6i) + 20*exp(c*7i + d*x*7i) + 15*exp(c*8i + d*x*8i) + 15*exp(c*9i + d*x*9i) + 6*exp(c*10i + d*x*10i) + 6*exp(c*11i + d*x*11i) + exp(c*12i + d*x*12i) + exp(c*13i + d*x*13i) + 1)","B"
1328,1,787,284,7.432643,"\text{Not used}","int((1/cos(c + d*x))^(13/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2840\,A+3212\,B+3795\,C\right)\,4{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(30\,A+41\,B+50\,C\right)\,8{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(30\,A+41\,B+50\,C\right)\,8{}\mathrm{i}}{15\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(160\,A+157\,B+165\,C\right)\,8{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(160\,A+157\,B+165\,C\right)\,8{}\mathrm{i}}{35\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(710\,A+803\,B+870\,C\right)\,8{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(710\,A+803\,B+870\,C\right)\,8{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2840\,A+3212\,B+3795\,C\right)\,4{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2\,B+5\,C\right)\,4{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2\,B+5\,C\right)\,4{}\mathrm{i}}{3\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+10\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+5\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+{\mathrm{e}}^{c\,10{}\mathrm{i}+d\,x\,10{}\mathrm{i}}+{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2840*A + 3212*B + 3795*C)*4i)/(3465*d) - (a^2*exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(30*A + 41*B + 50*C)*8i)/(15*d) + (a^2*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(30*A + 41*B + 50*C)*8i)/(15*d) + (a^2*exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(160*A + 157*B + 165*C)*8i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(160*A + 157*B + 165*C)*8i)/(35*d) + (a^2*exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(710*A + 803*B + 870*C)*8i)/(315*d) - (a^2*exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(710*A + 803*B + 870*C)*8i)/(315*d) - (a^2*exp(c*11i + d*x*11i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2840*A + 3212*B + 3795*C)*4i)/(3465*d) - (a^2*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2*B + 5*C)*4i)/(3*d) + (a^2*exp(c*8i + d*x*8i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2*B + 5*C)*4i)/(3*d)))/(exp(c*1i + d*x*1i) + 5*exp(c*2i + d*x*2i) + 5*exp(c*3i + d*x*3i) + 10*exp(c*4i + d*x*4i) + 10*exp(c*5i + d*x*5i) + 10*exp(c*6i + d*x*6i) + 10*exp(c*7i + d*x*7i) + 5*exp(c*8i + d*x*8i) + 5*exp(c*9i + d*x*9i) + exp(c*10i + d*x*10i) + exp(c*11i + d*x*11i) + 1)","B"
1329,1,749,234,7.754267,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\frac{\sqrt{\frac{1}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(584\,A+690\,B+903\,C\right)\,2{}\mathrm{i}}{315\,d}-\frac{C\,a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,2{}\mathrm{i}}{d}+\frac{C\,a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,2{}\mathrm{i}}{d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2\,A+5\,B+10\,C\right)\,4{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(2\,A+5\,B+10\,C\right)\,4{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(24\,A+25\,B+33\,C\right)\,4{}\mathrm{i}}{5\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(24\,A+25\,B+33\,C\right)\,4{}\mathrm{i}}{5\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(146\,A+155\,B+182\,C\right)\,4{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(146\,A+155\,B+182\,C\right)\,4{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\sqrt{a+a\,\left(\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}\right)}\,\left(584\,A+690\,B+903\,C\right)\,2{}\mathrm{i}}{315\,d}\right)}{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}+6\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\mathrm{i}}+4\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}+{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\mathrm{i}}+{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}+1}","Not used",1,"((1/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(584*A + 690*B + 903*C)*2i)/(315*d) - (C*a^2*exp(c*1i + d*x*1i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*2i)/d + (C*a^2*exp(c*8i + d*x*8i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*2i)/d - (a^2*exp(c*3i + d*x*3i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2*A + 5*B + 10*C)*4i)/(3*d) + (a^2*exp(c*6i + d*x*6i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(2*A + 5*B + 10*C)*4i)/(3*d) + (a^2*exp(c*4i + d*x*4i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(24*A + 25*B + 33*C)*4i)/(5*d) - (a^2*exp(c*5i + d*x*5i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(24*A + 25*B + 33*C)*4i)/(5*d) + (a^2*exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(146*A + 155*B + 182*C)*4i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(146*A + 155*B + 182*C)*4i)/(35*d) - (a^2*exp(c*9i + d*x*9i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(584*A + 690*B + 903*C)*2i)/(315*d)))/(exp(c*1i + d*x*1i) + 4*exp(c*2i + d*x*2i) + 4*exp(c*3i + d*x*3i) + 6*exp(c*4i + d*x*4i) + 6*exp(c*5i + d*x*5i) + 4*exp(c*6i + d*x*6i) + 4*exp(c*7i + d*x*7i) + exp(c*8i + d*x*8i) + exp(c*9i + d*x*9i) + 1)","B"
1330,0,-1,242,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1331,0,-1,243,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1332,0,-1,253,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1333,0,-1,251,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1334,0,-1,253,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1335,0,-1,301,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1336,0,-1,353,0.000000,"\text{Not used}","int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1337,0,-1,305,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(11/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(11/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1338,0,-1,257,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(9/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(9/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1339,0,-1,211,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1340,0,-1,163,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1341,0,-1,178,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1342,0,-1,181,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1343,0,-1,235,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
1344,0,-1,281,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
1345,0,-1,192,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(B\,b\,{\cos\left(c+d\,x\right)}^2+\left(A\,b+B\,a\right)\,\cos\left(c+d\,x\right)+A\,a\right)}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(1/2), x)","F"
1346,0,-1,333,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(9/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(9/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1347,0,-1,283,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1348,0,-1,233,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1349,0,-1,181,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1350,0,-1,189,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(3/2), x)","F"
1351,0,-1,242,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
1352,0,-1,300,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
1353,0,-1,333,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1354,0,-1,281,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1355,0,-1,231,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1356,0,-1,183,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + a*cos(c + d*x))^(5/2), x)","F"
1357,0,-1,241,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
1358,0,-1,294,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
1359,0,-1,352,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
1360,0,-1,205,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x)), x)","F"
1361,0,-1,172,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x)), x)","F"
1362,0,-1,135,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x)), x)","F"
1363,0,-1,135,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x)), x)","F"
1364,0,-1,141,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x)),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x)), x)","F"
1365,0,-1,174,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\left(a+b\,\cos\left(c+d\,x\right)\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(1/2), x)","F"
1366,0,-1,205,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\left(a+b\,\cos\left(c+d\,x\right)\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(3/2), x)","F"
1367,0,-1,292,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^2, x)","F"
1368,0,-1,243,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^2, x)","F"
1369,0,-1,209,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2, x)","F"
1370,0,-1,194,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2, x)","F"
1371,0,-1,206,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2, x)","F"
1372,0,-1,211,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2, x)","F"
1373,0,-1,245,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2), x)","F"
1374,0,-1,294,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^2)/(1/cos(c + d*x))^(3/2), x)","F"
1375,0,-1,333,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^3, x)","F"
1376,0,-1,283,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3, x)","F"
1377,0,-1,269,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3, x)","F"
1378,0,-1,258,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3, x)","F"
1379,0,-1,284,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3, x)","F"
1380,0,-1,285,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3, x)","F"
1381,0,-1,335,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2), x)","F"
1382,0,-1,386,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^3)/(1/cos(c + d*x))^(3/2), x)","F"
1383,0,-1,417,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^4,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^4, x)","F"
1384,0,-1,365,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^4,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^4, x)","F"
1385,0,-1,356,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^4,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^4, x)","F"
1386,0,-1,361,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^4,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^4, x)","F"
1387,0,-1,340,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^4,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^4, x)","F"
1388,0,-1,360,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^4,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^4, x)","F"
1389,0,-1,369,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^4,x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^4, x)","F"
1390,0,-1,422,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^4)/(1/cos(c + d*x))^(1/2), x)","F"
1391,0,-1,266,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x)), x)","F"
1392,0,-1,200,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x)), x)","F"
1393,0,-1,172,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x)), x)","F"
1394,0,-1,145,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x)),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x)), x)","F"
1395,0,-1,190,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))), x)","F"
1396,0,-1,241,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))), x)","F"
1397,0,-1,299,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))), x)","F"
1398,0,-1,396,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^2, x)","F"
1399,0,-1,330,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^2, x)","F"
1400,0,-1,274,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^2, x)","F"
1401,0,-1,277,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
1402,0,-1,352,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
1403,0,-1,430,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
1404,0,-1,554,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^3, x)","F"
1405,0,-1,477,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^3, x)","F"
1406,0,-1,405,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^3, x)","F"
1407,0,-1,408,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
1408,0,-1,405,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
1409,0,-1,493,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
1410,0,-1,579,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3), x)","F"
1411,0,-1,544,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
1412,0,-1,455,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
1413,0,-1,385,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
1414,0,-1,454,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
1415,0,-1,499,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
1416,0,-1,515,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
1417,0,-1,613,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2), x)","F"
1418,0,-1,698,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2), x)","F"
1419,0,-1,542,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
1420,0,-1,458,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
1421,0,-1,525,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
1422,0,-1,560,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
1423,0,-1,569,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
1424,0,-1,613,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
1425,0,-1,698,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2), x)","F"
1426,0,-1,627,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
1427,0,-1,544,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
1428,0,-1,600,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
1429,0,-1,666,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
1430,0,-1,627,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
1431,0,-1,669,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
1432,0,-1,695,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
1433,0,-1,806,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(a + b*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2), x)","F"
1434,0,-1,469,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(9/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1435,0,-1,394,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1436,0,-1,323,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1437,0,-1,403,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1438,0,-1,453,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1439,0,-1,515,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1440,0,-1,534,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1441,0,-1,432,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1442,0,-1,348,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1443,0,-1,481,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1444,0,-1,563,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1445,0,-1,664,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1446,0,-1,589,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1447,0,-1,489,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1448,0,-1,456,0.000000,"\text{Not used}","int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\left(C\,{\cos\left(c+d\,x\right)}^2+A\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*cos(c + d*x)^2)*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1449,0,-1,618,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
1450,0,-1,710,0.000000,"\text{Not used}","int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
1451,0,-1,230,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1452,0,-1,192,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1453,0,-1,151,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1454,0,-1,147,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1455,0,-1,156,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1456,0,-1,194,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1457,0,-1,230,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(a+b\,\cos\left(c+d\,x\right)\right)\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1458,0,-1,342,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1459,0,-1,288,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1460,0,-1,240,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1461,0,-1,220,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1462,0,-1,229,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1463,0,-1,243,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1464,0,-1,291,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1465,0,-1,345,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^2*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1466,0,-1,397,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1467,0,-1,334,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1468,0,-1,313,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1469,0,-1,311,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1470,0,-1,319,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1471,0,-1,336,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1472,0,-1,401,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1473,0,-1,463,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^3*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1474,0,-1,515,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1475,0,-1,441,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1476,0,-1,423,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1477,0,-1,426,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1478,0,-1,413,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1479,0,-1,419,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1480,0,-1,444,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1481,0,-1,517,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^4*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1482,0,-1,294,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1483,0,-1,218,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1484,0,-1,178,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1485,0,-1,157,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x)), x)","F"
1486,0,-1,207,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))), x)","F"
1487,0,-1,270,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))), x)","F"
1488,0,-1,345,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))), x)","F"
1489,0,-1,452,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
1490,0,-1,366,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
1491,0,-1,303,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^2, x)","F"
1492,0,-1,311,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
1493,0,-1,403,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
1494,0,-1,505,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
1495,0,-1,669,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
1496,0,-1,562,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
1497,0,-1,473,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^3, x)","F"
1498,0,-1,478,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
1499,0,-1,483,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
1500,0,-1,596,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
1501,0,-1,714,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3), x)","F"
1502,0,-1,592,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1503,0,-1,487,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1504,0,-1,400,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1505,0,-1,467,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1506,0,-1,509,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1507,0,-1,543,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1508,0,-1,646,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1509,0,-1,766,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{a+b\,\cos\left(c+d\,x\right)}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(3/2), x)","F"
1510,0,-1,590,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1511,0,-1,490,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1512,0,-1,550,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1513,0,-1,588,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1514,0,-1,595,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1515,0,-1,647,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1516,0,-1,764,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1517,0,-1,705,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{13/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1518,0,-1,592,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1519,0,-1,640,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1520,0,-1,703,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1521,0,-1,682,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1522,0,-1,707,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1523,0,-1,760,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right) \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2), x)","F"
1524,0,-1,894,0.000000,"\text{Not used}","int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(((a + b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(1/cos(c + d*x))^(1/2), x)","F"
1525,0,-1,506,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(9/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(9/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1526,0,-1,412,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1527,0,-1,333,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1528,0,-1,407,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1529,0,-1,461,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1530,0,-1,545,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1531,0,-1,653,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
1532,0,-1,445,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(B\,b\,{\cos\left(c+d\,x\right)}^2+\left(A\,b+B\,a\right)\,\cos\left(c+d\,x\right)+A\,a\right)}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A*a + cos(c + d*x)*(A*b + B*a) + B*b*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(1/2), x)","F"
1533,0,-1,585,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(7/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1534,0,-1,464,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1535,0,-1,362,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1536,0,-1,496,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(3/2), x)","F"
1537,0,-1,595,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1538,0,-1,720,0.000000,"\text{Not used}","int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x) + C*cos(c + d*x)^2)/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
1539,0,-1,660,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1540,0,-1,535,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"
1541,0,-1,495,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(C\,{\cos\left(c+d\,x\right)}^2+B\,\cos\left(c+d\,x\right)+A\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(A + B*cos(c + d*x) + C*cos(c + d*x)^2))/(a + b*cos(c + d*x))^(5/2), x)","F"