1,1,236,125,1.545524,"\text{Not used}","int(cos(c + d*x)^3*(A + B*cos(c + d*x))*(a + a*cos(c + d*x)),x)","\frac{\left(\frac{3\,A\,a}{4}+\frac{3\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{29\,A\,a}{6}+\frac{13\,B\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,A\,a}{3}+\frac{116\,B\,a}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{35\,A\,a}{6}+\frac{19\,B\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+\frac{13\,B\,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\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)\,\left(A+B\right)}{4\,d}+\frac{3\,a\,\mathrm{atan}\left(\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{4\,\left(\frac{3\,A\,a}{4}+\frac{3\,B\,a}{4}\right)}\right)\,\left(A+B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + (13*B*a)/4) + tan(c/2 + (d*x)/2)^9*((3*A*a)/4 + (3*B*a)/4) + tan(c/2 + (d*x)/2)^7*((29*A*a)/6 + (13*B*a)/6) + tan(c/2 + (d*x)/2)^3*((35*A*a)/6 + (19*B*a)/6) + tan(c/2 + (d*x)/2)^5*((20*A*a)/3 + (116*B*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(tan(c/2 + (d*x)/2)) - (d*x)/2)*(A + B))/(4*d) + (3*a*atan((3*a*tan(c/2 + (d*x)/2)*(A + B))/(4*((3*A*a)/4 + (3*B*a)/4)))*(A + B))/(4*d)","B"
2,1,212,97,1.227605,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x)),x)","\frac{\left(A\,a+\frac{3\,B\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{7\,A\,a}{3}+\frac{49\,B\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{13\,A\,a}{3}+\frac{31\,B\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+\frac{13\,B\,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\,B\right)}{4\,\left(A\,a+\frac{3\,B\,a}{4}\right)}\right)\,\left(4\,A+3\,B\right)}{4\,d}-\frac{a\,\left(4\,A+3\,B\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*B*a)/4) + tan(c/2 + (d*x)/2)^7*(A*a + (3*B*a)/4) + tan(c/2 + (d*x)/2)^3*((13*A*a)/3 + (31*B*a)/12) + tan(c/2 + (d*x)/2)^5*((7*A*a)/3 + (49*B*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*B))/(4*(A*a + (3*B*a)/4)))*(4*A + 3*B))/(4*d) - (a*(4*A + 3*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
3,1,84,77,0.233862,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x)),x)","\frac{A\,a\,x}{2}+\frac{B\,a\,x}{2}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,a\,\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\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}","Not used",1,"(A*a*x)/2 + (B*a*x)/2 + (A*a*sin(c + d*x))/d + (3*B*a*sin(c + d*x))/(4*d) + (A*a*sin(2*c + 2*d*x))/(4*d) + (B*a*sin(2*c + 2*d*x))/(4*d) + (B*a*sin(3*c + 3*d*x))/(12*d)","B"
4,1,50,47,0.194325,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x)),x)","A\,a\,x+\frac{B\,a\,x}{2}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"A*a*x + (B*a*x)/2 + (A*a*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (B*a*sin(2*c + 2*d*x))/(4*d)","B"
5,1,100,32,0.282986,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/cos(c + d*x),x)","\frac{B\,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{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}","Not used",1,"(B*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 + (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
6,1,100,32,0.306605,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/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}","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","B"
7,1,94,56,0.833630,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,A\,a+2\,B\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A\,a+2\,B\,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(A+2\,B\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*A*a + 2*B*a) - tan(c/2 + (d*x)/2)^3*(A*a + 2*B*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))*(A + 2*B))/d","B"
8,1,126,86,2.066735,"\text{Not used}","int(((A + B*cos(c + d*x))*(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+B\right)}{d}-\frac{\left(A\,a+B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A\,a}{3}-4\,B\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A\,a+3\,B\,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 + B))/d - (tan(c/2 + (d*x)/2)*(3*A*a + 3*B*a) + tan(c/2 + (d*x)/2)^5*(A*a + B*a) - tan(c/2 + (d*x)/2)^3*((4*A*a)/3 + 4*B*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"
9,1,166,106,2.664889,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/cos(c + d*x)^5,x)","\frac{\left(-\frac{3\,A\,a}{4}-B\,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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{31\,A\,a}{12}-\frac{13\,B\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a}{4}+3\,B\,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\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a)/4 + 3*B*a) - tan(c/2 + (d*x)/2)^7*((3*A*a)/4 + B*a) - tan(c/2 + (d*x)/2)^3*((31*A*a)/12 + (13*B*a)/3) + tan(c/2 + (d*x)/2)^5*((49*A*a)/12 + (7*B*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*A + 4*B))/(4*d)","B"
10,1,315,191,1.585455,"\text{Not used}","int(cos(c + d*x)^3*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2,x)","\frac{\left(\frac{3\,A\,a^2}{2}+\frac{11\,B\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{17\,A\,a^2}{2}+\frac{187\,B\,a^2}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{107\,A\,a^2}{5}+\frac{331\,B\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{117\,A\,a^2}{5}+\frac{501\,B\,a^2}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{31\,A\,a^2}{2}+\frac{87\,B\,a^2}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{13\,A\,a^2}{2}+\frac{53\,B\,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(12\,A+11\,B\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(12\,A+11\,B\right)}{8\,\left(\frac{3\,A\,a^2}{2}+\frac{11\,B\,a^2}{8}\right)}\right)\,\left(12\,A+11\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((13*A*a^2)/2 + (53*B*a^2)/8) + tan(c/2 + (d*x)/2)^11*((3*A*a^2)/2 + (11*B*a^2)/8) + tan(c/2 + (d*x)/2)^3*((31*A*a^2)/2 + (87*B*a^2)/8) + tan(c/2 + (d*x)/2)^9*((17*A*a^2)/2 + (187*B*a^2)/24) + tan(c/2 + (d*x)/2)^7*((107*A*a^2)/5 + (331*B*a^2)/20) + tan(c/2 + (d*x)/2)^5*((117*A*a^2)/5 + (501*B*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*(12*A + 11*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(12*A + 11*B))/(8*((3*A*a^2)/2 + (11*B*a^2)/8)))*(12*A + 11*B))/(8*d)","B"
11,1,277,160,1.499660,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2,x)","\frac{\left(\frac{7\,A\,a^2}{4}+\frac{3\,B\,a^2}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{49\,A\,a^2}{6}+7\,B\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{40\,A\,a^2}{3}+\frac{72\,B\,a^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{79\,A\,a^2}{6}+9\,B\,a^2\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}\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(7\,A+6\,B\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^2\,\mathrm{atan}\left(\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,A+6\,B\right)}{4\,\left(\frac{7\,A\,a^2}{4}+\frac{3\,B\,a^2}{2}\right)}\right)\,\left(7\,A+6\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + (13*B*a^2)/2) + tan(c/2 + (d*x)/2)^9*((7*A*a^2)/4 + (3*B*a^2)/2) + tan(c/2 + (d*x)/2)^7*((49*A*a^2)/6 + 7*B*a^2) + tan(c/2 + (d*x)/2)^3*((79*A*a^2)/6 + 9*B*a^2) + tan(c/2 + (d*x)/2)^5*((40*A*a^2)/3 + (72*B*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*(7*A + 6*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d) + (a^2*atan((a^2*tan(c/2 + (d*x)/2)*(7*A + 6*B))/(4*((7*A*a^2)/4 + (3*B*a^2)/2)))*(7*A + 6*B))/(4*d)","B"
12,1,134,129,0.290784,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2,x)","A\,a^2\,x+\frac{7\,B\,a^2\,x}{8}+\frac{7\,A\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,B\,a^2\,\sin\left(c+d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{A\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,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)}{6\,d}+\frac{B\,a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"A*a^2*x + (7*B*a^2*x)/8 + (7*A*a^2*sin(c + d*x))/(4*d) + (3*B*a^2*sin(c + d*x))/(2*d) + (A*a^2*sin(2*c + 2*d*x))/(2*d) + (A*a^2*sin(3*c + 3*d*x))/(12*d) + (B*a^2*sin(2*c + 2*d*x))/(2*d) + (B*a^2*sin(3*c + 3*d*x))/(6*d) + (B*a^2*sin(4*c + 4*d*x))/(32*d)","B"
13,1,98,94,0.233266,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2,x)","\frac{3\,A\,a^2\,x}{2}+B\,a^2\,x+\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{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}","Not used",1,"(3*A*a^2*x)/2 + B*a^2*x + (2*A*a^2*sin(c + d*x))/d + (7*B*a^2*sin(c + d*x))/(4*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)","B"
14,1,141,82,0.337011,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*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{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{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{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"(A*a^2*sin(c + d*x))/d + (2*B*a^2*sin(c + d*x))/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 + (3*B*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)","B"
15,1,161,74,0.320469,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,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{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{A\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(B*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 + (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 + (A*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
16,1,162,88,0.298748,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2)/cos(c + d*x)^3,x)","\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{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{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}+\frac{B\,a^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(3*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 + (4*B*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*a^2*sin(c + d*x))/(d*cos(c + d*x))","B"
17,1,145,113,2.082003,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2)/cos(c + d*x)^4,x)","\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A+\frac{3\,B}{2}\right)}{d}-\frac{\left(2\,A\,a^2+3\,B\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,A\,a^2}{3}-8\,B\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A\,a^2+5\,B\,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))*(A + (3*B)/2))/d - (tan(c/2 + (d*x)/2)*(6*A*a^2 + 5*B*a^2) + tan(c/2 + (d*x)/2)^5*(2*A*a^2 + 3*B*a^2) - tan(c/2 + (d*x)/2)^3*((16*A*a^2)/3 + 8*B*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"
18,1,183,144,2.681690,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2)/cos(c + d*x)^5,x)","\frac{\left(-\frac{7\,A\,a^2}{4}-2\,B\,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}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{25\,A\,a^2}{4}+6\,B\,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\,A}{8}+B\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((25*A*a^2)/4 + 6*B*a^2) - tan(c/2 + (d*x)/2)^7*((7*A*a^2)/4 + 2*B*a^2) + tan(c/2 + (d*x)/2)^5*((77*A*a^2)/12 + (22*B*a^2)/3) - tan(c/2 + (d*x)/2)^3*((83*A*a^2)/12 + (34*B*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*A)/8 + B))/d","B"
19,1,315,201,1.606122,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3,x)","\frac{\left(\frac{13\,A\,a^3}{4}+\frac{23\,B\,a^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{221\,A\,a^3}{12}+\frac{391\,B\,a^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{429\,A\,a^3}{10}+\frac{759\,B\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{499\,A\,a^3}{10}+\frac{969\,B\,a^3}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{419\,A\,a^3}{12}+\frac{211\,B\,a^3}{8}\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}\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(26\,A+23\,B\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+23\,B\right)}{8\,\left(\frac{13\,A\,a^3}{4}+\frac{23\,B\,a^3}{8}\right)}\right)\,\left(26\,A+23\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (105*B*a^3)/8) + tan(c/2 + (d*x)/2)^11*((13*A*a^3)/4 + (23*B*a^3)/8) + tan(c/2 + (d*x)/2)^3*((419*A*a^3)/12 + (211*B*a^3)/8) + tan(c/2 + (d*x)/2)^9*((221*A*a^3)/12 + (391*B*a^3)/24) + tan(c/2 + (d*x)/2)^7*((429*A*a^3)/10 + (759*B*a^3)/20) + tan(c/2 + (d*x)/2)^5*((499*A*a^3)/10 + (969*B*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*(26*A + 23*B)*(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 + 23*B))/(8*((13*A*a^3)/4 + (23*B*a^3)/8)))*(26*A + 23*B))/(8*d)","B"
20,1,277,154,1.504711,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3,x)","\frac{\left(\frac{15\,A\,a^3}{4}+\frac{13\,B\,a^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{35\,A\,a^3}{2}+\frac{91\,B\,a^3}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(32\,A\,a^3+\frac{416\,B\,a^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{61\,A\,a^3}{2}+\frac{133\,B\,a^3}{6}\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}\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(15\,A+13\,B\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(15\,A+13\,B\right)}{4\,\left(\frac{15\,A\,a^3}{4}+\frac{13\,B\,a^3}{4}\right)}\right)\,\left(15\,A+13\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((49*A*a^3)/4 + (51*B*a^3)/4) + tan(c/2 + (d*x)/2)^9*((15*A*a^3)/4 + (13*B*a^3)/4) + tan(c/2 + (d*x)/2)^7*((35*A*a^3)/2 + (91*B*a^3)/6) + tan(c/2 + (d*x)/2)^3*((61*A*a^3)/2 + (133*B*a^3)/6) + tan(c/2 + (d*x)/2)^5*(32*A*a^3 + (416*B*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*(15*A + 13*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d) + (a^3*atan((a^3*tan(c/2 + (d*x)/2)*(15*A + 13*B))/(4*((15*A*a^3)/4 + (13*B*a^3)/4)))*(15*A + 13*B))/(4*d)","B"
21,1,134,116,0.271531,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3,x)","\frac{5\,A\,a^3\,x}{2}+\frac{15\,B\,a^3\,x}{8}+\frac{15\,A\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{13\,B\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{B\,a^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(5*A*a^3*x)/2 + (15*B*a^3*x)/8 + (15*A*a^3*sin(c + d*x))/(4*d) + (13*B*a^3*sin(c + d*x))/(4*d) + (3*A*a^3*sin(2*c + 2*d*x))/(4*d) + (A*a^3*sin(3*c + 3*d*x))/(12*d) + (B*a^3*sin(2*c + 2*d*x))/d + (B*a^3*sin(3*c + 3*d*x))/(4*d) + (B*a^3*sin(4*c + 4*d*x))/(32*d)","B"
22,1,178,111,0.421320,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{15\,B\,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{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)}{d}+\frac{A\,a^3\,\sin\left(2\,c+2\,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}","Not used",1,"(3*A*a^3*sin(c + d*x))/d + (15*B*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 + (5*B*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))/(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)","B"
23,1,197,110,0.370542,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{3\,B\,a^3\,\sin\left(c+d\,x\right)}{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{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{A\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,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 + (3*B*a^3*sin(c + d*x))/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 + (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 + (A*a^3*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
24,1,207,114,0.372080,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{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{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{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{B\,a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(B*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 + (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 + (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) + (B*a^3*sin(c + d*x))/(d*cos(c + d*x))","B"
25,1,209,125,0.332415,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/cos(c + d*x)^4,x)","\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{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{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{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}","Not used",1,"(5*A*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/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 + (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) + (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)","B"
26,1,185,154,2.707543,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/cos(c + d*x)^5,x)","\frac{\left(-\frac{15\,A\,a^3}{4}-5\,B\,a^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{55\,A\,a^3}{4}+\frac{55\,B\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{73\,A\,a^3}{4}-\frac{73\,B\,a^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{49\,A\,a^3}{4}+11\,B\,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\,A+4\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((49*A*a^3)/4 + 11*B*a^3) - tan(c/2 + (d*x)/2)^7*((15*A*a^3)/4 + 5*B*a^3) + tan(c/2 + (d*x)/2)^5*((55*A*a^3)/4 + (55*B*a^3)/3) - tan(c/2 + (d*x)/2)^3*((73*A*a^3)/4 + (73*B*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*A + 4*B))/(4*d)","B"
27,1,224,185,2.815820,"\text{Not used}","int(((A + B*cos(c + d*x))*(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+15\,B\right)}{4\,d}-\frac{\left(\frac{13\,A\,a^3}{4}+\frac{15\,B\,a^3}{4}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{416\,A\,a^3}{15}+32\,B\,a^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}\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}\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 + 15*B))/(4*d) - (tan(c/2 + (d*x)/2)*((51*A*a^3)/4 + (49*B*a^3)/4) + tan(c/2 + (d*x)/2)^9*((13*A*a^3)/4 + (15*B*a^3)/4) - tan(c/2 + (d*x)/2)^7*((91*A*a^3)/6 + (35*B*a^3)/2) - tan(c/2 + (d*x)/2)^3*((133*A*a^3)/6 + (61*B*a^3)/2) + tan(c/2 + (d*x)/2)^5*((416*A*a^3)/15 + 32*B*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"
28,1,353,241,1.636557,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4,x)","\frac{\left(\frac{49\,A\,a^4}{8}+\frac{11\,B\,a^4}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{245\,A\,a^4}{6}+\frac{110\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{13867\,A\,a^4}{120}+\frac{3113\,B\,a^4}{30}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{896\,A\,a^4}{5}+\frac{5632\,B\,a^4}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{19157\,A\,a^4}{120}+\frac{1501\,B\,a^4}{10}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{523\,A\,a^4}{6}+70\,B\,a^4\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}\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(49\,A+44\,B\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^4\,\mathrm{atan}\left(\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(49\,A+44\,B\right)}{8\,\left(\frac{49\,A\,a^4}{8}+\frac{11\,B\,a^4}{2}\right)}\right)\,\left(49\,A+44\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + (53*B*a^4)/2) + tan(c/2 + (d*x)/2)^13*((49*A*a^4)/8 + (11*B*a^4)/2) + tan(c/2 + (d*x)/2)^11*((245*A*a^4)/6 + (110*B*a^4)/3) + tan(c/2 + (d*x)/2)^3*((523*A*a^4)/6 + 70*B*a^4) + tan(c/2 + (d*x)/2)^7*((896*A*a^4)/5 + (5632*B*a^4)/35) + tan(c/2 + (d*x)/2)^9*((13867*A*a^4)/120 + (3113*B*a^4)/30) + tan(c/2 + (d*x)/2)^5*((19157*A*a^4)/120 + (1501*B*a^4)/10))/(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*(49*A + 44*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d) + (a^4*atan((a^4*tan(c/2 + (d*x)/2)*(49*A + 44*B))/(8*((49*A*a^4)/8 + (11*B*a^4)/2)))*(49*A + 44*B))/(8*d)","B"
29,1,316,185,1.616350,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4,x)","\frac{\left(7\,A\,a^4+\frac{49\,B\,a^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{119\,A\,a^4}{3}+\frac{833\,B\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{462\,A\,a^4}{5}+\frac{1617\,B\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{562\,A\,a^4}{5}+\frac{1967\,B\,a^4}{20}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{233\,A\,a^4}{3}+\frac{1471\,B\,a^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{207\,B\,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(8\,A+7\,B\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(8\,A+7\,B\right)}{8\,\left(7\,A\,a^4+\frac{49\,B\,a^4}{8}\right)}\right)\,\left(8\,A+7\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(25*A*a^4 + (207*B*a^4)/8) + tan(c/2 + (d*x)/2)^11*(7*A*a^4 + (49*B*a^4)/8) + tan(c/2 + (d*x)/2)^9*((119*A*a^4)/3 + (833*B*a^4)/24) + tan(c/2 + (d*x)/2)^3*((233*A*a^4)/3 + (1471*B*a^4)/24) + tan(c/2 + (d*x)/2)^7*((462*A*a^4)/5 + (1617*B*a^4)/20) + tan(c/2 + (d*x)/2)^5*((562*A*a^4)/5 + (1967*B*a^4)/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)) - (7*a^4*(8*A + 7*B)*(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)*(8*A + 7*B))/(8*(7*A*a^4 + (49*B*a^4)/8)))*(8*A + 7*B))/(8*d)","B"
30,1,278,150,1.558463,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4,x)","\frac{\left(\frac{35\,A\,a^4}{4}+7\,B\,a^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{245\,A\,a^4}{6}+\frac{98\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{224\,A\,a^4}{3}+\frac{896\,B\,a^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{395\,A\,a^4}{6}+\frac{158\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{93\,A\,a^4}{4}+25\,B\,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{7\,a^4\,\left(5\,A+4\,B\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{7\,a^4\,\mathrm{atan}\left(\frac{7\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,A+4\,B\right)}{4\,\left(\frac{35\,A\,a^4}{4}+7\,B\,a^4\right)}\right)\,\left(5\,A+4\,B\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((93*A*a^4)/4 + 25*B*a^4) + tan(c/2 + (d*x)/2)^9*((35*A*a^4)/4 + 7*B*a^4) + tan(c/2 + (d*x)/2)^7*((245*A*a^4)/6 + (98*B*a^4)/3) + tan(c/2 + (d*x)/2)^3*((395*A*a^4)/6 + (158*B*a^4)/3) + tan(c/2 + (d*x)/2)^5*((224*A*a^4)/3 + (896*B*a^4)/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)) - (7*a^4*(5*A + 4*B)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d) + (7*a^4*atan((7*a^4*tan(c/2 + (d*x)/2)*(5*A + 4*B))/(4*((35*A*a^4)/4 + 7*B*a^4)))*(5*A + 4*B))/(4*d)","B"
31,1,188,151,0.672874,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4)/cos(c + d*x),x)","\frac{144\,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)+24\,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)+105\,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)+12\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+A\,a^4\,\sin\left(3\,c+3\,d\,x\right)+21\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)+4\,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}+81\,A\,a^4\,\sin\left(c+d\,x\right)+84\,B\,a^4\,\sin\left(c+d\,x\right)}{12\,d}","Not used",1,"(144*A*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 24*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 105*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 12*A*a^4*sin(2*c + 2*d*x) + A*a^4*sin(3*c + 3*d*x) + 21*B*a^4*sin(2*c + 2*d*x) + 4*B*a^4*sin(3*c + 3*d*x) + (3*B*a^4*sin(4*c + 4*d*x))/8 + 81*A*a^4*sin(c + d*x) + 84*B*a^4*sin(c + d*x))/(12*d)","B"
32,1,242,150,0.421349,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,B\,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{12\,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)}{d}+\frac{2\,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)}{d}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{A\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{2\,B\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(4*A*a^4*sin(c + d*x))/d + (20*B*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 + (12*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (A*a^4*cos(c + d*x)*sin(c + d*x))/(2*d) + (2*B*a^4*cos(c + d*x)*sin(c + d*x))/d","B"
33,1,243,162,0.402432,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{4\,B\,a^4\,\sin\left(c+d\,x\right)}{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{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)}{d}+\frac{8\,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)}{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{B\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(A*a^4*sin(c + d*x))/d + (4*B*a^4*sin(c + d*x))/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 + (13*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*B*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) + (B*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^4*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
34,1,254,165,0.406920,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4)/cos(c + d*x)^4,x)","\frac{B\,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{8\,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)}{d}+\frac{13\,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)}{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{4\,B\,a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(B*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 + (8*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*B*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) + (4*B*a^4*sin(c + d*x))/(d*cos(c + d*x)) + (B*a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
35,1,255,173,0.378117,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4)/cos(c + d*x)^5,x)","\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{2\,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)}{d}+\frac{12\,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)}{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{20\,B\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{2\,B\,a^4\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{B\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(35*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (2*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (12*B*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) + (20*B*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (2*B*a^4*sin(c + d*x))/(d*cos(c + d*x)^2) + (B*a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
36,1,224,198,2.791467,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4)/cos(c + d*x)^6,x)","\frac{7\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,A+5\,B\right)}{4\,d}-\frac{\left(7\,A\,a^4+\frac{35\,B\,a^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{98\,A\,a^4}{3}-\frac{245\,B\,a^4}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{896\,A\,a^4}{15}+\frac{224\,B\,a^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{158\,A\,a^4}{3}-\frac{395\,B\,a^4}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(25\,A\,a^4+\frac{93\,B\,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}-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,"(7*a^4*atanh(tan(c/2 + (d*x)/2))*(4*A + 5*B))/(4*d) - (tan(c/2 + (d*x)/2)*(25*A*a^4 + (93*B*a^4)/4) + tan(c/2 + (d*x)/2)^9*(7*A*a^4 + (35*B*a^4)/4) - tan(c/2 + (d*x)/2)^7*((98*A*a^4)/3 + (245*B*a^4)/6) - tan(c/2 + (d*x)/2)^3*((158*A*a^4)/3 + (395*B*a^4)/6) + tan(c/2 + (d*x)/2)^5*((896*A*a^4)/15 + (224*B*a^4)/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"
37,1,262,229,2.838641,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^4)/cos(c + d*x)^7,x)","\frac{\left(-\frac{49\,A\,a^4}{8}-7\,B\,a^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}\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}\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}\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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{207\,A\,a^4}{8}+25\,B\,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)}^{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+8\,B\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((207*A*a^4)/8 + 25*B*a^4) - tan(c/2 + (d*x)/2)^11*((49*A*a^4)/8 + 7*B*a^4) + tan(c/2 + (d*x)/2)^9*((833*A*a^4)/24 + (119*B*a^4)/3) - tan(c/2 + (d*x)/2)^3*((1471*A*a^4)/24 + (233*B*a^4)/3) - tan(c/2 + (d*x)/2)^7*((1617*A*a^4)/20 + (462*B*a^4)/5) + tan(c/2 + (d*x)/2)^5*((1967*A*a^4)/20 + (562*B*a^4)/5))/(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 + 8*B))/(8*d)","B"
38,1,170,153,0.379197,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x)),x)","\frac{15\,B\,x}{8\,a}-\frac{3\,A\,x}{2\,a}+\frac{7\,A\,\sin\left(c+d\,x\right)}{4\,a\,d}-\frac{7\,B\,\sin\left(c+d\,x\right)}{4\,a\,d}-\frac{A\,\sin\left(2\,c+2\,d\,x\right)}{4\,a\,d}+\frac{A\,\sin\left(3\,c+3\,d\,x\right)}{12\,a\,d}+\frac{A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}+\frac{B\,\sin\left(2\,c+2\,d\,x\right)}{2\,a\,d}-\frac{B\,\sin\left(3\,c+3\,d\,x\right)}{12\,a\,d}+\frac{B\,\sin\left(4\,c+4\,d\,x\right)}{32\,a\,d}-\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(15*B*x)/(8*a) - (3*A*x)/(2*a) + (7*A*sin(c + d*x))/(4*a*d) - (7*B*sin(c + d*x))/(4*a*d) - (A*sin(2*c + 2*d*x))/(4*a*d) + (A*sin(3*c + 3*d*x))/(12*a*d) + (A*tan(c/2 + (d*x)/2))/(a*d) + (B*sin(2*c + 2*d*x))/(2*a*d) - (B*sin(3*c + 3*d*x))/(12*a*d) + (B*sin(4*c + 4*d*x))/(32*a*d) - (B*tan(c/2 + (d*x)/2))/(a*d)","B"
39,1,138,122,1.357407,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x)),x)","\frac{3\,x\,\left(A-B\right)}{2\,a}-\frac{\left(3\,A-5\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,A-\frac{16\,B}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A-3\,B\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\right)}{a\,d}","Not used",1,"(3*x*(A - B))/(2*a) - (tan(c/2 + (d*x)/2)^5*(3*A - 5*B) + tan(c/2 + (d*x)/2)^3*(4*A - (16*B)/3) + tan(c/2 + (d*x)/2)*(A - 3*B))/(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))/(a*d)","B"
40,1,107,90,0.489983,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x)),x)","\frac{\left(2\,A-3\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-B\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-3\,B\right)}{2\,a}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(2*A - 3*B) + tan(c/2 + (d*x)/2)*(2*A - B))/(d*(a + 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4)) - (x*(2*A - 3*B))/(2*a) + (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
41,1,65,54,0.265252,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x)),x)","\frac{x\,\left(A-B\right)}{a}+\frac{2\,B\,\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(A-B\right)}{a\,d}","Not used",1,"(x*(A - B))/a + (2*B*tan(c/2 + (d*x)/2))/(d*(a + a*tan(c/2 + (d*x)/2)^2)) - (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
42,1,30,34,0.198287,"\text{Not used}","int((A + B*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(A-B\right)}{a}+\frac{B\,d\,x}{a}}{d}","Not used",1,"((tan(c/2 + (d*x)/2)*(A - B))/a + (B*d*x)/a)/d","B"
43,1,42,44,0.215768,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + a*cos(c + d*x))),x)","\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-B\right)}{a\,d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a*d) - (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
44,1,78,69,0.289880,"\text{Not used}","int((A + B*cos(c + d*x))/(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\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A-B\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\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*atanh(tan(c/2 + (d*x)/2))*(A - B))/(a*d) + (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
45,1,119,107,0.372865,"\text{Not used}","int((A + B*cos(c + d*x))/(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{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,A}{2}-B\right)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\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)) + (2*atanh(tan(c/2 + (d*x)/2))*((3*A)/2 - B))/(a*d) - (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
46,1,152,131,0.639334,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^4*(a + a*cos(c + d*x))),x)","\frac{\left(5\,A-3\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,B-\frac{16\,A}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A-B\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(A-B\right)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A-B\right)}{a\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(5*A - 3*B) - tan(c/2 + (d*x)/2)^3*((16*A)/3 - 4*B) + tan(c/2 + (d*x)/2)*(3*A - B))/(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))*(A - B))/(a*d) + (tan(c/2 + (d*x)/2)*(A - B))/(a*d)","B"
47,1,189,170,0.334645,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\frac{x\,\left(7\,A-10\,B\right)}{2\,a^2}-\frac{\left(5\,A-10\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,A-\frac{40\,B}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(3\,A-6\,B\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(A-B\right)}{a^2}+\frac{3\,A-5\,B}{2\,a^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2\,d}","Not used",1,"(x*(7*A - 10*B))/(2*a^2) - (tan(c/2 + (d*x)/2)^5*(5*A - 10*B) + tan(c/2 + (d*x)/2)^3*(8*A - (40*B)/3) + tan(c/2 + (d*x)/2)*(3*A - 6*B))/(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*(A - B))/a^2 + (3*A - 5*B)/(2*a^2)))/d + (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d)","B"
48,1,152,147,0.287643,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B\right)}{2\,a^2}+\frac{2\,A-4\,B}{2\,a^2}\right)}{d}-\frac{x\,\left(4\,A-7\,B\right)}{2\,a^2}+\frac{\left(2\,A-5\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-3\,B\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(A-B\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(A - B))/(2*a^2) + (2*A - 4*B)/(2*a^2)))/d - (x*(4*A - 7*B))/(2*a^2) + (tan(c/2 + (d*x)/2)^3*(2*A - 5*B) + tan(c/2 + (d*x)/2)*(2*A - 3*B))/(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))/(6*a^2*d)","B"
49,1,105,99,0.258734,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\frac{x\,\left(A-2\,B\right)}{a^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B}{a^2}+\frac{A-3\,B}{2\,a^2}\right)}{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{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,a^2\,d}","Not used",1,"(x*(A - 2*B))/a^2 - (tan(c/2 + (d*x)/2)*((A - B)/a^2 + (A - 3*B)/(2*a^2)))/d + (2*B*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))/(6*a^2*d)","B"
50,1,65,70,0.217635,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\frac{3\,A\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,B\,d\,x}{6\,a^2\,d}","Not used",1,"(3*A*tan(c/2 + (d*x)/2) - 9*B*tan(c/2 + (d*x)/2) - A*tan(c/2 + (d*x)/2)^3 + B*tan(c/2 + (d*x)/2)^3 + 6*B*d*x)/(6*a^2*d)","B"
51,1,45,65,0.188705,"\text{Not used}","int((A + B*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(A-B\right)}{6\,a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{2\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d) + (tan(c/2 + (d*x)/2)*(A + B))/(2*a^2*d)","B"
52,1,74,79,0.229317,"\text{Not used}","int((A + B*cos(c + d*x))/(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)}^3\,\left(A-B\right)}{6\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A}{a^2}+\frac{A-B}{2\,a^2}\right)}{d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d) - (tan(c/2 + (d*x)/2)*(A/a^2 + (A - B)/(2*a^2)))/d","B"
53,1,123,107,0.279501,"\text{Not used}","int((A + B*cos(c + d*x))/(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}{a^2}+\frac{3\,A-B}{2\,a^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{6\,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{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)/a^2 + (3*A - B)/(2*a^2)))/d + (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d) - (2*A*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*A - B))/(a^2*d)","B"
54,1,165,152,0.300991,"\text{Not used}","int((A + B*cos(c + d*x))/(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\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\right)}{6\,a^2\,d}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(7\,A-4\,B\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))/(2*a^2) + (4*A - 2*B)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^3*(A - B))/(6*a^2*d) + (atanh(tan(c/2 + (d*x)/2))*(7*A - 4*B))/(a^2*d)","B"
55,1,203,179,0.341019,"\text{Not used}","int((A + B*cos(c + d*x))/(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-B\right)}{a^2}+\frac{5\,A-3\,B}{2\,a^2}\right)}{d}-\frac{\left(10\,A-5\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,B-\frac{40\,A}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(6\,A-3\,B\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)}^3\,\left(A-B\right)}{6\,a^2\,d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(10\,A-7\,B\right)}{a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((2*(A - B))/a^2 + (5*A - 3*B)/(2*a^2)))/d - (tan(c/2 + (d*x)/2)^5*(10*A - 5*B) - tan(c/2 + (d*x)/2)^3*((40*A)/3 - 8*B) + tan(c/2 + (d*x)/2)*(6*A - 3*B))/(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)^3*(A - B))/(6*a^2*d) - (atanh(tan(c/2 + (d*x)/2))*(10*A - 7*B))/(a^2*d)","B"
56,1,238,218,0.332966,"\text{Not used}","int((cos(c + d*x)^5*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3,x)","\frac{x\,\left(13\,A-23\,B\right)}{2\,a^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,\left(A-B\right)}{2\,a^3}+\frac{4\,A-6\,B}{a^3}+\frac{5\,A-15\,B}{4\,a^3}\right)}{d}-\frac{\left(7\,A-17\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(12\,A-\frac{76\,B}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(5\,A-11\,B\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{A-B}{3\,a^3}+\frac{4\,A-6\,B}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}","Not used",1,"(x*(13*A - 23*B))/(2*a^3) - (tan(c/2 + (d*x)/2)*((5*(A - B))/(2*a^3) + (4*A - 6*B)/a^3 + (5*A - 15*B)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(7*A - 17*B) + tan(c/2 + (d*x)/2)^3*(12*A - (76*B)/3) + tan(c/2 + (d*x)/2)*(5*A - 11*B))/(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*((A - B)/(3*a^3) + (4*A - 6*B)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d)","B"
57,1,203,193,0.267257,"\text{Not used}","int((cos(c + d*x)^4*(A + B*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(\frac{3\,\left(A-B\right)}{2\,a^3}+\frac{3\,\left(3\,A-5\,B\right)}{4\,a^3}+\frac{2\,A-10\,B}{4\,a^3}\right)}{d}-\frac{x\,\left(6\,A-13\,B\right)}{2\,a^3}+\frac{\left(2\,A-7\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-5\,B\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{A-B}{4\,a^3}+\frac{3\,A-5\,B}{12\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((3*(A - B))/(2*a^3) + (3*(3*A - 5*B))/(4*a^3) + (2*A - 10*B)/(4*a^3)))/d - (x*(6*A - 13*B))/(2*a^3) + (tan(c/2 + (d*x)/2)^3*(2*A - 7*B) + tan(c/2 + (d*x)/2)*(2*A - 5*B))/(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*((A - B)/(4*a^3) + (3*A - 5*B)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d)","B"
58,1,152,147,0.262950,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(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}{6\,a^3}+\frac{2\,A-4\,B}{12\,a^3}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(A-B\right)}{4\,a^3}-\frac{3\,B}{2\,a^3}+\frac{2\,A-4\,B}{2\,a^3}\right)}{d}+\frac{x\,\left(A-3\,B\right)}{a^3}+\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{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((A - B)/(6*a^3) + (2*A - 4*B)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)*((3*(A - B))/(4*a^3) - (3*B)/(2*a^3) + (2*A - 4*B)/(2*a^3)))/d + (x*(A - 3*B))/a^3 + (2*B*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))/(20*a^3*d)","B"
59,1,134,116,0.383510,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3,x)","\frac{B\,x}{a^3}-\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{A\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}-\frac{B\,{\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{7\,B\,\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}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(B*x)/a^3 - (cos(c/2 + (d*x)/2)^2*((A*sin(c/2 + (d*x)/2)^3)/6 - (B*sin(c/2 + (d*x)/2)^3)/3) - cos(c/2 + (d*x)/2)^4*((A*sin(c/2 + (d*x)/2))/4 - (7*B*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)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
60,1,66,102,0.207838,"\text{Not used}","int((cos(c + d*x)*(A + B*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\,A+15\,B-3\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,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\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(15*A + 15*B - 3*A*tan(c/2 + (d*x)/2)^4 - 10*B*tan(c/2 + (d*x)/2)^2 + 3*B*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
61,1,66,102,0.195212,"\text{Not used}","int((A + B*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\,A+15\,B+10\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,A\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,B\,{\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*A + 15*B + 10*A*tan(c/2 + (d*x)/2)^2 + 3*A*tan(c/2 + (d*x)/2)^4 - 3*B*tan(c/2 + (d*x)/2)^4))/(60*a^3*d)","B"
62,1,130,117,0.245511,"\text{Not used}","int((A + B*cos(c + d*x))/(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)\,\left(\frac{A-B}{4\,a^3}+\frac{3\,A+B}{4\,a^3}+\frac{3\,A-B}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{12\,a^3}+\frac{3\,A-B}{12\,a^3}\right)}{d}","Not used",1,"(2*A*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (tan(c/2 + (d*x)/2)*((A - B)/(4*a^3) + (3*A + B)/(4*a^3) + (3*A - B)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d) - (tan(c/2 + (d*x)/2)^3*((A - B)/(12*a^3) + (3*A - B)/(12*a^3)))/d","B"
63,1,168,145,0.280018,"\text{Not used}","int((A + B*cos(c + d*x))/(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}{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\,A}{2\,a^3}+\frac{3\,\left(A-B\right)}{4\,a^3}+\frac{4\,A-2\,B}{2\,a^3}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,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{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)/(6*a^3) + (4*A - 2*B)/(12*a^3)))/d + (tan(c/2 + (d*x)/2)*((3*A)/(2*a^3) + (3*(A - B))/(4*a^3) + (4*A - 2*B)/(2*a^3)))/d + (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d) - (2*A*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*A - B))/(a^3*d)","B"
64,1,216,196,0.277124,"\text{Not used}","int((A + B*cos(c + d*x))/(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(A-B\right)}{2\,a^3}+\frac{3\,\left(5\,A-3\,B\right)}{4\,a^3}+\frac{10\,A-2\,B}{4\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{4\,a^3}+\frac{5\,A-3\,B}{12\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-B\right)}{20\,a^3\,d}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(13\,A-6\,B\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*(A - B))/(2*a^3) + (3*(5*A - 3*B))/(4*a^3) + (10*A - 2*B)/(4*a^3)))/d - (tan(c/2 + (d*x)/2)^3*((A - B)/(4*a^3) + (5*A - 3*B)/(12*a^3)))/d - (tan(c/2 + (d*x)/2)^5*(A - B))/(20*a^3*d) + (atanh(tan(c/2 + (d*x)/2))*(13*A - 6*B))/(a^3*d)","B"
65,1,259,229,0.306812,"\text{Not used}","int((cos(c + d*x)^5*(A + B*cos(c + d*x)))/(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-B\right)}{4\,a^4}-\frac{5\,B}{2\,a^4}+\frac{3\,\left(4\,A-6\,B\right)}{4\,a^4}+\frac{3\,\left(5\,A-15\,B\right)}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{4\,a^4}+\frac{4\,A-6\,B}{8\,a^4}+\frac{5\,A-15\,B}{24\,a^4}\right)}{d}-\frac{x\,\left(8\,A-21\,B\right)}{2\,a^4}+\frac{\left(2\,A-9\,B\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A-7\,B\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{3\,\left(A-B\right)}{40\,a^4}+\frac{4\,A-6\,B}{40\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*(A - B))/(4*a^4) - (5*B)/(2*a^4) + (3*(4*A - 6*B))/(4*a^4) + (3*(5*A - 15*B))/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((A - B)/(4*a^4) + (4*A - 6*B)/(8*a^4) + (5*A - 15*B)/(24*a^4)))/d - (x*(8*A - 21*B))/(2*a^4) + (tan(c/2 + (d*x)/2)^3*(2*A - 9*B) + tan(c/2 + (d*x)/2)*(2*A - 7*B))/(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*((3*(A - B))/(40*a^4) + (4*A - 6*B)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4*d)","B"
66,1,201,185,0.387734,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^4,x)","\frac{A\,d\,x-4\,B\,d\,x}{a^4\,d}-\frac{\left(\frac{52\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{21}-\frac{764\,B\,\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{143\,B\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{105}-\frac{16\,A\,\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{5\,A\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{28}-\frac{8\,B\,\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}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}+\frac{2\,B\,\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,"(A*d*x - 4*B*d*x)/(a^4*d) - ((B*sin(c/2 + (d*x)/2))/56 - (A*sin(c/2 + (d*x)/2))/56 + cos(c/2 + (d*x)/2)^2*((5*A*sin(c/2 + (d*x)/2))/28 - (8*B*sin(c/2 + (d*x)/2))/35) - cos(c/2 + (d*x)/2)^4*((16*A*sin(c/2 + (d*x)/2))/21 - (143*B*sin(c/2 + (d*x)/2))/105) + cos(c/2 + (d*x)/2)^6*((52*A*sin(c/2 + (d*x)/2))/21 - (764*B*sin(c/2 + (d*x)/2))/105))/(a^4*d*cos(c/2 + (d*x)/2)^7) + (2*B*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2))/(a^4*d)","B"
67,1,162,154,0.344768,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^4,x)","\frac{B\,x}{a^4}+\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}\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}\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}\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}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(B*x)/a^4 + ((B*sin(c/2 + (d*x)/2))/56 - (A*sin(c/2 + (d*x)/2))/56 + 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) + 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) - 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))/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
68,1,86,136,0.247368,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^4,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A+3\,B\right)}{24\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A-3\,B\right)}{40\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{8\,a^4}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)^3*(A + 3*B))/(24*a^4) + (tan(c/2 + (d*x)/2)^5*(A - 3*B))/(40*a^4) - (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4) - (tan(c/2 + (d*x)/2)*(A + B))/(8*a^4))/d","B"
69,1,84,138,0.247575,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^4,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(A+B\right)}{40\,a^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(A-B\right)}{24\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{8\,a^4}}{d}","Not used",1,"-((tan(c/2 + (d*x)/2)^5*(A + B))/(40*a^4) - (tan(c/2 + (d*x)/2)^3*(A - B))/(24*a^4) + (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4) - (tan(c/2 + (d*x)/2)*(A + B))/(8*a^4))/d","B"
70,1,87,138,0.243455,"\text{Not used}","int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,A+B\right)}{24\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A+B\right)}{8\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,A-B\right)}{40\,a^4}}{d}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(3*A + B))/(24*a^4) + (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4) + (tan(c/2 + (d*x)/2)*(A + B))/(8*a^4) + (tan(c/2 + (d*x)/2)^5*(3*A - B))/(40*a^4))/d","B"
71,1,199,147,0.360923,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + a*cos(c + d*x))^4),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)}{a^4\,d}-\frac{{\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)}^3}{24}-\frac{B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}\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}{8}-\frac{3\,B\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}\right)+{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{15\,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}\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}}{a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(2*A*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^4*d) - (cos(c/2 + (d*x)/2)^4*((11*A*sin(c/2 + (d*x)/2)^3)/24 - (B*sin(c/2 + (d*x)/2)^3)/8) + cos(c/2 + (d*x)/2)^2*((A*sin(c/2 + (d*x)/2)^5)/8 - (3*B*sin(c/2 + (d*x)/2)^5)/40) + cos(c/2 + (d*x)/2)^6*((15*A*sin(c/2 + (d*x)/2))/8 - (B*sin(c/2 + (d*x)/2))/8) + (A*sin(c/2 + (d*x)/2)^7)/56 - (B*sin(c/2 + (d*x)/2)^7)/56)/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
72,1,236,175,0.279793,"\text{Not used}","int((A + B*cos(c + d*x))/(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)}^3\,\left(\frac{A-B}{8\,a^4}+\frac{5\,A-3\,B}{12\,a^4}+\frac{10\,A-2\,B}{24\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{A-B}{20\,a^4}+\frac{5\,A-3\,B}{40\,a^4}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{A-B}{2\,a^4}+\frac{3\,\left(5\,A-3\,B\right)}{8\,a^4}+\frac{10\,A-2\,B}{4\,a^4}+\frac{10\,A+2\,B}{8\,a^4}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,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{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)^3*((A - B)/(8*a^4) + (5*A - 3*B)/(12*a^4) + (10*A - 2*B)/(24*a^4)))/d + (tan(c/2 + (d*x)/2)^5*((A - B)/(20*a^4) + (5*A - 3*B)/(40*a^4)))/d + (tan(c/2 + (d*x)/2)*((A - B)/(2*a^4) + (3*(5*A - 3*B))/(8*a^4) + (10*A - 2*B)/(4*a^4) + (10*A + 2*B)/(8*a^4)))/d + (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4*d) - (2*A*tan(c/2 + (d*x)/2))/(d*(a^4*tan(c/2 + (d*x)/2)^2 - a^4)) - (2*atanh(tan(c/2 + (d*x)/2))*(4*A - B))/(a^4*d)","B"
73,1,273,232,0.286501,"\text{Not used}","int((A + B*cos(c + d*x))/(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{5\,A}{2\,a^4}+\frac{5\,\left(A-B\right)}{4\,a^4}+\frac{3\,\left(6\,A-4\,B\right)}{4\,a^4}+\frac{3\,\left(15\,A-5\,B\right)}{8\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{A-B}{4\,a^4}+\frac{6\,A-4\,B}{8\,a^4}+\frac{15\,A-5\,B}{24\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{3\,\left(A-B\right)}{40\,a^4}+\frac{6\,A-4\,B}{40\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(A-B\right)}{56\,a^4\,d}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(21\,A-8\,B\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)*((5*A)/(2*a^4) + (5*(A - B))/(4*a^4) + (3*(6*A - 4*B))/(4*a^4) + (3*(15*A - 5*B))/(8*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((A - B)/(4*a^4) + (6*A - 4*B)/(8*a^4) + (15*A - 5*B)/(24*a^4)))/d - (tan(c/2 + (d*x)/2)^5*((3*(A - B))/(40*a^4) + (6*A - 4*B)/(40*a^4)))/d - (tan(c/2 + (d*x)/2)^7*(A - B))/(56*a^4*d) + (atanh(tan(c/2 + (d*x)/2))*(21*A - 8*B))/(a^4*d)","B"
74,0,-1,187,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+B\,\cos\left(c+d\,x\right)\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))*(a + a*cos(c + d*x))^(1/2), x)","F"
75,0,-1,144,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+B\,\cos\left(c+d\,x\right)\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))*(a + a*cos(c + d*x))^(1/2), x)","F"
76,0,-1,101,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+B\,\cos\left(c+d\,x\right)\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))*(a + a*cos(c + d*x))^(1/2), x)","F"
77,0,-1,62,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2), x)","F"
78,0,-1,66,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
79,0,-1,68,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
80,0,-1,117,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
81,0,-1,160,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^4, x)","F"
82,0,-1,234,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+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(cos(c + d*x)^3*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2), x)","F"
83,0,-1,189,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+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(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2), x)","F"
84,0,-1,138,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+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(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2), x)","F"
85,0,-1,101,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2),x)","\int \left(A+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((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2), x)","F"
86,0,-1,105,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
87,0,-1,103,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
88,0,-1,119,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
89,0,-1,164,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^4,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^4, x)","F"
90,0,-1,209,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^5,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^5, x)","F"
91,0,-1,237,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+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(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2), x)","F"
92,0,-1,175,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+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(cos(c + d*x)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2), x)","F"
93,0,-1,138,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2),x)","\int \left(A+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((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2), x)","F"
94,0,-1,142,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
95,0,-1,144,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
96,0,-1,156,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^3, x)","F"
97,0,-1,164,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^4,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^4, x)","F"
98,0,-1,209,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^5,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^5, x)","F"
99,0,-1,254,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^6,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^6, x)","F"
100,0,-1,202,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^(1/2), x)","F"
101,0,-1,159,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^(1/2), x)","F"
102,1,160,118,0.379416,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,A\,\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\,B\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,a\,d}-\frac{2\,B\,\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*A*(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*B*sin(c + d*x)*(a + a*cos(c + d*x))^(1/2))/(3*a*d) - (2*B*(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"
103,1,112,78,0.350269,"\text{Not used}","int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(1/2),x)","\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}}+2\,B\,\mathrm{E}\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}}-B\,\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)}}","Not used",1,"(A*ellipticF(c/2 + (d*x)/2, 1)*((2*(a + a*cos(c + d*x)))/a)^(1/2) + 2*B*ellipticE(c/2 + (d*x)/2, 1)*((2*(a + a*cos(c + d*x)))/a)^(1/2) - B*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))","B"
104,0,-1,91,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)), x)","F"
105,0,-1,119,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)), x)","F"
106,0,-1,165,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)), x)","F"
107,0,-1,261,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\left(A+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((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2), x)","F"
108,0,-1,216,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+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((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2), x)","F"
109,0,-1,171,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+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((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2), x)","F"
110,0,-1,118,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+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((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2), x)","F"
111,0,-1,87,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{A+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((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(3/2), x)","F"
112,0,-1,127,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)), x)","F"
113,0,-1,170,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)), x)","F"
114,0,-1,221,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)), x)","F"
115,0,-1,261,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\left(A+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((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2), x)","F"
116,0,-1,216,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+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((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2), x)","F"
117,0,-1,169,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+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((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2), x)","F"
118,0,-1,126,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+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((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2), x)","F"
119,0,-1,126,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{A+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((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(5/2), x)","F"
120,0,-1,164,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)), x)","F"
121,0,-1,207,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)), x)","F"
122,0,-1,264,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2)), x)","F"
123,1,177,159,1.085011,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
124,1,166,132,0.608633,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
125,1,128,101,0.521512,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
126,1,79,70,0.526405,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/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\,B\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,a\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}","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*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*A*a*(ellipticE(c/2 + (d*x)/2, 2) + ellipticF(c/2 + (d*x)/2, 2)))/d","B"
127,1,90,66,0.963974,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\frac{2\,A\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,a\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\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*A*a*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*a*(ellipticE(c/2 + (d*x)/2, 2) + 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))","B"
128,1,150,95,1.300034,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/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\,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*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"
129,1,177,132,1.606269,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\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\,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}}+\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}}","Not used",1,"(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*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)) + (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))","B"
130,1,266,194,1.071389,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
131,1,231,161,1.012339,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
132,1,153,126,1.003735,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*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\,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}}","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*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))","B"
133,1,134,118,1.135957,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(3/2),x)","\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\,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}}","Not used",1,"(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*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))","B"
134,1,196,120,1.691550,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^2)/cos(c + d*x)^(5/2),x)","\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*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"
135,1,229,159,1.974079,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,B\,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}}","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 + (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))","B"
136,1,235,194,2.298657,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{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}}","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))","B"
137,1,360,237,1.310079,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
138,1,323,204,1.074257,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(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{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}}","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))","B"
139,1,255,171,0.998479,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*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^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{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}}","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 + (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))","B"
140,1,229,169,1.042826,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(3/2),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\,\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}}","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*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))","B"
141,1,251,161,1.628193,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{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\,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}}","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*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))","B"
142,1,287,171,2.502775,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/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{2\,A\,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}}","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 + (2*A*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))","B"
143,1,307,204,2.665626,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(9/2),x)","\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}}","Not used",1,"(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))","B"
144,1,552,237,3.031176,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/cos(c + d*x)^(11/2),x)","\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{19\,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{9\,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{25\,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{3\,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}}\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{34\,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{27\,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}}\right)}{135\,d}+\frac{8\,\left(\frac{3\,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{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}}\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{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{136\,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{39\,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{153\,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{27\,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}}\right)}{45\,d}","Not used",1,"(2*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2)*((19*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (9*A*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2)) + (25*B*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (3*B*a^3*sin(c + d*x))/(cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))))/(21*d) - (8*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2)*((34*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)) + (27*B*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2))))/(135*d) + (8*((3*A*a^3*sin(c + d*x))/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x)^2)^(1/2)) + (B*a^3*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) + (2*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2)*((136*A*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (39*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)) + (153*B*a^3*sin(c + d*x))/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x)^2)^(1/2)) + (27*B*a^3*sin(c + d*x))/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))))/(45*d)","B"
145,0,-1,156,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x)), x)","F"
146,0,-1,123,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x)), x)","F"
147,0,-1,85,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x)), x)","F"
148,0,-1,83,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))), x)","F"
149,0,-1,119,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))), x)","F"
150,0,-1,153,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))), x)","F"
151,0,-1,203,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2, x)","F"
152,0,-1,166,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^2, x)","F"
153,0,-1,136,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^2, x)","F"
154,0,-1,121,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^2, x)","F"
155,0,-1,121,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
156,0,-1,168,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
157,0,-1,201,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
158,0,-1,254,0.000000,"\text{Not used}","int((cos(c + d*x)^(9/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{9/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^(9/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3, x)","F"
159,0,-1,219,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^3, x)","F"
160,0,-1,188,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^3, x)","F"
161,0,-1,180,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^3, x)","F"
162,0,-1,178,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^3, x)","F"
163,0,-1,182,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
164,0,-1,221,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
165,0,-1,254,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
166,0,-1,221,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{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))*(a + a*cos(c + d*x))^(1/2), x)","F"
167,0,-1,176,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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))*(a + a*cos(c + d*x))^(1/2), x)","F"
168,0,-1,131,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\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))*(a + a*cos(c + d*x))^(1/2), x)","F"
169,0,-1,78,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
170,0,-1,76,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
171,1,112,85,1.556847,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2),x)","\frac{2\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(2\,A\,\sin\left(c+d\,x\right)+3\,B\,\sin\left(c+d\,x\right)+2\,A\,\sin\left(2\,c+2\,d\,x\right)+2\,A\,\sin\left(3\,c+3\,d\,x\right)+3\,B\,\sin\left(3\,c+3\,d\,x\right)\right)}{3\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\left(3\,\cos\left(c+d\,x\right)+2\,\cos\left(2\,c+2\,d\,x\right)+\cos\left(3\,c+3\,d\,x\right)+2\right)}","Not used",1,"(2*(a*(cos(c + d*x) + 1))^(1/2)*(2*A*sin(c + d*x) + 3*B*sin(c + d*x) + 2*A*sin(2*c + 2*d*x) + 2*A*sin(3*c + 3*d*x) + 3*B*sin(3*c + 3*d*x)))/(3*d*cos(c + d*x)^(1/2)*(3*cos(c + d*x) + 2*cos(2*c + 2*d*x) + cos(3*c + 3*d*x) + 2))","B"
172,1,194,130,3.253433,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2),x)","\frac{4\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(14\,A\,\sin\left(c+d\,x\right)+10\,B\,\sin\left(c+d\,x\right)+8\,A\,\sin\left(2\,c+2\,d\,x\right)+18\,A\,\sin\left(3\,c+3\,d\,x\right)+4\,A\,\sin\left(4\,c+4\,d\,x\right)+4\,A\,\sin\left(5\,c+5\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)+15\,B\,\sin\left(3\,c+3\,d\,x\right)+5\,B\,\sin\left(4\,c+4\,d\,x\right)+5\,B\,\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,"(4*(a*(cos(c + d*x) + 1))^(1/2)*(14*A*sin(c + d*x) + 10*B*sin(c + d*x) + 8*A*sin(2*c + 2*d*x) + 18*A*sin(3*c + 3*d*x) + 4*A*sin(4*c + 4*d*x) + 4*A*sin(5*c + 5*d*x) + 10*B*sin(2*c + 2*d*x) + 15*B*sin(3*c + 3*d*x) + 5*B*sin(4*c + 4*d*x) + 5*B*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"
173,1,479,175,6.226111,"\text{Not used}","int(((A + B*cos(c + d*x))*(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+112\,B\right)\,1{}\mathrm{i}}{105\,d}-\frac{B\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}+\frac{B\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(96\,A+112\,B\right)\,1{}\mathrm{i}}{105\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(336\,A+392\,B\right)\,1{}\mathrm{i}}{105\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(336\,A+392\,B\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)*1i)/(105*d) - (B*exp(c*3i + d*x*3i)*8i)/(3*d) + (B*exp(c*4i + d*x*4i)*8i)/(3*d) - (exp(c*7i + d*x*7i)*(96*A + 112*B)*1i)/(105*d) + (exp(c*2i + d*x*2i)*(336*A + 392*B)*1i)/(105*d) - (exp(c*5i + d*x*5i)*(336*A + 392*B)*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"
174,0,-1,227,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2), x)","F"
175,0,-1,180,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+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(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2), x)","F"
176,0,-1,133,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
177,0,-1,126,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
178,0,-1,125,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2), x)","F"
179,1,195,134,3.093619,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2),x)","\frac{2\,a\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(48\,A\,\sin\left(c+d\,x\right)+50\,B\,\sin\left(c+d\,x\right)+36\,A\,\sin\left(2\,c+2\,d\,x\right)+66\,A\,\sin\left(3\,c+3\,d\,x\right)+18\,A\,\sin\left(4\,c+4\,d\,x\right)+18\,A\,\sin\left(5\,c+5\,d\,x\right)+20\,B\,\sin\left(2\,c+2\,d\,x\right)+75\,B\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(4\,c+4\,d\,x\right)+25\,B\,\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*(a*(cos(c + d*x) + 1))^(1/2)*(48*A*sin(c + d*x) + 50*B*sin(c + d*x) + 36*A*sin(2*c + 2*d*x) + 66*A*sin(3*c + 3*d*x) + 18*A*sin(4*c + 4*d*x) + 18*A*sin(5*c + 5*d*x) + 20*B*sin(2*c + 2*d*x) + 75*B*sin(3*c + 3*d*x) + 10*B*sin(4*c + 4*d*x) + 25*B*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"
180,1,236,181,6.719536,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{8\,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(2\,A+3\,B\right)}{3\,d}+\frac{16\,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(13\,A+12\,B\right)}{15\,d}+\frac{8\,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(52\,A+63\,B\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)*((16*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((3*c)/2 + (3*d*x)/2)*(13*A + 12*B))/(15*d) - (8*a*exp((c*7i)/2 + (d*x*7i)/2)*sin(c/2 + (d*x)/2)*(2*A + 3*B))/(3*d) + (8*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((7*c)/2 + (7*d*x)/2)*(52*A + 63*B))/(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"
181,1,289,228,7.022599,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{16\,B\,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)}{3\,d}+\frac{16\,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(34\,A+39\,B\right)}{35\,d}+\frac{32\,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(34\,A+39\,B\right)}{315\,d}+\frac{96\,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(A+B\right)}{5\,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)*((16*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2)*(34*A + 39*B))/(35*d) - (16*B*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((3*c)/2 + (3*d*x)/2))/(3*d) + (32*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2)*(34*A + 39*B))/(315*d) + (96*a*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2)*(A + B))/(5*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"
182,0,-1,274,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2), x)","F"
183,0,-1,227,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+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(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2), x)","F"
184,0,-1,180,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
185,0,-1,178,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
186,0,-1,173,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
187,0,-1,172,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2), x)","F"
188,1,551,181,6.864408,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/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{a^2\,\left(230\,A+301\,B\right)\,2{}\mathrm{i}}{105\,d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\left(10\,A+17\,B\right)\,2{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,\left(10\,A+17\,B\right)\,2{}\mathrm{i}}{3\,d}+\frac{a^2\,{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,\left(100\,A+113\,B\right)\,2{}\mathrm{i}}{15\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(100\,A+113\,B\right)\,2{}\mathrm{i}}{15\,d}-\frac{a^2\,{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,\left(230\,A+301\,B\right)\,2{}\mathrm{i}}{105\,d}-\frac{B\,a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,2{}\mathrm{i}}{d}+\frac{B\,a^2\,{\mathrm{e}}^{c\,6{}\mathrm{i}+d\,x\,6{}\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}}+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)*((a^2*(230*A + 301*B)*2i)/(105*d) - (a^2*exp(c*3i + d*x*3i)*(10*A + 17*B)*2i)/(3*d) + (a^2*exp(c*4i + d*x*4i)*(10*A + 17*B)*2i)/(3*d) + (a^2*exp(c*2i + d*x*2i)*(100*A + 113*B)*2i)/(15*d) - (a^2*exp(c*5i + d*x*5i)*(100*A + 113*B)*2i)/(15*d) - (a^2*exp(c*7i + d*x*7i)*(230*A + 301*B)*2i)/(105*d) - (B*a^2*exp(c*1i + d*x*1i)*2i)/d + (B*a^2*exp(c*6i + d*x*6i)*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) + 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"
189,1,647,228,8.235907,"\text{Not used}","int(((A + B*cos(c + d*x))*(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(292\,A+345\,B\right)\,4{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,\left(2\,A+5\,B\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\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\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\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\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\right)\,4{}\mathrm{i}}{35\,d}-\frac{a^2\,{\mathrm{e}}^{c\,9{}\mathrm{i}+d\,x\,9{}\mathrm{i}}\,\left(292\,A+345\,B\right)\,4{}\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*(292*A + 345*B)*4i)/(315*d) - (a^2*exp(c*3i + d*x*3i)*(2*A + 5*B)*4i)/(3*d) + (a^2*exp(c*6i + d*x*6i)*(2*A + 5*B)*4i)/(3*d) + (a^2*exp(c*4i + d*x*4i)*(24*A + 25*B)*4i)/(5*d) - (a^2*exp(c*5i + d*x*5i)*(24*A + 25*B)*4i)/(5*d) + (a^2*exp(c*2i + d*x*2i)*(146*A + 155*B)*4i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(146*A + 155*B)*4i)/(35*d) - (a^2*exp(c*9i + d*x*9i)*(292*A + 345*B)*4i)/(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"
190,1,773,275,7.322021,"\text{Not used}","int(((A + B*cos(c + d*x))*(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(710\,A+803\,B\right)\,16{}\mathrm{i}}{3465\,d}-\frac{a^2\,{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,\left(30\,A+41\,B\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\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\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\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\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\right)\,8{}\mathrm{i}}{315\,d}-\frac{a^2\,{\mathrm{e}}^{c\,11{}\mathrm{i}+d\,x\,11{}\mathrm{i}}\,\left(710\,A+803\,B\right)\,16{}\mathrm{i}}{3465\,d}-\frac{B\,a^2\,{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,8{}\mathrm{i}}{3\,d}+\frac{B\,a^2\,{\mathrm{e}}^{c\,8{}\mathrm{i}+d\,x\,8{}\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}}+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*(710*A + 803*B)*16i)/(3465*d) - (a^2*exp(c*5i + d*x*5i)*(30*A + 41*B)*8i)/(15*d) + (a^2*exp(c*6i + d*x*6i)*(30*A + 41*B)*8i)/(15*d) + (a^2*exp(c*4i + d*x*4i)*(160*A + 157*B)*8i)/(35*d) - (a^2*exp(c*7i + d*x*7i)*(160*A + 157*B)*8i)/(35*d) + (a^2*exp(c*2i + d*x*2i)*(710*A + 803*B)*8i)/(315*d) - (a^2*exp(c*9i + d*x*9i)*(710*A + 803*B)*8i)/(315*d) - (a^2*exp(c*11i + d*x*11i)*(710*A + 803*B)*16i)/(3465*d) - (B*a^2*exp(c*3i + d*x*3i)*8i)/(3*d) + (B*a^2*exp(c*8i + d*x*8i)*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) + 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"
191,0,-1,190,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^(1/2), x)","F"
192,0,-1,141,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\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)))/(a + a*cos(c + d*x))^(1/2), x)","F"
193,0,-1,100,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
194,0,-1,99,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
195,0,-1,142,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
196,0,-1,187,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
197,0,-1,197,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2), x)","F"
198,0,-1,145,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(3/2), x)","F"
199,0,-1,107,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
200,0,-1,156,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
201,0,-1,203,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
202,0,-1,246,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+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((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2), x)","F"
203,0,-1,194,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2), x)","F"
204,0,-1,154,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(5/2), x)","F"
205,0,-1,156,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
206,0,-1,203,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
207,0,-1,250,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\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))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
208,0,-1,293,0.000000,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2), x)","F"
209,0,-1,241,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2), x)","F"
210,0,-1,201,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2), x)","F"
211,0,-1,201,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + a*cos(c + d*x))^(7/2), x)","F"
212,0,-1,203,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
213,0,-1,250,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
214,0,-1,297,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
215,1,117,105,0.474266,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x)),x)","\frac{A\,a\,x}{2}+\frac{3\,B\,b\,x}{8}+\frac{3\,A\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,B\,a\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}","Not used",1,"(A*a*x)/2 + (3*B*b*x)/8 + (3*A*b*sin(c + d*x))/(4*d) + (3*B*a*sin(c + d*x))/(4*d) + (A*a*sin(2*c + 2*d*x))/(4*d) + (A*b*sin(3*c + 3*d*x))/(12*d) + (B*a*sin(3*c + 3*d*x))/(12*d) + (B*b*sin(2*c + 2*d*x))/(4*d) + (B*b*sin(4*c + 4*d*x))/(32*d)","B"
216,1,84,84,0.397114,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x)),x)","\frac{A\,b\,x}{2}+\frac{B\,a\,x}{2}+\frac{A\,a\,\sin\left(c+d\,x\right)}{d}+\frac{3\,B\,b\,\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}","Not used",1,"(A*b*x)/2 + (B*a*x)/2 + (A*a*sin(c + d*x))/d + (3*B*b*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)","B"
217,1,50,52,0.355770,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x)),x)","A\,a\,x+\frac{B\,b\,x}{2}+\frac{A\,b\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,\sin\left(c+d\,x\right)}{d}+\frac{B\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}","Not used",1,"A*a*x + (B*b*x)/2 + (A*b*sin(c + d*x))/d + (B*a*sin(c + d*x))/d + (B*b*sin(2*c + 2*d*x))/(4*d)","B"
218,1,100,35,0.479025,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/cos(c + d*x),x)","\frac{B\,b\,\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}","Not used",1,"(B*b*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","B"
219,1,114,35,0.484200,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/cos(c + d*x)^2,x)","\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{A\,a\,\sin\left(c+d\,x\right)}{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,"(2*B*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d - (A*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (A*a*sin(c + d*x))/(d*cos(c + d*x))","B"
220,1,104,61,1.273270,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/cos(c + d*x)^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a+2\,A\,b+2\,B\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,A\,b-A\,a+2\,B\,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(A\,a+2\,B\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A*a + 2*A*b + 2*B*a) - tan(c/2 + (d*x)/2)^3*(2*A*b - A*a + 2*B*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))*(A*a + 2*B*b))/d","B"
221,1,145,93,2.574210,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/cos(c + d*x)^4,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(A\,b+B\,a\right)}{d}-\frac{\left(2\,A\,a-A\,b-B\,a+2\,B\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A\,a}{3}-4\,B\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a+A\,b+B\,a+2\,B\,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))*(A*b + B*a))/d - (tan(c/2 + (d*x)/2)*(2*A*a + A*b + B*a + 2*B*b) - tan(c/2 + (d*x)/2)^3*((4*A*a)/3 + 4*B*b) + tan(c/2 + (d*x)/2)^5*(2*A*a - A*b - B*a + 2*B*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"
222,1,194,114,3.863395,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/cos(c + d*x)^5,x)","\frac{\left(\frac{5\,A\,a}{4}-2\,A\,b-2\,B\,a+B\,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\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\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\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\,A\,a}{4}+B\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*A*a)/4 + 2*A*b + 2*B*a + B*b) + tan(c/2 + (d*x)/2)^7*((5*A*a)/4 - 2*A*b - 2*B*a + B*b) - tan(c/2 + (d*x)/2)^3*((10*A*b)/3 - (3*A*a)/4 + (10*B*a)/3 + B*b) + tan(c/2 + (d*x)/2)^5*((3*A*a)/4 + (10*A*b)/3 + (10*B*a)/3 - B*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*A*a)/4 + B*b))/d","B"
223,1,307,189,3.933278,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^2,x)","\frac{x\,\left(A\,a^2+\frac{3\,B\,a\,b}{2}+\frac{3\,A\,b^2}{4}\right)}{2}+\frac{\left(2\,B\,a^2-\frac{5\,A\,b^2}{4}-A\,a^2+2\,B\,b^2+4\,A\,a\,b-\frac{5\,B\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{16\,B\,a^2}{3}-\frac{A\,b^2}{2}-2\,A\,a^2+\frac{8\,B\,b^2}{3}+\frac{32\,A\,a\,b}{3}-B\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,B\,a^2}{3}+\frac{40\,A\,a\,b}{3}+\frac{116\,B\,b^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,A\,a^2+\frac{A\,b^2}{2}+\frac{16\,B\,a^2}{3}+\frac{8\,B\,b^2}{3}+\frac{32\,A\,a\,b}{3}+B\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,a^2+\frac{5\,A\,b^2}{4}+2\,B\,a^2+2\,B\,b^2+4\,A\,a\,b+\frac{5\,B\,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*(A*a^2 + (3*A*b^2)/4 + (3*B*a*b)/2))/2 + (tan(c/2 + (d*x)/2)^5*((20*B*a^2)/3 + (116*B*b^2)/15 + (40*A*a*b)/3) - tan(c/2 + (d*x)/2)^9*(A*a^2 + (5*A*b^2)/4 - 2*B*a^2 - 2*B*b^2 - 4*A*a*b + (5*B*a*b)/2) + tan(c/2 + (d*x)/2)^3*(2*A*a^2 + (A*b^2)/2 + (16*B*a^2)/3 + (8*B*b^2)/3 + (32*A*a*b)/3 + B*a*b) - tan(c/2 + (d*x)/2)^7*(2*A*a^2 + (A*b^2)/2 - (16*B*a^2)/3 - (8*B*b^2)/3 - (32*A*a*b)/3 + B*a*b) + tan(c/2 + (d*x)/2)*(A*a^2 + (5*A*b^2)/4 + 2*B*a^2 + 2*B*b^2 + 4*A*a*b + (5*B*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"
224,1,169,170,0.512097,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^2,x)","\frac{B\,a^2\,x}{2}+\frac{3\,B\,b^2\,x}{8}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{d}+\frac{3\,A\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+A\,a\,b\,x+\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{A\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{B\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}","Not used",1,"(B*a^2*x)/2 + (3*B*b^2*x)/8 + (A*a^2*sin(c + d*x))/d + (3*A*b^2*sin(c + d*x))/(4*d) + A*a*b*x + (B*a^2*sin(2*c + 2*d*x))/(4*d) + (A*b^2*sin(3*c + 3*d*x))/(12*d) + (B*b^2*sin(2*c + 2*d*x))/(4*d) + (B*b^2*sin(4*c + 4*d*x))/(32*d) + (3*B*a*b*sin(c + d*x))/(2*d) + (A*a*b*sin(2*c + 2*d*x))/(2*d) + (B*a*b*sin(3*c + 3*d*x))/(6*d)","B"
225,1,115,107,0.452678,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^2,x)","A\,a^2\,x+\frac{A\,b^2\,x}{2}+\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{B\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{2\,A\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}","Not used",1,"A*a^2*x + (A*b^2*x)/2 + (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) + (B*b^2*sin(3*c + 3*d*x))/(12*d) + (2*A*a*b*sin(c + d*x))/d + (B*a*b*sin(2*c + 2*d*x))/(2*d)","B"
226,1,169,86,0.693442,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^2)/cos(c + d*x),x)","\frac{A\,b^2\,\sin\left(c+d\,x\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\,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{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}","Not used",1,"(A*b^2*sin(c + d*x))/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) + (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","B"
227,1,169,60,0.875843,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^2)/cos(c + d*x)^2,x)","\frac{A\,a^2\,\mathrm{tan}\left(c+d\,x\right)}{d}+\frac{2\,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}+\frac{B\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d\,\cos\left(c+d\,x\right)}+\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}-\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\,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*tan(c + d*x))/d + (2*A*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (B*a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/d + (B*b^2*sin(2*c + 2*d*x))/(2*d*cos(c + d*x)) - (A*a*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*4i)/d + (4*B*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
228,1,176,80,0.978136,"\text{Not used}","int(((A + B*cos(c + d*x))*(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)+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)+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)\right)}{d}+\frac{\frac{B\,a^2\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,a^2\,\sin\left(c+d\,x\right)}{2}+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)) + 2*B*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((B*a^2*sin(2*c + 2*d*x))/2 + (A*a^2*sin(c + d*x))/2 + A*a*b*sin(2*c + 2*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
229,1,227,116,3.659551,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*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{B\,a^2}{2}+A\,a\,b+B\,b^2\right)}{2\,B\,a^2+4\,A\,a\,b+4\,B\,b^2}\right)\,\left(B\,a^2+2\,A\,a\,b+2\,B\,b^2\right)}{d}-\frac{\left(2\,A\,a^2+2\,A\,b^2-B\,a^2-2\,A\,a\,b+4\,B\,a\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,A\,a^2}{3}-8\,B\,a\,b-4\,A\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,A\,a^2+2\,A\,b^2+B\,a^2+2\,A\,a\,b+4\,B\,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)*((B*a^2)/2 + B*b^2 + A*a*b))/(2*B*a^2 + 4*B*b^2 + 4*A*a*b))*(B*a^2 + 2*B*b^2 + 2*A*a*b))/d - (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 + 2*A*a*b + 4*B*a*b) - tan(c/2 + (d*x)/2)^3*((4*A*a^2)/3 + 4*A*b^2 + 8*B*a*b) + tan(c/2 + (d*x)/2)^5*(2*A*a^2 + 2*A*b^2 - B*a^2 - 2*A*a*b + 4*B*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"
230,1,314,156,3.868345,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{3\,A\,a^2}{8}+B\,a\,b+\frac{A\,b^2}{2}\right)}{\frac{3\,A\,a^2}{2}+4\,B\,a\,b+2\,A\,b^2}\right)\,\left(\frac{3\,A\,a^2}{4}+2\,B\,a\,b+A\,b^2\right)}{d}+\frac{\left(\frac{5\,A\,a^2}{4}+A\,b^2-2\,B\,a^2-2\,B\,b^2-4\,A\,a\,b+2\,B\,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+\frac{20\,A\,a\,b}{3}-2\,B\,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-\frac{20\,A\,a\,b}{3}-2\,B\,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+4\,A\,a\,b+2\,B\,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*A*a^2)/8 + (A*b^2)/2 + B*a*b))/((3*A*a^2)/2 + 2*A*b^2 + 4*B*a*b))*((3*A*a^2)/4 + A*b^2 + 2*B*a*b))/d + (tan(c/2 + (d*x)/2)^7*((5*A*a^2)/4 + A*b^2 - 2*B*a^2 - 2*B*b^2 - 4*A*a*b + 2*B*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 + (20*A*a*b)/3 + 2*B*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 + (20*A*a*b)/3 - 2*B*a*b) + tan(c/2 + (d*x)/2)*((5*A*a^2)/4 + A*b^2 + 2*B*a^2 + 2*B*b^2 + 4*A*a*b + 2*B*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"
231,1,352,269,1.108068,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3,x)","\frac{A\,a^3\,x}{2}+\frac{5\,B\,b^3\,x}{16}+\frac{9\,A\,a\,b^2\,x}{8}+\frac{9\,B\,a^2\,b\,x}{8}+\frac{5\,A\,b^3\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,B\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{A\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,A\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{B\,a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{A\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{15\,B\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,B\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{B\,b^3\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{3\,A\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{A\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)}{4\,d}+\frac{3\,A\,a\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{5\,B\,a\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{16\,d}+\frac{3\,B\,a^2\,b\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,B\,a\,b^2\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{9\,A\,a^2\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{15\,B\,a\,b^2\,\sin\left(c+d\,x\right)}{8\,d}","Not used",1,"(A*a^3*x)/2 + (5*B*b^3*x)/16 + (9*A*a*b^2*x)/8 + (9*B*a^2*b*x)/8 + (5*A*b^3*sin(c + d*x))/(8*d) + (3*B*a^3*sin(c + d*x))/(4*d) + (A*a^3*sin(2*c + 2*d*x))/(4*d) + (5*A*b^3*sin(3*c + 3*d*x))/(48*d) + (B*a^3*sin(3*c + 3*d*x))/(12*d) + (A*b^3*sin(5*c + 5*d*x))/(80*d) + (15*B*b^3*sin(2*c + 2*d*x))/(64*d) + (3*B*b^3*sin(4*c + 4*d*x))/(64*d) + (B*b^3*sin(6*c + 6*d*x))/(192*d) + (3*A*a*b^2*sin(2*c + 2*d*x))/(4*d) + (A*a^2*b*sin(3*c + 3*d*x))/(4*d) + (3*A*a*b^2*sin(4*c + 4*d*x))/(32*d) + (3*B*a^2*b*sin(2*c + 2*d*x))/(4*d) + (5*B*a*b^2*sin(3*c + 3*d*x))/(16*d) + (3*B*a^2*b*sin(4*c + 4*d*x))/(32*d) + (3*B*a*b^2*sin(5*c + 5*d*x))/(80*d) + (9*A*a^2*b*sin(c + d*x))/(4*d) + (15*B*a*b^2*sin(c + d*x))/(8*d)","B"
232,1,277,243,0.777966,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3,x)","\frac{3\,A\,b^3\,x}{8}+\frac{B\,a^3\,x}{2}+\frac{3\,A\,a^2\,b\,x}{2}+\frac{9\,B\,a\,b^2\,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{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{B\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{80\,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{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}","Not used",1,"(3*A*b^3*x)/8 + (B*a^3*x)/2 + (3*A*a^2*b*x)/2 + (9*B*a*b^2*x)/8 + (A*a^3*sin(c + d*x))/d + (5*B*b^3*sin(c + d*x))/(8*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) + (B*b^3*sin(5*c + 5*d*x))/(80*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) + (9*A*a*b^2*sin(c + d*x))/(4*d) + (9*B*a^2*b*sin(c + d*x))/(4*d)","B"
233,1,202,171,0.569205,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3,x)","A\,a^3\,x+\frac{3\,B\,b^3\,x}{8}+\frac{3\,A\,a\,b^2\,x}{2}+\frac{3\,B\,a^2\,b\,x}{2}+\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{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{B\,b^3\,\sin\left(4\,c+4\,d\,x\right)}{32\,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\,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}","Not used",1,"A*a^3*x + (3*B*b^3*x)/8 + (3*A*a*b^2*x)/2 + (3*B*a^2*b*x)/2 + (3*A*b^3*sin(c + d*x))/(4*d) + (B*a^3*sin(c + d*x))/d + (A*b^3*sin(3*c + 3*d*x))/(12*d) + (B*b^3*sin(2*c + 2*d*x))/(4*d) + (B*b^3*sin(4*c + 4*d*x))/(32*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*A*a^2*b*sin(c + d*x))/d + (9*B*a*b^2*sin(c + d*x))/(4*d)","B"
234,1,1924,137,1.910073,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3)/cos(c + d*x),x)","\frac{\left(2\,B\,b^3-A\,b^3+6\,A\,a\,b^2-3\,B\,a\,b^2+6\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(12\,B\,a^2\,b+12\,A\,a\,b^2+\frac{4\,B\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(A\,b^3+2\,B\,b^3+6\,A\,a\,b^2+3\,B\,a\,b^2+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)}^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}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{2}\right)\,1{}\mathrm{i}-\left(\left(1{}\mathrm{i}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{2}\right)\,1{}\mathrm{i}}{\left(\left(1{}\mathrm{i}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{2}\right)+\left(\left(1{}\mathrm{i}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{2}\right)\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)\right)\,\left(1{}\mathrm{i}\,B\,a^3+3{}\mathrm{i}\,A\,a^2\,b+\frac{3{}\mathrm{i}\,B\,a\,b^2}{2}+\frac{1{}\mathrm{i}\,A\,b^3}{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+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}\right)\,\left(2\,B\,a^3+6\,A\,a^2\,b+3\,B\,a\,b^2+A\,b^3\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)+A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+32\,B^2\,a^6+96\,B^2\,a^4\,b^2+72\,B^2\,a^2\,b^4\right)-A\,a^3\,\left(32\,A\,a^3+16\,A\,b^3+32\,B\,a^3+96\,A\,a^2\,b+48\,B\,a\,b^2\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+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}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(A*b^3 + 2*B*b^3 + 6*A*a*b^2 + 3*B*a*b^2 + 6*B*a^2*b) + tan(c/2 + (d*x)/2)^3*((4*B*b^3)/3 + 12*A*a*b^2 + 12*B*a^2*b) + tan(c/2 + (d*x)/2)^5*(2*B*b^3 - A*b^3 + 6*A*a*b^2 - 3*B*a*b^2 + 6*B*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(((((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2) + tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*3i)/2)*1i - (((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2) - tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*3i)/2)*1i)/((((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2) + tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*3i)/2) + (((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*3i)/2)*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2) - tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3))*((A*b^3*1i)/2 + B*a^3*1i + A*a^2*b*3i + (B*a*b^2*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 + 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))*(A*b^3 + 2*B*a^3 + 6*A*a^2*b + 3*B*a*b^2))/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 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3) + A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2))*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 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3) - A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2))*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 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3) + A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2)) - A*a^3*(tan(c/2 + (d*x)/2)*(32*A^2*a^6 + 8*A^2*b^6 + 32*B^2*a^6 + 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 + 48*A*B*a*b^5 + 192*A*B*a^5*b + 320*A*B*a^3*b^3) - A*a^3*(32*A*a^3 + 16*A*b^3 + 32*B*a^3 + 96*A*a^2*b + 48*B*a*b^2)) + 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 + 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))*2i)/d","B"
235,1,236,131,1.351279,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3)/cos(c + d*x)^2,x)","\frac{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)+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)+6\,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)-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}-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{B\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{8}+A\,a^3\,\sin\left(c+d\,x\right)+\frac{B\,b^3\,\sin\left(c+d\,x\right)}{8}+\frac{3\,B\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(B*b^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 + 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 + 6*B*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + ((A*b^3*sin(2*c + 2*d*x))/2 + (B*b^3*sin(3*c + 3*d*x))/8 + A*a^3*sin(c + d*x) + (B*b^3*sin(c + d*x))/8 + (3*B*a*b^2*sin(2*c + 2*d*x))/2)/(d*cos(c + d*x))","B"
236,1,249,124,1.556366,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3)/cos(c + d*x)^3,x)","\frac{\frac{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{B\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{B\,b^3\,\sin\left(c+d\,x\right)}{4}+\frac{3\,A\,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{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)\,1{}\mathrm{i}}{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)+A\,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\,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)+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)\,3{}\mathrm{i}\right)}{d}","Not used",1,"((B*a^3*sin(2*c + 2*d*x))/2 + (B*b^3*sin(3*c + 3*d*x))/4 + (A*a^3*sin(c + d*x))/2 + (B*b^3*sin(c + d*x))/4 + (3*A*a^2*b*sin(2*c + 2*d*x))/2)/(d*(cos(2*c + 2*d*x)/2 + 1/2)) - (2*((A*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*1i)/2 - A*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + A*a*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i - 3*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))*3i))/d","B"
237,1,526,145,1.948165,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{B\,a^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{A\,a^3\,\sin\left(c+d\,x\right)}{2}+\frac{3\,A\,a\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,B\,a^2\,b\,\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{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)\,3{}\mathrm{i}}{4}+\frac{3\,B\,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\,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{3\,B\,a^2\,b\,\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{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)\,1{}\mathrm{i}}{4}+\frac{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)\,\cos\left(3\,c+3\,d\,x\right)}{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{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)\,\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{B\,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,"((A*a^3*sin(3*c + 3*d*x))/6 + (B*a^3*sin(2*c + 2*d*x))/4 + (A*a^3*sin(c + d*x))/2 + (3*A*a*b^2*sin(c + d*x))/4 + (3*B*a^2*b*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 - (B*a^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/4 + (3*B*b^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/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 + (3*B*a^2*b*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 - (B*a^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/4 + (B*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/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 - (B*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 - (A*a^2*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i)/4 - (B*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"
238,1,395,188,3.945682,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3)/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^3}{8}+\frac{3\,B\,a^2\,b}{2}+\frac{3\,A\,a\,b^2}{2}+B\,b^3\right)}{\frac{3\,A\,a^3}{2}+6\,B\,a^2\,b+6\,A\,a\,b^2+4\,B\,b^3}\right)\,\left(\frac{3\,A\,a^3}{4}+3\,B\,a^2\,b+3\,A\,a\,b^2+2\,B\,b^3\right)}{d}-\frac{\left(2\,A\,b^3-\frac{5\,A\,a^3}{4}+2\,B\,a^3-3\,A\,a\,b^2+6\,A\,a^2\,b+6\,B\,a\,b^2-3\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(3\,A\,a\,b^2-6\,A\,b^3-\frac{10\,B\,a^3}{3}-\frac{3\,A\,a^3}{4}-10\,A\,a^2\,b-18\,B\,a\,b^2+3\,B\,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}+3\,A\,a\,b^2+10\,A\,a^2\,b+18\,B\,a\,b^2+3\,B\,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^3-3\,A\,a\,b^2-6\,A\,a^2\,b-6\,B\,a\,b^2-3\,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)}^8-4\,{\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^3)/8 + B*b^3 + (3*A*a*b^2)/2 + (3*B*a^2*b)/2))/((3*A*a^3)/2 + 4*B*b^3 + 6*A*a*b^2 + 6*B*a^2*b))*((3*A*a^3)/4 + 2*B*b^3 + 3*A*a*b^2 + 3*B*a^2*b))/d - (tan(c/2 + (d*x)/2)^7*(2*A*b^3 - (5*A*a^3)/4 + 2*B*a^3 - 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 - 3*B*a^2*b) + tan(c/2 + (d*x)/2)^3*(6*A*b^3 - (3*A*a^3)/4 + (10*B*a^3)/3 + 3*A*a*b^2 + 10*A*a^2*b + 18*B*a*b^2 + 3*B*a^2*b) - tan(c/2 + (d*x)/2)^5*((3*A*a^3)/4 + 6*A*b^3 + (10*B*a^3)/3 - 3*A*a*b^2 + 10*A*a^2*b + 18*B*a*b^2 - 3*B*a^2*b) - tan(c/2 + (d*x)/2)*((5*A*a^3)/4 + 2*A*b^3 + 2*B*a^3 + 3*A*a*b^2 + 6*A*a^2*b + 6*B*a*b^2 + 3*B*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"
239,1,470,236,3.894146,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{9\,A\,a^2\,b}{8}+\frac{3\,B\,a\,b^2}{2}+\frac{A\,b^3}{2}\right)}{\frac{3\,B\,a^3}{2}+\frac{9\,A\,a^2\,b}{2}+6\,B\,a\,b^2+2\,A\,b^3}\right)\,\left(\frac{3\,B\,a^3}{4}+\frac{9\,A\,a^2\,b}{4}+3\,B\,a\,b^2+A\,b^3\right)}{d}-\frac{\left(2\,A\,a^3-A\,b^3-\frac{5\,B\,a^3}{4}+2\,B\,b^3+6\,A\,a\,b^2-\frac{15\,A\,a^2\,b}{4}-3\,B\,a\,b^2+6\,B\,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^3-16\,A\,a\,b^2+\frac{3\,A\,a^2\,b}{2}+6\,B\,a\,b^2-16\,B\,a^2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^3}{15}+20\,B\,a^2\,b+20\,A\,a\,b^2+12\,B\,b^3\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^3-16\,A\,a\,b^2-\frac{3\,A\,a^2\,b}{2}-6\,B\,a\,b^2-16\,B\,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+6\,A\,a\,b^2+\frac{15\,A\,a^2\,b}{4}+3\,B\,a\,b^2+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)}^{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 + (9*A*a^2*b)/8 + (3*B*a*b^2)/2))/(2*A*b^3 + (3*B*a^3)/2 + (9*A*a^2*b)/2 + 6*B*a*b^2))*(A*b^3 + (3*B*a^3)/4 + (9*A*a^2*b)/4 + 3*B*a*b^2))/d - (tan(c/2 + (d*x)/2)*(2*A*a^3 + A*b^3 + (5*B*a^3)/4 + 2*B*b^3 + 6*A*a*b^2 + (15*A*a^2*b)/4 + 3*B*a*b^2 + 6*B*a^2*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^3)/15 + 12*B*b^3 + 20*A*a*b^2 + 20*B*a^2*b) + tan(c/2 + (d*x)/2)^9*(2*A*a^3 - A*b^3 - (5*B*a^3)/4 + 2*B*b^3 + 6*A*a*b^2 - (15*A*a^2*b)/4 - 3*B*a*b^2 + 6*B*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*A*a*b^2 + (3*A*a^2*b)/2 + 6*B*a*b^2 + 16*B*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*A*a*b^2 - (3*A*a^2*b)/2 - 6*B*a*b^2 + 16*B*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"
240,1,436,366,2.635188,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4,x)","\frac{420\,A\,a^4\,\sin\left(2\,c+2\,d\,x\right)+\frac{1575\,A\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4}+140\,B\,a^4\,\sin\left(3\,c+3\,d\,x\right)+\frac{315\,A\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{35\,A\,b^4\,\sin\left(6\,c+6\,d\,x\right)}{4}+\frac{735\,B\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{147\,B\,b^4\,\sin\left(5\,c+5\,d\,x\right)}{4}+\frac{15\,B\,b^4\,\sin\left(7\,c+7\,d\,x\right)}{4}+1260\,B\,a^4\,\sin\left(c+d\,x\right)+\frac{3675\,B\,b^4\,\sin\left(c+d\,x\right)}{4}+4200\,A\,a\,b^3\,\sin\left(c+d\,x\right)+5040\,A\,a^3\,b\,\sin\left(c+d\,x\right)+840\,A\,a^4\,d\,x+525\,A\,b^4\,d\,x+700\,A\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)+560\,A\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)+84\,A\,a\,b^3\,\sin\left(5\,c+5\,d\,x\right)+1575\,B\,a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+1680\,B\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+315\,B\,a\,b^3\,\sin\left(4\,c+4\,d\,x\right)+210\,B\,a^3\,b\,\sin\left(4\,c+4\,d\,x\right)+35\,B\,a\,b^3\,\sin\left(6\,c+6\,d\,x\right)+6300\,B\,a^2\,b^2\,\sin\left(c+d\,x\right)+2520\,A\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)+315\,A\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)+1050\,B\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)+126\,B\,a^2\,b^2\,\sin\left(5\,c+5\,d\,x\right)+2100\,B\,a\,b^3\,d\,x+2520\,B\,a^3\,b\,d\,x+3780\,A\,a^2\,b^2\,d\,x}{1680\,d}","Not used",1,"(420*A*a^4*sin(2*c + 2*d*x) + (1575*A*b^4*sin(2*c + 2*d*x))/4 + 140*B*a^4*sin(3*c + 3*d*x) + (315*A*b^4*sin(4*c + 4*d*x))/4 + (35*A*b^4*sin(6*c + 6*d*x))/4 + (735*B*b^4*sin(3*c + 3*d*x))/4 + (147*B*b^4*sin(5*c + 5*d*x))/4 + (15*B*b^4*sin(7*c + 7*d*x))/4 + 1260*B*a^4*sin(c + d*x) + (3675*B*b^4*sin(c + d*x))/4 + 4200*A*a*b^3*sin(c + d*x) + 5040*A*a^3*b*sin(c + d*x) + 840*A*a^4*d*x + 525*A*b^4*d*x + 700*A*a*b^3*sin(3*c + 3*d*x) + 560*A*a^3*b*sin(3*c + 3*d*x) + 84*A*a*b^3*sin(5*c + 5*d*x) + 1575*B*a*b^3*sin(2*c + 2*d*x) + 1680*B*a^3*b*sin(2*c + 2*d*x) + 315*B*a*b^3*sin(4*c + 4*d*x) + 210*B*a^3*b*sin(4*c + 4*d*x) + 35*B*a*b^3*sin(6*c + 6*d*x) + 6300*B*a^2*b^2*sin(c + d*x) + 2520*A*a^2*b^2*sin(2*c + 2*d*x) + 315*A*a^2*b^2*sin(4*c + 4*d*x) + 1050*B*a^2*b^2*sin(3*c + 3*d*x) + 126*B*a^2*b^2*sin(5*c + 5*d*x) + 2100*B*a*b^3*d*x + 2520*B*a^3*b*d*x + 3780*A*a^2*b^2*d*x)/(1680*d)","B"
241,1,403,325,1.370733,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4,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{A\,a^4\,\sin\left(c+d\,x\right)}{d}+\frac{5\,A\,b^4\,\sin\left(c+d\,x\right)}{8\,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{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{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{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\,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 + (A*a^4*sin(c + d*x))/d + (5*A*b^4*sin(c + d*x))/(8*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) + (3*B*b^4*sin(4*c + 4*d*x))/(64*d) + (B*b^4*sin(6*c + 6*d*x))/(192*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) + (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*B*a*b^3*sin(c + d*x))/(2*d) + (3*B*a^3*b*sin(c + d*x))/d","B"
242,1,307,241,0.878011,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4,x)","A\,a^4\,x+\frac{3\,A\,b^4\,x}{8}+\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{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{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{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{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\,A\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{4\,A\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"A*a^4*x + (3*A*b^4*x)/8 + (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 + (A*b^4*sin(2*c + 2*d*x))/(4*d) + (A*b^4*sin(4*c + 4*d*x))/(32*d) + (5*B*b^4*sin(3*c + 3*d*x))/(48*d) + (B*b^4*sin(5*c + 5*d*x))/(80*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) + (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*A*a*b^3*sin(c + d*x))/d + (4*A*a^3*b*sin(c + d*x))/d","B"
243,1,369,200,1.419309,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4)/cos(c + d*x),x)","\frac{3\,A\,b^4\,\sin\left(c+d\,x\right)}{4\,d}+\frac{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)}{d}+\frac{2\,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)}{d}+\frac{3\,B\,b^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\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{B\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{B\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{4\,A\,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)}{d}+\frac{8\,A\,a^3\,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\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{6\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{B\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{6\,B\,a^2\,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{3\,B\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,B\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{4\,B\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*A*b^4*sin(c + d*x))/(4*d) + (2*A*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*B*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*B*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (A*b^4*sin(3*c + 3*d*x))/(12*d) + (B*b^4*sin(2*c + 2*d*x))/(4*d) + (B*b^4*sin(4*c + 4*d*x))/(32*d) + (4*A*a*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*A*a^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (A*a*b^3*sin(2*c + 2*d*x))/d + (6*A*a^2*b^2*sin(c + d*x))/d + (B*a*b^3*sin(3*c + 3*d*x))/(3*d) + (6*B*a^2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*B*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*B*a*b^3*sin(c + d*x))/d + (4*B*a^3*b*sin(c + d*x))/d","B"
244,1,2522,195,2.268639,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4)/cos(c + d*x)^2,x)","\frac{\left(2\,A\,a^4+A\,b^4-2\,B\,b^4-12\,B\,a^2\,b^2-8\,A\,a\,b^3+4\,B\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,A\,a^4-A\,b^4+\frac{2\,B\,b^4}{3}-12\,B\,a^2\,b^2-8\,A\,a\,b^3-4\,B\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,A\,a^4-A\,b^4-\frac{2\,B\,b^4}{3}+12\,B\,a^2\,b^2+8\,A\,a\,b^3-4\,B\,a\,b^3\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+12\,B\,a^2\,b^2+8\,A\,a\,b^3+4\,B\,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)}^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(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+192\,A\,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+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\right)\right)\,1{}\mathrm{i}-\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+192\,A\,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+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\right)\right)\,1{}\mathrm{i}}{\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+192\,A\,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+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\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+192\,A\,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+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\right)\right)-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+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}\right)\,\left(2{}\mathrm{i}\,B\,a^4+8{}\mathrm{i}\,A\,b\,a^3\right)}{d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\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+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\right)-\frac{b\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+192\,A\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)}{2}+\frac{b\,\left(\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+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\right)+\frac{b\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+192\,A\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)}{2}}{64\,A^3\,a^3\,b^9-256\,B^3\,a^{11}\,b+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+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-\frac{b\,\left(\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+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\right)-\frac{b\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+192\,A\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)\,1{}\mathrm{i}}{2}+\frac{b\,\left(\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+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\right)+\frac{b\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)\,\left(16\,A\,b^4+32\,B\,a^4+192\,A\,a^2\,b^2+128\,A\,a^3\,b+64\,B\,a\,b^3+128\,B\,a^3\,b\right)\,1{}\mathrm{i}}{2}\right)\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)\,1{}\mathrm{i}}{2}}\right)\,\left(8\,B\,a^3+12\,A\,a^2\,b+4\,B\,a\,b^2+A\,b^3\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*A*a^4 + A*b^4 + 2*B*b^4 + 12*B*a^2*b^2 + 8*A*a*b^3 + 4*B*a*b^3) + tan(c/2 + (d*x)/2)^7*(2*A*a^4 + A*b^4 - 2*B*b^4 - 12*B*a^2*b^2 - 8*A*a*b^3 + 4*B*a*b^3) + tan(c/2 + (d*x)/2)^3*(6*A*a^4 - A*b^4 - (2*B*b^4)/3 + 12*B*a^2*b^2 + 8*A*a*b^3 - 4*B*a*b^3) - tan(c/2 + (d*x)/2)^5*(A*b^4 - 6*A*a^4 - (2*B*b^4)/3 + 12*B*a^2*b^2 + 8*A*a*b^3 + 4*B*a*b^3))/(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^4 + 4*A*a^3*b)*((B*a^4 + 4*A*a^3*b)*(16*A*b^4 + 32*B*a^4 + 192*A*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 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3))*1i - (B*a^4 + 4*A*a^3*b)*((B*a^4 + 4*A*a^3*b)*(16*A*b^4 + 32*B*a^4 + 192*A*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 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3))*1i)/((B*a^4 + 4*A*a^3*b)*((B*a^4 + 4*A*a^3*b)*(16*A*b^4 + 32*B*a^4 + 192*A*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 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*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 + 192*A*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 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3)) - 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 + 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))*(B*a^4*2i + A*a^3*b*8i))/d - (b*atan(((b*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3) - (b*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2)*(16*A*b^4 + 32*B*a^4 + 192*A*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)/2)*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2))/2 + (b*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3) + (b*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2)*(16*A*b^4 + 32*B*a^4 + 192*A*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)/2)*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2))/2)/(64*A^3*a^3*b^9 - 256*B^3*a^11*b + 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 - (b*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3) - (b*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2)*(16*A*b^4 + 32*B*a^4 + 192*A*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)/2)*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2)*1i)/2 + (b*(tan(c/2 + (d*x)/2)*(8*A^2*b^8 + 32*B^2*a^8 + 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 + 64*A*B*a*b^7 + 256*A*B*a^7*b + 896*A*B*a^3*b^5 + 1536*A*B*a^5*b^3) + (b*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2)*(16*A*b^4 + 32*B*a^4 + 192*A*a^2*b^2 + 128*A*a^3*b + 64*B*a*b^3 + 128*B*a^3*b)*1i)/2)*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2)*1i)/2 + 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))*(A*b^3 + 8*B*a^3 + 12*A*a^2*b + 4*B*a*b^2))/d","B"
245,1,330,209,2.314146,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4)/cos(c + d*x)^3,x)","\frac{2\,\left(\frac{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)}{2}+\frac{B\,b^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}+4\,A\,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)+4\,B\,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)+6\,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)+6\,B\,a^2\,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)\right)}{d}+\frac{\frac{B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{A\,b^4\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{B\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{8}+\frac{B\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{16}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{2}+\frac{A\,b^4\,\sin\left(c+d\,x\right)}{4}+B\,a\,b^3\,\sin\left(c+d\,x\right)+2\,A\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+B\,a\,b^3\,\sin\left(3\,c+3\,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^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (B*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + 4*A*a*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 4*B*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*A*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 6*B*a^2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))))/d + ((B*a^4*sin(2*c + 2*d*x))/2 + (A*b^4*sin(3*c + 3*d*x))/4 + (B*b^4*sin(2*c + 2*d*x))/8 + (B*b^4*sin(4*c + 4*d*x))/16 + (A*a^4*sin(c + d*x))/2 + (A*b^4*sin(c + d*x))/4 + B*a*b^3*sin(c + d*x) + 2*A*a^3*b*sin(2*c + 2*d*x) + B*a*b^3*sin(3*c + 3*d*x))/(d*(cos(2*c + 2*d*x)/2 + 1/2))","B"
246,1,636,198,2.831152,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4)/cos(c + d*x)^4,x)","\frac{\frac{A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{6}+\frac{B\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{B\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{8}+\frac{A\,a^4\,\sin\left(c+d\,x\right)}{2}+B\,a^3\,b\,\sin\left(c+d\,x\right)+\frac{3\,A\,b^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}+A\,a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+\frac{3\,A\,a^2\,b^2\,\sin\left(c+d\,x\right)}{2}+B\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)+\frac{A\,b^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}+\frac{3\,A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{2}+2\,B\,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)\,\cos\left(3\,c+3\,d\,x\right)+6\,B\,a\,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)-\frac{B\,a^4\,\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{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)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}}{4}-A\,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)\,2{}\mathrm{i}-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)\,\cos\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}-B\,a^2\,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}-B\,a^2\,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}-A\,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)\,6{}\mathrm{i}-A\,a^3\,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)\,3{}\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^4*sin(3*c + 3*d*x))/6 + (B*a^4*sin(2*c + 2*d*x))/4 + (B*b^4*sin(2*c + 2*d*x))/4 + (B*b^4*sin(4*c + 4*d*x))/8 + (A*a^4*sin(c + d*x))/2 + B*a^3*b*sin(c + d*x) + (3*A*b^4*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (B*a^4*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/4 + A*a^3*b*sin(2*c + 2*d*x) + (3*A*a^2*b^2*sin(c + d*x))/2 + B*a^3*b*sin(3*c + 3*d*x) + (A*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (B*a^4*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i)/4 + (3*A*a^2*b^2*sin(3*c + 3*d*x))/2 - A*a*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*2i - A*a^3*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*1i + 2*B*a*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x) - B*a^2*b^2*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*9i - B*a^2*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*3i - A*a*b^3*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*6i - A*a^3*b*cos(c + d*x)*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i + 6*B*a*b^3*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
247,1,1969,216,2.976052,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,A\,a^4\,\sin\left(3\,c+3\,d\,x\right)}{8}+4\,B\,a^4\,\sin\left(2\,c+2\,d\,x\right)+B\,a^4\,\sin\left(4\,c+4\,d\,x\right)+9\,B\,b^4\,\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+96\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+1792\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+512\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+256\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8}{\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+96\,A\,B\,a^7\,b+960\,A\,B\,a^5\,b^3+1792\,A\,B\,a^3\,b^5+512\,A\,B\,a\,b^7+256\,B^2\,a^6\,b^2+1024\,B^2\,a^4\,b^4+1024\,B^2\,a^2\,b^6+64\,B^2\,b^8\right)}\right)+\frac{33\,A\,a^4\,\sin\left(c+d\,x\right)}{8}+12\,B\,b^4\,\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+96\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+1792\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+512\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+256\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8}{\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+96\,A\,B\,a^7\,b+960\,A\,B\,a^5\,b^3+1792\,A\,B\,a^3\,b^5+512\,A\,B\,a\,b^7+256\,B^2\,a^6\,b^2+1024\,B^2\,a^4\,b^4+1024\,B^2\,a^2\,b^6+64\,B^2\,b^8\right)}\right)+3\,B\,b^4\,\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+96\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^7\,b+960\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^5\,b^3+1792\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a^3\,b^5+512\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,A\,B\,a\,b^7+256\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^6\,b^2+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^4\,b^4+1024\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,a^2\,b^6+64\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,B^2\,b^8}{\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+96\,A\,B\,a^7\,b+960\,A\,B\,a^5\,b^3+1792\,A\,B\,a^3\,b^5+512\,A\,B\,a\,b^7+256\,B^2\,a^6\,b^2+1024\,B^2\,a^4\,b^4+1024\,B^2\,a^2\,b^6+64\,B^2\,b^8\right)}\right)+6\,B\,a^3\,b\,\sin\left(c+d\,x\right)+36\,B\,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)+18\,B\,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)+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)+6\,B\,a^3\,b\,\sin\left(3\,c+3\,d\,x\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)+9\,A\,a^2\,b^2\,\sin\left(3\,c+3\,d\,x\right)+18\,B\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)+9\,B\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)+48\,B\,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(2\,c+2\,d\,x\right)+24\,B\,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(2\,c+2\,d\,x\right)+12\,B\,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(4\,c+4\,d\,x\right)+6\,B\,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(4\,c+4\,d\,x\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)}{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*A*a^4*sin(3*c + 3*d*x))/8 + 4*B*a^4*sin(2*c + 2*d*x) + B*a^4*sin(4*c + 4*d*x) + 9*B*b^4*atan((9*A^2*a^8*sin(c/2 + (d*x)/2) + 64*A^2*b^8*sin(c/2 + (d*x)/2) + 64*B^2*b^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*B^2*a^2*b^6*sin(c/2 + (d*x)/2) + 1024*B^2*a^4*b^4*sin(c/2 + (d*x)/2) + 256*B^2*a^6*b^2*sin(c/2 + (d*x)/2) + 1792*A*B*a^3*b^5*sin(c/2 + (d*x)/2) + 960*A*B*a^5*b^3*sin(c/2 + (d*x)/2) + 512*A*B*a*b^7*sin(c/2 + (d*x)/2) + 96*A*B*a^7*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^8 + 64*A^2*b^8 + 64*B^2*b^8 + 384*A^2*a^2*b^6 + 624*A^2*a^4*b^4 + 144*A^2*a^6*b^2 + 1024*B^2*a^2*b^6 + 1024*B^2*a^4*b^4 + 256*B^2*a^6*b^2 + 512*A*B*a*b^7 + 96*A*B*a^7*b + 1792*A*B*a^3*b^5 + 960*A*B*a^5*b^3))) + (33*A*a^4*sin(c + d*x))/8 + 12*B*b^4*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) + 64*B^2*b^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*B^2*a^2*b^6*sin(c/2 + (d*x)/2) + 1024*B^2*a^4*b^4*sin(c/2 + (d*x)/2) + 256*B^2*a^6*b^2*sin(c/2 + (d*x)/2) + 1792*A*B*a^3*b^5*sin(c/2 + (d*x)/2) + 960*A*B*a^5*b^3*sin(c/2 + (d*x)/2) + 512*A*B*a*b^7*sin(c/2 + (d*x)/2) + 96*A*B*a^7*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^8 + 64*A^2*b^8 + 64*B^2*b^8 + 384*A^2*a^2*b^6 + 624*A^2*a^4*b^4 + 144*A^2*a^6*b^2 + 1024*B^2*a^2*b^6 + 1024*B^2*a^4*b^4 + 256*B^2*a^6*b^2 + 512*A*B*a*b^7 + 96*A*B*a^7*b + 1792*A*B*a^3*b^5 + 960*A*B*a^5*b^3))) + 3*B*b^4*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) + 64*B^2*b^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*B^2*a^2*b^6*sin(c/2 + (d*x)/2) + 1024*B^2*a^4*b^4*sin(c/2 + (d*x)/2) + 256*B^2*a^6*b^2*sin(c/2 + (d*x)/2) + 1792*A*B*a^3*b^5*sin(c/2 + (d*x)/2) + 960*A*B*a^5*b^3*sin(c/2 + (d*x)/2) + 512*A*B*a*b^7*sin(c/2 + (d*x)/2) + 96*A*B*a^7*b*sin(c/2 + (d*x)/2))/(cos(c/2 + (d*x)/2)*(9*A^2*a^8 + 64*A^2*b^8 + 64*B^2*b^8 + 384*A^2*a^2*b^6 + 624*A^2*a^4*b^4 + 144*A^2*a^6*b^2 + 1024*B^2*a^2*b^6 + 1024*B^2*a^4*b^4 + 256*B^2*a^6*b^2 + 512*A*B*a*b^7 + 96*A*B*a^7*b + 1792*A*B*a^3*b^5 + 960*A*B*a^5*b^3))) + 6*B*a^3*b*sin(c + d*x) + 36*B*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 18*B*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (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) + 6*B*a^3*b*sin(3*c + 3*d*x) + (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) + 9*A*a^2*b^2*sin(3*c + 3*d*x) + 18*B*a^2*b^2*sin(2*c + 2*d*x) + 9*B*a^2*b^2*sin(4*c + 4*d*x) + 48*B*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 24*B*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + 12*B*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 6*B*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(4*c + 4*d*x) + 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))/(12*d*(cos(2*c + 2*d*x)/2 + cos(4*c + 4*d*x)/8 + 3/8))","B"
248,1,555,267,3.879051,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4)/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^4}{8}+\frac{3\,A\,a^3\,b}{2}+3\,B\,a^2\,b^2+2\,A\,a\,b^3+B\,b^4\right)}{\frac{3\,B\,a^4}{2}+6\,A\,a^3\,b+12\,B\,a^2\,b^2+8\,A\,a\,b^3+4\,B\,b^4}\right)\,\left(\frac{3\,B\,a^4}{4}+3\,A\,a^3\,b+6\,B\,a^2\,b^2+4\,A\,a\,b^3+2\,B\,b^4\right)}{d}-\frac{\left(2\,A\,a^4+2\,A\,b^4-\frac{5\,B\,a^4}{4}+12\,A\,a^2\,b^2-6\,B\,a^2\,b^2-4\,A\,a\,b^3-5\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,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}-32\,A\,a^2\,b^2+12\,B\,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}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,A\,a^4}{15}+\frac{80\,B\,a^3\,b}{3}+40\,A\,a^2\,b^2+48\,B\,a\,b^3+12\,A\,b^4\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}-32\,A\,a^2\,b^2-12\,B\,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}\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}+12\,A\,a^2\,b^2+6\,B\,a^2\,b^2+4\,A\,a\,b^3+5\,A\,a^3\,b+8\,B\,a\,b^3+8\,B\,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)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((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))/((3*B*a^4)/2 + 4*B*b^4 + 12*B*a^2*b^2 + 8*A*a*b^3 + 6*A*a^3*b))*((3*B*a^4)/4 + 2*B*b^4 + 6*B*a^2*b^2 + 4*A*a*b^3 + 3*A*a^3*b))/d - (tan(c/2 + (d*x)/2)*(2*A*a^4 + 2*A*b^4 + (5*B*a^4)/4 + 12*A*a^2*b^2 + 6*B*a^2*b^2 + 4*A*a*b^3 + 5*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b) + tan(c/2 + (d*x)/2)^5*((116*A*a^4)/15 + 12*A*b^4 + 40*A*a^2*b^2 + 48*B*a*b^3 + (80*B*a^3*b)/3) + tan(c/2 + (d*x)/2)^9*(2*A*a^4 + 2*A*b^4 - (5*B*a^4)/4 + 12*A*a^2*b^2 - 6*B*a^2*b^2 - 4*A*a*b^3 - 5*A*a^3*b + 8*B*a*b^3 + 8*B*a^3*b) - tan(c/2 + (d*x)/2)^3*((8*A*a^4)/3 + 8*A*b^4 + (B*a^4)/2 + 32*A*a^2*b^2 + 12*B*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) - tan(c/2 + (d*x)/2)^7*((8*A*a^4)/3 + 8*A*b^4 - (B*a^4)/2 + 32*A*a^2*b^2 - 12*B*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))/(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"
249,1,706,324,3.751099,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^4)/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^4}{16}+\frac{3\,B\,a^3\,b}{2}+\frac{9\,A\,a^2\,b^2}{4}+2\,B\,a\,b^3+\frac{A\,b^4}{2}\right)}{\frac{5\,A\,a^4}{4}+6\,B\,a^3\,b+9\,A\,a^2\,b^2+8\,B\,a\,b^3+2\,A\,b^4}\right)\,\left(\frac{5\,A\,a^4}{8}+3\,B\,a^3\,b+\frac{9\,A\,a^2\,b^2}{2}+4\,B\,a\,b^3+A\,b^4\right)}{d}+\frac{\left(\frac{11\,A\,a^4}{8}+A\,b^4-2\,B\,a^4-2\,B\,b^4+\frac{15\,A\,a^2\,b^2}{2}-12\,B\,a^2\,b^2-8\,A\,a\,b^3-8\,A\,a^3\,b+4\,B\,a\,b^3+5\,B\,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{21\,A\,a^2\,b^2}{2}+44\,B\,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\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+3\,A\,a^2\,b^2-72\,B\,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\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+3\,A\,a^2\,b^2+72\,B\,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\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{21\,A\,a^2\,b^2}{2}-44\,B\,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\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{15\,A\,a^2\,b^2}{2}+12\,B\,a^2\,b^2+8\,A\,a\,b^3+8\,A\,a^3\,b+4\,B\,a\,b^3+5\,B\,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)}","Not used",1,"(atanh((4*tan(c/2 + (d*x)/2)*((5*A*a^4)/16 + (A*b^4)/2 + (9*A*a^2*b^2)/4 + 2*B*a*b^3 + (3*B*a^3*b)/2))/((5*A*a^4)/4 + 2*A*b^4 + 9*A*a^2*b^2 + 8*B*a*b^3 + 6*B*a^3*b))*((5*A*a^4)/8 + A*b^4 + (9*A*a^2*b^2)/2 + 4*B*a*b^3 + 3*B*a^3*b))/d + (tan(c/2 + (d*x)/2)*((11*A*a^4)/8 + A*b^4 + 2*B*a^4 + 2*B*b^4 + (15*A*a^2*b^2)/2 + 12*B*a^2*b^2 + 8*A*a*b^3 + 8*A*a^3*b + 4*B*a*b^3 + 5*B*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 + (15*A*a^2*b^2)/2 - 12*B*a^2*b^2 - 8*A*a*b^3 - 8*A*a^3*b + 4*B*a*b^3 + 5*B*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 + (21*A*a^2*b^2)/2 + 44*B*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) + 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 - (21*A*a^2*b^2)/2 + 44*B*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) + 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 + 3*A*a^2*b^2 + 72*B*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) + 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 + 3*A*a^2*b^2 - 72*B*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))/(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"
250,1,4568,178,5.088368,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,b^2+2\,B\,a^2+2\,B\,b^2-2\,A\,a\,b-B\,a\,b\right)}{b^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,B\,a^2-A\,b^2+2\,B\,b^2-2\,A\,a\,b+B\,a\,b\right)}{b^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,B\,a^2-3\,A\,a\,b+B\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}+\frac{\left(2\,a^2+b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}+\frac{\left(2\,a^2+b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}-\frac{\left(2\,a^2+b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,1{}\mathrm{i}}{2\,b^4}\right)}{2\,b^4}}{\frac{16\,\left(-4\,A^3\,a^8\,b^3+6\,A^3\,a^7\,b^4-6\,A^3\,a^6\,b^5+5\,A^3\,a^5\,b^6-2\,A^3\,a^4\,b^7+A^3\,a^3\,b^8+12\,A^2\,B\,a^9\,b^2-18\,A^2\,B\,a^8\,b^3+18\,A^2\,B\,a^7\,b^4-15\,A^2\,B\,a^6\,b^5+6\,A^2\,B\,a^5\,b^6-3\,A^2\,B\,a^4\,b^7-12\,A\,B^2\,a^{10}\,b+18\,A\,B^2\,a^9\,b^2-18\,A\,B^2\,a^8\,b^3+15\,A\,B^2\,a^7\,b^4-6\,A\,B^2\,a^6\,b^5+3\,A\,B^2\,a^5\,b^6+4\,B^3\,a^{11}-6\,B^3\,a^{10}\,b+6\,B^3\,a^9\,b^2-5\,B^3\,a^8\,b^3+2\,B^3\,a^7\,b^4-B^3\,a^6\,b^5\right)}{b^9}-\frac{\left(2\,a^2+b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}+\frac{\left(2\,a^2+b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(2\,a^2+b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^2\,a^2\,b^7\right)}{b^6}-\frac{\left(2\,a^2+b^2\right)\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,a\right)\,\left(8\,a^3\,b^8-16\,a^2\,b^9+8\,a\,b^{10}\right)\,4{}\mathrm{i}}{b^{10}}\right)\,1{}\mathrm{i}}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}}\right)\,\left(2\,a^2+b^2\right)\,\left(A\,b-B\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,a\right)}{b^6-a^2\,b^4}\right)\,1{}\mathrm{i}}{b^6-a^2\,b^4}}{\frac{16\,\left(-4\,A^3\,a^8\,b^3+6\,A^3\,a^7\,b^4-6\,A^3\,a^6\,b^5+5\,A^3\,a^5\,b^6-2\,A^3\,a^4\,b^7+A^3\,a^3\,b^8+12\,A^2\,B\,a^9\,b^2-18\,A^2\,B\,a^8\,b^3+18\,A^2\,B\,a^7\,b^4-15\,A^2\,B\,a^6\,b^5+6\,A^2\,B\,a^5\,b^6-3\,A^2\,B\,a^4\,b^7-12\,A\,B^2\,a^{10}\,b+18\,A\,B^2\,a^9\,b^2-18\,A\,B^2\,a^8\,b^3+15\,A\,B^2\,a^7\,b^4-6\,A\,B^2\,a^6\,b^5+3\,A\,B^2\,a^5\,b^6+4\,B^3\,a^{11}-6\,B^3\,a^{10}\,b+6\,B^3\,a^9\,b^2-5\,B^3\,a^8\,b^3+2\,B^3\,a^7\,b^4-B^3\,a^6\,b^5\right)}{b^9}-\frac{a^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,A^2\,a^7\,b^2+16\,A^2\,a^6\,b^3-16\,A^2\,a^5\,b^4+16\,A^2\,a^4\,b^5-13\,A^2\,a^3\,b^6+7\,A^2\,a^2\,b^7-3\,A^2\,a\,b^8+A^2\,b^9+16\,A\,B\,a^8\,b-32\,A\,B\,a^7\,b^2+32\,A\,B\,a^6\,b^3-32\,A\,B\,a^5\,b^4+26\,A\,B\,a^4\,b^5-14\,A\,B\,a^3\,b^6+6\,A\,B\,a^2\,b^7-2\,A\,B\,a\,b^8-8\,B^2\,a^9+16\,B^2\,a^8\,b-16\,B^2\,a^7\,b^2+16\,B^2\,a^6\,b^3-13\,B^2\,a^5\,b^4+7\,B^2\,a^4\,b^5-3\,B^2\,a^3\,b^6+B^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\,A\,b^{13}+2\,A\,a^2\,b^{11}-6\,A\,a^3\,b^{10}+4\,A\,a^4\,b^9+2\,B\,a^2\,b^{11}-2\,B\,a^3\,b^{10}+6\,B\,a^4\,b^9-4\,B\,a^5\,b^8-2\,A\,a\,b^{12}-2\,B\,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(A\,b-B\,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(A\,b-B\,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(A\,b-B\,a\right)\,2{}\mathrm{i}}{d\,\left(b^6-a^2\,b^4\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 - 2*A*a*b - B*a*b))/b^3 + (tan(c/2 + (d*x)/2)^5*(2*B*a^2 - A*b^2 + 2*B*b^2 - 2*A*a*b + B*a*b))/b^3 + (4*tan(c/2 + (d*x)/2)^3*(3*B*a^2 + B*b^2 - 3*A*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)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + ((2*a^2 + b^2)*(A*b - B*a)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 - (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*1i)/(2*b^4)))/(2*b^4) + ((2*a^2 + b^2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - ((2*a^2 + b^2)*(A*b - B*a)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 + (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*1i)/(2*b^4)))/(2*b^4))/((16*(4*B^3*a^11 - 6*B^3*a^10*b + A^3*a^3*b^8 - 2*A^3*a^4*b^7 + 5*A^3*a^5*b^6 - 6*A^3*a^6*b^5 + 6*A^3*a^7*b^4 - 4*A^3*a^8*b^3 - B^3*a^6*b^5 + 2*B^3*a^7*b^4 - 5*B^3*a^8*b^3 + 6*B^3*a^9*b^2 - 12*A*B^2*a^10*b + 3*A*B^2*a^5*b^6 - 6*A*B^2*a^6*b^5 + 15*A*B^2*a^7*b^4 - 18*A*B^2*a^8*b^3 + 18*A*B^2*a^9*b^2 - 3*A^2*B*a^4*b^7 + 6*A^2*B*a^5*b^6 - 15*A^2*B*a^6*b^5 + 18*A^2*B*a^7*b^4 - 18*A^2*B*a^8*b^3 + 12*A^2*B*a^9*b^2))/b^9 - ((2*a^2 + b^2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + ((2*a^2 + b^2)*(A*b - B*a)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 - (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*1i)/(2*b^4))*1i)/(2*b^4) + ((2*a^2 + b^2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - ((2*a^2 + b^2)*(A*b - B*a)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 + (tan(c/2 + (d*x)/2)*(2*a^2 + b^2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8)*4i)/b^10)*1i)/(2*b^4))*1i)/(2*b^4)))*(2*a^2 + b^2)*(A*b - B*a))/(b^4*d) + (a^3*atan(((a^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4) + (a^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4))*1i)/(b^6 - a^2*b^4))/((16*(4*B^3*a^11 - 6*B^3*a^10*b + A^3*a^3*b^8 - 2*A^3*a^4*b^7 + 5*A^3*a^5*b^6 - 6*A^3*a^6*b^5 + 6*A^3*a^7*b^4 - 4*A^3*a^8*b^3 - B^3*a^6*b^5 + 2*B^3*a^7*b^4 - 5*B^3*a^8*b^3 + 6*B^3*a^9*b^2 - 12*A*B^2*a^10*b + 3*A*B^2*a^5*b^6 - 6*A*B^2*a^6*b^5 + 15*A*B^2*a^7*b^4 - 18*A*B^2*a^8*b^3 + 18*A*B^2*a^9*b^2 - 3*A^2*B*a^4*b^7 + 6*A^2*B*a^5*b^6 - 15*A^2*B*a^6*b^5 + 18*A^2*B*a^7*b^4 - 18*A^2*B*a^8*b^3 + 12*A^2*B*a^9*b^2))/b^9 - (a^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 + (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 - (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4) + (a^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(A^2*b^9 - 8*B^2*a^9 - 3*A^2*a*b^8 + 16*B^2*a^8*b + 7*A^2*a^2*b^7 - 13*A^2*a^3*b^6 + 16*A^2*a^4*b^5 - 16*A^2*a^5*b^4 + 16*A^2*a^6*b^3 - 8*A^2*a^7*b^2 + B^2*a^2*b^7 - 3*B^2*a^3*b^6 + 7*B^2*a^4*b^5 - 13*B^2*a^5*b^4 + 16*B^2*a^6*b^3 - 16*B^2*a^7*b^2 - 2*A*B*a*b^8 + 16*A*B*a^8*b + 6*A*B*a^2*b^7 - 14*A*B*a^3*b^6 + 26*A*B*a^4*b^5 - 32*A*B*a^5*b^4 + 32*A*B*a^6*b^3 - 32*A*B*a^7*b^2))/b^6 - (a^3*(-(a + b)*(a - b))^(1/2)*((8*(2*A*b^13 + 2*A*a^2*b^11 - 6*A*a^3*b^10 + 4*A*a^4*b^9 + 2*B*a^2*b^11 - 2*B*a^3*b^10 + 6*B*a^4*b^9 - 4*B*a^5*b^8 - 2*A*a*b^12 - 2*B*a*b^12))/b^9 + (8*a^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^10 - 16*a^2*b^9 + 8*a^3*b^8))/(b^6*(b^6 - a^2*b^4)))*(A*b - B*a))/(b^6 - a^2*b^4)))/(b^6 - a^2*b^4)))*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*2i)/(d*(b^6 - a^2*b^4))","B"
251,1,3761,134,3.997971,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A\,b-2\,B\,a+B\,b\right)}{b^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,B\,a-2\,A\,b+B\,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\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,a\,b^9\right)}{b^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,b^3}-\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,a\,b^9\right)}{b^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,b^3}}{\frac{16\,\left(-4\,A^3\,a^5\,b^3+4\,A^3\,a^4\,b^4+12\,A^2\,B\,a^6\,b^2-14\,A^2\,B\,a^5\,b^3+6\,A^2\,B\,a^4\,b^4-4\,A^2\,B\,a^3\,b^5-12\,A\,B^2\,a^7\,b+16\,A\,B^2\,a^6\,b^2-12\,A\,B^2\,a^5\,b^3+9\,A\,B^2\,a^4\,b^4-2\,A\,B^2\,a^3\,b^5+A\,B^2\,a^2\,b^6+4\,B^3\,a^8-6\,B^3\,a^7\,b+6\,B^3\,a^6\,b^2-5\,B^3\,a^5\,b^3+2\,B^3\,a^4\,b^4-B^3\,a^3\,b^5\right)}{b^6}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,a\,b^9\right)}{b^6}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^3}+\frac{\left(\frac{\left(\frac{8\,\left(2\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,a\,b^9\right)}{b^6}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^3}}\right)\,\left(2{}\mathrm{i}\,B\,a^2-2{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,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(A\,b-B\,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)}{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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,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(A\,b-B\,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)}{b^5-a^2\,b^3}\right)\,1{}\mathrm{i}}{b^5-a^2\,b^3}}{\frac{16\,\left(-4\,A^3\,a^5\,b^3+4\,A^3\,a^4\,b^4+12\,A^2\,B\,a^6\,b^2-14\,A^2\,B\,a^5\,b^3+6\,A^2\,B\,a^4\,b^4-4\,A^2\,B\,a^3\,b^5-12\,A\,B^2\,a^7\,b+16\,A\,B^2\,a^6\,b^2-12\,A\,B^2\,a^5\,b^3+9\,A\,B^2\,a^4\,b^4-2\,A\,B^2\,a^3\,b^5+A\,B^2\,a^2\,b^6+4\,B^3\,a^8-6\,B^3\,a^7\,b+6\,B^3\,a^6\,b^2-5\,B^3\,a^5\,b^3+2\,B^3\,a^4\,b^4-B^3\,a^3\,b^5\right)}{b^6}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}+\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,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(A\,b-B\,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)}{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(A\,b-B\,a\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^5\,b^2-16\,A^2\,a^4\,b^3+12\,A^2\,a^3\,b^4-4\,A^2\,a^2\,b^5-16\,A\,B\,a^6\,b+32\,A\,B\,a^5\,b^2-28\,A\,B\,a^4\,b^3+20\,A\,B\,a^3\,b^4-12\,A\,B\,a^2\,b^5+4\,A\,B\,a\,b^6+8\,B^2\,a^7-16\,B^2\,a^6\,b+16\,B^2\,a^5\,b^2-16\,B^2\,a^4\,b^3+13\,B^2\,a^3\,b^4-7\,B^2\,a^2\,b^5+3\,B^2\,a\,b^6-B^2\,b^7\right)}{b^4}-\frac{a^2\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,\left(\frac{8\,\left(2\,B\,b^{10}+8\,A\,a^2\,b^8-4\,A\,a^3\,b^7+2\,B\,a^2\,b^8-6\,B\,a^3\,b^7+4\,B\,a^4\,b^6-4\,A\,a\,b^9-2\,B\,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(A\,b-B\,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)}{b^5-a^2\,b^3}\right)}{b^5-a^2\,b^3}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{d\,\left(b^5-a^2\,b^3\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(2*A*b - 2*B*a + B*b))/b^2 - (tan(c/2 + (d*x)/2)^3*(2*B*a - 2*A*b + B*b))/b^2)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (atan(((((((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 - (4*tan(c/2 + (d*x)/2)*(B*a^2*2i + B*b^2*1i - A*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(B*a^2*2i + B*b^2*1i - A*a*b*2i))/(2*b^3) - (8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4)*(B*a^2*2i + B*b^2*1i - A*a*b*2i)*1i)/(2*b^3) - (((((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 + (4*tan(c/2 + (d*x)/2)*(B*a^2*2i + B*b^2*1i - A*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(B*a^2*2i + B*b^2*1i - A*a*b*2i))/(2*b^3) + (8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4)*(B*a^2*2i + B*b^2*1i - A*a*b*2i)*1i)/(2*b^3))/((16*(4*B^3*a^8 - 6*B^3*a^7*b + 4*A^3*a^4*b^4 - 4*A^3*a^5*b^3 - B^3*a^3*b^5 + 2*B^3*a^4*b^4 - 5*B^3*a^5*b^3 + 6*B^3*a^6*b^2 - 12*A*B^2*a^7*b + A*B^2*a^2*b^6 - 2*A*B^2*a^3*b^5 + 9*A*B^2*a^4*b^4 - 12*A*B^2*a^5*b^3 + 16*A*B^2*a^6*b^2 - 4*A^2*B*a^3*b^5 + 6*A^2*B*a^4*b^4 - 14*A^2*B*a^5*b^3 + 12*A^2*B*a^6*b^2))/b^6 + (((((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 - (4*tan(c/2 + (d*x)/2)*(B*a^2*2i + B*b^2*1i - A*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(B*a^2*2i + B*b^2*1i - A*a*b*2i))/(2*b^3) - (8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4)*(B*a^2*2i + B*b^2*1i - A*a*b*2i))/(2*b^3) + (((((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 + (4*tan(c/2 + (d*x)/2)*(B*a^2*2i + B*b^2*1i - A*a*b*2i)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/b^7)*(B*a^2*2i + B*b^2*1i - A*a*b*2i))/(2*b^3) + (8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4)*(B*a^2*2i + B*b^2*1i - A*a*b*2i))/(2*b^3)))*(B*a^2*2i + B*b^2*1i - A*a*b*2i)*1i)/(b^3*d) + (a^2*atan(((a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4 + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3))))/(b^5 - a^2*b^3))*1i)/(b^5 - a^2*b^3) + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4 - (a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3))))/(b^5 - a^2*b^3))*1i)/(b^5 - a^2*b^3))/((16*(4*B^3*a^8 - 6*B^3*a^7*b + 4*A^3*a^4*b^4 - 4*A^3*a^5*b^3 - B^3*a^3*b^5 + 2*B^3*a^4*b^4 - 5*B^3*a^5*b^3 + 6*B^3*a^6*b^2 - 12*A*B^2*a^7*b + A*B^2*a^2*b^6 - 2*A*B^2*a^3*b^5 + 9*A*B^2*a^4*b^4 - 12*A*B^2*a^5*b^3 + 16*A*B^2*a^6*b^2 - 4*A^2*B*a^3*b^5 + 6*A^2*B*a^4*b^4 - 14*A^2*B*a^5*b^3 + 12*A^2*B*a^6*b^2))/b^6 + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4 + (a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 + (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(b^5 - a^2*b^3))))/(b^5 - a^2*b^3)))/(b^5 - a^2*b^3) - (a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*tan(c/2 + (d*x)/2)*(8*B^2*a^7 - B^2*b^7 + 3*B^2*a*b^6 - 16*B^2*a^6*b - 4*A^2*a^2*b^5 + 12*A^2*a^3*b^4 - 16*A^2*a^4*b^3 + 8*A^2*a^5*b^2 - 7*B^2*a^2*b^5 + 13*B^2*a^3*b^4 - 16*B^2*a^4*b^3 + 16*B^2*a^5*b^2 + 4*A*B*a*b^6 - 16*A*B*a^6*b - 12*A*B*a^2*b^5 + 20*A*B*a^3*b^4 - 28*A*B*a^4*b^3 + 32*A*B*a^5*b^2))/b^4 - (a^2*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((8*(2*B*b^10 + 8*A*a^2*b^8 - 4*A*a^3*b^7 + 2*B*a^2*b^8 - 6*B*a^3*b^7 + 4*B*a^4*b^6 - 4*A*a*b^9 - 2*B*a*b^9))/b^6 - (8*a^2*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a*b^8 - 16*a^2*b^7 + 8*a^3*b^6))/(b^4*(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 - B*a)*2i)/(d*(b^5 - a^2*b^3))","B"
252,1,541,89,1.117125,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\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\,\left(a^2-b^2\right)}-\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\,\left(a^2-b^2\right)}-\frac{B\,b\,\sin\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}+\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)}{b\,d\,\left(a^2-b^2\right)}-\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)}{b^2\,d\,\left(a^2-b^2\right)}+\frac{A\,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{A\,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{B\,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{B\,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{B\,a^2\,\sin\left(c+d\,x\right)}{b\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (2*A*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^2 - b^2)) - (B*b*sin(c + d*x))/(d*(a^2 - b^2)) + (2*A*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d*(a^2 - b^2)) - (2*B*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d*(a^2 - b^2)) + (A*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)) - (A*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)) - (B*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)) + (B*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)) + (B*a^2*sin(c + d*x))/(b*d*(a^2 - b^2))","B"
253,1,344,67,1.719996,"\text{Not used}","int((A + B*cos(c + d*x))/(a + b*cos(c + d*x)),x)","\frac{a\,\left(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\,\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)-A\,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)}+A\,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\,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)}{b\,d}","Not used",1,"(a*(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*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*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) + A*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*B*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d)","B"
254,1,342,76,1.600172,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + b*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)}{a\,d}+\frac{b\,\left(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)}-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}\right)-B\,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)}+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)\,\sqrt{b^2-a^2}}{a\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*A*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) + (b*(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) - 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)) - B*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) + 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^2 - a^2)^(1/2))/(a*d*(a^2 - b^2))","B"
255,1,675,99,1.988492,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))),x)","\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\,\left(a^2-b^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)\,2{}\mathrm{i}}{d\,\left(a^2-b^2\right)}+\frac{A\,a\,\mathrm{tan}\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}-\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)\,2{}\mathrm{i}}{a^2\,d\,\left(a^2-b^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)\,2{}\mathrm{i}}{a\,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{B\,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{A\,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,"(A*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(d*(a^2 - b^2)) - (B*a*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(d*(a^2 - b^2)) + (A*a*tan(c + d*x))/(d*(a^2 - b^2)) - (A*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(a^2*d*(a^2 - b^2)) + (B*b^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*2i)/(a*d*(a^2 - b^2)) - (A*b^2*tan(c + d*x))/(a*d*(a^2 - b^2)) - (B*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)) + (A*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"
256,1,4051,143,4.206571,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))),x)","\frac{B\,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{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\,\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\,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{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)\,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{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)\,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{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{B\,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{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{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)\,\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{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}-A^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\,B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,A\,B\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,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(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4-4\,A\,B\,a^6\,b+4\,A\,B\,a^2\,b^5+4\,B^2\,a^5\,b^2-4\,B^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{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{B\,b^2\,\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}-A^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\,B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,A\,B\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,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(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4-4\,A\,B\,a^6\,b+4\,A\,B\,a^2\,b^5+4\,B^2\,a^5\,b^2-4\,B^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{\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{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}-A^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\,B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,A\,B\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,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(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4-4\,A\,B\,a^6\,b+4\,A\,B\,a^2\,b^5+4\,B^2\,a^5\,b^2-4\,B^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{B\,b^2\,\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}-A^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\,B^2\,a^2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,B^2\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+12\,B^2\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,B^2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,B^2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-16\,A\,B\,a\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+16\,A\,B\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-4\,A\,B\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-20\,A\,B\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+4\,A\,B\,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(A^2\,a^7+2\,A^2\,a^5\,b^2-3\,A^2\,a^3\,b^4-4\,A\,B\,a^6\,b+4\,A\,B\,a^2\,b^5+4\,B^2\,a^5\,b^2-4\,B^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,"(B*a*sin(2*c + 2*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*sin(c + 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)) + (B*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)) - (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)) - (B*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)) + (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)) - (B*b^2*sin(2*c + 2*d*x))/(2*a*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)) + (B*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)) - (A*b^2*sin(c + d*x))/(2*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) - A^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*B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*A*B*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*A*B*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*B*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*A*B*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*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)*(A^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*B^2*a^3*b^4 + 4*B^2*a^5*b^2 - 4*A*B*a^6*b + 4*A*B*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)) - (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)) - (B*b^2*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) - A^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*B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*A*B*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*A*B*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*B*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*A*B*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*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)*(A^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*B^2*a^3*b^4 + 4*B^2*a^5*b^2 - 4*A*B*a^6*b + 4*A*B*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((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)) + (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) - A^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*B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*A*B*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*A*B*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*B*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*A*B*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*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)*(A^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*B^2*a^3*b^4 + 4*B^2*a^5*b^2 - 4*A*B*a^6*b + 4*A*B*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)) - (B*b^2*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) - A^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*B^2*a^2*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*B^2*a^2*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 12*B^2*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*B^2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*B^2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 16*A*B*a*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + 16*A*B*a*b^8*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 4*A*B*a^8*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 20*A*B*a^3*b^6*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 4*A*B*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)*(A^2*a^7 - 3*A^2*a^3*b^4 + 2*A^2*a^5*b^2 - 4*B^2*a^3*b^4 + 4*B^2*a^5*b^2 - 4*A*B*a^6*b + 4*A*B*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"
257,1,4696,187,4.895360,"\text{Not used}","int((A + B*cos(c + d*x))/(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-A\,a\,b-2\,B\,a\,b\right)}{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+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\,B\,a\,b+3\,A\,b^2\right)}{3\,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-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\right)}{a^6}+\frac{\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}-\frac{4\,\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(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{a^{10}}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{2\,a^4}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{2\,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-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\right)}{a^6}-\frac{\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}+\frac{4\,\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(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{a^{10}}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{2\,a^4}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{2\,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}-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+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\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-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\right)}{a^6}+\frac{\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}-\frac{4\,\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(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{a^{10}}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{2\,a^4}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{2\,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-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\right)}{a^6}-\frac{\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}+\frac{4\,\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(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{a^{10}}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{2\,a^4}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)}{2\,a^4}}\right)\,\left(-B\,a^3+A\,a^2\,b-2\,B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{a^4\,d}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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-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\right)}{a^6}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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(A\,b-B\,a\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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-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\right)}{a^6}-\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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(A\,b-B\,a\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}+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}-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+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\right)}{a^9}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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-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\right)}{a^6}+\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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(A\,b-B\,a\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}-\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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-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\right)}{a^6}-\frac{b^3\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,B\,a^{13}-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\,B\,a^9\,b^4-6\,B\,a^{10}\,b^3+2\,B\,a^{11}\,b^2-2\,A\,a^{12}\,b-2\,B\,a^{12}\,b\right)}{a^9}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(A\,b-B\,a\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(A\,b-B\,a\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(A\,b-B\,a\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"(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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + (((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (4*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/a^10)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/(2*a^4))*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2)*1i)/(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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - (((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (4*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/a^10)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/(2*a^4))*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2)*1i)/(2*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 - 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))/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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + (((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (4*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/a^10)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/(2*a^4))*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/(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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - (((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (4*tan(c/2 + (d*x)/2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/a^10)*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/(2*a^4))*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2))/(2*a^4)))*(2*A*b^3 - B*a^3 + A*a^2*b - 2*B*a*b^2)*1i)/(a^4*d) - ((tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 - A*a*b - 2*B*a*b))/a^3 + (tan(c/2 + (d*x)/2)^5*(2*A*a^2 + 2*A*b^2 - B*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*B*a*b))/(3*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^3*atan(((b^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + (b^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (8*b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - (b^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (8*b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(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*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 - 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))/a^9 + (b^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 + (b^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 - (8*b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) - (b^3*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*((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 - 16*A*B*a*b^8 + 2*A*B*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))/a^6 - (b^3*(-(a + b)*(a - b))^(1/2)*((8*(2*B*a^13 - 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*B*a^9*b^4 - 6*B*a^10*b^3 + 2*B*a^11*b^2 - 2*A*a^12*b - 2*B*a^12*b))/a^9 + (8*b^3*tan(c/2 + (d*x)/2)*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(A*b - B*a))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*(-(a + b)*(a - b))^(1/2)*(A*b - B*a)*2i)/(d*(a^6 - a^4*b^2))","B"
258,1,6744,263,9.208595,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,B\,a^4-2\,A\,b^4+B\,b^4+2\,A\,a^2\,b^2-5\,B\,a^2\,b^2+2\,A\,a\,b^3-4\,A\,a^3\,b+3\,B\,a\,b^3-3\,B\,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\,A\,b^4+6\,B\,a^4+B\,b^4-2\,A\,a^2\,b^2-5\,B\,a^2\,b^2+2\,A\,a\,b^3-4\,A\,a^3\,b-3\,B\,a\,b^3+3\,B\,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\,B\,a^4+4\,A\,a^3\,b+3\,B\,a^2\,b^2-2\,A\,a\,b^3+B\,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\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(-32\,A^3\,a^8\,b^3+16\,A^3\,a^7\,b^4+80\,A^3\,a^6\,b^5-24\,A^3\,a^5\,b^6-48\,A^3\,a^4\,b^7+144\,A^2\,B\,a^9\,b^2-72\,A^2\,B\,a^8\,b^3-336\,A^2\,B\,a^7\,b^4+108\,A^2\,B\,a^6\,b^5+168\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+24\,A^2\,B\,a^3\,b^8-216\,A\,B^2\,a^{10}\,b+108\,A\,B^2\,a^9\,b^2+468\,A\,B^2\,a^8\,b^3-162\,A\,B^2\,a^7\,b^4-186\,A\,B^2\,a^6\,b^5+15\,A\,B^2\,a^5\,b^6-63\,A\,B^2\,a^4\,b^7+3\,A\,B^2\,a^3\,b^8-3\,A\,B^2\,a^2\,b^9+108\,B^3\,a^{11}-54\,B^3\,a^{10}\,b-216\,B^3\,a^9\,b^2+81\,B^3\,a^8\,b^3+63\,B^3\,a^7\,b^4-9\,B^3\,a^6\,b^5+41\,B^3\,a^5\,b^6-4\,B^3\,a^4\,b^7+4\,B^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\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^2\,b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(\frac{8\,\left(2\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,a^7\,b^8-8\,A\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^4}\right)\,\left(6{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^4}}\right)\,\left(6{}\mathrm{i}\,B\,a^2-4{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{b^4\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\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(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,\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(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,A^3\,a^8\,b^3+16\,A^3\,a^7\,b^4+80\,A^3\,a^6\,b^5-24\,A^3\,a^5\,b^6-48\,A^3\,a^4\,b^7+144\,A^2\,B\,a^9\,b^2-72\,A^2\,B\,a^8\,b^3-336\,A^2\,B\,a^7\,b^4+108\,A^2\,B\,a^6\,b^5+168\,A^2\,B\,a^5\,b^6-6\,A^2\,B\,a^4\,b^7+24\,A^2\,B\,a^3\,b^8-216\,A\,B^2\,a^{10}\,b+108\,A\,B^2\,a^9\,b^2+468\,A\,B^2\,a^8\,b^3-162\,A\,B^2\,a^7\,b^4-186\,A\,B^2\,a^6\,b^5+15\,A\,B^2\,a^5\,b^6-63\,A\,B^2\,a^4\,b^7+3\,A\,B^2\,a^3\,b^8-3\,A\,B^2\,a^2\,b^9+108\,B^3\,a^{11}-54\,B^3\,a^{10}\,b-216\,B^3\,a^9\,b^2+81\,B^3\,a^8\,b^3+63\,B^3\,a^7\,b^4-9\,B^3\,a^6\,b^5+41\,B^3\,a^5\,b^6-4\,B^3\,a^4\,b^7+4\,B^3\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a^2\,\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(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a^2\,\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(32\,A^2\,a^8\,b^2-32\,A^2\,a^7\,b^3-64\,A^2\,a^6\,b^4+64\,A^2\,a^5\,b^5+20\,A^2\,a^4\,b^6-32\,A^2\,a^3\,b^7+16\,A^2\,a^2\,b^8-96\,A\,B\,a^9\,b+96\,A\,B\,a^8\,b^2+176\,A\,B\,a^7\,b^3-176\,A\,B\,a^6\,b^4-40\,A\,B\,a^5\,b^5+64\,A\,B\,a^4\,b^6-40\,A\,B\,a^3\,b^7+16\,A\,B\,a^2\,b^8-8\,A\,B\,a\,b^9+72\,B^2\,a^{10}-72\,B^2\,a^9\,b-120\,B^2\,a^8\,b^2+120\,B^2\,a^7\,b^3+17\,B^2\,a^6\,b^4-26\,B^2\,a^5\,b^5+23\,B^2\,a^4\,b^6-20\,B^2\,a^3\,b^7+11\,B^2\,a^2\,b^8-2\,B^2\,a\,b^9+B^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\,B\,b^{15}+12\,A\,a^2\,b^{13}+12\,A\,a^3\,b^{12}-20\,A\,a^4\,b^{11}-4\,A\,a^5\,b^{10}+8\,A\,a^6\,b^9+6\,B\,a^2\,b^{13}-16\,B\,a^3\,b^{12}-14\,B\,a^4\,b^{11}+28\,B\,a^5\,b^{10}+6\,B\,a^6\,b^9-12\,B\,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^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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,b^3\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,\left(3\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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\,B\,a^3-2\,A\,a^2\,b-4\,B\,a\,b^2+3\,A\,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,"(a^2*atan(((a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2)*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*B^3*a^11 - 54*B^3*a^10*b - 48*A^3*a^4*b^7 - 24*A^3*a^5*b^6 + 80*A^3*a^6*b^5 + 16*A^3*a^7*b^4 - 32*A^3*a^8*b^3 + 4*B^3*a^3*b^8 - 4*B^3*a^4*b^7 + 41*B^3*a^5*b^6 - 9*B^3*a^6*b^5 + 63*B^3*a^7*b^4 + 81*B^3*a^8*b^3 - 216*B^3*a^9*b^2 - 216*A*B^2*a^10*b - 3*A*B^2*a^2*b^9 + 3*A*B^2*a^3*b^8 - 63*A*B^2*a^4*b^7 + 15*A*B^2*a^5*b^6 - 186*A*B^2*a^6*b^5 - 162*A*B^2*a^7*b^4 + 468*A*B^2*a^8*b^3 + 108*A*B^2*a^9*b^2 + 24*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 168*A^2*B*a^5*b^6 + 108*A^2*B*a^6*b^5 - 336*A^2*B*a^7*b^4 - 72*A^2*B*a^8*b^3 + 144*A^2*B*a^9*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*(3*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*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*A*b^3 + 3*B*a^3 - 2*A*a^2*b - 4*B*a*b^2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)) - (atan(-((((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(B*a^2*6i + B*b^2*1i - A*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)))*(B*a^2*6i + B*b^2*1i - A*a*b*4i))/(2*b^4))*(B*a^2*6i + B*b^2*1i - A*a*b*4i)*1i)/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(B*a^2*6i + B*b^2*1i - A*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)))*(B*a^2*6i + B*b^2*1i - A*a*b*4i))/(2*b^4))*(B*a^2*6i + B*b^2*1i - A*a*b*4i)*1i)/(2*b^4))/((16*(108*B^3*a^11 - 54*B^3*a^10*b - 48*A^3*a^4*b^7 - 24*A^3*a^5*b^6 + 80*A^3*a^6*b^5 + 16*A^3*a^7*b^4 - 32*A^3*a^8*b^3 + 4*B^3*a^3*b^8 - 4*B^3*a^4*b^7 + 41*B^3*a^5*b^6 - 9*B^3*a^6*b^5 + 63*B^3*a^7*b^4 + 81*B^3*a^8*b^3 - 216*B^3*a^9*b^2 - 216*A*B^2*a^10*b - 3*A*B^2*a^2*b^9 + 3*A*B^2*a^3*b^8 - 63*A*B^2*a^4*b^7 + 15*A*B^2*a^5*b^6 - 186*A*B^2*a^6*b^5 - 162*A*B^2*a^7*b^4 + 468*A*B^2*a^8*b^3 + 108*A*B^2*a^9*b^2 + 24*A^2*B*a^3*b^8 - 6*A^2*B*a^4*b^7 + 168*A^2*B*a^5*b^6 + 108*A^2*B*a^6*b^5 - 336*A^2*B*a^7*b^4 - 72*A^2*B*a^8*b^3 + 144*A^2*B*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*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(B*a^2*6i + B*b^2*1i - A*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)))*(B*a^2*6i + B*b^2*1i - A*a*b*4i))/(2*b^4))*(B*a^2*6i + B*b^2*1i - A*a*b*4i))/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*B^2*a^10 + B^2*b^10 - 2*B^2*a*b^9 - 72*B^2*a^9*b + 16*A^2*a^2*b^8 - 32*A^2*a^3*b^7 + 20*A^2*a^4*b^6 + 64*A^2*a^5*b^5 - 64*A^2*a^6*b^4 - 32*A^2*a^7*b^3 + 32*A^2*a^8*b^2 + 11*B^2*a^2*b^8 - 20*B^2*a^3*b^7 + 23*B^2*a^4*b^6 - 26*B^2*a^5*b^5 + 17*B^2*a^6*b^4 + 120*B^2*a^7*b^3 - 120*B^2*a^8*b^2 - 8*A*B*a*b^9 - 96*A*B*a^9*b + 16*A*B*a^2*b^8 - 40*A*B*a^3*b^7 + 64*A*B*a^4*b^6 - 40*A*B*a^5*b^5 - 176*A*B*a^6*b^4 + 176*A*B*a^7*b^3 + 96*A*B*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (((8*(2*B*b^15 + 12*A*a^2*b^13 + 12*A*a^3*b^12 - 20*A*a^4*b^11 - 4*A*a^5*b^10 + 8*A*a^6*b^9 + 6*B*a^2*b^13 - 16*B*a^3*b^12 - 14*B*a^4*b^11 + 28*B*a^5*b^10 + 6*B*a^6*b^9 - 12*B*a^7*b^8 - 8*A*a*b^14))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(B*a^2*6i + B*b^2*1i - A*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)))*(B*a^2*6i + B*b^2*1i - A*a*b*4i))/(2*b^4))*(B*a^2*6i + B*b^2*1i - A*a*b*4i))/(2*b^4)))*(B*a^2*6i + B*b^2*1i - A*a*b*4i)*1i)/(b^4*d) - ((tan(c/2 + (d*x)/2)^5*(6*B*a^4 - 2*A*b^4 + B*b^4 + 2*A*a^2*b^2 - 5*B*a^2*b^2 + 2*A*a*b^3 - 4*A*a^3*b + 3*B*a*b^3 - 3*B*a^3*b))/((a*b^3 - b^4)*(a + b)) + (tan(c/2 + (d*x)/2)*(2*A*b^4 + 6*B*a^4 + B*b^4 - 2*A*a^2*b^2 - 5*B*a^2*b^2 + 2*A*a*b^3 - 4*A*a^3*b - 3*B*a*b^3 + 3*B*a^3*b))/((a*b^3 - b^4)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(B*b^4 - 6*B*a^4 + 3*B*a^2*b^2 - 2*A*a*b^3 + 4*A*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)))","B"
259,1,3276,155,5.169694,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(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^2\,b-B\,b^3-2\,B\,a^3+B\,a\,b^2+B\,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(B\,b^3-2\,B\,a^3+A\,a^2\,b+B\,a\,b^2-B\,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(A\,b-2\,B\,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(A\,b\,1{}\mathrm{i}-B\,a\,2{}\mathrm{i}\right)}{b^3\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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(-A^3\,a^5\,b^3+A^3\,a^4\,b^4+3\,A^3\,a^3\,b^5-2\,A^3\,a^2\,b^6-2\,A^3\,a\,b^7+6\,A^2\,B\,a^6\,b^2-5\,A^2\,B\,a^5\,b^3-17\,A^2\,B\,a^4\,b^4+9\,A^2\,B\,a^3\,b^5+11\,A^2\,B\,a^2\,b^6-12\,A\,B^2\,a^7\,b+8\,A\,B^2\,a^6\,b^2+32\,A\,B^2\,a^5\,b^3-13\,A\,B^2\,a^4\,b^4-20\,A\,B^2\,a^3\,b^5+8\,B^3\,a^8-4\,B^3\,a^7\,b-20\,B^3\,a^6\,b^2+6\,B^3\,a^5\,b^3+12\,B^3\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,b^3\right)}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,A^2\,a^6\,b^2-2\,A^2\,a^5\,b^3-5\,A^2\,a^4\,b^4+4\,A^2\,a^3\,b^5+3\,A^2\,a^2\,b^6-2\,A^2\,a\,b^7+A^2\,b^8-8\,A\,B\,a^7\,b+8\,A\,B\,a^6\,b^2+18\,A\,B\,a^5\,b^3-16\,A\,B\,a^4\,b^4-8\,A\,B\,a^3\,b^5+8\,A\,B\,a^2\,b^6-4\,A\,B\,a\,b^7+8\,B^2\,a^8-8\,B^2\,a^7\,b-16\,B^2\,a^6\,b^2+16\,B^2\,a^5\,b^3+5\,B^2\,a^4\,b^4-8\,B^2\,a^3\,b^5+4\,B^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(A\,a^2\,b^{10}-A\,b^{12}-3\,A\,a^3\,b^9+A\,a^5\,b^7-3\,B\,a^2\,b^{10}-3\,B\,a^3\,b^9+5\,B\,a^4\,b^8+B\,a^5\,b^7-2\,B\,a^6\,b^6+2\,A\,a\,b^{11}+2\,B\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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\,B\,a^3-A\,a^2\,b-3\,B\,a\,b^2+2\,A\,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)*(A*b - 2*B*a)*1i)/(b^3*d) - ((2*tan(c/2 + (d*x)/2)^3*(A*a^2*b - B*b^3 - 2*B*a^3 + B*a*b^2 + B*a^2*b))/(b^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(B*b^3 - 2*B*a^3 + A*a^2*b + B*a*b^2 - B*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)*(A*b*1i - B*a*2i))/(b^3*d) - (a*atan(((a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*B^3*a^8 - 2*A^3*a*b^7 - 4*B^3*a^7*b - 2*A^3*a^2*b^6 + 3*A^3*a^3*b^5 + A^3*a^4*b^4 - A^3*a^5*b^3 + 12*B^3*a^4*b^4 + 6*B^3*a^5*b^3 - 20*B^3*a^6*b^2 - 12*A*B^2*a^7*b - 20*A*B^2*a^3*b^5 - 13*A*B^2*a^4*b^4 + 32*A*B^2*a^5*b^3 + 8*A*B^2*a^6*b^2 + 11*A^2*B*a^2*b^6 + 9*A^2*B*a^3*b^5 - 17*A^2*B*a^4*b^4 - 5*A^2*B*a^5*b^3 + 6*A^2*B*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a*((32*tan(c/2 + (d*x)/2)*(A^2*b^8 + 8*B^2*a^8 - 2*A^2*a*b^7 - 8*B^2*a^7*b + 3*A^2*a^2*b^6 + 4*A^2*a^3*b^5 - 5*A^2*a^4*b^4 - 2*A^2*a^5*b^3 + 2*A^2*a^6*b^2 + 4*B^2*a^2*b^6 - 8*B^2*a^3*b^5 + 5*B^2*a^4*b^4 + 16*B^2*a^5*b^3 - 16*B^2*a^6*b^2 - 4*A*B*a*b^7 - 8*A*B*a^7*b + 8*A*B*a^2*b^6 - 8*A*B*a^3*b^5 - 16*A*B*a^4*b^4 + 18*A*B*a^5*b^3 + 8*A*B*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(A*a^2*b^10 - A*b^12 - 3*A*a^3*b^9 + A*a^5*b^7 - 3*B*a^2*b^10 - 3*B*a^3*b^9 + 5*B*a^4*b^8 + B*a^5*b^7 - 2*B*a^6*b^6 + 2*A*a*b^11 + 2*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*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*A*b^3 + 2*B*a^3 - A*a^2*b - 3*B*a*b^2)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
260,1,3775,122,7.786304,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\frac{2\,B\,\mathrm{atan}\left(\frac{\frac{B\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{B\,\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{B\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{B\,\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\,B\,b^5+A\,B^2\,a^3\,b^2+A\,B^2\,a^2\,b^3-3\,A\,B^2\,a\,b^4-A\,B^2\,b^5+B^3\,a^5-B^3\,a^4\,b-3\,B^3\,a^3\,b^2+2\,B^3\,a^2\,b^3+2\,B^3\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{B\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{B\,\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{B\,\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{B\,\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,a\,b^8\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{B\,\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(B\,a^2-A\,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(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(A^2\,B\,b^5+A\,B^2\,a^3\,b^2+A\,B^2\,a^2\,b^3-3\,A\,B^2\,a\,b^4-A\,B^2\,b^5+B^3\,a^5-B^3\,a^4\,b-3\,B^3\,a^3\,b^2+2\,B^3\,a^2\,b^3+2\,B^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\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(A^2\,b^6+2\,A\,B\,a^3\,b^3-4\,A\,B\,a\,b^5+2\,B^2\,a^6-2\,B^2\,a^5\,b-5\,B^2\,a^4\,b^2+4\,B^2\,a^3\,b^3+3\,B^2\,a^2\,b^4-2\,B^2\,a\,b^5+B^2\,b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{\left(\frac{32\,\left(A\,a^2\,b^7-B\,b^9-A\,b^9-A\,a^3\,b^6+B\,a^2\,b^7-3\,B\,a^3\,b^6+B\,a^5\,b^4+A\,a\,b^8+2\,B\,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\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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(B\,a^3-2\,B\,a\,b^2+A\,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*B*atan(((B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2 - (B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/b^2)/((64*(B^3*a^5 - A*B^2*b^5 + A^2*B*b^5 + 2*B^3*a*b^4 - B^3*a^4*b + 2*B^3*a^2*b^3 - 3*B^3*a^3*b^2 - 3*A*B^2*a*b^4 + A*B^2*a^2*b^3 + A*B^2*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2 + (B*((B*((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*a*b^8))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*a*b^2)*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(B^3*a^5 - A*B^2*b^5 + A^2*B*b^5 + 2*B^3*a*b^4 - B^3*a^4*b + 2*B^3*a^2*b^3 - 3*B^3*a^3*b^2 - 3*A*B^2*a*b^4 + A*B^2*a^2*b^3 + A*B^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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A^2*b^6 + 2*B^2*a^6 + B^2*b^6 - 2*B^2*a*b^5 - 2*B^2*a^5*b + 3*B^2*a^2*b^4 + 4*B^2*a^3*b^3 - 5*B^2*a^4*b^2 - 4*A*B*a*b^5 + 2*A*B*a^3*b^3))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (((32*(A*a^2*b^7 - B*b^9 - A*b^9 - A*a^3*b^6 + B*a^2*b^7 - 3*B*a^3*b^6 + B*a^5*b^4 + A*a*b^8 + 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(A*b^3 + B*a^3 - 2*B*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)*(B*a^2 - A*a*b))/(d*(a + b)*(a*b - b^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
261,1,113,100,0.732032,"\text{Not used}","int((A + B*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(A\,a-B\,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(A\,b-B\,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)))*(A*a - B*b))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (2*tan(c/2 + (d*x)/2)*(A*b - B*a))/(d*(a + b)*(a - b)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
262,1,3763,133,7.811291,"\text{Not used}","int((A + B*cos(c + d*x))/(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(A\,b^2-B\,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{A\,\mathrm{atan}\left(\frac{\frac{A\,\left(\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+2\,A\,a^8\,b+B\,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\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+B^2\,a^6\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-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+2\,A\,a^8\,b+B\,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\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+B^2\,a^6\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-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+2\,A\,a^8\,b+B\,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\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+B^2\,a^6\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\,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\,B^2\,a^5\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-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+2\,A\,a^8\,b+B\,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\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+B^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{\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\,B\,a^5\,b+2\,A\,B\,a^3\,b^3+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\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\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,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\,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\,B^2\,a^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\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\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\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\,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+B^2\,a^6\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+2\,A\,a^8\,b+B\,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(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,b^3\right)}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(B\,a^3-2\,A\,a^2\,b+A\,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(B\,a^3-2\,A\,a^2\,b+A\,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,"- (A*atan(((A*((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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2 - (A*((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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2)/((A*((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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/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*B*a^2*b^3 + A^2*B*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 - 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 + 2*A*a^8*b + B*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 + 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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))/a^2))*2i)/(a^2*d) - (atan((((-(a + b)^3*(a - b)^3)^(1/2)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*a^2*b)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + ((-(a + b)^3*(a - b)^3)^(1/2)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*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*B*a^2*b^3 + A^2*B*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - ((-(a + b)^3*(a - b)^3)^(1/2)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*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)*((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 - 4*A*B*a^5*b + 2*A*B*a^3*b^3))/(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 + 2*A*a^8*b + B*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)*(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))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(A*b^3 + B*a^3 - 2*A*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)*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 - B*a*b))/(d*(a + b)*(a*b - a^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
263,1,5464,189,8.515521,"\text{Not used}","int((A + B*cos(c + d*x))/(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\,b^2-2\,A\,b^3-A\,a^3+A\,a^2\,b+B\,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(A\,a^3-2\,A\,b^3-A\,a\,b^2+A\,a^2\,b+B\,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(\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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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)\,\left(2\,A\,b-B\,a\right)}{a^3}\right)\,\left(2\,A\,b-B\,a\right)\,1{}\mathrm{i}}{a^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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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)\,\left(2\,A\,b-B\,a\right)}{a^3}\right)\,\left(2\,A\,b-B\,a\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+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^6-2\,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\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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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)\,\left(2\,A\,b-B\,a\right)}{a^3}\right)\,\left(2\,A\,b-B\,a\right)}{a^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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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)\,\left(2\,A\,b-B\,a\right)}{a^3}\right)\,\left(2\,A\,b-B\,a\right)}{a^3}}\right)\,\left(2\,A\,b-B\,a\right)\,2{}\mathrm{i}}{a^3\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,b^3\right)\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,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+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^6-2\,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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,b^3\right)}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}-\frac{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^8-4\,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+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\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b\,\left(\frac{32\,\left(A\,a^7\,b^5-2\,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+2\,A\,a^{11}\,b+2\,B\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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\,B\,a^3-3\,A\,a^2\,b-B\,a\,b^2+2\,A\,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(((((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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)))*(2*A*b - B*a))/a^3)*(2*A*b - B*a)*1i)/a^3 + (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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)))*(2*A*b - B*a))/a^3)*(2*A*b - B*a)*1i)/a^3)/((64*(8*A^3*b^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 + 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))/(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 - 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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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)))*(2*A*b - B*a))/a^3)*(2*A*b - B*a))/a^3 - (((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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)))*(2*A*b - B*a))/a^3)*(2*A*b - B*a))/a^3))*(2*A*b - B*a)*2i)/(a^3*d) - ((2*tan(c/2 + (d*x)/2)^3*(A*a*b^2 - 2*A*b^3 - A*a^3 + A*a^2*b + B*a*b^2))/(a^2*(a + b)*(a - b)) - (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))/(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*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*b^2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*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 - 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 + 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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*b^2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) - (b*((32*tan(c/2 + (d*x)/2)*(8*A^2*b^8 + B^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 + 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))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b*((32*(A*a^7*b^5 - 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 + 2*A*a^11*b + 2*B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*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*A*b^3 + 2*B*a^3 - 3*A*a^2*b - B*a*b^2)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
264,1,6692,270,9.278940,"\text{Not used}","int((A + B*cos(c + d*x))/(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)}^5\,\left(A\,a^4+6\,A\,b^4-2\,B\,a^4-5\,A\,a^2\,b^2+2\,B\,a^2\,b^2-3\,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)\,\left(A\,a^4+6\,A\,b^4+2\,B\,a^4-5\,A\,a^2\,b^2-2\,B\,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^4-2\,B\,a^3\,b+3\,A\,a^2\,b^2+4\,B\,a\,b^3-6\,A\,b^4\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{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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,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(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)}{2\,a^4}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)\,1{}\mathrm{i}}{2\,a^4}+\frac{\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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,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(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)}{2\,a^4}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}+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^9-48\,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\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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,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(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)}{2\,a^4}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)}{2\,a^4}+\frac{\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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,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(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)}{2\,a^4}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)}{2\,a^4}}\right)\,\left(A\,a^2-4\,B\,a\,b+6\,A\,b^2\right)\,1{}\mathrm{i}}{a^4\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b^2\,\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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\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}+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^9-48\,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\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{b^2\,\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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}-\frac{b^2\,\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(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+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\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^2\,\left(\frac{8\,\left(2\,A\,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^2-8\,B\,a^{14}\,b\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\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(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,\left(3\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\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\,B\,a^3-4\,A\,a^2\,b-2\,B\,a\,b^2+3\,A\,b^3\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*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(A*a^2 + 6*A*b^2 - 4*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)))*(A*a^2 + 6*A*b^2 - 4*B*a*b))/(2*a^4))*(A*a^2 + 6*A*b^2 - 4*B*a*b)*1i)/(2*a^4) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(A*a^2 + 6*A*b^2 - 4*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)))*(A*a^2 + 6*A*b^2 - 4*B*a*b))/(2*a^4))*(A*a^2 + 6*A*b^2 - 4*B*a*b)*1i)/(2*a^4))/((16*(108*A^3*b^11 - 54*A^3*a*b^10 - 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 - 216*A^2*B*a*b^10 + 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))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(A*a^2 + 6*A*b^2 - 4*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)))*(A*a^2 + 6*A*b^2 - 4*B*a*b))/(2*a^4))*(A*a^2 + 6*A*b^2 - 4*B*a*b))/(2*a^4) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(A*a^2 + 6*A*b^2 - 4*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)))*(A*a^2 + 6*A*b^2 - 4*B*a*b))/(2*a^4))*(A*a^2 + 6*A*b^2 - 4*B*a*b))/(2*a^4)))*(A*a^2 + 6*A*b^2 - 4*B*a*b)*1i)/(a^4*d) - ((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 - 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)*(A*a^4 + 6*A*b^4 + 2*B*a^4 - 5*A*a^2*b^2 - 2*B*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 + 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^2*atan(((b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^2*((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*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)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2)*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^2*((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*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)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*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 - 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 - 216*A^2*B*a*b^10 + 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))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^2*((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*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)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) - (b^2*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^10 + 72*A^2*b^10 - 72*A^2*a*b^9 - 2*A^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 - 96*A*B*a*b^9 - 8*A*B*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))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^2*((8*(2*A*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 - 8*B*a^14*b))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*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)))*(-(a + b)^3*(a - b)^3)^(1/2)*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*(3*A*b^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*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^3 + 3*B*a^3 - 4*A*a^2*b - 2*B*a*b^2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
265,1,10598,398,12.006094,"\text{Not used}","int((cos(c + d*x)^4*(A + B*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)}^5\,\left(3\,B\,b^7-36\,B\,a^7-2\,A\,b^7+10\,A\,a^2\,b^5+16\,A\,a^3\,b^4-35\,A\,a^4\,b^3-9\,A\,a^5\,b^2+5\,B\,a^2\,b^5-26\,B\,a^3\,b^4-29\,B\,a^4\,b^3+67\,B\,a^5\,b^2-4\,A\,a\,b^6+18\,A\,a^6\,b+4\,B\,a\,b^6+18\,B\,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\,A\,b^7+36\,B\,a^7+3\,B\,b^7-10\,A\,a^2\,b^5+16\,A\,a^3\,b^4+35\,A\,a^4\,b^3-9\,A\,a^5\,b^2+5\,B\,a^2\,b^5+26\,B\,a^3\,b^4-29\,B\,a^4\,b^3-67\,B\,a^5\,b^2-4\,A\,a\,b^6-18\,A\,a^6\,b-4\,B\,a\,b^6+18\,B\,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(B\,b^6-12\,B\,a^6-2\,A\,b^6+4\,A\,a^2\,b^4-12\,A\,a^3\,b^3-3\,A\,a^4\,b^2-8\,B\,a^2\,b^4-10\,B\,a^3\,b^3+23\,B\,a^4\,b^2+2\,A\,a\,b^5+6\,A\,a^5\,b+5\,B\,a\,b^5+6\,B\,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\,A\,b^6-12\,B\,a^6+B\,b^6-4\,A\,a^2\,b^4-12\,A\,a^3\,b^3+3\,A\,a^4\,b^2-8\,B\,a^2\,b^4+10\,B\,a^3\,b^3+23\,B\,a^4\,b^2+2\,A\,a\,b^5+6\,A\,a^5\,b-5\,B\,a\,b^5-6\,B\,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{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{8\,\left(-216\,A^3\,a^{12}\,b^3+108\,A^3\,a^{11}\,b^4+972\,A^3\,a^{10}\,b^5-486\,A^3\,a^9\,b^6-1728\,A^3\,a^8\,b^7+756\,A^3\,a^7\,b^8+1404\,A^3\,a^6\,b^9-432\,A^3\,a^5\,b^{10}-432\,A^3\,a^4\,b^{11}+1296\,A^2\,B\,a^{13}\,b^2-648\,A^2\,B\,a^{12}\,b^3-5724\,A^2\,B\,a^{11}\,b^4+2808\,A^2\,B\,a^{10}\,b^5+9828\,A^2\,B\,a^9\,b^6-4203\,A^2\,B\,a^8\,b^7-7524\,A^2\,B\,a^7\,b^8+2268\,A^2\,B\,a^6\,b^9+1980\,A^2\,B\,a^5\,b^{10}+144\,A^2\,B\,a^3\,b^{12}-2592\,A\,B^2\,a^{14}\,b+1296\,A\,B^2\,a^{13}\,b^2+11232\,A\,B^2\,a^{12}\,b^3-5400\,A\,B^2\,a^{11}\,b^4-18594\,A\,B^2\,a^{10}\,b^5+7767\,A\,B^2\,a^9\,b^6+13347\,A\,B^2\,a^8\,b^7-3972\,A\,B^2\,a^7\,b^8-2892\,A\,B^2\,a^6\,b^9+9\,A\,B^2\,a^5\,b^{10}-489\,A\,B^2\,a^4\,b^{11}+12\,A\,B^2\,a^3\,b^{12}-12\,A\,B^2\,a^2\,b^{13}+1728\,B^3\,a^{15}-864\,B^3\,a^{14}\,b-7344\,B^3\,a^{13}\,b^2+3456\,B^3\,a^{12}\,b^3+11700\,B^3\,a^{11}\,b^4-4770\,B^3\,a^{10}\,b^5-7829\,B^3\,a^9\,b^6+2326\,B^3\,a^8\,b^7+1314\,B^3\,a^7\,b^8-11\,B^3\,a^6\,b^9+411\,B^3\,a^5\,b^{10}-20\,B^3\,a^4\,b^{11}+20\,B^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\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,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}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^5}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)}{2\,b^5}}\right)\,\left(12{}\mathrm{i}\,B\,a^2-6{}\mathrm{i}\,A\,a\,b+1{}\mathrm{i}\,B\,b^2\right)\,1{}\mathrm{i}}{b^5\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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)\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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)\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,A^3\,a^{12}\,b^3+108\,A^3\,a^{11}\,b^4+972\,A^3\,a^{10}\,b^5-486\,A^3\,a^9\,b^6-1728\,A^3\,a^8\,b^7+756\,A^3\,a^7\,b^8+1404\,A^3\,a^6\,b^9-432\,A^3\,a^5\,b^{10}-432\,A^3\,a^4\,b^{11}+1296\,A^2\,B\,a^{13}\,b^2-648\,A^2\,B\,a^{12}\,b^3-5724\,A^2\,B\,a^{11}\,b^4+2808\,A^2\,B\,a^{10}\,b^5+9828\,A^2\,B\,a^9\,b^6-4203\,A^2\,B\,a^8\,b^7-7524\,A^2\,B\,a^7\,b^8+2268\,A^2\,B\,a^6\,b^9+1980\,A^2\,B\,a^5\,b^{10}+144\,A^2\,B\,a^3\,b^{12}-2592\,A\,B^2\,a^{14}\,b+1296\,A\,B^2\,a^{13}\,b^2+11232\,A\,B^2\,a^{12}\,b^3-5400\,A\,B^2\,a^{11}\,b^4-18594\,A\,B^2\,a^{10}\,b^5+7767\,A\,B^2\,a^9\,b^6+13347\,A\,B^2\,a^8\,b^7-3972\,A\,B^2\,a^7\,b^8-2892\,A\,B^2\,a^6\,b^9+9\,A\,B^2\,a^5\,b^{10}-489\,A\,B^2\,a^4\,b^{11}+12\,A\,B^2\,a^3\,b^{12}-12\,A\,B^2\,a^2\,b^{13}+1728\,B^3\,a^{15}-864\,B^3\,a^{14}\,b-7344\,B^3\,a^{13}\,b^2+3456\,B^3\,a^{12}\,b^3+11700\,B^3\,a^{11}\,b^4-4770\,B^3\,a^{10}\,b^5-7829\,B^3\,a^9\,b^6+2326\,B^3\,a^8\,b^7+1314\,B^3\,a^7\,b^8-11\,B^3\,a^6\,b^9+411\,B^3\,a^5\,b^{10}-20\,B^3\,a^4\,b^{11}+20\,B^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\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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)\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,\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(72\,A^2\,a^{12}\,b^2-72\,A^2\,a^{11}\,b^3-288\,A^2\,a^{10}\,b^4+288\,A^2\,a^9\,b^5+441\,A^2\,a^8\,b^6-432\,A^2\,a^7\,b^7-288\,A^2\,a^6\,b^8+288\,A^2\,a^5\,b^9+36\,A^2\,a^4\,b^{10}-72\,A^2\,a^3\,b^{11}+36\,A^2\,a^2\,b^{12}-288\,A\,B\,a^{13}\,b+288\,A\,B\,a^{12}\,b^2+1128\,A\,B\,a^{11}\,b^3-1128\,A\,B\,a^{10}\,b^4-1650\,A\,B\,a^9\,b^5+1632\,A\,B\,a^8\,b^6+984\,A\,B\,a^7\,b^7-1008\,A\,B\,a^6\,b^8-72\,A\,B\,a^5\,b^9+192\,A\,B\,a^4\,b^{10}-108\,A\,B\,a^3\,b^{11}+24\,A\,B\,a^2\,b^{12}-12\,A\,B\,a\,b^{13}+288\,B^2\,a^{14}-288\,B^2\,a^{13}\,b-1104\,B^2\,a^{12}\,b^2+1104\,B^2\,a^{11}\,b^3+1538\,B^2\,a^{10}\,b^4-1538\,B^2\,a^9\,b^5-827\,B^2\,a^8\,b^6+872\,B^2\,a^7\,b^7+18\,B^2\,a^6\,b^8-108\,B^2\,a^5\,b^9+74\,B^2\,a^4\,b^{10}-40\,B^2\,a^3\,b^{11}+21\,B^2\,a^2\,b^{12}-2\,B^2\,a\,b^{13}+B^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\,B\,b^{21}+48\,A\,a^2\,b^{19}+72\,A\,a^3\,b^{18}-156\,A\,a^4\,b^{17}-84\,A\,a^5\,b^{16}+192\,A\,a^6\,b^{15}+48\,A\,a^7\,b^{14}-108\,A\,a^8\,b^{13}-12\,A\,a^9\,b^{12}+24\,A\,a^{10}\,b^{11}+28\,B\,a^2\,b^{19}-80\,B\,a^3\,b^{18}-120\,B\,a^4\,b^{17}+276\,B\,a^5\,b^{16}+164\,B\,a^6\,b^{15}-360\,B\,a^7\,b^{14}-100\,B\,a^8\,b^{13}+212\,B\,a^9\,b^{12}+24\,B\,a^{10}\,b^{11}-48\,B\,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^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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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)\,\left(-12\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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\,B\,a^5+6\,A\,a^4\,b+29\,B\,a^3\,b^2-15\,A\,a^2\,b^3-20\,B\,a\,b^4+12\,A\,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)^5*(3*B*b^7 - 36*B*a^7 - 2*A*b^7 + 10*A*a^2*b^5 + 16*A*a^3*b^4 - 35*A*a^4*b^3 - 9*A*a^5*b^2 + 5*B*a^2*b^5 - 26*B*a^3*b^4 - 29*B*a^4*b^3 + 67*B*a^5*b^2 - 4*A*a*b^6 + 18*A*a^6*b + 4*B*a*b^6 + 18*B*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^3*(2*A*b^7 + 36*B*a^7 + 3*B*b^7 - 10*A*a^2*b^5 + 16*A*a^3*b^4 + 35*A*a^4*b^3 - 9*A*a^5*b^2 + 5*B*a^2*b^5 + 26*B*a^3*b^4 - 29*B*a^4*b^3 - 67*B*a^5*b^2 - 4*A*a*b^6 - 18*A*a^6*b - 4*B*a*b^6 + 18*B*a^6*b))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) + (tan(c/2 + (d*x)/2)^7*(B*b^6 - 12*B*a^6 - 2*A*b^6 + 4*A*a^2*b^4 - 12*A*a^3*b^3 - 3*A*a^4*b^2 - 8*B*a^2*b^4 - 10*B*a^3*b^3 + 23*B*a^4*b^2 + 2*A*a*b^5 + 6*A*a^5*b + 5*B*a*b^5 + 6*B*a^5*b))/((a*b^4 - b^5)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*A*b^6 - 12*B*a^6 + B*b^6 - 4*A*a^2*b^4 - 12*A*a^3*b^3 + 3*A*a^4*b^2 - 8*B*a^2*b^4 + 10*B*a^3*b^3 + 23*B*a^4*b^2 + 2*A*a*b^5 + 6*A*a^5*b - 5*B*a*b^5 - 6*B*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(((((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(B*a^2*12i + B*b^2*1i - A*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)))*(B*a^2*12i + B*b^2*1i - A*a*b*6i))/(2*b^5))*(B*a^2*12i + B*b^2*1i - A*a*b*6i)*1i)/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(B*a^2*12i + B*b^2*1i - A*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)))*(B*a^2*12i + B*b^2*1i - A*a*b*6i))/(2*b^5))*(B*a^2*12i + B*b^2*1i - A*a*b*6i)*1i)/(2*b^5))/((8*(1728*B^3*a^15 - 864*B^3*a^14*b - 432*A^3*a^4*b^11 - 432*A^3*a^5*b^10 + 1404*A^3*a^6*b^9 + 756*A^3*a^7*b^8 - 1728*A^3*a^8*b^7 - 486*A^3*a^9*b^6 + 972*A^3*a^10*b^5 + 108*A^3*a^11*b^4 - 216*A^3*a^12*b^3 + 20*B^3*a^3*b^12 - 20*B^3*a^4*b^11 + 411*B^3*a^5*b^10 - 11*B^3*a^6*b^9 + 1314*B^3*a^7*b^8 + 2326*B^3*a^8*b^7 - 7829*B^3*a^9*b^6 - 4770*B^3*a^10*b^5 + 11700*B^3*a^11*b^4 + 3456*B^3*a^12*b^3 - 7344*B^3*a^13*b^2 - 2592*A*B^2*a^14*b - 12*A*B^2*a^2*b^13 + 12*A*B^2*a^3*b^12 - 489*A*B^2*a^4*b^11 + 9*A*B^2*a^5*b^10 - 2892*A*B^2*a^6*b^9 - 3972*A*B^2*a^7*b^8 + 13347*A*B^2*a^8*b^7 + 7767*A*B^2*a^9*b^6 - 18594*A*B^2*a^10*b^5 - 5400*A*B^2*a^11*b^4 + 11232*A*B^2*a^12*b^3 + 1296*A*B^2*a^13*b^2 + 144*A^2*B*a^3*b^12 + 1980*A^2*B*a^5*b^10 + 2268*A^2*B*a^6*b^9 - 7524*A^2*B*a^7*b^8 - 4203*A^2*B*a^8*b^7 + 9828*A^2*B*a^9*b^6 + 2808*A^2*B*a^10*b^5 - 5724*A^2*B*a^11*b^4 - 648*A^2*B*a^12*b^3 + 1296*A^2*B*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*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(B*a^2*12i + B*b^2*1i - A*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)))*(B*a^2*12i + B*b^2*1i - A*a*b*6i))/(2*b^5))*(B*a^2*12i + B*b^2*1i - A*a*b*6i))/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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*tan(c/2 + (d*x)/2)*(B*a^2*12i + B*b^2*1i - A*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)))*(B*a^2*12i + B*b^2*1i - A*a*b*6i))/(2*b^5))*(B*a^2*12i + B*b^2*1i - A*a*b*6i))/(2*b^5)))*(B*a^2*12i + B*b^2*1i - A*a*b*6i)*1i)/(b^5*d) + (a^2*atan(((a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*B^3*a^15 - 864*B^3*a^14*b - 432*A^3*a^4*b^11 - 432*A^3*a^5*b^10 + 1404*A^3*a^6*b^9 + 756*A^3*a^7*b^8 - 1728*A^3*a^8*b^7 - 486*A^3*a^9*b^6 + 972*A^3*a^10*b^5 + 108*A^3*a^11*b^4 - 216*A^3*a^12*b^3 + 20*B^3*a^3*b^12 - 20*B^3*a^4*b^11 + 411*B^3*a^5*b^10 - 11*B^3*a^6*b^9 + 1314*B^3*a^7*b^8 + 2326*B^3*a^8*b^7 - 7829*B^3*a^9*b^6 - 4770*B^3*a^10*b^5 + 11700*B^3*a^11*b^4 + 3456*B^3*a^12*b^3 - 7344*B^3*a^13*b^2 - 2592*A*B^2*a^14*b - 12*A*B^2*a^2*b^13 + 12*A*B^2*a^3*b^12 - 489*A*B^2*a^4*b^11 + 9*A*B^2*a^5*b^10 - 2892*A*B^2*a^6*b^9 - 3972*A*B^2*a^7*b^8 + 13347*A*B^2*a^8*b^7 + 7767*A*B^2*a^9*b^6 - 18594*A*B^2*a^10*b^5 - 5400*A*B^2*a^11*b^4 + 11232*A*B^2*a^12*b^3 + 1296*A*B^2*a^13*b^2 + 144*A^2*B*a^3*b^12 + 1980*A^2*B*a^5*b^10 + 2268*A^2*B*a^6*b^9 - 7524*A^2*B*a^7*b^8 - 4203*A^2*B*a^8*b^7 + 9828*A^2*B*a^9*b^6 + 2808*A^2*B*a^10*b^5 - 5724*A^2*B*a^11*b^4 - 648*A^2*B*a^12*b^3 + 1296*A^2*B*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*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(288*B^2*a^14 + B^2*b^14 - 2*B^2*a*b^13 - 288*B^2*a^13*b + 36*A^2*a^2*b^12 - 72*A^2*a^3*b^11 + 36*A^2*a^4*b^10 + 288*A^2*a^5*b^9 - 288*A^2*a^6*b^8 - 432*A^2*a^7*b^7 + 441*A^2*a^8*b^6 + 288*A^2*a^9*b^5 - 288*A^2*a^10*b^4 - 72*A^2*a^11*b^3 + 72*A^2*a^12*b^2 + 21*B^2*a^2*b^12 - 40*B^2*a^3*b^11 + 74*B^2*a^4*b^10 - 108*B^2*a^5*b^9 + 18*B^2*a^6*b^8 + 872*B^2*a^7*b^7 - 827*B^2*a^8*b^6 - 1538*B^2*a^9*b^5 + 1538*B^2*a^10*b^4 + 1104*B^2*a^11*b^3 - 1104*B^2*a^12*b^2 - 12*A*B*a*b^13 - 288*A*B*a^13*b + 24*A*B*a^2*b^12 - 108*A*B*a^3*b^11 + 192*A*B*a^4*b^10 - 72*A*B*a^5*b^9 - 1008*A*B*a^6*b^8 + 984*A*B*a^7*b^7 + 1632*A*B*a^8*b^6 - 1650*A*B*a^9*b^5 - 1128*A*B*a^10*b^4 + 1128*A*B*a^11*b^3 + 288*A*B*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*B*b^21 + 48*A*a^2*b^19 + 72*A*a^3*b^18 - 156*A*a^4*b^17 - 84*A*a^5*b^16 + 192*A*a^6*b^15 + 48*A*a^7*b^14 - 108*A*a^8*b^13 - 12*A*a^9*b^12 + 24*A*a^10*b^11 + 28*B*a^2*b^19 - 80*B*a^3*b^18 - 120*B*a^4*b^17 + 276*B*a^5*b^16 + 164*B*a^6*b^15 - 360*B*a^7*b^14 - 100*B*a^8*b^13 + 212*B*a^9*b^12 + 24*B*a^10*b^11 - 48*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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)))*(12*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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*A*b^5 - 12*B*a^5 - 15*A*a^2*b^3 + 29*B*a^3*b^2 + 6*A*a^4*b - 20*B*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"
266,1,5542,280,7.663377,"\text{Not used}","int((cos(c + d*x)^3*(A + B*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)}^5\,\left(6\,B\,a^5-2\,B\,b^5+6\,A\,a^2\,b^3+A\,a^3\,b^2+4\,B\,a^2\,b^3-12\,B\,a^3\,b^2-2\,A\,a^4\,b+2\,B\,a\,b^4-3\,B\,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\,B\,a^5+2\,B\,b^5+6\,A\,a^2\,b^3-A\,a^3\,b^2-4\,B\,a^2\,b^3-12\,B\,a^3\,b^2-2\,A\,a^4\,b+2\,B\,a\,b^4+3\,B\,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\,B\,a^6-2\,A\,a^5\,b-13\,B\,a^4\,b^2+5\,A\,a^3\,b^3+6\,B\,a^2\,b^4-2\,B\,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(A\,b-3\,B\,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(A\,b\,1{}\mathrm{i}-B\,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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,A^3\,a^9\,b^3+2\,A^3\,a^8\,b^4+18\,A^3\,a^7\,b^5-13\,A^3\,a^6\,b^6-36\,A^3\,a^5\,b^7+26\,A^3\,a^4\,b^8+34\,A^3\,a^3\,b^9-24\,A^3\,a^2\,b^{10}-12\,A^3\,a\,b^{11}+36\,A^2\,B\,a^{10}\,b^2-18\,A^2\,B\,a^9\,b^3-162\,A^2\,B\,a^8\,b^4+105\,A^2\,B\,a^7\,b^5+312\,A^2\,B\,a^6\,b^6-198\,A^2\,B\,a^5\,b^7-282\,A^2\,B\,a^4\,b^8+156\,A^2\,B\,a^3\,b^9+96\,A^2\,B\,a^2\,b^{10}-108\,A\,B^2\,a^{11}\,b+54\,A\,B^2\,a^{10}\,b^2+486\,A\,B^2\,a^9\,b^3-279\,A\,B^2\,a^8\,b^4-900\,A\,B^2\,a^7\,b^5+486\,A\,B^2\,a^6\,b^6+774\,A\,B^2\,a^5\,b^7-324\,A\,B^2\,a^4\,b^8-252\,A\,B^2\,a^3\,b^9+108\,B^3\,a^{12}-54\,B^3\,a^{11}\,b-486\,B^3\,a^{10}\,b^2+243\,B^3\,a^9\,b^3+864\,B^3\,a^8\,b^4-378\,B^3\,a^7\,b^5-702\,B^3\,a^6\,b^6+216\,B^3\,a^5\,b^7+216\,B^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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,A^2\,a^{10}\,b^2-8\,A^2\,a^9\,b^3-32\,A^2\,a^8\,b^4+32\,A^2\,a^7\,b^5+57\,A^2\,a^6\,b^6-48\,A^2\,a^5\,b^7-52\,A^2\,a^4\,b^8+32\,A^2\,a^3\,b^9+24\,A^2\,a^2\,b^{10}-8\,A^2\,a\,b^{11}+4\,A^2\,b^{12}-48\,A\,B\,a^{11}\,b+48\,A\,B\,a^{10}\,b^2+192\,A\,B\,a^9\,b^3-192\,A\,B\,a^8\,b^4-318\,A\,B\,a^7\,b^5+288\,A\,B\,a^6\,b^6+252\,A\,B\,a^5\,b^7-192\,A\,B\,a^4\,b^8-72\,A\,B\,a^3\,b^9+48\,A\,B\,a^2\,b^{10}-24\,A\,B\,a\,b^{11}+72\,B^2\,a^{12}-72\,B^2\,a^{11}\,b-288\,B^2\,a^{10}\,b^2+288\,B^2\,a^9\,b^3+441\,B^2\,a^8\,b^4-432\,B^2\,a^7\,b^5-288\,B^2\,a^6\,b^6+288\,B^2\,a^5\,b^7+36\,B^2\,a^4\,b^8-72\,B^2\,a^3\,b^9+36\,B^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\,A\,b^{18}-8\,A\,a^2\,b^{16}+34\,A\,a^3\,b^{15}+6\,A\,a^4\,b^{14}-36\,A\,a^5\,b^{13}-4\,A\,a^6\,b^{12}+18\,A\,a^7\,b^{11}+2\,A\,a^8\,b^{10}-4\,A\,a^9\,b^9+24\,B\,a^2\,b^{16}+36\,B\,a^3\,b^{15}-78\,B\,a^4\,b^{14}-42\,B\,a^5\,b^{13}+96\,B\,a^6\,b^{12}+24\,B\,a^7\,b^{11}-54\,B\,a^8\,b^{10}-6\,B\,a^9\,b^9+12\,B\,a^{10}\,b^8-12\,A\,a\,b^{17}-12\,B\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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\,B\,a^5+2\,A\,a^4\,b+15\,B\,a^3\,b^2-5\,A\,a^2\,b^3-12\,B\,a\,b^4+6\,A\,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*B*a^5 - 2*B*b^5 + 6*A*a^2*b^3 + A*a^3*b^2 + 4*B*a^2*b^3 - 12*B*a^3*b^2 - 2*A*a^4*b + 2*B*a*b^4 - 3*B*a^4*b))/((a*b^3 - b^4)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(6*B*a^5 + 2*B*b^5 + 6*A*a^2*b^3 - A*a^3*b^2 - 4*B*a^2*b^3 - 12*B*a^3*b^2 - 2*A*a^4*b + 2*B*a*b^4 + 3*B*a^4*b))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) + (2*tan(c/2 + (d*x)/2)^3*(6*B*a^6 - 2*B*b^6 + 5*A*a^3*b^3 + 6*B*a^2*b^4 - 13*B*a^4*b^2 - 2*A*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)*(A*b - 3*B*a)*1i)/(b^4*d) - (log(tan(c/2 + (d*x)/2) - 1i)*(A*b*1i - B*a*3i))/(b^4*d) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*B^3*a^12 - 12*A^3*a*b^11 - 54*B^3*a^11*b - 24*A^3*a^2*b^10 + 34*A^3*a^3*b^9 + 26*A^3*a^4*b^8 - 36*A^3*a^5*b^7 - 13*A^3*a^6*b^6 + 18*A^3*a^7*b^5 + 2*A^3*a^8*b^4 - 4*A^3*a^9*b^3 + 216*B^3*a^4*b^8 + 216*B^3*a^5*b^7 - 702*B^3*a^6*b^6 - 378*B^3*a^7*b^5 + 864*B^3*a^8*b^4 + 243*B^3*a^9*b^3 - 486*B^3*a^10*b^2 - 108*A*B^2*a^11*b - 252*A*B^2*a^3*b^9 - 324*A*B^2*a^4*b^8 + 774*A*B^2*a^5*b^7 + 486*A*B^2*a^6*b^6 - 900*A*B^2*a^7*b^5 - 279*A*B^2*a^8*b^4 + 486*A*B^2*a^9*b^3 + 54*A*B^2*a^10*b^2 + 96*A^2*B*a^2*b^10 + 156*A^2*B*a^3*b^9 - 282*A^2*B*a^4*b^8 - 198*A^2*B*a^5*b^7 + 312*A^2*B*a^6*b^6 + 105*A^2*B*a^7*b^5 - 162*A^2*B*a^8*b^4 - 18*A^2*B*a^9*b^3 + 36*A^2*B*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*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A^2*b^12 + 72*B^2*a^12 - 8*A^2*a*b^11 - 72*B^2*a^11*b + 24*A^2*a^2*b^10 + 32*A^2*a^3*b^9 - 52*A^2*a^4*b^8 - 48*A^2*a^5*b^7 + 57*A^2*a^6*b^6 + 32*A^2*a^7*b^5 - 32*A^2*a^8*b^4 - 8*A^2*a^9*b^3 + 8*A^2*a^10*b^2 + 36*B^2*a^2*b^10 - 72*B^2*a^3*b^9 + 36*B^2*a^4*b^8 + 288*B^2*a^5*b^7 - 288*B^2*a^6*b^6 - 432*B^2*a^7*b^5 + 441*B^2*a^8*b^4 + 288*B^2*a^9*b^3 - 288*B^2*a^10*b^2 - 24*A*B*a*b^11 - 48*A*B*a^11*b + 48*A*B*a^2*b^10 - 72*A*B*a^3*b^9 - 192*A*B*a^4*b^8 + 252*A*B*a^5*b^7 + 288*A*B*a^6*b^6 - 318*A*B*a^7*b^5 - 192*A*B*a^8*b^4 + 192*A*B*a^9*b^3 + 48*A*B*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*A*b^18 - 8*A*a^2*b^16 + 34*A*a^3*b^15 + 6*A*a^4*b^14 - 36*A*a^5*b^13 - 4*A*a^6*b^12 + 18*A*a^7*b^11 + 2*A*a^8*b^10 - 4*A*a^9*b^9 + 24*B*a^2*b^16 + 36*B*a^3*b^15 - 78*B*a^4*b^14 - 42*B*a^5*b^13 + 96*B*a^6*b^12 + 24*B*a^7*b^11 - 54*B*a^8*b^10 - 6*B*a^9*b^9 + 12*B*a^10*b^8 - 12*A*a*b^17 - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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*A*b^5 - 6*B*a^5 - 5*A*a^2*b^3 + 15*B*a^3*b^2 + 2*A*a^4*b - 12*B*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"
267,1,6923,211,9.948512,"\text{Not used}","int((cos(c + d*x)^2*(A + B*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\,B\,a^4+A\,a^2\,b^2-6\,B\,a^2\,b^2+4\,A\,a\,b^3-B\,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\,B\,a^4-A\,a^2\,b^2-6\,B\,a^2\,b^2+4\,A\,a\,b^3+B\,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\,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^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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{B\,\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{B\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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{B\,\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(A^2\,B\,a^4\,b^5+4\,A^2\,B\,a^2\,b^7+4\,A^2\,B\,b^9-2\,A\,B^2\,a^7\,b^2-2\,A\,B^2\,a^6\,b^3+2\,A\,B^2\,a^5\,b^4+2\,A\,B^2\,a^3\,b^6+6\,A\,B^2\,a^2\,b^7-20\,A\,B^2\,a\,b^8-4\,A\,B^2\,b^9+4\,B^3\,a^9-2\,B^3\,a^8\,b-18\,B^3\,a^7\,b^2+13\,B^3\,a^6\,b^3+36\,B^3\,a^5\,b^4-26\,B^3\,a^4\,b^5-34\,B^3\,a^3\,b^6+24\,B^3\,a^2\,b^7+12\,B^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{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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{B\,\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{B\,\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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{B\,\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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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(A^2\,B\,a^4\,b^5+4\,A^2\,B\,a^2\,b^7+4\,A^2\,B\,b^9-2\,A\,B^2\,a^7\,b^2-2\,A\,B^2\,a^6\,b^3+2\,A\,B^2\,a^5\,b^4+2\,A\,B^2\,a^3\,b^6+6\,A\,B^2\,a^2\,b^7-20\,A\,B^2\,a\,b^8-4\,A\,B^2\,b^9+4\,B^3\,a^9-2\,B^3\,a^8\,b-18\,B^3\,a^7\,b^2+13\,B^3\,a^6\,b^3+36\,B^3\,a^5\,b^4-26\,B^3\,a^4\,b^5-34\,B^3\,a^3\,b^6+24\,B^3\,a^2\,b^7+12\,B^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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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{\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(A^2\,a^4\,b^6+4\,A^2\,a^2\,b^8+4\,A^2\,b^{10}-4\,A\,B\,a^7\,b^3+2\,A\,B\,a^5\,b^5+8\,A\,B\,a^3\,b^7-24\,A\,B\,a\,b^9+8\,B^2\,a^{10}-8\,B^2\,a^9\,b-32\,B^2\,a^8\,b^2+32\,B^2\,a^7\,b^3+57\,B^2\,a^6\,b^4-48\,B^2\,a^5\,b^5-52\,B^2\,a^4\,b^6+32\,B^2\,a^3\,b^7+24\,B^2\,a^2\,b^8-8\,B^2\,a\,b^9+4\,B^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\,A\,b^{15}+4\,B\,b^{15}-6\,A\,a^2\,b^{13}+6\,A\,a^3\,b^{12}+2\,A\,a^6\,b^9-2\,A\,a^7\,b^8-8\,B\,a^2\,b^{13}+34\,B\,a^3\,b^{12}+6\,B\,a^4\,b^{11}-36\,B\,a^5\,b^{10}-4\,B\,a^6\,b^9+18\,B\,a^7\,b^8+2\,B\,a^8\,b^7-4\,B\,a^9\,b^6-4\,A\,a\,b^{14}-12\,B\,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\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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)\,\left(-2\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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\,B\,a^5+5\,B\,a^3\,b^2+A\,a^2\,b^3-6\,B\,a\,b^4+2\,A\,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*B*atan(-((B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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) - (B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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 - (B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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) + (B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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)/((B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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) - (B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*B^3*a^9 - 4*A*B^2*b^9 + 4*A^2*B*b^9 + 12*B^3*a*b^8 - 2*B^3*a^8*b + 24*B^3*a^2*b^7 - 34*B^3*a^3*b^6 - 26*B^3*a^4*b^5 + 36*B^3*a^5*b^4 + 13*B^3*a^6*b^3 - 18*B^3*a^7*b^2 - 20*A*B^2*a*b^8 + 6*A*B^2*a^2*b^7 + 2*A*B^2*a^3*b^6 + 2*A*B^2*a^5*b^4 - 2*A*B^2*a^6*b^3 - 2*A*B^2*a^7*b^2 + 4*A^2*B*a^2*b^7 + A^2*B*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) + (B*((B*((8*(4*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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) + (B*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*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*B*a^4 + A*a^2*b^2 - 6*B*a^2*b^2 + 4*A*a*b^3 - B*a^3*b))/((a*b^2 - b^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*B*a^4 - A*a^2*b^2 - 6*B*a^2*b^2 + 4*A*a*b^3 + B*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((((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)) + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*B^3*a^9 - 4*A*B^2*b^9 + 4*A^2*B*b^9 + 12*B^3*a*b^8 - 2*B^3*a^8*b + 24*B^3*a^2*b^7 - 34*B^3*a^3*b^6 - 26*B^3*a^4*b^5 + 36*B^3*a^5*b^4 + 13*B^3*a^6*b^3 - 18*B^3*a^7*b^2 - 20*A*B^2*a*b^8 + 6*A*B^2*a^2*b^7 + 2*A*B^2*a^3*b^6 + 2*A*B^2*a^5*b^4 - 2*A*B^2*a^6*b^3 - 2*A*B^2*a^7*b^2 + 4*A^2*B*a^2*b^7 + A^2*B*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) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^10 + 8*B^2*a^10 + 4*B^2*b^10 - 8*B^2*a*b^9 - 8*B^2*a^9*b + 4*A^2*a^2*b^8 + A^2*a^4*b^6 + 24*B^2*a^2*b^8 + 32*B^2*a^3*b^7 - 52*B^2*a^4*b^6 - 48*B^2*a^5*b^5 + 57*B^2*a^6*b^4 + 32*B^2*a^7*b^3 - 32*B^2*a^8*b^2 - 24*A*B*a*b^9 + 8*A*B*a^3*b^7 + 2*A*B*a^5*b^5 - 4*A*B*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*A*b^15 + 4*B*b^15 - 6*A*a^2*b^13 + 6*A*a^3*b^12 + 2*A*a^6*b^9 - 2*A*a^7*b^8 - 8*B*a^2*b^13 + 34*B*a^3*b^12 + 6*B*a^4*b^11 - 36*B*a^5*b^10 - 4*B*a^6*b^9 + 18*B*a^7*b^8 + 2*B*a^8*b^7 - 4*B*a^9*b^6 - 4*A*a*b^14 - 12*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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)))*(2*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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*A*b^5 - 2*B*a^5 + A*a^2*b^3 + 5*B*a^3*b^2 - 6*B*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"
268,1,248,180,3.742107,"\text{Not used}","int((cos(c + d*x)*(A + B*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\,A\,a^2+2\,A\,b^2-B\,a^2+A\,a\,b-4\,B\,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\,A\,a^2+2\,A\,b^2+B\,a^2-A\,a\,b-4\,B\,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(B\,a^2-3\,A\,a\,b+2\,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*A*a^2 + 2*A*b^2 - B*a^2 + A*a*b - 4*B*a*b))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(2*A*a^2 + 2*A*b^2 + B*a^2 - A*a*b - 4*B*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)))*(B*a^2 + 2*B*b^2 - 3*A*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
269,1,248,164,3.544138,"\text{Not used}","int((A + B*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\,B\,a^2-A\,b^2+2\,B\,b^2-4\,A\,a\,b+B\,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^2-4\,A\,a\,b-B\,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\,A\,a^2-3\,B\,a\,b+A\,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 - A*b^2 + 2*B*b^2 - 4*A*a*b + B*a*b))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(A*b^2 + 2*B*a^2 + 2*B*b^2 - 4*A*a*b - B*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*A*a^2 + A*b^2 - 3*B*a*b))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
270,1,6913,214,9.627359,"\text{Not used}","int((A + B*cos(c + d*x))/(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\,A\,b^4-6\,A\,a^2\,b^2+B\,a^2\,b^2-A\,a\,b^3+4\,B\,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^4-6\,A\,a^2\,b^2-B\,a^2\,b^2+A\,a\,b^3+4\,B\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^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{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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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{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^2-12\,A\,a^{14}\,b-4\,B\,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{\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(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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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)\,\left(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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{\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(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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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)\,\left(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,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+4\,A\,B^2\,a^9+4\,A\,B^2\,a^7\,b^2+A\,B^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{\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(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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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)\,\left(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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{\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(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+4\,B^2\,a^{10}+4\,B^2\,a^8\,b^2+B^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\,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^2-12\,A\,a^{14}\,b-4\,B\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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)\,\left(2\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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\,B\,a^5-6\,A\,a^4\,b+B\,a^3\,b^2+5\,A\,a^2\,b^3-2\,A\,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*A*b^4 - 6*A*a^2*b^2 + B*a^2*b^2 - A*a*b^3 + 4*B*a^3*b))/((a^2*b - a^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(2*A*b^4 - 6*A*a^2*b^2 - B*a^2*b^2 + A*a*b^3 + 4*B*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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 + 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))/(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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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 - 12*A*a^14*b - 4*B*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((((-(a + b)^5*(a - b)^5)^(1/2)*((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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)) + ((-(a + b)^5*(a - b)^5)^(1/2)*((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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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 + 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))/(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*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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)*((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 - 24*A*B*a^9*b - 4*A*B*a^3*b^7 + 2*A*B*a^5*b^5 + 8*A*B*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*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 - 12*A*a^14*b - 4*B*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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)))*(2*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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*B*a^5 - 2*A*b^5 + 5*A*a^2*b^3 + B*a^3*b^2 - 6*A*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"
271,1,9312,299,12.905405,"\text{Not used}","int((A + B*cos(c + d*x))/(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\,A\,b^5-2\,A\,a^5-12\,A\,a^2\,b^3+4\,A\,a^3\,b^2+B\,a^2\,b^3+6\,B\,a^3\,b^2-3\,A\,a\,b^4+2\,A\,a^4\,b-2\,B\,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\,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+3\,A\,a\,b^4+2\,A\,a^4\,b-2\,B\,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\,A\,a^6-6\,A\,a^4\,b^2-5\,B\,a^3\,b^3+13\,A\,a^2\,b^4+2\,B\,a\,b^5-6\,A\,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(\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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)\,\left(3\,A\,b-B\,a\right)}{a^4}\right)\,\left(3\,A\,b-B\,a\right)\,1{}\mathrm{i}}{a^4}+\frac{\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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)\,\left(3\,A\,b-B\,a\right)}{a^4}\right)\,\left(3\,A\,b-B\,a\right)\,1{}\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}-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}+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}-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\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(\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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)\,\left(3\,A\,b-B\,a\right)}{a^4}\right)\,\left(3\,A\,b-B\,a\right)}{a^4}+\frac{\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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)\,\left(3\,A\,b-B\,a\right)}{a^4}\right)\,\left(3\,A\,b-B\,a\right)}{a^4}}\right)\,\left(3\,A\,b-B\,a\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(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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,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}+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}-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\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\,\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,\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}+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}\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\,B\,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^2-12\,A\,a^{17}\,b-12\,B\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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\,B\,a^5+12\,A\,a^4\,b+5\,B\,a^3\,b^2-15\,A\,a^2\,b^3-2\,B\,a\,b^4+6\,A\,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*A*b^5 - 2*A*a^5 - 12*A*a^2*b^3 + 4*A*a^3*b^2 + B*a^2*b^3 + 6*B*a^3*b^2 - 3*A*a*b^4 + 2*A*a^4*b - 2*B*a*b^4))/((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 + 3*A*a*b^4 + 2*A*a^4*b - 2*B*a*b^4))/((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 + 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(((((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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)))*(3*A*b - B*a))/a^4)*(3*A*b - B*a)*1i)/a^4 + (((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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)))*(3*A*b - B*a))/a^4)*(3*A*b - B*a)*1i)/a^4)/((16*(108*A^3*b^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 + 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))/(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)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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)))*(3*A*b - B*a))/a^4)*(3*A*b - B*a))/a^4 + (((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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)))*(3*A*b - B*a))/a^4)*(3*A*b - B*a))/a^4))*(3*A*b - B*a)*2i)/(a^4*d) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A^3*b^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 + 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))/(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*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*((8*tan(c/2 + (d*x)/2)*(72*A^2*b^12 + 4*B^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 - 48*A*B*a*b^11 - 24*A*B*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))/(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*B*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 - 12*A*a^17*b - 12*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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*A*b^5 - 6*B*a^5 - 15*A*a^2*b^3 + 5*B*a^3*b^2 + 12*A*a^4*b - 2*B*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"
272,1,10547,402,12.558052,"\text{Not used}","int((A + B*cos(c + d*x))/(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+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+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+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^2-6\,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{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}+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}\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(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,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(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)}{2\,a^5}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,A\,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^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}+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}\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(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,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(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)}{2\,a^5}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}+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}-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}\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{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}+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}\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(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,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(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)}{2\,a^5}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)}{2\,a^5}+\frac{\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}+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}\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(\frac{4\,\left(4\,A\,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^2-24\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,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(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)}{2\,a^5}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)}{2\,a^5}}\right)\,\left(A\,a^2-6\,B\,a\,b+12\,A\,b^2\right)\,1{}\mathrm{i}}{a^5\,d}-\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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}-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}+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}-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}\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^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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^2\,\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(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}+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}\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^2\,\left(\frac{4\,\left(4\,A\,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^2-24\,B\,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^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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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)\,\left(-12\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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\,B\,a^5+20\,A\,a^4\,b+15\,B\,a^3\,b^2-29\,A\,a^2\,b^3-6\,B\,a\,b^4+12\,A\,b^5\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 + 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 + 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 + 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 - 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(((((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) - (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 12*A*b^2 - 6*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)))*(A*a^2 + 12*A*b^2 - 6*B*a*b))/(2*a^5))*(A*a^2 + 12*A*b^2 - 6*B*a*b)*1i)/(2*a^5) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) + (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 12*A*b^2 - 6*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)))*(A*a^2 + 12*A*b^2 - 6*B*a*b))/(2*a^5))*(A*a^2 + 12*A*b^2 - 6*B*a*b)*1i)/(2*a^5))/((8*(1728*A^3*b^15 - 864*A^3*a*b^14 - 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 - 2592*A^2*B*a*b^14 + 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))/(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)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) - (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 12*A*b^2 - 6*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)))*(A*a^2 + 12*A*b^2 - 6*B*a*b))/(2*a^5))*(A*a^2 + 12*A*b^2 - 6*B*a*b))/(2*a^5) + (((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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) + (((4*(4*A*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 - 24*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 12*A*b^2 - 6*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)))*(A*a^2 + 12*A*b^2 - 6*B*a*b))/(2*a^5))*(A*a^2 + 12*A*b^2 - 6*B*a*b))/(2*a^5)))*(A*a^2 + 12*A*b^2 - 6*B*a*b)*1i)/(a^5*d) - (b^2*atan(((b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*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^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*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 - 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 - 2592*A^2*B*a*b^14 + 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))/(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^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(A^2*a^14 + 288*A^2*b^14 - 288*A^2*a*b^13 - 2*A^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 - 288*A*B*a*b^13 - 12*A*B*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))/(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^2*((4*(4*A*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 - 24*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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)))*(12*A*b^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4))/(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^5 - 12*B*a^5 - 29*A*a^2*b^3 + 15*B*a^3*b^2 + 20*A*a^4*b - 6*B*a*b^4)*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"
273,1,7823,409,12.514810,"\text{Not used}","int((cos(c + d*x)^4*(A + B*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)}^7\,\left(12\,A\,a^2\,b^5-2\,B\,b^7-8\,B\,a^7+4\,A\,a^3\,b^4-6\,A\,a^4\,b^3-A\,a^5\,b^2+6\,B\,a^2\,b^5-26\,B\,a^3\,b^4-11\,B\,a^4\,b^3+24\,B\,a^5\,b^2+2\,A\,a^6\,b+2\,B\,a\,b^6+4\,B\,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)}^3\,\left(72\,B\,a^8+18\,B\,b^8+36\,A\,a^2\,b^6-96\,A\,a^3\,b^5-14\,A\,a^4\,b^4+59\,A\,a^5\,b^3+3\,A\,a^6\,b^2-72\,B\,a^2\,b^6-60\,B\,a^3\,b^5+273\,B\,a^4\,b^4+47\,B\,a^5\,b^3-236\,B\,a^6\,b^2-18\,A\,a^7\,b-12\,B\,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\,B\,a^8+18\,B\,b^8-36\,A\,a^2\,b^6-96\,A\,a^3\,b^5+14\,A\,a^4\,b^4+59\,A\,a^5\,b^3-3\,A\,a^6\,b^2-72\,B\,a^2\,b^6+60\,B\,a^3\,b^5+273\,B\,a^4\,b^4-47\,B\,a^5\,b^3-236\,B\,a^6\,b^2-18\,A\,a^7\,b+12\,B\,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(2\,B\,b^7-8\,B\,a^7+12\,A\,a^2\,b^5-4\,A\,a^3\,b^4-6\,A\,a^4\,b^3+A\,a^5\,b^2-6\,B\,a^2\,b^5-26\,B\,a^3\,b^4+11\,B\,a^4\,b^3+24\,B\,a^5\,b^2+2\,A\,a^6\,b+2\,B\,a\,b^6-4\,B\,a^6\,b\right)}{b^4\,\left(a+b\right)\,{\left(a-b\right)}^3}}{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(A\,b-4\,B\,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(A\,b\,1{}\mathrm{i}-B\,a\,4{}\mathrm{i}\right)}{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^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,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\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,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\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(-4\,A^3\,a^{13}\,b^3+2\,A^3\,a^{12}\,b^4+26\,A^3\,a^{11}\,b^5-11\,A^3\,a^{10}\,b^6-70\,A^3\,a^9\,b^7+34\,A^3\,a^8\,b^8+110\,A^3\,a^7\,b^9-66\,A^3\,a^6\,b^{10}-110\,A^3\,a^5\,b^{11}+64\,A^3\,a^4\,b^{12}+64\,A^3\,a^3\,b^{13}-48\,A^3\,a^2\,b^{14}-16\,A^3\,a\,b^{15}+48\,A^2\,B\,a^{14}\,b^2-24\,A^2\,B\,a^{13}\,b^3-312\,A^2\,B\,a^{12}\,b^4+138\,A^2\,B\,a^{11}\,b^5+846\,A^2\,B\,a^{10}\,b^6-408\,A^2\,B\,a^9\,b^7-1314\,A^2\,B\,a^8\,b^8+726\,A^2\,B\,a^7\,b^9+1266\,A^2\,B\,a^6\,b^{10}-690\,A^2\,B\,a^5\,b^{11}-702\,A^2\,B\,a^4\,b^{12}+408\,A^2\,B\,a^3\,b^{13}+168\,A^2\,B\,a^2\,b^{14}-192\,A\,B^2\,a^{15}\,b+96\,A\,B^2\,a^{14}\,b^2+1248\,A\,B^2\,a^{13}\,b^3-576\,A\,B^2\,a^{12}\,b^4-3408\,A\,B^2\,a^{11}\,b^5+1632\,A\,B^2\,a^{10}\,b^6+5232\,A\,B^2\,a^9\,b^7-2649\,A\,B^2\,a^8\,b^8-4848\,A\,B^2\,a^7\,b^9+2376\,A\,B^2\,a^6\,b^{10}+2544\,A\,B^2\,a^5\,b^{11}-1104\,A\,B^2\,a^4\,b^{12}-576\,A\,B^2\,a^3\,b^{13}+256\,B^3\,a^{16}-128\,B^3\,a^{15}\,b-1664\,B^3\,a^{14}\,b^2+800\,B^3\,a^{13}\,b^3+4576\,B^3\,a^{12}\,b^4-2176\,B^3\,a^{11}\,b^5-6944\,B^3\,a^{10}\,b^6+3204\,B^3\,a^9\,b^7+6176\,B^3\,a^8\,b^8-2560\,B^3\,a^7\,b^9-3040\,B^3\,a^6\,b^{10}+960\,B^3\,a^5\,b^{11}+640\,B^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{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,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\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,A^2\,a^{14}\,b^2-8\,A^2\,a^{13}\,b^3-48\,A^2\,a^{12}\,b^4+48\,A^2\,a^{11}\,b^5+117\,A^2\,a^{10}\,b^6-120\,A^2\,a^9\,b^7-164\,A^2\,a^8\,b^8+160\,A^2\,a^7\,b^9+156\,A^2\,a^6\,b^{10}-120\,A^2\,a^5\,b^{11}-92\,A^2\,a^4\,b^{12}+48\,A^2\,a^3\,b^{13}+44\,A^2\,a^2\,b^{14}-8\,A^2\,a\,b^{15}+4\,A^2\,b^{16}-64\,A\,B\,a^{15}\,b+64\,A\,B\,a^{14}\,b^2+384\,A\,B\,a^{13}\,b^3-384\,A\,B\,a^{12}\,b^4-948\,A\,B\,a^{11}\,b^5+960\,A\,B\,a^{10}\,b^6+1306\,A\,B\,a^9\,b^7-1280\,A\,B\,a^8\,b^8-1128\,A\,B\,a^7\,b^9+960\,A\,B\,a^6\,b^{10}+592\,A\,B\,a^5\,b^{11}-384\,A\,B\,a^4\,b^{12}-160\,A\,B\,a^3\,b^{13}+64\,A\,B\,a^2\,b^{14}-32\,A\,B\,a\,b^{15}+128\,B^2\,a^{16}-128\,B^2\,a^{15}\,b-768\,B^2\,a^{14}\,b^2+768\,B^2\,a^{13}\,b^3+1920\,B^2\,a^{12}\,b^4-1920\,B^2\,a^{11}\,b^5-2600\,B^2\,a^{10}\,b^6+2560\,B^2\,a^9\,b^7+2025\,B^2\,a^8\,b^8-1920\,B^2\,a^7\,b^9-824\,B^2\,a^6\,b^{10}+768\,B^2\,a^5\,b^{11}+80\,B^2\,a^4\,b^{12}-128\,B^2\,a^3\,b^{13}+64\,B^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{a\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,A\,b^{24}-12\,A\,a^2\,b^{22}+64\,A\,a^3\,b^{21}+20\,A\,a^4\,b^{20}-110\,A\,a^5\,b^{19}-30\,A\,a^6\,b^{18}+110\,A\,a^7\,b^{17}+30\,A\,a^8\,b^{16}-70\,A\,a^9\,b^{15}-14\,A\,a^{10}\,b^{14}+26\,A\,a^{11}\,b^{13}+2\,A\,a^{12}\,b^{12}-4\,A\,a^{13}\,b^{11}+40\,B\,a^2\,b^{22}+72\,B\,a^3\,b^{21}-190\,B\,a^4\,b^{20}-146\,B\,a^5\,b^{19}+386\,B\,a^6\,b^{18}+174\,B\,a^7\,b^{17}-434\,B\,a^8\,b^{16}-126\,B\,a^9\,b^{15}+286\,B\,a^{10}\,b^{14}+50\,B\,a^{11}\,b^{13}-104\,B\,a^{12}\,b^{12}-8\,B\,a^{13}\,b^{11}+16\,B\,a^{14}\,b^{10}-16\,A\,a\,b^{23}-16\,B\,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\,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\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-2\,A\,a^6\,b-28\,B\,a^5\,b^2+7\,A\,a^4\,b^3+35\,B\,a^3\,b^4-8\,A\,a^2\,b^5-20\,B\,a\,b^6+8\,A\,b^7\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,"(log(tan(c/2 + (d*x)/2) + 1i)*(A*b - 4*B*a)*1i)/(b^5*d) - ((tan(c/2 + (d*x)/2)^7*(12*A*a^2*b^5 - 2*B*b^7 - 8*B*a^7 + 4*A*a^3*b^4 - 6*A*a^4*b^3 - A*a^5*b^2 + 6*B*a^2*b^5 - 26*B*a^3*b^4 - 11*B*a^4*b^3 + 24*B*a^5*b^2 + 2*A*a^6*b + 2*B*a*b^6 + 4*B*a^6*b))/(b^4*(a + b)^3*(a - b)) - (tan(c/2 + (d*x)/2)^3*(72*B*a^8 + 18*B*b^8 + 36*A*a^2*b^6 - 96*A*a^3*b^5 - 14*A*a^4*b^4 + 59*A*a^5*b^3 + 3*A*a^6*b^2 - 72*B*a^2*b^6 - 60*B*a^3*b^5 + 273*B*a^4*b^4 + 47*B*a^5*b^3 - 236*B*a^6*b^2 - 18*A*a^7*b - 12*B*a^7*b))/(3*b^4*(a + b)^2*(a - b)^3) - (tan(c/2 + (d*x)/2)^5*(72*B*a^8 + 18*B*b^8 - 36*A*a^2*b^6 - 96*A*a^3*b^5 + 14*A*a^4*b^4 + 59*A*a^5*b^3 - 3*A*a^6*b^2 - 72*B*a^2*b^6 + 60*B*a^3*b^5 + 273*B*a^4*b^4 - 47*B*a^5*b^3 - 236*B*a^6*b^2 - 18*A*a^7*b + 12*B*a^7*b))/(3*b^4*(a + b)^3*(a - b)^2) + (tan(c/2 + (d*x)/2)*(2*B*b^7 - 8*B*a^7 + 12*A*a^2*b^5 - 4*A*a^3*b^4 - 6*A*a^4*b^3 + A*a^5*b^2 - 6*B*a^2*b^5 - 26*B*a^3*b^4 + 11*B*a^4*b^3 + 24*B*a^5*b^2 + 2*A*a^6*b + 2*B*a*b^6 - 4*B*a^6*b))/(b^4*(a + b)*(a - b)^3))/(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)*(A*b*1i - B*a*4i))/(b^5*d) - (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*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)) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*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*B^3*a^16 - 16*A^3*a*b^15 - 128*B^3*a^15*b - 48*A^3*a^2*b^14 + 64*A^3*a^3*b^13 + 64*A^3*a^4*b^12 - 110*A^3*a^5*b^11 - 66*A^3*a^6*b^10 + 110*A^3*a^7*b^9 + 34*A^3*a^8*b^8 - 70*A^3*a^9*b^7 - 11*A^3*a^10*b^6 + 26*A^3*a^11*b^5 + 2*A^3*a^12*b^4 - 4*A^3*a^13*b^3 + 640*B^3*a^4*b^12 + 960*B^3*a^5*b^11 - 3040*B^3*a^6*b^10 - 2560*B^3*a^7*b^9 + 6176*B^3*a^8*b^8 + 3204*B^3*a^9*b^7 - 6944*B^3*a^10*b^6 - 2176*B^3*a^11*b^5 + 4576*B^3*a^12*b^4 + 800*B^3*a^13*b^3 - 1664*B^3*a^14*b^2 - 192*A*B^2*a^15*b - 576*A*B^2*a^3*b^13 - 1104*A*B^2*a^4*b^12 + 2544*A*B^2*a^5*b^11 + 2376*A*B^2*a^6*b^10 - 4848*A*B^2*a^7*b^9 - 2649*A*B^2*a^8*b^8 + 5232*A*B^2*a^9*b^7 + 1632*A*B^2*a^10*b^6 - 3408*A*B^2*a^11*b^5 - 576*A*B^2*a^12*b^4 + 1248*A*B^2*a^13*b^3 + 96*A*B^2*a^14*b^2 + 168*A^2*B*a^2*b^14 + 408*A^2*B*a^3*b^13 - 702*A^2*B*a^4*b^12 - 690*A^2*B*a^5*b^11 + 1266*A^2*B*a^6*b^10 + 726*A^2*B*a^7*b^9 - 1314*A^2*B*a^8*b^8 - 408*A^2*B*a^9*b^7 + 846*A^2*B*a^10*b^6 + 138*A^2*B*a^11*b^5 - 312*A^2*B*a^12*b^4 - 24*A^2*B*a^13*b^3 + 48*A^2*B*a^14*b^2))/(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) + (a*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) + (a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^16 + 128*B^2*a^16 - 8*A^2*a*b^15 - 128*B^2*a^15*b + 44*A^2*a^2*b^14 + 48*A^2*a^3*b^13 - 92*A^2*a^4*b^12 - 120*A^2*a^5*b^11 + 156*A^2*a^6*b^10 + 160*A^2*a^7*b^9 - 164*A^2*a^8*b^8 - 120*A^2*a^9*b^7 + 117*A^2*a^10*b^6 + 48*A^2*a^11*b^5 - 48*A^2*a^12*b^4 - 8*A^2*a^13*b^3 + 8*A^2*a^14*b^2 + 64*B^2*a^2*b^14 - 128*B^2*a^3*b^13 + 80*B^2*a^4*b^12 + 768*B^2*a^5*b^11 - 824*B^2*a^6*b^10 - 1920*B^2*a^7*b^9 + 2025*B^2*a^8*b^8 + 2560*B^2*a^9*b^7 - 2600*B^2*a^10*b^6 - 1920*B^2*a^11*b^5 + 1920*B^2*a^12*b^4 + 768*B^2*a^13*b^3 - 768*B^2*a^14*b^2 - 32*A*B*a*b^15 - 64*A*B*a^15*b + 64*A*B*a^2*b^14 - 160*A*B*a^3*b^13 - 384*A*B*a^4*b^12 + 592*A*B*a^5*b^11 + 960*A*B*a^6*b^10 - 1128*A*B*a^7*b^9 - 1280*A*B*a^8*b^8 + 1306*A*B*a^9*b^7 + 960*A*B*a^10*b^6 - 948*A*B*a^11*b^5 - 384*A*B*a^12*b^4 + 384*A*B*a^13*b^3 + 64*A*B*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) - (a*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*A*b^24 - 12*A*a^2*b^22 + 64*A*a^3*b^21 + 20*A*a^4*b^20 - 110*A*a^5*b^19 - 30*A*a^6*b^18 + 110*A*a^7*b^17 + 30*A*a^8*b^16 - 70*A*a^9*b^15 - 14*A*a^10*b^14 + 26*A*a^11*b^13 + 2*A*a^12*b^12 - 4*A*a^13*b^11 + 40*B*a^2*b^22 + 72*B*a^3*b^21 - 190*B*a^4*b^20 - 146*B*a^5*b^19 + 386*B*a^6*b^18 + 174*B*a^7*b^17 - 434*B*a^8*b^16 - 126*B*a^9*b^15 + 286*B*a^10*b^14 + 50*B*a^11*b^13 - 104*B*a^12*b^12 - 8*B*a^13*b^11 + 16*B*a^14*b^10 - 16*A*a*b^23 - 16*B*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*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 8*A*a^2*b^5 + 7*A*a^4*b^3 + 35*B*a^3*b^4 - 28*B*a^5*b^2 - 2*A*a^6*b - 20*B*a*b^6)*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"
274,1,9733,301,12.575204,"\text{Not used}","int((cos(c + d*x)^3*(A + B*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)}^5\,\left(3\,A\,a^2\,b^4-2\,B\,a^6+2\,A\,a^3\,b^3-12\,B\,a^2\,b^4-4\,B\,a^3\,b^3+6\,B\,a^4\,b^2+6\,A\,a\,b^5+B\,a^5\,b\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^3}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,B\,a^6+3\,A\,a^2\,b^4-2\,A\,a^3\,b^3+12\,B\,a^2\,b^4-4\,B\,a^3\,b^3-6\,B\,a^4\,b^2-6\,A\,a\,b^5+B\,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\,B\,a^6+11\,B\,a^4\,b^2+A\,a^3\,b^3-18\,B\,a^2\,b^4+9\,A\,a\,b^5\right)}{3\,{\left(a+b\right)}^2\,\left(a^2\,b^3-2\,a\,b^4+b^5\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{2\,B\,\mathrm{atan}\left(\frac{\frac{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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{B\,\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{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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{B\,\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(9\,A^2\,B\,a^4\,b^9+12\,A^2\,B\,a^2\,b^{11}+4\,A^2\,B\,b^{13}+6\,A\,B^2\,a^9\,b^4+6\,A\,B^2\,a^8\,b^5-20\,A\,B^2\,a^7\,b^6-14\,A\,B^2\,a^6\,b^7+14\,A\,B^2\,a^5\,b^8+6\,A\,B^2\,a^4\,b^9-22\,A\,B^2\,a^3\,b^{10}+6\,A\,B^2\,a^2\,b^{11}-28\,A\,B^2\,a\,b^{12}-4\,A\,B^2\,b^{13}+4\,B^3\,a^{13}-2\,B^3\,a^{12}\,b-26\,B^3\,a^{11}\,b^2+11\,B^3\,a^{10}\,b^3+70\,B^3\,a^9\,b^4-34\,B^3\,a^8\,b^5-110\,B^3\,a^7\,b^6+66\,B^3\,a^6\,b^7+110\,B^3\,a^5\,b^8-64\,B^3\,a^4\,b^9-64\,B^3\,a^3\,b^{10}+48\,B^3\,a^2\,b^{11}+16\,B^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{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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{B\,\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{B\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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{B\,\left(\frac{8\,\left(4\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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{B\,\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{\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^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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(9\,A^2\,B\,a^4\,b^9+12\,A^2\,B\,a^2\,b^{11}+4\,A^2\,B\,b^{13}+6\,A\,B^2\,a^9\,b^4+6\,A\,B^2\,a^8\,b^5-20\,A\,B^2\,a^7\,b^6-14\,A\,B^2\,a^6\,b^7+14\,A\,B^2\,a^5\,b^8+6\,A\,B^2\,a^4\,b^9-22\,A\,B^2\,a^3\,b^{10}+6\,A\,B^2\,a^2\,b^{11}-28\,A\,B^2\,a\,b^{12}-4\,A\,B^2\,b^{13}+4\,B^3\,a^{13}-2\,B^3\,a^{12}\,b-26\,B^3\,a^{11}\,b^2+11\,B^3\,a^{10}\,b^3+70\,B^3\,a^9\,b^4-34\,B^3\,a^8\,b^5-110\,B^3\,a^7\,b^6+66\,B^3\,a^6\,b^7+110\,B^3\,a^5\,b^8-64\,B^3\,a^4\,b^9-64\,B^3\,a^3\,b^{10}+48\,B^3\,a^2\,b^{11}+16\,B^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(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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(9\,A^2\,a^4\,b^{10}+12\,A^2\,a^2\,b^{12}+4\,A^2\,b^{14}+12\,A\,B\,a^9\,b^5-34\,A\,B\,a^7\,b^7+20\,A\,B\,a^5\,b^9-16\,A\,B\,a^3\,b^{11}-32\,A\,B\,a\,b^{13}+8\,B^2\,a^{14}-8\,B^2\,a^{13}\,b-48\,B^2\,a^{12}\,b^2+48\,B^2\,a^{11}\,b^3+117\,B^2\,a^{10}\,b^4-120\,B^2\,a^9\,b^5-164\,B^2\,a^8\,b^6+160\,B^2\,a^7\,b^7+156\,B^2\,a^6\,b^8-120\,B^2\,a^5\,b^9-92\,B^2\,a^4\,b^{10}+48\,B^2\,a^3\,b^{11}+44\,B^2\,a^2\,b^{12}-8\,B^2\,a\,b^{13}+4\,B^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\,A\,b^{21}+4\,B\,b^{21}-6\,A\,a^2\,b^{19}+6\,A\,a^3\,b^{18}-6\,A\,a^4\,b^{17}+6\,A\,a^5\,b^{16}+14\,A\,a^6\,b^{15}-14\,A\,a^7\,b^{14}-6\,A\,a^8\,b^{13}+6\,A\,a^9\,b^{12}-12\,B\,a^2\,b^{19}+64\,B\,a^3\,b^{18}+20\,B\,a^4\,b^{17}-110\,B\,a^5\,b^{16}-30\,B\,a^6\,b^{15}+110\,B\,a^7\,b^{14}+30\,B\,a^8\,b^{13}-70\,B\,a^9\,b^{12}-14\,B\,a^{10}\,b^{11}+26\,B\,a^{11}\,b^{10}+2\,B\,a^{12}\,b^9-4\,B\,a^{13}\,b^8-4\,A\,a\,b^{20}-16\,B\,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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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\,a^7-7\,B\,a^5\,b^2+8\,B\,a^3\,b^4+3\,A\,a^2\,b^5-8\,B\,a\,b^6+2\,A\,b^7\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,"((tan(c/2 + (d*x)/2)^5*(3*A*a^2*b^4 - 2*B*a^6 + 2*A*a^3*b^3 - 12*B*a^2*b^4 - 4*B*a^3*b^3 + 6*B*a^4*b^2 + 6*A*a*b^5 + B*a^5*b))/((a*b^3 - b^4)*(a + b)^3) - (tan(c/2 + (d*x)/2)*(2*B*a^6 + 3*A*a^2*b^4 - 2*A*a^3*b^3 + 12*B*a^2*b^4 - 4*B*a^3*b^3 - 6*B*a^4*b^2 - 6*A*a*b^5 + B*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*(A*a^3*b^3 - 3*B*a^6 - 18*B*a^2*b^4 + 11*B*a^4*b^2 + 9*A*a*b^5))/(3*(a + b)^2*(b^5 - 2*a*b^4 + a^2*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))) + (2*B*atan(((B*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) + (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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) - (B*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 + (B*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) - (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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) + (B*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*B^3*a^13 - 4*A*B^2*b^13 + 4*A^2*B*b^13 + 16*B^3*a*b^12 - 2*B^3*a^12*b + 48*B^3*a^2*b^11 - 64*B^3*a^3*b^10 - 64*B^3*a^4*b^9 + 110*B^3*a^5*b^8 + 66*B^3*a^6*b^7 - 110*B^3*a^7*b^6 - 34*B^3*a^8*b^5 + 70*B^3*a^9*b^4 + 11*B^3*a^10*b^3 - 26*B^3*a^11*b^2 - 28*A*B^2*a*b^12 + 6*A*B^2*a^2*b^11 - 22*A*B^2*a^3*b^10 + 6*A*B^2*a^4*b^9 + 14*A*B^2*a^5*b^8 - 14*A*B^2*a^6*b^7 - 20*A*B^2*a^7*b^6 + 6*A*B^2*a^8*b^5 + 6*A*B^2*a^9*b^4 + 12*A^2*B*a^2*b^11 + 9*A^2*B*a^4*b^9))/(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) - (B*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) + (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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) - (B*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*((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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) - (B*((8*(4*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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) + (B*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) + (atan(((((8*tan(c/2 + (d*x)/2)*(4*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*B^3*a^13 - 4*A*B^2*b^13 + 4*A^2*B*b^13 + 16*B^3*a*b^12 - 2*B^3*a^12*b + 48*B^3*a^2*b^11 - 64*B^3*a^3*b^10 - 64*B^3*a^4*b^9 + 110*B^3*a^5*b^8 + 66*B^3*a^6*b^7 - 110*B^3*a^7*b^6 - 34*B^3*a^8*b^5 + 70*B^3*a^9*b^4 + 11*B^3*a^10*b^3 - 26*B^3*a^11*b^2 - 28*A*B^2*a*b^12 + 6*A*B^2*a^2*b^11 - 22*A*B^2*a^3*b^10 + 6*A*B^2*a^4*b^9 + 14*A*B^2*a^5*b^8 - 14*A*B^2*a^6*b^7 - 20*A*B^2*a^7*b^6 + 6*A*B^2*a^8*b^5 + 6*A*B^2*a^9*b^4 + 12*A^2*B*a^2*b^11 + 9*A^2*B*a^4*b^9))/(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*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A^2*b^14 + 8*B^2*a^14 + 4*B^2*b^14 - 8*B^2*a*b^13 - 8*B^2*a^13*b + 12*A^2*a^2*b^12 + 9*A^2*a^4*b^10 + 44*B^2*a^2*b^12 + 48*B^2*a^3*b^11 - 92*B^2*a^4*b^10 - 120*B^2*a^5*b^9 + 156*B^2*a^6*b^8 + 160*B^2*a^7*b^7 - 164*B^2*a^8*b^6 - 120*B^2*a^9*b^5 + 117*B^2*a^10*b^4 + 48*B^2*a^11*b^3 - 48*B^2*a^12*b^2 - 32*A*B*a*b^13 - 16*A*B*a^3*b^11 + 20*A*B*a^5*b^9 - 34*A*B*a^7*b^7 + 12*A*B*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*A*b^21 + 4*B*b^21 - 6*A*a^2*b^19 + 6*A*a^3*b^18 - 6*A*a^4*b^17 + 6*A*a^5*b^16 + 14*A*a^6*b^15 - 14*A*a^7*b^14 - 6*A*a^8*b^13 + 6*A*a^9*b^12 - 12*B*a^2*b^19 + 64*B*a^3*b^18 + 20*B*a^4*b^17 - 110*B*a^5*b^16 - 30*B*a^6*b^15 + 110*B*a^7*b^14 + 30*B*a^8*b^13 - 70*B*a^9*b^12 - 14*B*a^10*b^11 + 26*B*a^11*b^10 + 2*B*a^12*b^9 - 4*B*a^13*b^8 - 4*A*a*b^20 - 16*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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*A*b^7 + 2*B*a^7 + 3*A*a^2*b^5 + 8*B*a^3*b^4 - 7*B*a^5*b^2 - 8*B*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"
275,1,440,274,4.147083,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(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(A\,a^3-3\,B\,a^2\,b+4\,A\,a\,b^2-2\,B\,b^3\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(-B\,a^3+7\,A\,a^2\,b-9\,B\,a\,b^2+3\,A\,b^3\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(A\,a^3+2\,A\,b^3-2\,B\,a^3+2\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2-3\,B\,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(A\,a^3-2\,A\,b^3+2\,B\,a^3+2\,A\,a\,b^2-6\,A\,a^2\,b+6\,B\,a\,b^2-3\,B\,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,"(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*a^3 - 2*B*b^3 + 4*A*a*b^2 - 3*B*a^2*b))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((4*tan(c/2 + (d*x)/2)^3*(3*A*b^3 - B*a^3 + 7*A*a^2*b - 9*B*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(A*a^3 + 2*A*b^3 - 2*B*a^3 + 2*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 - 3*B*a^2*b))/((a + b)^3*(a - b)) - (tan(c/2 + (d*x)/2)*(A*a^3 - 2*A*b^3 + 2*B*a^3 + 2*A*a*b^2 - 6*A*a^2*b + 6*B*a*b^2 - 3*B*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"
276,1,451,263,4.032481,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(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^3-7\,B\,a^2\,b+7\,A\,a\,b^2-3\,B\,b^3\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)\,\left(2\,A\,a^3-A\,b^3+B\,a^3-2\,B\,b^3+6\,A\,a\,b^2-2\,A\,a^2\,b+2\,B\,a\,b^2-6\,B\,a^2\,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(2\,A\,a^3+A\,b^3-B\,a^3-2\,B\,b^3+6\,A\,a\,b^2+2\,A\,a^2\,b-2\,B\,a\,b^2-6\,B\,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(-B\,a^3+4\,A\,a^2\,b-4\,B\,a\,b^2+A\,b^3\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 - 3*B*b^3 + 7*A*a*b^2 - 7*B*a^2*b))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)*(2*A*a^3 - A*b^3 + B*a^3 - 2*B*b^3 + 6*A*a*b^2 - 2*A*a^2*b + 2*B*a*b^2 - 6*B*a^2*b))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)) + (tan(c/2 + (d*x)/2)^5*(2*A*a^3 + A*b^3 - B*a^3 - 2*B*b^3 + 6*A*a*b^2 + 2*A*a^2*b - 2*B*a*b^2 - 6*B*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 + 4*A*a^2*b - 4*B*a*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
277,1,440,237,4.002428,"\text{Not used}","int((A + B*cos(c + d*x))/(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^3-4\,B\,a^2\,b+3\,A\,a\,b^2-B\,b^3\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(-3\,B\,a^3+9\,A\,a^2\,b-7\,B\,a\,b^2+A\,b^3\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\,B\,a^3-2\,A\,b^3+B\,b^3-3\,A\,a\,b^2-6\,A\,a^2\,b+6\,B\,a\,b^2+2\,B\,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^3-2\,B\,a^3+B\,b^3-3\,A\,a\,b^2+6\,A\,a^2\,b-6\,B\,a\,b^2+2\,B\,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,"(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 + 3*A*a*b^2 - 4*B*a^2*b))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((4*tan(c/2 + (d*x)/2)^3*(A*b^3 - 3*B*a^3 + 9*A*a^2*b - 7*B*a*b^2))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) - (tan(c/2 + (d*x)/2)^5*(2*B*a^3 - 2*A*b^3 + B*b^3 - 3*A*a*b^2 - 6*A*a^2*b + 6*B*a*b^2 + 2*B*a^2*b))/((a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(2*A*b^3 - 2*B*a^3 + B*b^3 - 3*A*a*b^2 + 6*A*a^2*b - 6*B*a*b^2 + 2*B*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"
278,1,9727,301,12.810113,"\text{Not used}","int((A + B*cos(c + d*x))/(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^6-6\,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+A\,a\,b^5-6\,B\,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{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,A\,a^2\,b^4-2\,A\,b^6-4\,A\,a^3\,b^3-12\,A\,a^4\,b^2+2\,B\,a^3\,b^3+3\,B\,a^4\,b^2+A\,a\,b^5+6\,B\,a^5\,b\right)}{\left(a^3\,b-a^4\right)\,{\left(a+b\right)}^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,B\,a^5\,b-18\,A\,a^4\,b^2+B\,a^3\,b^3+11\,A\,a^2\,b^4-3\,A\,b^6\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,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{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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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+4\,A\,B^2\,a^{13}+12\,A\,B^2\,a^{11}\,b^2+9\,A\,B^2\,a^9\,b^4\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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+4\,B^2\,a^{14}+12\,B^2\,a^{12}\,b^2+9\,B^2\,a^{10}\,b^4\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^2-16\,A\,a^{20}\,b-4\,B\,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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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\,B\,a^7-8\,A\,a^6\,b+3\,B\,a^5\,b^2+8\,A\,a^4\,b^3-7\,A\,a^2\,b^5+2\,A\,b^7\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,"(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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 + 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^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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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) - ((tan(c/2 + (d*x)/2)*(2*A*b^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 + A*a*b^5 - 6*B*a^5*b))/((a + b)*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*b^2)) - (tan(c/2 + (d*x)/2)^5*(6*A*a^2*b^4 - 2*A*b^6 - 4*A*a^3*b^3 - 12*A*a^4*b^2 + 2*B*a^3*b^3 + 3*B*a^4*b^2 + A*a*b^5 + 6*B*a^5*b))/((a^3*b - a^4)*(a + b)^3) + (4*tan(c/2 + (d*x)/2)^3*(11*A*a^2*b^4 - 3*A*b^6 - 18*A*a^4*b^2 + B*a^3*b^3 + 9*B*a^5*b))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*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(((((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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 + 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^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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 - 32*A*B*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))/(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 - 16*A*a^20*b - 4*B*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 - 8*A*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 - 8*A*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 - 8*A*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 - 8*A*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"
279,1,13119,420,18.113980,"\text{Not used}","int((A + B*cos(c + d*x))/(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+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^2-12\,A\,a\,b^7-18\,B\,a\,b^7\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)}^7\,\left(24\,A\,a^2\,b^5-8\,A\,b^7-2\,A\,a^7-11\,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+4\,A\,a\,b^6+2\,A\,a^6\,b+2\,B\,a\,b^6\right)}{a^4\,{\left(a+b\right)}^3\,\left(a-b\right)}+\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+12\,A\,a\,b^7-18\,B\,a\,b^7\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(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^2-4\,A\,a\,b^6+2\,A\,a^6\,b+2\,B\,a\,b^6\right)}{a^4\,\left(a+b\right)\,{\left(a-b\right)}^3}}{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(\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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}+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}\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)\,\left(4\,A\,b-B\,a\right)\,1{}\mathrm{i}}{a^5}-\frac{\left(\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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}+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}\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)\,\left(4\,A\,b-B\,a\right)\,1{}\mathrm{i}}{a^5}}{\frac{\left(\frac{\left(4\,A\,b-B\,a\right)\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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}+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}\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)\,\left(4\,A\,b-B\,a\right)}{a^5}-\frac{16\,\left(640\,A^3\,a^{12}\,b^4+960\,A^3\,a^{11}\,b^5-3040\,A^3\,a^{10}\,b^6-2560\,A^3\,a^9\,b^7+6176\,A^3\,a^8\,b^8+3204\,A^3\,a^7\,b^9-6944\,A^3\,a^6\,b^{10}-2176\,A^3\,a^5\,b^{11}+4576\,A^3\,a^4\,b^{12}+800\,A^3\,a^3\,b^{13}-1664\,A^3\,a^2\,b^{14}-128\,A^3\,a\,b^{15}+256\,A^3\,b^{16}-576\,A^2\,B\,a^{13}\,b^3-1104\,A^2\,B\,a^{12}\,b^4+2544\,A^2\,B\,a^{11}\,b^5+2376\,A^2\,B\,a^{10}\,b^6-4848\,A^2\,B\,a^9\,b^7-2649\,A^2\,B\,a^8\,b^8+5232\,A^2\,B\,a^7\,b^9+1632\,A^2\,B\,a^6\,b^{10}-3408\,A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10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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{16\,\left(640\,A^3\,a^{12}\,b^4+960\,A^3\,a^{11}\,b^5-3040\,A^3\,a^{10}\,b^6-2560\,A^3\,a^9\,b^7+6176\,A^3\,a^8\,b^8+3204\,A^3\,a^7\,b^9-6944\,A^3\,a^6\,b^{10}-2176\,A^3\,a^5\,b^{11}+4576\,A^3\,a^4\,b^{12}+800\,A^3\,a^3\,b^{13}-1664\,A^3\,a^2\,b^{14}-128\,A^3\,a\,b^{15}+256\,A^3\,b^{16}-576\,A^2\,B\,a^{13}\,b^3-1104\,A^2\,B\,a^{12}\,b^4+2544\,A^2\,B\,a^{11}\,b^5+2376\,A^2\,B\,a^{10}\,b^6-4848\,A^2\,B\,a^9\,b^7-2649\,A^2\,B\,a^8\,b^8+5232\,A^2\,B\,a^7\,b^9+1632\,A^2\,B\,a^6\,b^{10}-3408\,A^2\,B\,a^5\,b^{11}-576\,A^2\,B\,a^4\,b^{12}+1248\,A^2\,B\,a^3\,b^{13}+96\,A^2\,B\,a^2\,b^{14}-192\,A^2\,B\,a\,b^{15}+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}-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}\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{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}-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}+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}\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{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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\,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\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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{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}-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}+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}\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{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(4\,B\,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^2-16\,A\,a^{23}\,b-16\,B\,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\,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\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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)\,\left(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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(8\,B\,a^7-20\,A\,a^6\,b-8\,B\,a^5\,b^2+35\,A\,a^4\,b^3+7\,B\,a^3\,b^4-28\,A\,a^2\,b^5-2\,B\,a\,b^6+8\,A\,b^7\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 + 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 - 12*A*a*b^7 - 18*B*a*b^7))/(3*a^4*(a + b)^2*(a - b)^3) - (tan(c/2 + (d*x)/2)^7*(24*A*a^2*b^5 - 8*A*b^7 - 2*A*a^7 - 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 + 4*A*a*b^6 + 2*A*a^6*b + 2*B*a*b^6))/(a^4*(a + b)^3*(a - b)) + (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 + 12*A*a*b^7 - 18*B*a*b^7))/(3*a^4*(a + b)^3*(a - b)^2) + (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 - 4*A*a*b^6 + 2*A*a^6*b + 2*B*a*b^6))/(a^4*(a + b)*(a - b)^3))/(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)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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 - 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 - 64*A*B*a*b^15 - 32*A*B*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))/(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 - B*a)*1i)/a^5 - ((((4*A*b - B*a)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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 - 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 - 64*A*B*a*b^15 - 32*A*B*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))/(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 - B*a)*1i)/a^5)/(((((4*A*b - B*a)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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 - 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 - 64*A*B*a*b^15 - 32*A*B*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))/(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 - B*a))/a^5 - (16*(256*A^3*b^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 + 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))/(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)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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 - 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 - 64*A*B*a*b^15 - 32*A*B*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))/(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 - B*a))/a^5))*(4*A*b - B*a)*2i)/(a^5*d) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) - (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*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)) + (b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) + (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*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 - 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 + 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))/(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) + (b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) - (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)) - (b*((8*tan(c/2 + (d*x)/2)*(128*A^2*b^16 + 4*B^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 - 64*A*B*a*b^15 - 32*A*B*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))/(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) + (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(4*B*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 - 16*A*a^23*b - 16*B*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*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*(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)))*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6))/(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)*(8*A*b^7 + 8*B*a^7 - 28*A*a^2*b^5 + 35*A*a^4*b^3 + 7*B*a^3*b^4 - 8*B*a^5*b^2 - 20*A*a^6*b - 2*B*a*b^6)*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"
280,1,14398,547,13.935848,"\text{Not used}","int((A + B*cos(c + d*x))/(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+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+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}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,A\,a^{10}-18\,B\,a^9\,b+36\,A\,a^8\,b^2+132\,B\,a^7\,b^3-324\,A\,a^6\,b^4-320\,B\,a^5\,b^5+740\,A\,a^4\,b^6+248\,B\,a^3\,b^7-611\,A\,a^2\,b^8-72\,B\,a\,b^9+180\,A\,b^{10}\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)}^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^2-10\,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^2-30\,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^2-30\,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}}{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}-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}\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}-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^2-32\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-8\,B\,a\,b+20\,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(A\,a^2-8\,B\,a\,b+20\,A\,b^2\right)}{2\,a^6}\right)\,\left(A\,a^2-8\,B\,a\,b+20\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}-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}\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}-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^2-32\,B\,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\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(A\,a^2-8\,B\,a\,b+20\,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(A\,a^2-8\,B\,a\,b+20\,A\,b^2\right)}{2\,a^6}\right)\,\left(A\,a^2-8\,B\,a\,b+20\,A\,b^2\right)\,1{}\mathrm{i}}{2\,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}-20\,A^2\,B\,a^{17}\,b^2+20\,A^2\,B\,a^{16}\,b^3-1345\,A^2\,B\,a^{15}\,b^4-255\,A^2\,B\,a^{14}\,b^5-13929\,A^2\,B\,a^{13}\,b^6-24711\,A^2\,B\,a^{12}\,b^7+88721\,A^2\,B\,a^{11}\,b^8+77359\,A^2\,B\,a^{10}\,b^9-201479\,A^2\,B\,a^9\,b^{10}-105755\,A^2\,B\,a^8\,b^{11}+241596\,A^2\,B\,a^7\,b^{12}+76812\,A^2\,B\,a^6\,b^{13}-165384\,A^2\,B\,a^5\,b^{14}-29520\,A^2\,B\,a^4\,b^{15}+61440\,A^2\,B\,a^3\,b^{16}+4800\,A^2\,B\,a^2\,b^{17}-9600\,A^2\,B\,a\,b^{18}+320\,A\,B^2\,a^{16}\,b^3+80\,A\,B^2\,a^{15}\,b^4+7440\,A\,B^2\,a^{14}\,b^5+11960\,A\,B^2\,a^{13}\,b^6-40368\,A\,B^2\,a^{12}\,b^7-34567\,A\,B^2\,a^{11}\,b^8+86512\,A\,B^2\,a^{10}\,b^9+45148\,A\,B^2\,a^9\,b^{10}-100368\,A\,B^2\,a^8\,b^{11}-31680\,A\,B^2\,a^7\,b^{12}+67392\,A\,B^2\,a^6\,b^{13}+11904\,A\,B^2\,a^5\,b^{14}-24768\,A\,B^2\,a^4\,b^{15}-1920\,A\,B^2\,a^3\,b^{16}+3840\,A\,B^2\,a^2\,b^{17}-1280\,B^3\,a^{15}\,b^4-1920\,B^3\,a^{14}\,b^5+6080\,B^3\,a^{13}\,b^6+5120\,B^3\,a^{12}\,b^7-12352\,B^3\,a^{11}\,b^8-6408\,B^3\,a^{10}\,b^9+13888\,B^3\,a^9\,b^{10}+4352\,B^3\,a^8\,b^{11}-9152\,B^3\,a^7\,b^{12}-1600\,B^3\,a^6\,b^{13}+3328\,B^3\,a^5\,b^{14}+256\,B^3\,a^4\,b^{15}-512\,B^3\,a^3\,b^{16}\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(\frac{8\,\mathrm{tan}\le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,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}-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}\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^2\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,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^2-32\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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^2\,\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}-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}\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^2\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{4\,\left(4\,A\,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^2-32\,B\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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\,B\,a^7-40\,A\,a^6\,b-35\,B\,a^5\,b^2+84\,A\,a^4\,b^3+28\,B\,a^3\,b^4-69\,A\,a^2\,b^5-8\,B\,a\,b^6+20\,A\,b^7\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 + 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 + 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) + (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 - 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)^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 - 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 - 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 - 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))/(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)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 20*A*b^2 - 8*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)))*(A*a^2 + 20*A*b^2 - 8*B*a*b))/(2*a^6))*(A*a^2 + 20*A*b^2 - 8*B*a*b)*1i)/(2*a^6) + (((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 20*A*b^2 - 8*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)))*(A*a^2 + 20*A*b^2 - 8*B*a*b))/(2*a^6))*(A*a^2 + 20*A*b^2 - 8*B*a*b)*1i)/(2*a^6))/((8*(8000*A^3*b^19 - 4000*A^3*a*b^18 - 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 - 9600*A^2*B*a*b^18 + 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))/(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)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 20*A*b^2 - 8*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)))*(A*a^2 + 20*A*b^2 - 8*B*a*b))/(2*a^6))*(A*a^2 + 20*A*b^2 - 8*B*a*b))/(2*a^6) - (((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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 - 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 - 32*B*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*tan(c/2 + (d*x)/2)*(A*a^2 + 20*A*b^2 - 8*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)))*(A*a^2 + 20*A*b^2 - 8*B*a*b))/(2*a^6))*(A*a^2 + 20*A*b^2 - 8*B*a*b))/(2*a^6)))*(A*a^2 + 20*A*b^2 - 8*B*a*b)*1i)/(a^6*d) + (b^2*atan(((b^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*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^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*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 - 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 - 9600*A^2*B*a*b^18 + 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))/(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^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^2*((8*tan(c/2 + (d*x)/2)*(800*A^2*a*b^17 - 800*A^2*b^18 - A^2*a^18 + 2*A^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 + 640*A*B*a*b^17 + 16*A*B*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))/(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^2*(-(a + b)^7*(a - b)^7)^(1/2)*((4*(4*A*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 - 32*B*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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*A*b^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6))/(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^7 + 20*B*a^7 - 69*A*a^2*b^5 + 84*A*a^4*b^3 + 28*B*a^3*b^4 - 35*B*a^5*b^2 - 40*A*a^6*b - 8*B*a*b^6)*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"
281,1,24,28,0.479004,"\text{Not used}","int((cos(c + d*x)^3*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\frac{B\,\left(9\,\sin\left(c+d\,x\right)+\sin\left(3\,c+3\,d\,x\right)\right)}{12\,d}","Not used",1,"(B*(9*sin(c + d*x) + sin(3*c + 3*d*x)))/(12*d)","B"
282,1,50,27,0.867268,"\text{Not used}","int((cos(c + d*x)^2*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\frac{B\,x}{2}+\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(B*x)/2 + (B*tan(c/2 + (d*x)/2) - B*tan(c/2 + (d*x)/2)^3)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
283,1,11,11,0.472175,"\text{Not used}","int((cos(c + d*x)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\frac{B\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(B*sin(c + d*x))/d","B"
284,1,3,3,0.446133,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(a + b*cos(c + d*x)),x)","B\,x","Not used",1,"B*x","B"
285,1,16,12,0.487423,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))),x)","\frac{2\,B\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(2*B*atanh(tan(c/2 + (d*x)/2)))/d","B"
286,1,30,11,0.473792,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))),x)","-\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*B*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
287,1,73,36,0.855371,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))),x)","\frac{B\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+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)}^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,"(B*tan(c/2 + (d*x)/2) + B*tan(c/2 + (d*x)/2)^3)/(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"
288,1,39,28,0.519641,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^4*(a + b*cos(c + d*x))),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,{\cos\left(c+d\,x\right)}^2+B\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}","Not used",1,"(B*sin(c + d*x) + 2*B*cos(c + d*x)^2*sin(c + d*x))/(3*d*cos(c + d*x)^3)","B"
289,1,173,114,1.166750,"\text{Not used}","int((cos(c + d*x)^3*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\frac{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)}{b\,d}+\frac{B\,\sin\left(2\,c+2\,d\,x\right)}{4\,b\,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)}{b^3\,d}-\frac{B\,a\,\sin\left(c+d\,x\right)}{b^2\,d}-\frac{B\,a^3\,\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)\,2{}\mathrm{i}}{b^3\,d\,\sqrt{b^2-a^2}}","Not used",1,"(B*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d) + (B*sin(2*c + 2*d*x))/(4*b*d) + (2*B*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^3*d) - (B*a*sin(c + d*x))/(b^2*d) - (B*a^3*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)))*2i)/(b^3*d*(b^2 - a^2)^(1/2))","B"
290,1,193,79,0.893845,"\text{Not used}","int((cos(c + d*x)^2*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\frac{B\,\sin\left(c+d\,x\right)}{b\,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)}{b^2\,d}-\frac{B\,a^2\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2+1{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}+a^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}\right)\,2{}\mathrm{i}}{b^2\,d\,\sqrt{b^2-a^2}}","Not used",1,"(B*sin(c + d*x))/(b*d) - (2*B*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d) - (B*a^2*atan((b^3*sin(c/2 + (d*x)/2)*1i - a*b^2*sin(c/2 + (d*x)/2)*2i + a^2*b*sin(c/2 + (d*x)/2)*1i)/(cos(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) + a^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a*b*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)))*2i)/(b^2*d*(b^2 - a^2)^(1/2))","B"
291,1,101,61,0.798615,"\text{Not used}","int((cos(c + d*x)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\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)}{b\,d}+\frac{2\,B\,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)}{b\,d\,\sqrt{b^2-a^2}}","Not used",1,"(2*B*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d) + (2*B*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))))/(b*d*(b^2 - a^2)^(1/2))","B"
292,1,44,50,0.504397,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(a + b*cos(c + d*x))^2,x)","\frac{2\,B\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a-b\right)}{\sqrt{a^2-b^2}}\right)}{d\,\sqrt{a^2-b^2}}","Not used",1,"(2*B*atan((tan(c/2 + (d*x)/2)*(a - b))/(a^2 - b^2)^(1/2)))/(d*(a^2 - b^2)^(1/2))","B"
293,1,101,70,0.758057,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)*(a + b*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)}{a\,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)}{a\,d\,\sqrt{b^2-a^2}}","Not used",1,"(2*B*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*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))))/(a*d*(b^2 - a^2)^(1/2))","B"
294,1,326,88,1.058405,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))^2),x)","\frac{2\,B\,\left(\frac{a^3\,\sin\left(c+d\,x\right)}{2}-\frac{a\,b^2\,\sin\left(c+d\,x\right)}{2}\right)}{a^2\,d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)}-\frac{2\,B\,\left(a^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)-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)+b^2\,\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^2\,d\,\left(a^2-b^2\right)}","Not used",1,"(2*B*((a^3*sin(c + d*x))/2 - (a*b^2*sin(c + d*x))/2))/(a^2*d*cos(c + d*x)*(a^2 - b^2)) - (2*B*(a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + b^2*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))","B"
295,1,1099,123,1.825735,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))^2),x)","\frac{\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)}{2}-\frac{B\,b^2\,\sin\left(c+d\,x\right)}{2}+\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(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{a\,\left(\frac{B\,\sin\left(c+d\,x\right)}{2}+\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)}{2}+\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)\,\cos\left(2\,c+2\,d\,x\right)}{2}\right)}{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\,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)}{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{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{B\,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)}{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{B\,b^3\,\mathrm{atan}\left(\frac{\left(a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,b^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)\,\sqrt{b^2-a^2}+3\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^8\,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)\,\left(a^7+2\,a^5\,b^2-3\,a^3\,b^4\right)}\right)\,1{}\mathrm{i}}{a^3\,d\,\sqrt{b^2-a^2}\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{B\,b^3\,\mathrm{atan}\left(\frac{\left(a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+8\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(b^2-a^2\right)}^{3/2}-8\,b^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)\,\sqrt{b^2-a^2}+3\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-3\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}+2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}-a^8\,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)\,\left(a^7+2\,a^5\,b^2-3\,a^3\,b^4\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)\,1{}\mathrm{i}}{a^3\,d\,\sqrt{b^2-a^2}\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"((B*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (B*b^2*sin(c + d*x))/2 + (B*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/2)/(a*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (a*((B*sin(c + d*x))/2 + (B*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (B*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(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*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^3*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)) - (B*b^3*atan(((a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*b^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)^(1/2) + 3*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^8*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)*(a^7 - 3*a^3*b^4 + 2*a^5*b^2)))*1i)/(a^3*d*(b^2 - a^2)^(1/2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b^3*atan(((a^9*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 8*b^7*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(3/2) - 8*b^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)^(1/2) + 3*a^4*b^5*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 3*a^5*b^4*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - 2*a^6*b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) + 2*a^7*b^2*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2) - a^8*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)*(a^7 - 3*a^3*b^4 + 2*a^5*b^2)))*cos(2*c + 2*d*x)*1i)/(a^3*d*(b^2 - a^2)^(1/2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (B*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/(a^3*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2))","B"
296,0,-1,386,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\left(A+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*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2), x)","F"
297,0,-1,303,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+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)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2), x)","F"
298,0,-1,231,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2), x)","F"
299,0,-1,171,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2), x)","F"
300,0,-1,178,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x), x)","F"
301,0,-1,213,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^2, x)","F"
302,0,-1,292,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^3, x)","F"
303,0,-1,378,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^4,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^4, x)","F"
304,0,-1,378,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+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*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2), x)","F"
305,0,-1,297,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2), x)","F"
306,0,-1,225,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2),x)","\int \left(A+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((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2), x)","F"
307,0,-1,236,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x), x)","F"
308,0,-1,232,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^2, x)","F"
309,0,-1,295,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^3, x)","F"
310,0,-1,375,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^4,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^4, x)","F"
311,0,-1,462,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\left(A+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*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2), x)","F"
312,0,-1,372,0.000000,"\text{Not used}","int(cos(c + d*x)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2), x)","F"
313,0,-1,288,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+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((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2), x)","F"
314,0,-1,292,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x), x)","F"
315,0,-1,296,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^2,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^2, x)","F"
316,0,-1,315,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^3,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^3, x)","F"
317,0,-1,376,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^4,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^4, x)","F"
318,0,-1,465,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^5,x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^5, x)","F"
319,0,-1,320,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+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*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2), x)","F"
320,0,-1,246,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+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)^2*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2), x)","F"
321,1,199,183,0.799642,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{3\,b\,d}+\frac{2\,A\,\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\,B\,\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*B*sin(c + d*x)*(a + b*cos(c + d*x))^(1/2))/(3*b*d) + (2*A*(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*B*((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"
322,1,135,130,0.885269,"\text{Not used}","int((A + B*cos(c + d*x))/(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\,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)}}","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*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))","B"
323,0,-1,118,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\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))/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)), x)","F"
324,0,-1,216,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)), x)","F"
325,0,-1,299,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)), x)","F"
326,0,-1,387,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+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*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
327,0,-1,262,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+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*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
328,0,-1,204,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
329,0,-1,185,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{A+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((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(3/2), x)","F"
330,0,-1,190,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)), x)","F"
331,0,-1,303,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)), x)","F"
332,0,-1,398,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)), x)","F"
333,0,-1,550,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4\,\left(A+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)^4*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2), x)","F"
334,0,-1,413,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,\left(A+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*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2), x)","F"
335,0,-1,331,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+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*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2), x)","F"
336,0,-1,307,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2), x)","F"
337,0,-1,275,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{A+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((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(5/2), x)","F"
338,0,-1,349,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)), x)","F"
339,0,-1,437,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)), x)","F"
340,0,-1,532,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2)), x)","F"
341,0,-1,58,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(a + b*cos(c + d*x))^(3/2), x)","F"
342,0,-1,59,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)), x)","F"
343,0,-1,108,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(a + b*cos(c + d*x))^(5/2), x)","F"
344,0,-1,179,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)), x)","F"
345,1,177,170,1.348604,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B*cos(c + d*x))*(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\,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\,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)^(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*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*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"
346,1,166,140,1.155704,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
347,1,128,108,1.011215,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(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\,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}}","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))","B"
348,1,85,75,0.992587,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,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}","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*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","B"
349,1,96,71,1.440361,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\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\,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*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*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"
350,1,150,103,1.965099,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,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*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"
351,1,177,140,2.393712,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/cos(c + d*x)^(7/2),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\,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\,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}}","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*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*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))","B"
352,1,275,264,1.534503,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^2,x)","-\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\,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\,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}}-\frac{2\,B\,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)}^{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\,B\,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)^(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*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)) - (2*B*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)^(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*B*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"
353,1,264,223,1.350039,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(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\,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\,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{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}}","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*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)) - (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))","B"
354,1,229,182,1.342264,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(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\,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\,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{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}}","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*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)) - (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))","B"
355,1,177,140,1.340453,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,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}}","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*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))","B"
356,1,158,121,1.569626,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,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{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}}","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 + (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))","B"
357,1,194,126,2.287578,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^2)/cos(c + d*x)^(5/2),x)","\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{4\,B\,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{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,"(2*A*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*B*a*b*ellipticF(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"
358,1,227,172,2.616173,"\text{Not used}","int(((A + B*cos(c + d*x))*(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\,B\,b^2\,\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{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*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)) + (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"
359,1,364,305,1.738366,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + b*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{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\,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{2\,B\,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^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\,A\,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\,B\,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\,B\,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,"(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 - (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*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)) - (2*B*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^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*A*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*B*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*B*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"
360,1,328,255,1.539078,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(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{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\,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{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}}","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*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)) - (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))","B"
361,1,275,205,1.432495,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{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{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}}","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 + (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)) - (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))","B"
362,1,248,202,1.457577,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3)/cos(c + d*x)^(3/2),x)","\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}}","Not used",1,"(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))","B"
363,1,255,192,2.338651,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{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{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{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{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 + (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 + (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)) + (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"
364,1,291,204,3.587102,"\text{Not used}","int(((A + B*cos(c + d*x))*(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{2\,A\,b^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{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{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 + (2*A*b^3*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)) + (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"
365,0,-1,182,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
366,0,-1,137,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
367,0,-1,89,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
368,0,-1,61,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))), x)","F"
369,0,-1,86,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))), x)","F"
370,0,-1,150,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))), x)","F"
371,0,-1,303,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2, x)","F"
372,0,-1,224,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2, x)","F"
373,0,-1,198,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^2, x)","F"
374,0,-1,200,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
375,0,-1,256,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
376,0,-1,345,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
377,0,-1,367,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^3, x)","F"
378,0,-1,344,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^3, x)","F"
379,0,-1,337,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^3, x)","F"
380,0,-1,345,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
381,0,-1,420,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
382,0,-1,523,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
383,0,-1,44,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
384,0,-1,44,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
385,0,-1,17,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
386,0,-1,17,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))), x)","F"
387,0,-1,40,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))), x)","F"
388,0,-1,44,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))), x)","F"
389,0,-1,116,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2, x)","F"
390,0,-1,78,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2, x)","F"
391,0,-1,55,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^2, x)","F"
392,0,-1,30,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
393,0,-1,80,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
394,0,-1,133,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
395,0,-1,560,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2), x)","F"
396,0,-1,473,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2), x)","F"
397,0,-1,385,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(1/2), x)","F"
398,0,-1,351,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(3/2), x)","F"
399,0,-1,284,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(5/2), x)","F"
400,0,-1,350,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(7/2), x)","F"
401,0,-1,433,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/cos(c + d*x)^(9/2), x)","F"
402,0,-1,670,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2), x)","F"
403,0,-1,566,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2), x)","F"
404,0,-1,472,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(1/2), x)","F"
405,0,-1,449,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(3/2), x)","F"
406,0,-1,419,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(5/2), x)","F"
407,0,-1,353,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(7/2), x)","F"
408,0,-1,433,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(9/2), x)","F"
409,0,-1,522,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(11/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/cos(c + d*x)^(11/2), x)","F"
410,0,-1,779,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2), x)","F"
411,0,-1,664,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2), x)","F"
412,0,-1,564,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(1/2), x)","F"
413,0,-1,547,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(3/2), x)","F"
414,0,-1,536,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
415,0,-1,493,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(7/2), x)","F"
416,0,-1,434,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(9/2), x)","F"
417,0,-1,522,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(11/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(11/2), x)","F"
418,0,-1,622,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(13/2),x)","\int \frac{\left(A+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(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(13/2), x)","F"
419,0,-1,418,0.000000,"\text{Not used}","int(((B*cos(c + d*x) + (3*B*b)/(2*a))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2),x)","\int \frac{\left(B\,\cos\left(c+d\,x\right)+\frac{3\,B\,b}{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(((B*cos(c + d*x) + (3*B*b)/(2*a))*(a + b*cos(c + d*x))^(5/2))/cos(c + d*x)^(5/2), x)","F"
420,0,-1,479,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2), x)","F"
421,0,-1,427,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(1/2), x)","F"
422,0,-1,228,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
423,0,-1,230,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
424,0,-1,290,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
425,0,-1,363,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
426,0,-1,500,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
427,0,-1,416,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
428,0,-1,284,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
429,0,-1,305,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
430,0,-1,393,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
431,0,-1,674,0.000000,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}\,\left(A+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)^(5/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2), x)","F"
432,0,-1,545,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2), x)","F"
433,0,-1,391,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(A+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)*(A + B*cos(c + d*x)))/(a + b*cos(c + d*x))^(5/2), x)","F"
434,0,-1,429,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
435,0,-1,456,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
436,0,-1,567,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+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((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
437,0,-1,419,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
438,0,-1,117,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}\,\left(B\,a+B\,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*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
439,0,-1,110,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
440,0,-1,226,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{B\,a+B\,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*a + B*b*cos(c + d*x))/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
441,0,-1,72,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(3*cos(c + d*x) + 2)^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{3\,\cos\left(c+d\,x\right)+2}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(3*cos(c + d*x) + 2)^(1/2)), x)","F"
442,0,-1,70,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(3*cos(c + d*x) - 2)^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(3*cos(c + d*x) - 2)^(1/2)), x)","F"
443,0,-1,93,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(2 - 3*cos(c + d*x))^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{2-3\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(2 - 3*cos(c + d*x))^(1/2)), x)","F"
444,0,-1,95,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(- 3*cos(c + d*x) - 2)^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{-3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(- 3*cos(c + d*x) - 2)^(1/2)), x)","F"
445,0,-1,72,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(2*cos(c + d*x) + 3)^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{2\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(2*cos(c + d*x) + 3)^(1/2)), x)","F"
446,0,-1,74,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(3 - 2*cos(c + d*x))^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{3-2\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(3 - 2*cos(c + d*x))^(1/2)), x)","F"
447,0,-1,98,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(2*cos(c + d*x) - 3)^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(2*cos(c + d*x) - 3)^(1/2)), x)","F"
448,0,-1,96,0.000000,"\text{Not used}","int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(- 2*cos(c + d*x) - 3)^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)+1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{-2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int((cos(c + d*x) + 1)/(cos(c + d*x)^(3/2)*(- 2*cos(c + d*x) - 3)^(1/2)), x)","F"
449,0,-1,36,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^n,x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^n \,d x","Not used",0,"int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^n, x)","F"
450,0,-1,595,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^4,x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^4 \,d x","Not used",1,"int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^4, x)","F"
451,0,-1,406,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^3,x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^3, x)","F"
452,0,-1,287,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^2,x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^2, x)","F"
453,0,-1,196,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x)),x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,\left(a+b\,\cos\left(e+f\,x\right)\right) \,d x","Not used",1,"int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x)), x)","F"
454,0,-1,286,0.000000,"\text{Not used}","int(((c*cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x)),x)","\int \frac{{\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)}{a+b\,\cos\left(e+f\,x\right)} \,d x","Not used",1,"int(((c*cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x)), x)","F"
455,0,-1,181,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(3/2),x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",0,"int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(3/2), x)","F"
456,0,-1,38,0.000000,"\text{Not used}","int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(1/2),x)","\int {\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,\sqrt{a+b\,\cos\left(e+f\,x\right)} \,d x","Not used",0,"int((c*cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(1/2), x)","F"
457,0,-1,38,0.000000,"\text{Not used}","int(((c*cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(1/2),x)","\int \frac{{\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)}{\sqrt{a+b\,\cos\left(e+f\,x\right)}} \,d x","Not used",0,"int(((c*cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(1/2), x)","F"
458,0,-1,191,0.000000,"\text{Not used}","int(((c*cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(3/2),x)","\int \frac{{\left(c\,\cos\left(e+f\,x\right)\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)}{{\left(a+b\,\cos\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",0,"int(((c*cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(3/2), x)","F"
459,0,-1,172,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x)), x)","F"
460,0,-1,135,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x)), x)","F"
461,0,-1,106,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x)), x)","F"
462,0,-1,110,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x)), x)","F"
463,0,-1,141,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(1/2), x)","F"
464,0,-1,172,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x)))/(1/cos(c + d*x))^(3/2), x)","F"
465,0,-1,199,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2, x)","F"
466,0,-1,160,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2, x)","F"
467,0,-1,160,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2, x)","F"
468,0,-1,166,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2, x)","F"
469,0,-1,201,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*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(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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2), x)","F"
470,0,-1,244,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3, x)","F"
471,0,-1,211,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3, x)","F"
472,0,-1,199,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3, x)","F"
473,0,-1,211,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3, x)","F"
474,0,-1,211,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3, x)","F"
475,0,-1,244,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2), x)","F"
476,0,-1,193,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x)),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x)), x)","F"
477,0,-1,159,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x)),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x)), x)","F"
478,0,-1,123,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x)),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x)), x)","F"
479,0,-1,125,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))), x)","F"
480,0,-1,163,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))), x)","F"
481,0,-1,196,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))), x)","F"
482,0,-1,208,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^2, x)","F"
483,0,-1,161,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^2, x)","F"
484,0,-1,168,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
485,0,-1,176,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
486,0,-1,206,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
487,0,-1,261,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^3, x)","F"
488,0,-1,222,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^3,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^3, x)","F"
489,0,-1,216,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
490,0,-1,222,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
491,0,-1,228,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
492,0,-1,259,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3), x)","F"
493,1,479,220,5.604678,"\text{Not used}","int((A + B*cos(c + d*x))*(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+288\,B\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+288\,B\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\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\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\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\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)*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 + 288*B)*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)*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)*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)*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)*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"
494,1,441,175,4.551818,"\text{Not used}","int((A + B*cos(c + d*x))*(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(96\,A+112\,B\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\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\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\right)\,1{}\mathrm{i}}{105\,d}-\frac{B\,{\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{B\,{\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)}\,8{}\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)*(96*A + 112*B)*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)*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)*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)*1i)/(105*d) - (B*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) + (B*exp(c*4i + d*x*4i)*(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) + 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"
495,1,196,130,2.688893,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(1/2),x)","\frac{4\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(14\,A\,\sin\left(c+d\,x\right)+10\,B\,\sin\left(c+d\,x\right)+8\,A\,\sin\left(2\,c+2\,d\,x\right)+18\,A\,\sin\left(3\,c+3\,d\,x\right)+4\,A\,\sin\left(4\,c+4\,d\,x\right)+4\,A\,\sin\left(5\,c+5\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)+15\,B\,\sin\left(3\,c+3\,d\,x\right)+5\,B\,\sin\left(4\,c+4\,d\,x\right)+5\,B\,\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,"(4*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(14*A*sin(c + d*x) + 10*B*sin(c + d*x) + 8*A*sin(2*c + 2*d*x) + 18*A*sin(3*c + 3*d*x) + 4*A*sin(4*c + 4*d*x) + 4*A*sin(5*c + 5*d*x) + 10*B*sin(2*c + 2*d*x) + 15*B*sin(3*c + 3*d*x) + 5*B*sin(4*c + 4*d*x) + 5*B*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"
496,1,114,85,1.074206,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(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(2\,A\,\sin\left(c+d\,x\right)+3\,B\,\sin\left(c+d\,x\right)+2\,A\,\sin\left(2\,c+2\,d\,x\right)+2\,A\,\sin\left(3\,c+3\,d\,x\right)+3\,B\,\sin\left(3\,c+3\,d\,x\right)\right)}{3\,d\,\left(3\,\cos\left(c+d\,x\right)+2\,\cos\left(2\,c+2\,d\,x\right)+\cos\left(3\,c+3\,d\,x\right)+2\right)}","Not used",1,"(2*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(2*A*sin(c + d*x) + 3*B*sin(c + d*x) + 2*A*sin(2*c + 2*d*x) + 2*A*sin(3*c + 3*d*x) + 3*B*sin(3*c + 3*d*x)))/(3*d*(3*cos(c + d*x) + 2*cos(2*c + 2*d*x) + cos(3*c + 3*d*x) + 2))","B"
497,0,-1,96,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
498,0,-1,98,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
499,0,-1,151,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2), x)","F"
500,0,-1,196,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2), x)","F"
501,1,348,275,5.141944,"\text{Not used}","int((A + B*cos(c + d*x))*(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{32\,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(2\,A+3\,B\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{5\,d}+\frac{64\,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(21\,A+19\,B\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{35\,d}+\frac{32\,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(168\,A+187\,B\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{315\,d}+\frac{64\,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(168\,A+187\,B\right)\,\sqrt{a+a\,\cos\left(c+d\,x\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)*((64*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((3*c)/2 + (3*d*x)/2)*(21*A + 19*B)*(a + a*cos(c + d*x))^(1/2))/(35*d) - (32*a*exp((c*11i)/2 + (d*x*11i)/2)*sin(c/2 + (d*x)/2)*(2*A + 3*B)*(a + a*cos(c + d*x))^(1/2))/(5*d) + (32*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((7*c)/2 + (7*d*x)/2)*(168*A + 187*B)*(a + a*cos(c + d*x))^(1/2))/(315*d) + (64*a*exp((c*11i)/2 + (d*x*11i)/2)*sin((11*c)/2 + (11*d*x)/2)*(168*A + 187*B)*(a + a*cos(c + d*x))^(1/2))/(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"
502,1,316,228,4.914848,"\text{Not used}","int((A + B*cos(c + d*x))*(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{96\,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(A+B\right)}{5\,d}-\frac{16\,B\,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)}}{3\,d}+\frac{16\,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(34\,A+39\,B\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{35\,d}+\frac{32\,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(34\,A+39\,B\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)*((96*a*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2)*(A + B))/(5*d) - (16*B*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))/(3*d) + (16*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2)*(34*A + 39*B)*(a + a*cos(c + d*x))^(1/2))/(35*d) + (32*a*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2)*(34*A + 39*B)*(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"
503,1,259,181,4.804463,"\text{Not used}","int((A + B*cos(c + d*x))*(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{8\,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(2\,A+3\,B\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,d}+\frac{16\,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(13\,A+12\,B\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{15\,d}+\frac{8\,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(52\,A+63\,B\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)*((16*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((3*c)/2 + (3*d*x)/2)*(13*A + 12*B)*(a + a*cos(c + d*x))^(1/2))/(15*d) - (8*a*exp((c*7i)/2 + (d*x*7i)/2)*sin(c/2 + (d*x)/2)*(2*A + 3*B)*(a + a*cos(c + d*x))^(1/2))/(3*d) + (8*a*exp((c*7i)/2 + (d*x*7i)/2)*sin((7*c)/2 + (7*d*x)/2)*(52*A + 63*B)*(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"
504,1,197,134,2.443951,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(3/2),x)","\frac{2\,a\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(48\,A\,\sin\left(c+d\,x\right)+50\,B\,\sin\left(c+d\,x\right)+36\,A\,\sin\left(2\,c+2\,d\,x\right)+66\,A\,\sin\left(3\,c+3\,d\,x\right)+18\,A\,\sin\left(4\,c+4\,d\,x\right)+18\,A\,\sin\left(5\,c+5\,d\,x\right)+20\,B\,\sin\left(2\,c+2\,d\,x\right)+75\,B\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(4\,c+4\,d\,x\right)+25\,B\,\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*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(48*A*sin(c + d*x) + 50*B*sin(c + d*x) + 36*A*sin(2*c + 2*d*x) + 66*A*sin(3*c + 3*d*x) + 18*A*sin(4*c + 4*d*x) + 18*A*sin(5*c + 5*d*x) + 20*B*sin(2*c + 2*d*x) + 75*B*sin(3*c + 3*d*x) + 10*B*sin(4*c + 4*d*x) + 25*B*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"
505,0,-1,145,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
506,0,-1,146,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
507,0,-1,153,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
508,0,-1,200,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2), x)","F"
509,0,-1,247,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2), x)","F"
510,1,789,322,6.192210,"\text{Not used}","int((A + B*cos(c + d*x))*(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(4184\,A+4615\,B\right)\,32{}\mathrm{i}}{45045\,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(2\,A+5\,B\right)\,16{}\mathrm{i}}{5\,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\,A+5\,B\right)\,16{}\mathrm{i}}{5\,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(116\,A+115\,B\right)\,16{}\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(116\,A+115\,B\right)\,16{}\mathrm{i}}{35\,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\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\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(4184\,A+4615\,B\right)\,16{}\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(4184\,A+4615\,B\right)\,16{}\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(4184\,A+4615\,B\right)\,32{}\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)*(4184*A + 4615*B)*32i)/(45045*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)*(2*A + 5*B)*16i)/(5*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*A + 5*B)*16i)/(5*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)*(116*A + 115*B)*16i)/(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)*(116*A + 115*B)*16i)/(35*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)*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)*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)*(4184*A + 4615*B)*16i)/(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)*(4184*A + 4615*B)*16i)/(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)*(4184*A + 4615*B)*32i)/(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"
511,1,751,275,5.810460,"\text{Not used}","int((A + B*cos(c + d*x))*(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(710\,A+803\,B\right)\,16{}\mathrm{i}}{3465\,d}-\frac{B\,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{B\,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)}\,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(30\,A+41\,B\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\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\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\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\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\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(710\,A+803\,B\right)\,16{}\mathrm{i}}{3465\,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)*(710*A + 803*B)*16i)/(3465*d) - (B*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) + (B*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)*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)*(30*A + 41*B)*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)*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)*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)*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)*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)*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)*(710*A + 803*B)*16i)/(3465*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"
512,1,617,228,5.725490,"\text{Not used}","int((A + B*cos(c + d*x))*(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(292\,A+345\,B\right)\,4{}\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(2\,A+5\,B\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\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\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\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\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\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(292\,A+345\,B\right)\,4{}\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)*(292*A + 345*B)*4i)/(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)*(2*A + 5*B)*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)*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)*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)*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)*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)*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)*(292*A + 345*B)*4i)/(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"
513,1,579,181,4.995313,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(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(230\,A+301\,B\right)\,2{}\mathrm{i}}{105\,d}-\frac{B\,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{B\,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)}\,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(10\,A+17\,B\right)\,2{}\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(10\,A+17\,B\right)\,2{}\mathrm{i}}{3\,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(100\,A+113\,B\right)\,2{}\mathrm{i}}{15\,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(100\,A+113\,B\right)\,2{}\mathrm{i}}{15\,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(230\,A+301\,B\right)\,2{}\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^2*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(230*A + 301*B)*2i)/(105*d) - (B*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 + (B*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)*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)*(10*A + 17*B)*2i)/(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)*(10*A + 17*B)*2i)/(3*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)*(100*A + 113*B)*2i)/(15*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)*(100*A + 113*B)*2i)/(15*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)*(230*A + 301*B)*2i)/(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"
514,0,-1,192,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
515,0,-1,193,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
516,0,-1,198,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
517,0,-1,200,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
518,0,-1,247,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2), x)","F"
519,0,-1,294,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + a*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2), x)","F"
520,0,-1,295,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(11/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(11/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
521,0,-1,250,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
522,0,-1,207,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
523,0,-1,162,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
524,0,-1,119,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
525,0,-1,140,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(1/2), x)","F"
526,0,-1,181,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
527,0,-1,230,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
528,0,-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"
529,0,-1,317,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
530,0,-1,270,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
531,0,-1,223,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
532,0,-1,176,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
533,0,-1,127,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(3/2), x)","F"
534,0,-1,185,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
535,0,-1,237,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
536,0,-1,317,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
537,0,-1,270,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
538,0,-1,223,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
539,0,-1,176,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(5/2), x)","F"
540,0,-1,174,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
541,0,-1,234,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
542,0,-1,286,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
543,0,-1,317,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + a*cos(c + d*x))^(7/2), x)","F"
544,0,-1,270,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + a*cos(c + d*x))^(7/2), x)","F"
545,0,-1,223,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + a*cos(c + d*x))^(7/2), x)","F"
546,0,-1,221,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
547,0,-1,221,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
548,0,-1,281,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
549,0,-1,333,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
550,0,-1,180,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x)), x)","F"
551,0,-1,143,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x)), x)","F"
552,0,-1,111,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x)), x)","F"
553,0,-1,115,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x)),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x)), x)","F"
554,0,-1,148,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(1/2), x)","F"
555,0,-1,180,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + b*cos(c + d*x)))/(1/cos(c + d*x))^(3/2), x)","F"
556,0,-1,221,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2, x)","F"
557,0,-1,177,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2, x)","F"
558,0,-1,161,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2, x)","F"
559,0,-1,171,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2, x)","F"
560,0,-1,213,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*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(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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^2)/(1/cos(c + d*x))^(1/2), x)","F"
561,0,-1,295,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3, x)","F"
562,0,-1,244,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3, x)","F"
563,0,-1,239,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3, x)","F"
564,0,-1,237,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3, x)","F"
565,0,-1,245,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3,x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3, x)","F"
566,0,-1,295,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^3)/(1/cos(c + d*x))^(1/2), x)","F"
567,0,-1,210,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x)),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x)), x)","F"
568,0,-1,126,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x)),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x)), x)","F"
569,0,-1,101,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x)),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x)), x)","F"
570,0,-1,149,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))), x)","F"
571,0,-1,197,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))), x)","F"
572,0,-1,405,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^2, x)","F"
573,0,-1,316,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^2, x)","F"
574,0,-1,260,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^2,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^2, x)","F"
575,0,-1,258,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
576,0,-1,284,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
577,0,-1,363,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
578,0,-1,480,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^3, x)","F"
579,0,-1,405,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^3,x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^3, x)","F"
580,0,-1,402,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
581,0,-1,400,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
582,0,-1,427,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
583,0,-1,521,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3), x)","F"
584,0,-1,64,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(5/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,\left(B\,a+B\,b\,\cos\left(c+d\,x\right)\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(5/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
585,0,-1,60,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(B\,a+B\,b\,\cos\left(c+d\,x\right)\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(3/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
586,0,-1,37,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(B\,a+B\,b\,\cos\left(c+d\,x\right)\right)}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((1/cos(c + d*x))^(1/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x)), x)","F"
587,0,-1,37,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{B\,a+B\,b\,\cos\left(c+d\,x\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((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))), x)","F"
588,0,-1,64,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{B\,a+B\,b\,\cos\left(c+d\,x\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((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))), x)","F"
589,0,-1,64,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{B\,a+B\,b\,\cos\left(c+d\,x\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((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))), x)","F"
590,0,-1,473,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
591,0,-1,390,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
592,0,-1,324,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
593,0,-1,411,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
594,0,-1,445,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
595,0,-1,533,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(1/2), x)","F"
596,0,-1,620,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/2))/(1/cos(c + d*x))^(3/2), x)","F"
597,0,-1,562,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
598,0,-1,473,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
599,0,-1,393,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
600,0,-1,479,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
601,0,-1,509,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
602,0,-1,532,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
603,0,-1,626,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(1/2), x)","F"
604,0,-1,730,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^(3/2))/(1/cos(c + d*x))^(3/2), x)","F"
605,0,-1,662,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(13/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
606,0,-1,562,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
607,0,-1,474,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
608,0,-1,553,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
609,0,-1,596,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
610,0,-1,607,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
611,0,-1,624,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
612,0,-1,724,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(1/2), x)","F"
613,0,-1,839,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\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 + B*cos(c + d*x))*(a + b*cos(c + d*x))^(5/2))/(1/cos(c + d*x))^(3/2), x)","F"
614,0,-1,403,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
615,0,-1,330,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
616,0,-1,270,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
617,0,-1,268,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(1/2), x)","F"
618,0,-1,487,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
619,0,-1,539,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
620,0,-1,433,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(3/2), x)","F"
621,0,-1,345,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(3/2), x)","F"
622,0,-1,324,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(3/2), x)","F"
623,0,-1,476,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
624,0,-1,560,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
625,0,-1,607,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2))/(a + b*cos(c + d*x))^(5/2), x)","F"
626,0,-1,496,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2))/(a + b*cos(c + d*x))^(5/2), x)","F"
627,0,-1,469,0.000000,"\text{Not used}","int(((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\left(A+B\,\cos\left(c+d\,x\right)\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 + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2))/(a + b*cos(c + d*x))^(5/2), x)","F"
628,0,-1,431,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
629,0,-1,602,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
630,0,-1,733,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{A+B\,\cos\left(c+d\,x\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 + B*cos(c + d*x))/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
631,0,-1,266,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(3/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,\left(B\,a+B\,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(((1/cos(c + d*x))^(3/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
632,0,-1,130,0.000000,"\text{Not used}","int(((1/cos(c + d*x))^(1/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(B\,a+B\,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(((1/cos(c + d*x))^(1/2)*(B*a + B*b*cos(c + d*x)))/(a + b*cos(c + d*x))^(3/2), x)","F"
633,0,-1,137,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{B\,a+B\,b\,\cos\left(c+d\,x\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((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
634,0,-1,479,0.000000,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{B\,a+B\,b\,\cos\left(c+d\,x\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((B*a + B*b*cos(c + d*x))/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
635,0,-1,59,0.000000,"\text{Not used}","int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^n,x)","\int {\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^n \,d x","Not used",0,"int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^n, x)","F"
636,0,-1,644,0.000000,"\text{Not used}","int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^4,x)","\int {\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^4 \,d x","Not used",1,"int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^4, x)","F"
637,0,-1,455,0.000000,"\text{Not used}","int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^3,x)","\int {\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^3, x)","F"
638,0,-1,327,0.000000,"\text{Not used}","int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^2,x)","\int {\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^2, x)","F"
639,0,-1,217,0.000000,"\text{Not used}","int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x)),x)","\int {\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,\left(a+b\,\cos\left(e+f\,x\right)\right) \,d x","Not used",1,"int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x)), x)","F"
640,0,-1,299,0.000000,"\text{Not used}","int(((c/cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x)),x)","\int \frac{{\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)}{a+b\,\cos\left(e+f\,x\right)} \,d x","Not used",1,"int(((c/cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x)), x)","F"
641,0,-1,210,0.000000,"\text{Not used}","int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(3/2),x)","\int {\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",0,"int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(3/2), x)","F"
642,0,-1,61,0.000000,"\text{Not used}","int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(1/2),x)","\int {\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)\,\sqrt{a+b\,\cos\left(e+f\,x\right)} \,d x","Not used",0,"int((c/cos(e + f*x))^m*(A + B*cos(e + f*x))*(a + b*cos(e + f*x))^(1/2), x)","F"
643,0,-1,61,0.000000,"\text{Not used}","int(((c/cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(1/2),x)","\int \frac{{\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)}{\sqrt{a+b\,\cos\left(e+f\,x\right)}} \,d x","Not used",0,"int(((c/cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(1/2), x)","F"
644,0,-1,213,0.000000,"\text{Not used}","int(((c/cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(3/2),x)","\int \frac{{\left(\frac{c}{\cos\left(e+f\,x\right)}\right)}^m\,\left(A+B\,\cos\left(e+f\,x\right)\right)}{{\left(a+b\,\cos\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",0,"int(((c/cos(e + f*x))^m*(A + B*cos(e + f*x)))/(a + b*cos(e + f*x))^(3/2), x)","F"