1,1,107,114,2.976115,"\text{Not used}","int(cos(c + d*x)^5*(a + a*cos(c + d*x)),x)","\frac{5\,a\,x}{16}+\frac{\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{39\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}+\frac{133\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{283\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{107\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{27\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(5*a*x)/16 + ((27*a*tan(c/2 + (d*x)/2))/8 + (107*a*tan(c/2 + (d*x)/2)^3)/24 + (283*a*tan(c/2 + (d*x)/2)^5)/20 + (133*a*tan(c/2 + (d*x)/2)^7)/20 + (39*a*tan(c/2 + (d*x)/2)^9)/8 + (5*a*tan(c/2 + (d*x)/2)^11)/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
2,1,93,92,2.852382,"\text{Not used}","int(cos(c + d*x)^4*(a + a*cos(c + d*x)),x)","\frac{3\,a\,x}{8}+\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6}+\frac{116\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\frac{19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{13\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a*x)/8 + ((13*a*tan(c/2 + (d*x)/2))/4 + (19*a*tan(c/2 + (d*x)/2)^3)/6 + (116*a*tan(c/2 + (d*x)/2)^5)/15 + (13*a*tan(c/2 + (d*x)/2)^7)/6 + (3*a*tan(c/2 + (d*x)/2)^9)/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
3,1,79,76,3.602411,"\text{Not used}","int(cos(c + d*x)^3*(a + a*cos(c + d*x)),x)","\frac{3\,a\,x}{8}+\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{49\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{31\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{13\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(3*a*x)/8 + ((13*a*tan(c/2 + (d*x)/2))/4 + (31*a*tan(c/2 + (d*x)/2)^3)/12 + (49*a*tan(c/2 + (d*x)/2)^5)/12 + (3*a*tan(c/2 + (d*x)/2)^7)/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
4,1,55,54,0.378634,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x)),x)","\frac{a\,x}{2}+\frac{2\,a\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(a*x)/2 + (2*a*sin(c + d*x))/(3*d) + (a*cos(c + d*x)*sin(c + d*x))/(2*d) + (a*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
5,1,50,38,0.745229,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x)),x)","\frac{a\,x}{2}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(a*x)/2 + (3*a*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^3)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
6,1,15,15,0.311275,"\text{Not used}","int(a + a*cos(c + d*x),x)","a\,x+\frac{a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"a*x + (a*sin(c + d*x))/d","B"
7,1,20,16,0.342702,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x),x)","a\,x+\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"a*x + (2*a*atanh(tan(c/2 + (d*x)/2)))/d","B"
8,1,47,24,0.385014,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^2,x)","\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)))/d - (2*a*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
9,1,75,47,0.711748,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^3,x)","\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,{\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)}^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)}{d}","Not used",1,"(3*a*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^3)/(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)))/d","B"
10,1,102,63,2.038155,"\text{Not used}","int((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)}{d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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)))/d - (3*a*tan(c/2 + (d*x)/2) - (4*a*tan(c/2 + (d*x)/2)^3)/3 + a*tan(c/2 + (d*x)/2)^5)/(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"
11,1,130,85,3.338614,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^5,x)","\frac{-\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{49\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}-\frac{31\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{13\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"((13*a*tan(c/2 + (d*x)/2))/4 - (31*a*tan(c/2 + (d*x)/2)^3)/12 + (49*a*tan(c/2 + (d*x)/2)^5)/12 - (3*a*tan(c/2 + (d*x)/2)^7)/4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (3*a*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
12,1,158,101,4.770285,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^6,x)","\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}-\frac{13\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6}+\frac{116\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}-\frac{19\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{13\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(3*a*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((13*a*tan(c/2 + (d*x)/2))/4 - (19*a*tan(c/2 + (d*x)/2)^3)/6 + (116*a*tan(c/2 + (d*x)/2)^5)/15 - (13*a*tan(c/2 + (d*x)/2)^7)/6 + (3*a*tan(c/2 + (d*x)/2)^9)/4)/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
13,1,121,129,2.863593,"\text{Not used}","int(cos(c + d*x)^4*(a + a*cos(c + d*x))^2,x)","\frac{11\,a^2\,x}{16}+\frac{\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{187\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{331\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{501\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{87\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}+\frac{53\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(11*a^2*x)/16 + ((87*a^2*tan(c/2 + (d*x)/2)^3)/8 + (501*a^2*tan(c/2 + (d*x)/2)^5)/20 + (331*a^2*tan(c/2 + (d*x)/2)^7)/20 + (187*a^2*tan(c/2 + (d*x)/2)^9)/24 + (11*a^2*tan(c/2 + (d*x)/2)^11)/8 + (53*a^2*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
14,1,105,103,3.627710,"\text{Not used}","int(cos(c + d*x)^3*(a + a*cos(c + d*x))^2,x)","\frac{3\,a^2\,x}{4}+\frac{\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}+7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{72\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+9\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{13\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(3*a^2*x)/4 + (9*a^2*tan(c/2 + (d*x)/2)^3 + (72*a^2*tan(c/2 + (d*x)/2)^5)/5 + 7*a^2*tan(c/2 + (d*x)/2)^7 + (3*a^2*tan(c/2 + (d*x)/2)^9)/2 + (13*a^2*tan(c/2 + (d*x)/2))/2)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
15,1,89,87,3.495170,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^2,x)","\frac{7\,a^2\,x}{8}+\frac{\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{77\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{83\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(7*a^2*x)/8 + ((83*a^2*tan(c/2 + (d*x)/2)^3)/12 + (77*a^2*tan(c/2 + (d*x)/2)^5)/12 + (7*a^2*tan(c/2 + (d*x)/2)^7)/4 + (25*a^2*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
16,1,61,57,0.378690,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^2,x)","a^2\,x+\frac{5\,a^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}","Not used",1,"a^2*x + (5*a^2*sin(c + d*x))/(3*d) + (a^2*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (a^2*cos(c + d*x)*sin(c + d*x))/d","B"
17,1,57,45,0.723958,"\text{Not used}","int((a + a*cos(c + d*x))^2,x)","\frac{3\,a^2\,x}{2}+\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,a^2\,\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)}^2}","Not used",1,"(3*a^2*x)/2 + (3*a^2*tan(c/2 + (d*x)/2)^3 + 5*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
18,1,33,34,0.398962,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x),x)","2\,a^2\,x+\frac{a^2\,\left(2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\sin\left(c+d\,x\right)\right)}{d}","Not used",1,"2*a^2*x + (a^2*(2*atanh(tan(c/2 + (d*x)/2)) + sin(c + d*x)))/d","B"
19,1,56,34,0.390286,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x)^2,x)","a^2\,x+\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a^2\,\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,"a^2*x + (4*a^2*atanh(tan(c/2 + (d*x)/2)))/d - (2*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
20,1,83,54,0.705725,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x)^3,x)","\frac{3\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-5\,a^2\,\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)}","Not used",1,"(3*a^2*atanh(tan(c/2 + (d*x)/2)))/d - (3*a^2*tan(c/2 + (d*x)/2)^3 - 5*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
21,1,112,66,2.008376,"\text{Not used}","int((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)}{d}-\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+6\,a^2\,\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)))/d - (2*a^2*tan(c/2 + (d*x)/2)^5 - (16*a^2*tan(c/2 + (d*x)/2)^3)/3 + 6*a^2*tan(c/2 + (d*x)/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"
22,1,141,96,3.352465,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x)^5,x)","\frac{7\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{7\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-\frac{77\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{83\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}-\frac{25\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(7*a^2*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((83*a^2*tan(c/2 + (d*x)/2)^3)/12 - (77*a^2*tan(c/2 + (d*x)/2)^5)/12 + (7*a^2*tan(c/2 + (d*x)/2)^7)/4 - (25*a^2*tan(c/2 + (d*x)/2))/4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
23,1,121,129,2.868823,"\text{Not used}","int(cos(c + d*x)^3*(a + a*cos(c + d*x))^3,x)","\frac{23\,a^3\,x}{16}+\frac{\frac{23\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{391\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{759\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{969\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{211\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}+\frac{105\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(23*a^3*x)/16 + ((211*a^3*tan(c/2 + (d*x)/2)^3)/8 + (969*a^3*tan(c/2 + (d*x)/2)^5)/20 + (759*a^3*tan(c/2 + (d*x)/2)^7)/20 + (391*a^3*tan(c/2 + (d*x)/2)^9)/24 + (23*a^3*tan(c/2 + (d*x)/2)^11)/8 + (105*a^3*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
24,1,105,105,3.711355,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^3,x)","\frac{13\,a^3\,x}{8}+\frac{\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{91\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6}+\frac{416\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\frac{133\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{51\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(13*a^3*x)/8 + ((133*a^3*tan(c/2 + (d*x)/2)^3)/6 + (416*a^3*tan(c/2 + (d*x)/2)^5)/15 + (91*a^3*tan(c/2 + (d*x)/2)^7)/6 + (13*a^3*tan(c/2 + (d*x)/2)^9)/4 + (51*a^3*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
25,1,89,85,3.485886,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^3,x)","\frac{15\,a^3\,x}{8}+\frac{\frac{15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{55\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{73\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{49\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(15*a^3*x)/8 + ((73*a^3*tan(c/2 + (d*x)/2)^3)/4 + (55*a^3*tan(c/2 + (d*x)/2)^5)/4 + (15*a^3*tan(c/2 + (d*x)/2)^7)/4 + (49*a^3*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
26,1,63,63,0.395572,"\text{Not used}","int((a + a*cos(c + d*x))^3,x)","\frac{5\,a^3\,x}{2}+\frac{11\,a^3\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{3\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(5*a^3*x)/2 + (11*a^3*sin(c + d*x))/(3*d) + (a^3*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (3*a^3*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
27,1,88,59,0.436663,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x),x)","\frac{7\,a^3\,x}{2}+\frac{2\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+7\,a^3\,\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)}","Not used",1,"(7*a^3*x)/2 + (2*a^3*atanh(tan(c/2 + (d*x)/2)))/d + (5*a^3*tan(c/2 + (d*x)/2)^3 + 7*a^3*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1))","B"
28,1,57,48,0.410015,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^2,x)","3\,a^3\,x+\frac{6\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{4\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}","Not used",1,"3*a^3*x + (6*a^3*atanh(tan(c/2 + (d*x)/2)))/d - (4*a^3*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^4 - 1))","B"
29,1,88,59,0.440267,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^3,x)","a^3\,x+\frac{7\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-7\,a^3\,\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)}","Not used",1,"a^3*x + (7*a^3*atanh(tan(c/2 + (d*x)/2)))/d - (5*a^3*tan(c/2 + (d*x)/2)^3 - 7*a^3*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
30,1,112,72,2.039003,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^4,x)","\frac{5\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{40\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+11\,a^3\,\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,"(5*a^3*atanh(tan(c/2 + (d*x)/2)))/d - (5*a^3*tan(c/2 + (d*x)/2)^5 - (40*a^3*tan(c/2 + (d*x)/2)^3)/3 + 11*a^3*tan(c/2 + (d*x)/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"
31,1,141,93,3.292692,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^5,x)","\frac{15\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-\frac{55\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{73\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-\frac{49\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(15*a^3*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((73*a^3*tan(c/2 + (d*x)/2)^3)/4 - (55*a^3*tan(c/2 + (d*x)/2)^5)/4 + (15*a^3*tan(c/2 + (d*x)/2)^7)/4 - (49*a^3*tan(c/2 + (d*x)/2))/4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
32,1,170,114,4.626236,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^6,x)","\frac{13\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}-\frac{91\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6}+\frac{416\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}-\frac{133\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{51\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{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,"(13*a^3*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((416*a^3*tan(c/2 + (d*x)/2)^5)/15 - (133*a^3*tan(c/2 + (d*x)/2)^3)/6 - (91*a^3*tan(c/2 + (d*x)/2)^7)/6 + (13*a^3*tan(c/2 + (d*x)/2)^9)/4 + (51*a^3*tan(c/2 + (d*x)/2))/4)/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
33,1,121,127,2.854970,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^4,x)","\frac{49\,a^4\,x}{16}+\frac{\frac{49\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{833\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{1617\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{1967\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{1471\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{207\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(49*a^4*x)/16 + ((1471*a^4*tan(c/2 + (d*x)/2)^3)/24 + (1967*a^4*tan(c/2 + (d*x)/2)^5)/20 + (1617*a^4*tan(c/2 + (d*x)/2)^7)/20 + (833*a^4*tan(c/2 + (d*x)/2)^9)/24 + (49*a^4*tan(c/2 + (d*x)/2)^11)/8 + (207*a^4*tan(c/2 + (d*x)/2))/8)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
34,1,105,102,3.685466,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^4,x)","\frac{7\,a^4\,x}{2}+\frac{7\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{98\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{896\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\frac{158\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+25\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^5}","Not used",1,"(7*a^4*x)/2 + ((158*a^4*tan(c/2 + (d*x)/2)^3)/3 + (896*a^4*tan(c/2 + (d*x)/2)^5)/15 + (98*a^4*tan(c/2 + (d*x)/2)^7)/3 + 7*a^4*tan(c/2 + (d*x)/2)^9 + 25*a^4*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
35,1,89,87,3.557192,"\text{Not used}","int((a + a*cos(c + d*x))^4,x)","\frac{35\,a^4\,x}{8}+\frac{\frac{35\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{385\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{511\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{93\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(35*a^4*x)/8 + ((511*a^4*tan(c/2 + (d*x)/2)^3)/12 + (385*a^4*tan(c/2 + (d*x)/2)^5)/12 + (35*a^4*tan(c/2 + (d*x)/2)^7)/4 + (93*a^4*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
36,1,93,73,0.410836,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x),x)","6\,a^4\,x+\frac{20\,a^4\,\sin\left(c+d\,x\right)}{3\,d}+\frac{2\,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^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{2\,a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}","Not used",1,"6*a^4*x + (20*a^4*sin(c + d*x))/(3*d) + (2*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (2*a^4*cos(c + d*x)*sin(c + d*x))/d","B"
37,1,117,73,0.595782,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^2,x)","\frac{13\,a^4\,x}{2}+\frac{8\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{-5\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+11\,a^4\,\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-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(13*a^4*x)/2 + (8*a^4*atanh(tan(c/2 + (d*x)/2)))/d + (2*a^4*tan(c/2 + (d*x)/2)^3 - 5*a^4*tan(c/2 + (d*x)/2)^5 + 11*a^4*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 + 1))","B"
38,1,115,73,0.588958,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^3,x)","4\,a^4\,x+\frac{13\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{5\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-11\,a^4\,\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+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"4*a^4*x + (13*a^4*atanh(tan(c/2 + (d*x)/2)))/d + (2*a^4*tan(c/2 + (d*x)/2)^3 + 5*a^4*tan(c/2 + (d*x)/2)^5 - 11*a^4*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 - 1))","B"
39,1,117,73,0.620870,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^4,x)","a^4\,x+\frac{12\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{10\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{76\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+18\,a^4\,\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^4*x + (12*a^4*atanh(tan(c/2 + (d*x)/2)))/d - (10*a^4*tan(c/2 + (d*x)/2)^5 - (76*a^4*tan(c/2 + (d*x)/2)^3)/3 + 18*a^4*tan(c/2 + (d*x)/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"
40,1,141,96,3.502268,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^5,x)","\frac{35\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{35\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-\frac{385\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{511\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}-\frac{93\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(35*a^4*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((511*a^4*tan(c/2 + (d*x)/2)^3)/12 - (385*a^4*tan(c/2 + (d*x)/2)^5)/12 + (35*a^4*tan(c/2 + (d*x)/2)^7)/4 - (93*a^4*tan(c/2 + (d*x)/2))/4)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
41,1,170,111,4.611745,"\text{Not used}","int((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)}{d}-\frac{7\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{98\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{896\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}-\frac{158\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+25\,a^4\,\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)))/d - ((896*a^4*tan(c/2 + (d*x)/2)^5)/15 - (158*a^4*tan(c/2 + (d*x)/2)^3)/3 - (98*a^4*tan(c/2 + (d*x)/2)^7)/3 + 7*a^4*tan(c/2 + (d*x)/2)^9 + 25*a^4*tan(c/2 + (d*x)/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"
42,1,199,136,3.874261,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^7,x)","\frac{49\,a^4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{\frac{49\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}-\frac{833\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{1617\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}-\frac{1967\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{1471\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}-\frac{207\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{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,"(49*a^4*atanh(tan(c/2 + (d*x)/2)))/(8*d) - ((1471*a^4*tan(c/2 + (d*x)/2)^3)/24 - (1967*a^4*tan(c/2 + (d*x)/2)^5)/20 + (1617*a^4*tan(c/2 + (d*x)/2)^7)/20 - (833*a^4*tan(c/2 + (d*x)/2)^9)/24 + (49*a^4*tan(c/2 + (d*x)/2)^11)/8 - (207*a^4*tan(c/2 + (d*x)/2))/8)/(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"
43,1,98,118,1.942838,"\text{Not used}","int(cos(c + d*x)^5/(a + a*cos(c + d*x)),x)","\frac{15\,x}{8\,a}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}-\frac{\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{115\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{109\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(15*x)/(8*a) - tan(c/2 + (d*x)/2)/(a*d) - ((7*tan(c/2 + (d*x)/2))/4 + (109*tan(c/2 + (d*x)/2)^3)/12 + (115*tan(c/2 + (d*x)/2)^5)/12 + (25*tan(c/2 + (d*x)/2)^7)/4)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
44,1,70,94,0.597371,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x)),x)","\frac{\frac{15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{3\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{4}-\frac{\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{12}+\frac{\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{24}}{a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{3\,x}{2\,a}","Not used",1,"((15*sin(c/2 + (d*x)/2))/8 + (3*sin((3*c)/2 + (3*d*x)/2))/4 - sin((5*c)/2 + (5*d*x)/2)/12 + sin((7*c)/2 + (7*d*x)/2)/24)/(a*d*cos(c/2 + (d*x)/2)) - (3*x)/(2*a)","B"
45,1,89,76,0.408834,"\text{Not used}","int(cos(c + d*x)^3/(a + a*cos(c + d*x)),x)","-\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(c+d\,x\right)}{2}+3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"-(sin(c/2 + (d*x)/2) - (3*cos(c/2 + (d*x)/2)*(c + d*x))/2 + 3*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) - 2*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2))/(a*d*cos(c/2 + (d*x)/2))","B"
46,1,66,43,0.399909,"\text{Not used}","int(cos(c + d*x)^2/(a + a*cos(c + d*x)),x)","\frac{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(-c-d\,x\right)\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(sin(c/2 + (d*x)/2) - cos(c/2 + (d*x)/2)*(c + d*x) + 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2))/(a*d*cos(c/2 + (d*x)/2))","B"
47,1,23,29,0.331413,"\text{Not used}","int(cos(c + d*x)/(a + a*cos(c + d*x)),x)","\frac{x}{a}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"x/a - tan(c/2 + (d*x)/2)/(a*d)","B"
48,1,16,22,0.314754,"\text{Not used}","int(1/(a + a*cos(c + d*x)),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(a*d)","B"
49,1,31,38,0.353796,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)) - tan(c/2 + (d*x)/2))/(a*d)","B"
50,1,67,53,0.395264,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))),x)","\frac{2\,\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)}{a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}","Not used",1,"(2*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*d) + tan(c/2 + (d*x)/2)/(a*d)","B"
51,1,95,83,0.454323,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))),x)","\frac{3\,\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)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2)))/(a*d) - tan(c/2 + (d*x)/2)/(a*d) - (tan(c/2 + (d*x)/2) - 3*tan(c/2 + (d*x)/2)^3)/(d*(a - 2*a*tan(c/2 + (d*x)/2)^2 + a*tan(c/2 + (d*x)/2)^4))","B"
52,1,96,103,0.570734,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*cos(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d}-\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^3}","Not used",1,"tan(c/2 + (d*x)/2)/(a*d) - (3*atanh(tan(c/2 + (d*x)/2)))/(a*d) - (3*tan(c/2 + (d*x)/2) - (16*tan(c/2 + (d*x)/2)^3)/3 + 5*tan(c/2 + (d*x)/2)^5)/(a*d*(tan(c/2 + (d*x)/2)^2 - 1)^3)","B"
53,1,135,124,0.498750,"\text{Not used}","int(cos(c + d*x)^5/(a + a*cos(c + d*x))^2,x)","-\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-28\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+30\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(c+d\,x\right)}{6\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"-(sin(c/2 + (d*x)/2) - 28*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) - 60*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 40*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) - 16*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) + 30*cos(c/2 + (d*x)/2)^3*(c + d*x))/(6*a^2*d*cos(c/2 + (d*x)/2)^3)","B"
54,1,113,114,0.453325,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^2,x)","\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-22\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-30\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(c+d\,x\right)}{6\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"(sin(c/2 + (d*x)/2) - 22*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) - 30*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 12*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) + 21*cos(c/2 + (d*x)/2)^3*(c + d*x))/(6*a^2*d*cos(c/2 + (d*x)/2)^3)","B"
55,1,91,80,0.421963,"\text{Not used}","int(cos(c + d*x)^3/(a + a*cos(c + d*x))^2,x)","-\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(c+d\,x\right)}{6\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"-(sin(c/2 + (d*x)/2) - 16*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) - 12*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 12*cos(c/2 + (d*x)/2)^3*(c + d*x))/(6*a^2*d*cos(c/2 + (d*x)/2)^3)","B"
56,1,35,57,0.357692,"\text{Not used}","int(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)}^3-9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+6\,d\,x}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3 - 9*tan(c/2 + (d*x)/2) + 6*d*x)/(6*a^2*d)","B"
57,1,30,55,0.333599,"\text{Not used}","int(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({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-3\right)}{6\,a^2\,d}","Not used",1,"-(tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)^2 - 3))/(6*a^2*d)","B"
58,1,30,55,0.334468,"\text{Not used}","int(1/(a + a*cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\right)}{6\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)^2 + 3))/(6*a^2*d)","B"
59,1,43,66,0.373353,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^2),x)","-\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6\,a^2\,d}","Not used",1,"-(9*tan(c/2 + (d*x)/2) - 12*atanh(tan(c/2 + (d*x)/2)) + tan(c/2 + (d*x)/2)^3)/(6*a^2*d)","B"
60,1,92,81,0.413085,"\text{Not used}","int(1/(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)}^3}{6\,a^2\,d}-\frac{4\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{2\,\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{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(6*a^2*d) - (4*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (2*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 - a^2)) + (5*tan(c/2 + (d*x)/2))/(2*a^2*d)","B"
61,1,122,119,0.427593,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^2),x)","\frac{7\,\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}{6\,a^2\,d}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}","Not used",1,"(7*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - tan(c/2 + (d*x)/2)^3/(6*a^2*d) - (3*tan(c/2 + (d*x)/2) - 5*tan(c/2 + (d*x)/2)^3)/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2)) - (7*tan(c/2 + (d*x)/2))/(2*a^2*d)","B"
62,1,153,133,0.446634,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*cos(c + d*x))^2),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6\,a^2\,d}-\frac{10\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+6\,\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{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(6*a^2*d) - (10*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - (6*tan(c/2 + (d*x)/2) - (40*tan(c/2 + (d*x)/2)^3)/3 + 10*tan(c/2 + (d*x)/2)^5)/(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)) + (9*tan(c/2 + (d*x)/2))/(2*a^2*d)","B"
63,1,137,153,0.472455,"\text{Not used}","int(cos(c + d*x)^5/(a + a*cos(c + d*x))^3,x)","-\frac{3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-46\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+508\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+420\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-390\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(c+d\,x\right)}{60\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(3*sin(c/2 + (d*x)/2) - 46*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) + 508*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 420*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) - 120*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) - 390*cos(c/2 + (d*x)/2)^5*(c + d*x))/(60*a^3*d*cos(c/2 + (d*x)/2)^5)","B"
64,1,113,119,0.437528,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^3,x)","\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+96\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+40\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-60\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(c+d\,x\right)}{20\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"(sin(c/2 + (d*x)/2) - 12*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) + 96*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 40*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) - 60*cos(c/2 + (d*x)/2)^5*(c + d*x))/(20*a^3*d*cos(c/2 + (d*x)/2)^5)","B"
65,1,81,96,0.421075,"\text{Not used}","int(cos(c + d*x)^3/(a + a*cos(c + d*x))^3,x)","\frac{x}{a^3}-\frac{\frac{32\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}-\frac{13\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{30}+\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{20}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"x/a^3 - (sin(c/2 + (d*x)/2)/20 - (13*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2))/30 + (32*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2))/15)/(a^3*d*cos(c/2 + (d*x)/2)^5)","B"
66,1,45,83,0.354729,"\text{Not used}","int(cos(c + d*x)^2/(a + a*cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(3*tan(c/2 + (d*x)/2)^4 - 10*tan(c/2 + (d*x)/2)^2 + 15))/(60*a^3*d)","B"
67,1,30,83,0.337950,"\text{Not used}","int(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({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-5\right)}{20\,a^3\,d}","Not used",1,"-(tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)^4 - 5))/(20*a^3*d)","B"
68,1,45,83,0.350777,"\text{Not used}","int(1/(a + a*cos(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15\right)}{60\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(10*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + 15))/(60*a^3*d)","B"
69,1,58,97,0.404729,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^3),x)","-\frac{105\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-120\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{60\,a^3\,d}","Not used",1,"-(105*tan(c/2 + (d*x)/2) - 120*atanh(tan(c/2 + (d*x)/2)) + 20*tan(c/2 + (d*x)/2)^3 + 3*tan(c/2 + (d*x)/2)^5)/(60*a^3*d)","B"
70,1,111,112,0.400542,"\text{Not used}","int(1/(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}{2\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20\,a^3\,d}-\frac{6\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{2\,\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{17\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(2*a^3*d) + tan(c/2 + (d*x)/2)^5/(20*a^3*d) - (6*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - (2*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3)) + (17*tan(c/2 + (d*x)/2))/(4*a^3*d)","B"
71,1,141,156,0.393272,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^3),x)","\frac{13\,\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)}^5}{20\,a^3\,d}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,a^3\,d}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}-\frac{31\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^3\,d}","Not used",1,"(13*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - tan(c/2 + (d*x)/2)^5/(20*a^3*d) - (2*tan(c/2 + (d*x)/2)^3)/(3*a^3*d) - (5*tan(c/2 + (d*x)/2) - 7*tan(c/2 + (d*x)/2)^3)/(d*(a^3*tan(c/2 + (d*x)/2)^4 - 2*a^3*tan(c/2 + (d*x)/2)^2 + a^3)) - (31*tan(c/2 + (d*x)/2))/(4*a^3*d)","B"
72,1,159,184,0.517853,"\text{Not used}","int(cos(c + d*x)^6/(a + a*cos(c + d*x))^4,x)","\frac{5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-78\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+596\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4408\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+560\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2940\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(c+d\,x\right)}{280\,a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(5*sin(c/2 + (d*x)/2) - 78*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) + 596*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) - 4408*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) - 2520*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) + 560*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2) + 2940*cos(c/2 + (d*x)/2)^7*(c + d*x))/(280*a^4*d*cos(c/2 + (d*x)/2)^7)","B"
73,1,137,150,0.472462,"\text{Not used}","int(cos(c + d*x)^5/(a + a*cos(c + d*x))^4,x)","-\frac{15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-192\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1144\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-6112\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(c+d\,x\right)}{840\,a^4\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(15*sin(c/2 + (d*x)/2) - 192*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) + 1144*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) - 6112*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) - 1680*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) + 3360*cos(c/2 + (d*x)/2)^7*(c + d*x))/(840*a^4*d*cos(c/2 + (d*x)/2)^7)","B"
74,1,102,127,0.429278,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^4,x)","\frac{x}{a^4}+\frac{-\frac{52\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{21}+\frac{16\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{21}-\frac{5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{28}+\frac{\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,"x/a^4 + (sin(c/2 + (d*x)/2)/56 - (5*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2))/28 + (16*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2))/21 - (52*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2))/21)/(a^4*d*cos(c/2 + (d*x)/2)^7)","B"
75,1,58,114,0.386836,"\text{Not used}","int(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)\,\left(5\,{\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+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-35\right)}{280\,a^4\,d}","Not used",1,"-(tan(c/2 + (d*x)/2)*(35*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 5*tan(c/2 + (d*x)/2)^6 - 35))/(280*a^4*d)","B"
76,1,58,112,0.389813,"\text{Not used}","int(cos(c + d*x)^2/(a + a*cos(c + d*x))^4,x)","-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-15\,{\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+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-105\right)}{840\,a^4\,d}","Not used",1,"-(tan(c/2 + (d*x)/2)*(35*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 - 15*tan(c/2 + (d*x)/2)^6 - 105))/(840*a^4*d)","B"
77,1,58,112,0.388682,"\text{Not used}","int(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(-15\,{\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+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+105\right)}{840\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(35*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 - 15*tan(c/2 + (d*x)/2)^6 + 105))/(840*a^4*d)","B"
78,1,58,112,0.379894,"\text{Not used}","int(1/(a + a*cos(c + d*x))^4,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,{\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+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+35\right)}{280\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(35*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 5*tan(c/2 + (d*x)/2)^6 + 35))/(280*a^4*d)","B"
79,1,83,120,0.372546,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^4),x)","-\frac{\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56\,a^4}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4}+\frac{15\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^4}}{d}","Not used",1,"-((11*tan(c/2 + (d*x)/2)^3)/(24*a^4) + tan(c/2 + (d*x)/2)^5/(8*a^4) + tan(c/2 + (d*x)/2)^7/(56*a^4) - (2*atanh(tan(c/2 + (d*x)/2)))/a^4 + (15*tan(c/2 + (d*x)/2))/(8*a^4))/d","B"
80,1,130,135,0.419513,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^4),x)","\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^4\,d}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40\,a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56\,a^4\,d}-\frac{8\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{2\,\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{49\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^4\,d}","Not used",1,"(23*tan(c/2 + (d*x)/2)^3)/(24*a^4*d) + (7*tan(c/2 + (d*x)/2)^5)/(40*a^4*d) + tan(c/2 + (d*x)/2)^7/(56*a^4*d) - (8*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (2*tan(c/2 + (d*x)/2))/(d*(a^4*tan(c/2 + (d*x)/2)^2 - a^4)) + (49*tan(c/2 + (d*x)/2))/(8*a^4*d)","B"
81,1,160,185,0.465563,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^4),x)","\frac{21\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56\,a^4\,d}-\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^4\,d}-\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4\right)}-\frac{111\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^4\,d}","Not used",1,"(21*atanh(tan(c/2 + (d*x)/2)))/(a^4*d) - (9*tan(c/2 + (d*x)/2)^5)/(40*a^4*d) - tan(c/2 + (d*x)/2)^7/(56*a^4*d) - (13*tan(c/2 + (d*x)/2)^3)/(8*a^4*d) - (7*tan(c/2 + (d*x)/2) - 9*tan(c/2 + (d*x)/2)^3)/(d*(a^4*tan(c/2 + (d*x)/2)^4 - 2*a^4*tan(c/2 + (d*x)/2)^2 + a^4)) - (111*tan(c/2 + (d*x)/2))/(8*a^4*d)","B"
82,1,181,225,0.582935,"\text{Not used}","int(cos(c + d*x)^7/(a + a*cos(c + d*x))^5,x)","-\frac{35\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-590\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4584\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-23288\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+129824\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+55440\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-10080\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-78120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(c+d\,x\right)}{5040\,a^5\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(35*sin(c/2 + (d*x)/2) - 590*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) + 4584*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) - 23288*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) + 129824*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) + 55440*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2) - 10080*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2) - 78120*cos(c/2 + (d*x)/2)^9*(c + d*x))/(5040*a^5*d*cos(c/2 + (d*x)/2)^9)","B"
83,1,159,191,0.513428,"\text{Not used}","int(cos(c + d*x)^6/(a + a*cos(c + d*x))^5,x)","\frac{7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-100\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+636\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2512\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+10096\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+2016\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5040\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(c+d\,x\right)}{1008\,a^5\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"(7*sin(c/2 + (d*x)/2) - 100*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) + 636*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) - 2512*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) + 10096*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2) + 2016*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2) - 5040*cos(c/2 + (d*x)/2)^9*(c + d*x))/(1008*a^5*d*cos(c/2 + (d*x)/2)^9)","B"
84,1,125,168,0.477697,"\text{Not used}","int(cos(c + d*x)^5/(a + a*cos(c + d*x))^5,x)","\frac{x}{a^5}-\frac{\frac{863\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{315}-\frac{356\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{315}+\frac{169\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{420}-\frac{41\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{504}+\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{144}}{a^5\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"x/a^5 - (sin(c/2 + (d*x)/2)/144 - (41*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2))/504 + (169*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2))/420 - (356*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2))/315 + (863*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2))/315)/(a^5*d*cos(c/2 + (d*x)/2)^9)","B"
85,1,127,155,0.431748,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^5,x)","\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-420\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+378\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-180\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\right)}{5040\,a^5\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"(sin(c/2 + (d*x)/2)*(315*cos(c/2 + (d*x)/2)^8 + 35*sin(c/2 + (d*x)/2)^8 - 180*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 + 378*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 - 420*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2))/(5040*a^5*d*cos(c/2 + (d*x)/2)^9)","B"
86,1,58,147,0.392743,"\text{Not used}","int(cos(c + d*x)^3/(a + a*cos(c + d*x))^5,x)","-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+42\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-63\right)}{1008\,a^5\,d}","Not used",1,"-(tan(c/2 + (d*x)/2)*(42*tan(c/2 + (d*x)/2)^2 - 18*tan(c/2 + (d*x)/2)^6 + 7*tan(c/2 + (d*x)/2)^8 - 63))/(1008*a^5*d)","B"
87,1,45,139,0.357251,"\text{Not used}","int(cos(c + d*x)^2/(a + a*cos(c + d*x))^5,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+45\right)}{720\,a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(5*tan(c/2 + (d*x)/2)^8 - 18*tan(c/2 + (d*x)/2)^4 + 45))/(720*a^5*d)","B"
88,1,58,143,0.396512,"\text{Not used}","int(cos(c + d*x)/(a + a*cos(c + d*x))^5,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+42\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+63\right)}{1008\,a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(42*tan(c/2 + (d*x)/2)^2 - 18*tan(c/2 + (d*x)/2)^6 - 7*tan(c/2 + (d*x)/2)^8 + 63))/(1008*a^5*d)","B"
89,1,127,143,0.416739,"\text{Not used}","int(1/(a + a*cos(c + d*x))^5,x)","\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+420\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+378\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+180\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\right)}{5040\,a^5\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"(sin(c/2 + (d*x)/2)*(315*cos(c/2 + (d*x)/2)^8 + 35*sin(c/2 + (d*x)/2)^8 + 180*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 + 378*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 + 420*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2))/(5040*a^5*d*cos(c/2 + (d*x)/2)^9)","B"
90,1,99,153,0.392328,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^5),x)","-\frac{\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5\,a^5}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56\,a^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{144\,a^5}-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^5}+\frac{31\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a^5}}{d}","Not used",1,"-((13*tan(c/2 + (d*x)/2)^3)/(24*a^5) + tan(c/2 + (d*x)/2)^5/(5*a^5) + (3*tan(c/2 + (d*x)/2)^7)/(56*a^5) + tan(c/2 + (d*x)/2)^9/(144*a^5) - (2*atanh(tan(c/2 + (d*x)/2)))/a^5 + (31*tan(c/2 + (d*x)/2))/(16*a^5))/d","B"
91,1,149,168,0.448005,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^5),x)","\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2\,a^5\,d}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8\,a^5\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{14\,a^5\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{144\,a^5\,d}-\frac{10\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^5\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^5\right)}+\frac{129\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a^5\,d}","Not used",1,"(3*tan(c/2 + (d*x)/2)^3)/(2*a^5*d) + (3*tan(c/2 + (d*x)/2)^5)/(8*a^5*d) + tan(c/2 + (d*x)/2)^7/(14*a^5*d) + tan(c/2 + (d*x)/2)^9/(144*a^5*d) - (10*atanh(tan(c/2 + (d*x)/2)))/(a^5*d) - (2*tan(c/2 + (d*x)/2))/(d*(a^5*tan(c/2 + (d*x)/2)^2 - a^5)) + (129*tan(c/2 + (d*x)/2))/(16*a^5*d)","B"
92,1,179,224,0.477897,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^5),x)","\frac{31\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^5\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5\,a^5\,d}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{56\,a^5\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{144\,a^5\,d}-\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^5\,d}-\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^5\right)}-\frac{351\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a^5\,d}","Not used",1,"(31*atanh(tan(c/2 + (d*x)/2)))/(a^5*d) - (3*tan(c/2 + (d*x)/2)^5)/(5*a^5*d) - (5*tan(c/2 + (d*x)/2)^7)/(56*a^5*d) - tan(c/2 + (d*x)/2)^9/(144*a^5*d) - (25*tan(c/2 + (d*x)/2)^3)/(8*a^5*d) - (9*tan(c/2 + (d*x)/2) - 11*tan(c/2 + (d*x)/2)^3)/(d*(a^5*tan(c/2 + (d*x)/2)^4 - 2*a^5*tan(c/2 + (d*x)/2)^2 + a^5)) - (351*tan(c/2 + (d*x)/2))/(16*a^5*d)","B"
93,1,75,184,0.882083,"\text{Not used}","int(cos(c + d*x)^5/(a + a*cos(c + d*x))^6,x)","\frac{\frac{495\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{495\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{16}+\frac{275\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}+\frac{55\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}{8}+\frac{73\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)}{16}}{22176\,a^6\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}","Not used",1,"((495*sin((3*c)/2 + (3*d*x)/2))/8 + (495*sin((5*c)/2 + (5*d*x)/2))/16 + (275*sin((7*c)/2 + (7*d*x)/2))/8 + (55*sin((9*c)/2 + (9*d*x)/2))/8 + (73*sin((11*c)/2 + (11*d*x)/2))/16)/(22176*a^6*d*cos(c/2 + (d*x)/2)^11)","B"
94,1,151,176,0.462647,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^6,x)","\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(1155\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-1155\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+462\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+330\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-385\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+105\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\right)}{36960\,a^6\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}","Not used",1,"(sin(c/2 + (d*x)/2)*(1155*cos(c/2 + (d*x)/2)^10 + 105*sin(c/2 + (d*x)/2)^10 - 385*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 330*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 + 462*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 - 1155*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2))/(36960*a^6*d*cos(c/2 + (d*x)/2)^11)","B"
95,0,-1,158,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2), x)","F"
96,0,-1,122,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2), x)","F"
97,0,-1,86,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2), x)","F"
98,0,-1,56,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2), x)","F"
99,1,33,26,0.464005,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2),x)","\frac{2\,\sin\left(c+d\,x\right)\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}}{d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(2*sin(c + d*x)*(a*(cos(c + d*x) + 1))^(1/2))/(d*(cos(c + d*x) + 1))","B"
100,0,-1,37,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x), x)","F"
101,0,-1,62,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^2,x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^2, x)","F"
102,0,-1,102,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^3,x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^3, x)","F"
103,0,-1,138,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^4,x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^4, x)","F"
104,0,-1,162,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2),x)","\int {\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(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2), x)","F"
105,0,-1,116,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2),x)","\int {\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(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2), x)","F"
106,0,-1,86,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2), x)","F"
107,0,-1,59,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2),x)","\int {\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(3/2), x)","F"
108,0,-1,66,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x),x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/cos(c + d*x), x)","F"
109,0,-1,65,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^2,x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/cos(c + d*x)^2, x)","F"
110,0,-1,106,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^3,x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/cos(c + d*x)^3, x)","F"
111,0,-1,144,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^4,x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/cos(c + d*x)^4, x)","F"
112,0,-1,203,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2),x)","\int {\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(cos(c + d*x)^3*(a + a*cos(c + d*x))^(5/2), x)","F"
113,0,-1,146,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2),x)","\int {\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(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2), x)","F"
114,0,-1,116,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2),x)","\int \cos\left(c+d\,x\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2), x)","F"
115,0,-1,89,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2),x)","\int {\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(5/2), x)","F"
116,0,-1,98,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x),x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x), x)","F"
117,0,-1,92,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^2,x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x)^2, x)","F"
118,0,-1,106,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^3,x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x)^3, x)","F"
119,0,-1,144,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^4,x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x)^4, x)","F"
120,0,-1,182,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^5,x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x)^5, x)","F"
121,0,-1,119,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(7/2),x)","\int {\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(7/2), x)","F"
122,0,-1,174,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + a*cos(c + d*x))^(1/2), x)","F"
123,0,-1,140,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + a*cos(c + d*x))^(1/2), x)","F"
124,1,97,104,0.380887,"\text{Not used}","int(cos(c + d*x)^2/(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,\sin\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{3\,a\,d}-\frac{2\,\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*sin(c + d*x)*(a + a*cos(c + d*x))^(1/2))/(3*a*d) - (2*(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"
125,1,60,73,0.395805,"\text{Not used}","int(cos(c + d*x)/(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,\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)}}","Not used",1,"(2*(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))","B"
126,1,45,46,0.356569,"\text{Not used}","int(1/(a + a*cos(c + d*x))^(1/2),x)","\frac{\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,"(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"
127,0,-1,85,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^(1/2)), x)","F"
128,0,-1,108,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(1/2)), x)","F"
129,0,-1,147,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(1/2)), x)","F"
130,0,-1,181,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a*cos(c + d*x))^(1/2)), x)","F"
131,0,-1,183,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + a*cos(c + d*x))^(3/2), x)","F"
132,0,-1,145,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\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(cos(c + d*x)^3/(a + a*cos(c + d*x))^(3/2), x)","F"
133,0,-1,105,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\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(cos(c + d*x)^2/(a + a*cos(c + d*x))^(3/2), x)","F"
134,0,-1,77,0.000000,"\text{Not used}","int(cos(c + d*x)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)/(a + a*cos(c + d*x))^(3/2), x)","F"
135,0,-1,77,0.000000,"\text{Not used}","int(1/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{1}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + a*cos(c + d*x))^(3/2), x)","F"
136,0,-1,114,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)),x)","\int \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(1/(cos(c + d*x)*(a + a*cos(c + d*x))^(3/2)), x)","F"
137,0,-1,144,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(3/2)), x)","F"
138,0,-1,185,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^3*(a + a*cos(c + d*x))^(3/2)), x)","F"
139,0,-1,183,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^4}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + a*cos(c + d*x))^(5/2), x)","F"
140,0,-1,145,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\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(cos(c + d*x)^3/(a + a*cos(c + d*x))^(5/2), x)","F"
141,0,-1,107,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\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(cos(c + d*x)^2/(a + a*cos(c + d*x))^(5/2), x)","F"
142,0,-1,107,0.000000,"\text{Not used}","int(cos(c + d*x)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)/(a + a*cos(c + d*x))^(5/2), x)","F"
143,0,-1,107,0.000000,"\text{Not used}","int(1/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{1}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + a*cos(c + d*x))^(5/2), x)","F"
144,0,-1,144,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)),x)","\int \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(1/(cos(c + d*x)*(a + a*cos(c + d*x))^(5/2)), x)","F"
145,0,-1,174,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^2*(a + a*cos(c + d*x))^(5/2)), x)","F"
146,1,87,111,0.763539,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x)),x)","-\frac{2\,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\,{\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*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*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"
147,1,80,87,0.131130,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x)),x)","\frac{2\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,a\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,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*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*a*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*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"
148,1,53,61,0.120791,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x)),x)","\frac{2\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,a\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*a*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*a*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
149,1,27,35,0.461105,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^(1/2),x)","\frac{2\,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*a*(ellipticE(c/2 + (d*x)/2, 2) + ellipticF(c/2 + (d*x)/2, 2)))/d","B"
150,1,60,57,0.644999,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^(3/2),x)","\frac{2\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{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*ellipticF(c/2 + (d*x)/2, 2))/d + (2*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
151,1,87,83,0.779596,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^(5/2),x)","\frac{2\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
152,1,87,111,0.870613,"\text{Not used}","int((a + a*cos(c + d*x))/cos(c + d*x)^(7/2),x)","\frac{2\,a\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,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}}","Not used",1,"(2*a*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*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))","B"
153,1,136,147,0.768978,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2,x)","-\frac{2\,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\,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^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^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*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^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"
154,1,129,121,0.648604,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2,x)","\frac{2\,\left(a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}-\frac{4\,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^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^2*ellipticF(c/2 + (d*x)/2, 2) + a^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) - (4*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^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"
155,1,104,95,0.741793,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{4\,a^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,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*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*a^2*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (4*a^2*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*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"
156,1,59,67,0.679516,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x)^(1/2),x)","\frac{4\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,a^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(4*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (8*a^2*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*a^2*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
157,1,82,44,0.801924,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x)^(3/2),x)","\frac{2\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,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^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*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"
158,1,109,91,0.867285,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x)^(5/2),x)","\frac{2\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,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^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (4*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^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"
159,1,114,121,0.988536,"\text{Not used}","int((a + a*cos(c + d*x))^2/cos(c + d*x)^(7/2),x)","\frac{6\,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^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^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,"(6*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 20*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 30*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"
160,1,206,147,0.781933,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3,x)","\frac{2\,\left(a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}-\frac{2\,\left(\frac{33\,a^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{5\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{77\,d}-\frac{2\,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{104\,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{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{385\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(a^3*ellipticF(c/2 + (d*x)/2, 2) + a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) - (2*((33*a^3*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (5*a^3*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2))*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(77*d) - (2*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)) - (104*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 19/4, cos(c + d*x)^2))/(385*d*(sin(c + d*x)^2)^(1/2))","B"
161,1,143,121,0.648682,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3,x)","\frac{2\,\left(a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{6\,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^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*(a^3*ellipticE(c/2 + (d*x)/2, 2) + a^3*ellipticF(c/2 + (d*x)/2, 2) + a^3*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (6*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^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"
162,1,104,91,0.617627,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^(1/2),x)","\frac{6\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{2\,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,"(6*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (4*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (2*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"
163,1,104,91,0.644621,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^(3/2),x)","\frac{6\,a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{20\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}+\frac{2\,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,"(6*a^3*ellipticE(c/2 + (d*x)/2, 2))/d + (20*a^3*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) + (2*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"
164,1,126,91,1.017761,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^(5/2),x)","\frac{2\,\left(a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{6\,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^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*(a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*a^3*ellipticF(c/2 + (d*x)/2, 2)))/d + (6*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^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"
165,1,154,117,1.096726,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^(7/2),x)","\frac{2\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,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^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^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*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*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^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^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"
166,1,145,147,1.210135,"\text{Not used}","int((a + a*cos(c + d*x))^3/cos(c + d*x)^(9/2),x)","\frac{\frac{2\,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^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^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^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}}","Not used",1,"((2*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + (6*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^3*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 2*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))","B"
167,1,221,173,0.879831,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^4,x)","\frac{2\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{8\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,a^4\,{\cos\left(c+d\,x\right)}^{13/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{13}{4};\ \frac{17}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{13\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^4*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*a^4*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (8*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (4*a^4*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)) - (8*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*a^4*cos(c + d*x)^(13/2)*sin(c + d*x)*hypergeom([1/2, 13/4], 17/4, cos(c + d*x)^2))/(13*d*(sin(c + d*x)^2)^(1/2))","B"
168,1,223,147,0.807176,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^4,x)","\frac{2\,\left(3\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}-\frac{2\,\left(\frac{66\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{17\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)}{\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{77\,d}-\frac{8\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{208\,a^4\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{19}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{385\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(3*a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*a^4*ellipticF(c/2 + (d*x)/2, 2) + 4*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) - (2*((66*a^4*cos(c + d*x)^(7/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2) - (17*a^4*cos(c + d*x)^(11/2)*sin(c + d*x))/(sin(c + d*x)^2)^(1/2))*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(77*d) - (8*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (208*a^4*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 19/4, cos(c + d*x)^2))/(385*d*(sin(c + d*x)^2)^(1/2))","B"
169,1,146,121,0.705480,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^(1/2),x)","\frac{2\,\left(4\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+3\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+2\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{8\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,a^4\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(4*a^4*ellipticE(c/2 + (d*x)/2, 2) + 3*a^4*ellipticF(c/2 + (d*x)/2, 2) + 2*a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (8*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*a^4*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2))","B"
170,1,149,119,0.793634,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^(3/2),x)","\frac{12\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{32\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{8\,a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}+\frac{2\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,a^4\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(12*a^4*ellipticE(c/2 + (d*x)/2, 2))/d + (32*a^4*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (8*a^4*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) + (2*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) - (2*a^4*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
171,1,145,98,0.839694,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^(5/2),x)","\frac{2\,\left(12\,a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+19\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^4\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}+\frac{8\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(12*a^4*ellipticE(c/2 + (d*x)/2, 2) + 19*a^4*ellipticF(c/2 + (d*x)/2, 2) + a^4*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) + (8*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
172,1,202,121,1.301486,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^(7/2),x)","\frac{2\,\left(a^4\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+4\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d}+\frac{2\,\left(\frac{34\,a^4\,\sin\left(c+d\,x\right)}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{a^4\,\sin\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d}+\frac{8\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{8\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{7}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(a^4*ellipticE(c/2 + (d*x)/2, 2) + 4*a^4*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*((34*a^4*sin(c + d*x))/(cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (a^4*sin(c + d*x))/(cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)))*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(5*d) + (8*a^4*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) - (8*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 7/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
173,1,199,147,1.336841,"\text{Not used}","int((a + a*cos(c + d*x))^4/cos(c + d*x)^(9/2),x)","\frac{2\,a^4\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{8\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{8\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,a^4\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^4*ellipticF(c/2 + (d*x)/2, 2))/d + (8*a^4*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (4*a^4*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)) + (8*a^4*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2)) + (2*a^4*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/(7*d*cos(c + d*x)^(7/2)*(sin(c + d*x)^2)^(1/2))","B"
174,0,-1,128,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x)), x)","F"
175,0,-1,100,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x)), x)","F"
176,0,-1,72,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x)), x)","F"
177,0,-1,70,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x)), x)","F"
178,0,-1,70,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))), x)","F"
179,0,-1,96,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))), x)","F"
180,0,-1,124,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))), x)","F"
181,0,-1,160,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{9/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)/(a + a*cos(c + d*x))^2, x)","F"
182,0,-1,138,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^2, x)","F"
183,0,-1,112,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{{\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(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^2, x)","F"
184,0,-1,109,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{{\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(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^2, x)","F"
185,0,-1,57,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{\sqrt{\cos\left(c+d\,x\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 + a*cos(c + d*x))^2, x)","F"
186,0,-1,109,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
187,0,-1,136,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
188,0,-1,162,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
189,0,-1,207,0.000000,"\text{Not used}","int(cos(c + d*x)^(11/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{11/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(11/2)/(a + a*cos(c + d*x))^3, x)","F"
190,0,-1,181,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{9/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)/(a + a*cos(c + d*x))^3, x)","F"
191,0,-1,155,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^3, x)","F"
192,0,-1,155,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{{\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(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^3, x)","F"
193,0,-1,155,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{{\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(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^3, x)","F"
194,0,-1,155,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{\sqrt{\cos\left(c+d\,x\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 + a*cos(c + d*x))^3, x)","F"
195,0,-1,155,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
196,0,-1,181,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
197,0,-1,207,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
198,0,-1,154,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
199,0,-1,116,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
200,0,-1,72,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2), x)","F"
201,0,-1,37,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2), x)","F"
202,1,41,36,0.453961,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^(3/2),x)","\frac{2\,\sin\left(c+d\,x\right)\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(2*sin(c + d*x)*(a*(cos(c + d*x) + 1))^(1/2))/(d*cos(c + d*x)^(1/2)*(cos(c + d*x) + 1))","B"
203,1,82,77,1.269971,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^(5/2),x)","\frac{4\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(\sin\left(c+d\,x\right)+\sin\left(2\,c+2\,d\,x\right)+\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,"(4*(a*(cos(c + d*x) + 1))^(1/2)*(sin(c + d*x) + sin(2*c + 2*d*x) + 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"
204,1,132,115,2.366853,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/cos(c + d*x)^(7/2),x)","\frac{8\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(7\,\sin\left(c+d\,x\right)+4\,\sin\left(2\,c+2\,d\,x\right)+9\,\sin\left(3\,c+3\,d\,x\right)+2\,\sin\left(4\,c+4\,d\,x\right)+2\,\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,"(8*(a*(cos(c + d*x) + 1))^(1/2)*(7*sin(c + d*x) + 4*sin(2*c + 2*d*x) + 9*sin(3*c + 3*d*x) + 2*sin(4*c + 4*d*x) + 2*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"
205,1,415,153,5.642033,"\text{Not used}","int((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{32{}\mathrm{i}}{35\,d}+\frac{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,16{}\mathrm{i}}{5\,d}-\frac{{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,16{}\mathrm{i}}{5\,d}-\frac{{\mathrm{e}}^{c\,7{}\mathrm{i}+d\,x\,7{}\mathrm{i}}\,32{}\mathrm{i}}{35\,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)*(32i/(35*d) + (exp(c*2i + d*x*2i)*16i)/(5*d) - (exp(c*5i + d*x*5i)*16i)/(5*d) - (exp(c*7i + d*x*7i)*32i)/(35*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"
206,0,-1,160,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2),x)","\int {\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(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
207,0,-1,120,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \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(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
208,0,-1,75,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(1/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(1/2), x)","F"
209,0,-1,76,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(3/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(3/2), x)","F"
210,1,89,81,1.217125,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(5/2),x)","\frac{2\,a\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(5\,\sin\left(c+d\,x\right)+2\,\sin\left(2\,c+2\,d\,x\right)+5\,\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*(a*(cos(c + d*x) + 1))^(1/2)*(5*sin(c + d*x) + 2*sin(2*c + 2*d*x) + 5*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"
211,1,133,121,2.103174,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(7/2),x)","\frac{4\,a\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(8\,\sin\left(c+d\,x\right)+6\,\sin\left(2\,c+2\,d\,x\right)+11\,\sin\left(3\,c+3\,d\,x\right)+3\,\sin\left(4\,c+4\,d\,x\right)+3\,\sin\left(5\,c+5\,d\,x\right)\right)}{5\,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*(a*(cos(c + d*x) + 1))^(1/2)*(8*sin(c + d*x) + 6*sin(2*c + 2*d*x) + 11*sin(3*c + 3*d*x) + 3*sin(4*c + 4*d*x) + 3*sin(5*c + 5*d*x)))/(5*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"
212,1,157,161,4.588487,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(9/2),x)","\frac{91\,a\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}-35\,a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}+26\,a\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{\frac{315\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{315\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{105\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{105\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}}","Not used",1,"(91*a*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2) - 35*a*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2) + 26*a*sin((7*c)/2 + (7*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/((315*d*cos(c + d*x)^(1/2)*cos(c/2 + (d*x)/2))/8 + (315*d*cos(c + d*x)^(1/2)*cos((3*c)/2 + (3*d*x)/2))/8 + (105*d*cos(c + d*x)^(1/2)*cos((5*c)/2 + (5*d*x)/2))/8 + (105*d*cos(c + d*x)^(1/2)*cos((7*c)/2 + (7*d*x)/2))/8)","B"
213,0,-1,200,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2),x)","\int {\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(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
214,0,-1,160,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \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(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
215,0,-1,120,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(1/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(1/2), x)","F"
216,0,-1,114,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(3/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(3/2), x)","F"
217,0,-1,118,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(5/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(5/2), x)","F"
218,1,135,121,2.139547,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(7/2),x)","\frac{2\,a^2\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\left(98\,\sin\left(c+d\,x\right)+56\,\sin\left(2\,c+2\,d\,x\right)+141\,\sin\left(3\,c+3\,d\,x\right)+28\,\sin\left(4\,c+4\,d\,x\right)+43\,\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^2*(a*(cos(c + d*x) + 1))^(1/2)*(98*sin(c + d*x) + 56*sin(2*c + 2*d*x) + 141*sin(3*c + 3*d*x) + 28*sin(4*c + 4*d*x) + 43*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"
219,1,163,161,4.457479,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(9/2),x)","\frac{35\,a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}-\frac{35\,a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{2}+\frac{23\,a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{2}}{\frac{63\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{63\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{21\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{21\,d\,\sqrt{\cos\left(c+d\,x\right)}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}}","Not used",1,"(35*a^2*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2) - (35*a^2*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2))/2 + (23*a^2*sin((7*c)/2 + (7*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/2)/((63*d*cos(c + d*x)^(1/2)*cos(c/2 + (d*x)/2))/8 + (63*d*cos(c + d*x)^(1/2)*cos((3*c)/2 + (3*d*x)/2))/8 + (21*d*cos(c + d*x)^(1/2)*cos((5*c)/2 + (5*d*x)/2))/8 + (21*d*cos(c + d*x)^(1/2)*cos((7*c)/2 + (7*d*x)/2))/8)","B"
220,1,279,201,6.414827,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/cos(c + d*x)^(11/2),x)","\frac{\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\left(\frac{192\,a^2\,{\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)}{5\,d}-\frac{16\,a^2\,{\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{1168\,a^2\,{\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)}{35\,d}+\frac{2336\,a^2\,{\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)}{315\,d}\right)}{12\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)+8\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)+2\,\sqrt{\cos\left(c+d\,x\right)}\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\cos\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)}","Not used",1,"((a + a*cos(c + d*x))^(1/2)*((192*a^2*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2))/(5*d) - (16*a^2*exp((c*9i)/2 + (d*x*9i)/2)*sin((3*c)/2 + (3*d*x)/2))/(3*d) + (1168*a^2*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2))/(35*d) + (2336*a^2*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2))/(315*d)))/(12*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos(c/2 + (d*x)/2) + 8*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((3*c)/2 + (3*d*x)/2) + 8*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((5*c)/2 + (5*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((7*c)/2 + (7*d*x)/2) + 2*cos(c + d*x)^(1/2)*exp((c*9i)/2 + (d*x*9i)/2)*cos((9*c)/2 + (9*d*x)/2))","B"
221,1,42,38,0.581034,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/cos(c + d*x)^(5/4),x)","\frac{4\,a\,\sin\left(c+d\,x\right)\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}}{d\,{\cos\left(c+d\,x\right)}^{1/4}\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(4*a*sin(c + d*x)*(a*(cos(c + d*x) + 1))^(1/2))/(d*cos(c + d*x)^(1/4)*(cos(c + d*x) + 1))","B"
222,0,-1,37,0.000000,"\text{Not used}","int((a + a*cos(e + f*x))^(1/2)/cos(e + f*x)^(1/2),x)","\int \frac{\sqrt{a+a\,\cos\left(e+f\,x\right)}}{\sqrt{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a*cos(e + f*x))^(1/2)/cos(e + f*x)^(1/2), x)","F"
223,0,-1,38,0.000000,"\text{Not used}","int((a - a*cos(e + f*x))^(1/2)/(-cos(e + f*x))^(1/2),x)","\int \frac{\sqrt{a-a\,\cos\left(e+f\,x\right)}}{\sqrt{-\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((a - a*cos(e + f*x))^(1/2)/(-cos(e + f*x))^(1/2), x)","F"
224,0,-1,171,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(1/2), x)","F"
225,0,-1,128,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(1/2), x)","F"
226,0,-1,95,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(1/2), x)","F"
227,0,-1,56,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\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))^(1/2)), x)","F"
228,0,-1,93,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
229,0,-1,131,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
230,0,-1,169,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(7/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
231,0,-1,126,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(cos(c + d*x) + 1)^(1/2), x)","F"
232,0,-1,85,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(cos(c + d*x) + 1)^(1/2), x)","F"
233,0,-1,54,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(cos(c + d*x) + 1)^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(cos(c + d*x) + 1)^(1/2), x)","F"
234,0,-1,27,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(cos(c + d*x) + 1)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(cos(c + d*x) + 1)^(1/2)), x)","F"
235,0,-1,62,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(cos(c + d*x) + 1)^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(3/2)*(cos(c + d*x) + 1)^(1/2)), x)","F"
236,0,-1,98,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(cos(c + d*x) + 1)^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(5/2)*(cos(c + d*x) + 1)^(1/2)), x)","F"
237,0,-1,134,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(cos(c + d*x) + 1)^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(7/2)*(cos(c + d*x) + 1)^(1/2)), x)","F"
238,0,-1,174,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\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(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(3/2), x)","F"
239,0,-1,134,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\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(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(3/2), x)","F"
240,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\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(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(3/2), x)","F"
241,0,-1,97,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{\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(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
242,0,-1,137,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
243,0,-1,177,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
244,0,-1,214,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^(5/2), x)","F"
245,0,-1,174,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\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(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(5/2), x)","F"
246,0,-1,137,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\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(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(5/2), x)","F"
247,0,-1,137,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\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(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(5/2), x)","F"
248,0,-1,137,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{\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(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
249,0,-1,177,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
250,0,-1,217,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
251,0,-1,254,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{9/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)/(a + a*cos(c + d*x))^(7/2), x)","F"
252,0,-1,214,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}}{{\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 + a*cos(c + d*x))^(7/2), x)","F"
253,0,-1,177,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\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(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(7/2), x)","F"
254,0,-1,177,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\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(cos(c + d*x)^(3/2)/(a + a*cos(c + d*x))^(7/2), x)","F"
255,0,-1,177,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{\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(cos(c + d*x)^(1/2)/(a + a*cos(c + d*x))^(7/2), x)","F"
256,0,-1,177,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{\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(1/(cos(c + d*x)^(1/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
257,0,-1,217,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
258,0,-1,257,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
259,0,-1,217,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^(9/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)/(a + a*cos(c + d*x))^(9/2), x)","F"
260,0,-1,217,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(9/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(a + a*cos(c + d*x))^(9/2), x)","F"
261,0,-1,16,0.000000,"\text{Not used}","int(1/(cos(x)^(1/2)*(cos(x) + 1)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(x\right)}\,\sqrt{\cos\left(x\right)+1}} \,d x","Not used",1,"int(1/(cos(x)^(1/2)*(cos(x) + 1)^(1/2)), x)","F"
262,0,-1,41,0.000000,"\text{Not used}","int(1/(cos(x)^(1/2)*(a + a*cos(x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(x\right)}\,\sqrt{a+a\,\cos\left(x\right)}} \,d x","Not used",1,"int(1/(cos(x)^(1/2)*(a + a*cos(x))^(1/2)), x)","F"
263,0,-1,129,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a - a*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a-a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a - a*cos(c + d*x))^(1/2), x)","F"
264,0,-1,85,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a - a*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a-a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a - a*cos(c + d*x))^(1/2), x)","F"
265,0,-1,48,0.000000,"\text{Not used}","int((a - a*cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a-a\,\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a - a*cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2), x)","F"
266,1,42,37,0.794104,"\text{Not used}","int((a - a*cos(c + d*x))^(1/2)/cos(c + d*x)^(3/2),x)","-\frac{2\,\sin\left(c+d\,x\right)\,\sqrt{-a\,\left(\cos\left(c+d\,x\right)-1\right)}}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\left(\cos\left(c+d\,x\right)-1\right)}","Not used",1,"-(2*sin(c + d*x)*(-a*(cos(c + d*x) - 1))^(1/2))/(d*cos(c + d*x)^(1/2)*(cos(c + d*x) - 1))","B"
267,1,85,79,1.385250,"\text{Not used}","int((a - a*cos(c + d*x))^(1/2)/cos(c + d*x)^(5/2),x)","\frac{4\,\sqrt{-a\,\left(\cos\left(c+d\,x\right)-1\right)}\,\left(\sin\left(c+d\,x\right)-\sin\left(2\,c+2\,d\,x\right)+\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,"(4*(-a*(cos(c + d*x) - 1))^(1/2)*(sin(c + d*x) - sin(2*c + 2*d*x) + 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"
268,1,158,118,2.889538,"\text{Not used}","int((a - a*cos(c + d*x))^(1/2)/cos(c + d*x)^(7/2),x)","\frac{8\,\sqrt{2\,a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\,\left(7\,\sin\left(c+d\,x\right)-4\,\sin\left(2\,c+2\,d\,x\right)+9\,\sin\left(3\,c+3\,d\,x\right)-2\,\sin\left(4\,c+4\,d\,x\right)+2\,\sin\left(5\,c+5\,d\,x\right)\right)}{15\,d\,\sqrt{1-2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\,\left(-16\,{\sin\left(c+d\,x\right)}^2-4\,{\sin\left(2\,c+2\,d\,x\right)}^2+20\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+10\,{\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}^2+2\,{\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}^2\right)}","Not used",1,"(8*(2*a*sin(c/2 + (d*x)/2)^2)^(1/2)*(7*sin(c + d*x) - 4*sin(2*c + 2*d*x) + 9*sin(3*c + 3*d*x) - 2*sin(4*c + 4*d*x) + 2*sin(5*c + 5*d*x)))/(15*d*(1 - 2*sin(c/2 + (d*x)/2)^2)^(1/2)*(20*sin(c/2 + (d*x)/2)^2 - 4*sin(2*c + 2*d*x)^2 + 10*sin((3*c)/2 + (3*d*x)/2)^2 + 2*sin((5*c)/2 + (5*d*x)/2)^2 - 16*sin(c + d*x)^2))","B"
269,0,-1,114,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(1 - cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(1 - cos(c + d*x))^(1/2), x)","F"
270,0,-1,72,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(1 - cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(1 - cos(c + d*x))^(1/2), x)","F"
271,0,-1,37,0.000000,"\text{Not used}","int((1 - cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{1-\cos\left(c+d\,x\right)}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((1 - cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2), x)","F"
272,1,31,35,0.872417,"\text{Not used}","int((1 - cos(c + d*x))^(1/2)/cos(c + d*x)^(3/2),x)","\frac{2\,\sin\left(c+d\,x\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-\cos\left(c+d\,x\right)}}","Not used",1,"(2*sin(c + d*x))/(d*cos(c + d*x)^(1/2)*(1 - cos(c + d*x))^(1/2))","B"
273,1,84,75,1.554767,"\text{Not used}","int((1 - cos(c + d*x))^(1/2)/cos(c + d*x)^(5/2),x)","\frac{4\,\sqrt{1-\cos\left(c+d\,x\right)}\,\left(\sin\left(c+d\,x\right)-\sin\left(2\,c+2\,d\,x\right)+\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,"(4*(1 - cos(c + d*x))^(1/2)*(sin(c + d*x) - sin(2*c + 2*d*x) + 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"
274,1,156,112,2.003989,"\text{Not used}","int((1 - cos(c + d*x))^(1/2)/cos(c + d*x)^(7/2),x)","\frac{8\,\sqrt{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\,\left(7\,\sin\left(c+d\,x\right)-4\,\sin\left(2\,c+2\,d\,x\right)+9\,\sin\left(3\,c+3\,d\,x\right)-2\,\sin\left(4\,c+4\,d\,x\right)+2\,\sin\left(5\,c+5\,d\,x\right)\right)}{15\,d\,\sqrt{1-2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\,\left(-16\,{\sin\left(c+d\,x\right)}^2-4\,{\sin\left(2\,c+2\,d\,x\right)}^2+20\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+10\,{\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}^2+2\,{\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}^2\right)}","Not used",1,"(8*(2*sin(c/2 + (d*x)/2)^2)^(1/2)*(7*sin(c + d*x) - 4*sin(2*c + 2*d*x) + 9*sin(3*c + 3*d*x) - 2*sin(4*c + 4*d*x) + 2*sin(5*c + 5*d*x)))/(15*d*(1 - 2*sin(c/2 + (d*x)/2)^2)^(1/2)*(20*sin(c/2 + (d*x)/2)^2 - 4*sin(2*c + 2*d*x)^2 + 10*sin((3*c)/2 + (3*d*x)/2)^2 + 2*sin((5*c)/2 + (5*d*x)/2)^2 - 16*sin(c + d*x)^2))","B"
275,0,-1,185,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a - a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{\sqrt{a-a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(a - a*cos(c + d*x))^(1/2), x)","F"
276,0,-1,141,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a - a*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}}{\sqrt{a-a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(a - a*cos(c + d*x))^(1/2), x)","F"
277,0,-1,107,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a - a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{a-a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(a - a*cos(c + d*x))^(1/2), x)","F"
278,0,-1,58,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a - a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\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))^(1/2)), x)","F"
279,0,-1,95,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a - a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a-a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(3/2)*(a - a*cos(c + d*x))^(1/2)), x)","F"
280,0,-1,135,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a - a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a-a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(5/2)*(a - a*cos(c + d*x))^(1/2)), x)","F"
281,0,-1,173,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a - a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a-a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(7/2)*(a - a*cos(c + d*x))^(1/2)), x)","F"
282,0,-1,161,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(1 - cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{\sqrt{1-\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(1 - cos(c + d*x))^(1/2), x)","F"
283,0,-1,118,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(1 - cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}}{\sqrt{1-\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(1 - cos(c + d*x))^(1/2), x)","F"
284,0,-1,85,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(1 - cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{1-\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(1 - cos(c + d*x))^(1/2), x)","F"
285,0,-1,47,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{1-\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(1 - cos(c + d*x))^(1/2)), x)","F"
286,0,-1,83,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{1-\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(3/2)*(1 - cos(c + d*x))^(1/2)), x)","F"
287,0,-1,122,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(5/2)*(1 - cos(c + d*x))^(1/2)), x)","F"
288,0,-1,78,0.000000,"\text{Not used}","int(cos(c + d*x)^(4/3)*(a + a*cos(c + d*x))^(1/3),x)","\int {\cos\left(c+d\,x\right)}^{4/3}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{1/3} \,d x","Not used",1,"int(cos(c + d*x)^(4/3)*(a + a*cos(c + d*x))^(1/3), x)","F"
289,0,-1,79,0.000000,"\text{Not used}","int(cos(c + d*x)^(4/3)*(a + a*cos(c + d*x))^(2/3),x)","\int {\cos\left(c+d\,x\right)}^{4/3}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int(cos(c + d*x)^(4/3)*(a + a*cos(c + d*x))^(2/3), x)","F"
290,0,-1,79,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/3)*(a + a*cos(c + d*x))^(2/3),x)","\int {\cos\left(c+d\,x\right)}^{5/3}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int(cos(c + d*x)^(5/3)*(a + a*cos(c + d*x))^(2/3), x)","F"
291,0,-1,151,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x)),x)","\int {\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((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x)), x)","F"
292,0,-1,123,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x)),x)","\int {\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((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x)), x)","F"
293,0,-1,97,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x)),x)","\int {\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((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x)), x)","F"
294,0,-1,75,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x)),x)","\int \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((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x)), x)","F"
295,0,-1,101,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))/(1/cos(c + d*x))^(1/2),x)","\int \frac{a+a\,\cos\left(c+d\,x\right)}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + a*cos(c + d*x))/(1/cos(c + d*x))^(1/2), x)","F"
296,0,-1,127,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))/(1/cos(c + d*x))^(3/2),x)","\int \frac{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 + a*cos(c + d*x))/(1/cos(c + d*x))^(3/2), x)","F"
297,0,-1,151,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))/(1/cos(c + d*x))^(5/2),x)","\int \frac{a+a\,\cos\left(c+d\,x\right)}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + a*cos(c + d*x))/(1/cos(c + d*x))^(5/2), x)","F"
298,0,-1,161,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2, x)","F"
299,0,-1,131,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2, x)","F"
300,0,-1,64,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2, x)","F"
301,0,-1,107,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2,x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2, x)","F"
302,0,-1,135,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^2/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + a*cos(c + d*x))^2/(1/cos(c + d*x))^(1/2), x)","F"
303,0,-1,161,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^2/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + a*cos(c + d*x))^2/(1/cos(c + d*x))^(3/2), x)","F"
304,0,-1,187,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3, x)","F"
305,0,-1,157,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3, x)","F"
306,0,-1,131,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3, x)","F"
307,0,-1,131,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3, x)","F"
308,0,-1,131,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3,x)","\int \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((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3, x)","F"
309,0,-1,161,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^3/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\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 + a*cos(c + d*x))^3/(1/cos(c + d*x))^(1/2), x)","F"
310,0,-1,187,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^3/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + a*cos(c + d*x))^3/(1/cos(c + d*x))^(3/2), x)","F"
311,0,-1,187,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^4,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^4, x)","F"
312,0,-1,161,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^4,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^4, x)","F"
313,0,-1,118,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^4,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^4, x)","F"
314,0,-1,159,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^4,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^4, x)","F"
315,0,-1,161,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^4,x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^4, x)","F"
316,0,-1,187,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^4/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^4}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + a*cos(c + d*x))^4/(1/cos(c + d*x))^(1/2), x)","F"
317,0,-1,164,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x)),x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x)), x)","F"
318,0,-1,136,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x)),x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x)), x)","F"
319,0,-1,110,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x)),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{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)), x)","F"
320,0,-1,110,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))), x)","F"
321,0,-1,112,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))), x)","F"
322,0,-1,140,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))), x)","F"
323,0,-1,168,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))), x)","F"
324,0,-1,202,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^2, x)","F"
325,0,-1,176,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^2, x)","F"
326,0,-1,149,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^2,x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^2, x)","F"
327,0,-1,77,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^2), x)","F"
328,0,-1,149,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^2), x)","F"
329,0,-1,152,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^2), x)","F"
330,0,-1,178,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^2), x)","F"
331,0,-1,200,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^2),x)","\int \frac{1}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^2), x)","F"
332,0,-1,221,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^3, x)","F"
333,0,-1,195,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^3,x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^3, x)","F"
334,0,-1,195,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^3), x)","F"
335,0,-1,195,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^3), x)","F"
336,0,-1,195,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^3), x)","F"
337,0,-1,195,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^3), x)","F"
338,0,-1,221,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^3), x)","F"
339,1,163,153,5.190830,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(1/2),x)","\frac{14\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}+4\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}}{\frac{105\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{105\,d\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{35\,d\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{35\,d\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}}","Not used",1,"(14*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2) + 4*sin((7*c)/2 + (7*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2))/((105*d*cos(c/2 + (d*x)/2))/8 + (105*d*cos((3*c)/2 + (3*d*x)/2))/8 + (35*d*cos((5*c)/2 + (5*d*x)/2))/8 + (35*d*cos((7*c)/2 + (7*d*x)/2))/8)","B"
340,1,134,115,1.839093,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(1/2),x)","\frac{8\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(7\,\sin\left(c+d\,x\right)+4\,\sin\left(2\,c+2\,d\,x\right)+9\,\sin\left(3\,c+3\,d\,x\right)+2\,\sin\left(4\,c+4\,d\,x\right)+2\,\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,"(8*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(7*sin(c + d*x) + 4*sin(2*c + 2*d*x) + 9*sin(3*c + 3*d*x) + 2*sin(4*c + 4*d*x) + 2*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"
341,1,84,77,0.784717,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(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(\sin\left(c+d\,x\right)+\sin\left(2\,c+2\,d\,x\right)+\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,"(4*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(sin(c + d*x) + sin(2*c + 2*d*x) + 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"
342,1,43,36,0.294242,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,\sin\left(c+d\,x\right)\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(2*sin(c + d*x)*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2))/(d*(cos(c + d*x) + 1))","B"
343,0,-1,57,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\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))^(1/2), x)","F"
344,0,-1,92,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\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 + a*cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(1/2), x)","F"
345,0,-1,136,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\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 + a*cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(3/2), x)","F"
346,1,221,161,4.144531,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(3/2),x)","\frac{-35\,a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}+91\,a\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}+26\,a\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}}{\frac{315\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{315\,d\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{105\,d\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{105\,d\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}}","Not used",1,"(91*a*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2) - 35*a*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2) + 26*a*sin((7*c)/2 + (7*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2))/((315*d*cos(c/2 + (d*x)/2))/8 + (315*d*cos((3*c)/2 + (3*d*x)/2))/8 + (105*d*cos((5*c)/2 + (5*d*x)/2))/8 + (105*d*cos((7*c)/2 + (7*d*x)/2))/8)","B"
347,1,135,121,1.626344,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(3/2),x)","\frac{4\,a\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(8\,\sin\left(c+d\,x\right)+6\,\sin\left(2\,c+2\,d\,x\right)+11\,\sin\left(3\,c+3\,d\,x\right)+3\,\sin\left(4\,c+4\,d\,x\right)+3\,\sin\left(5\,c+5\,d\,x\right)\right)}{5\,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*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(8*sin(c + d*x) + 6*sin(2*c + 2*d*x) + 11*sin(3*c + 3*d*x) + 3*sin(4*c + 4*d*x) + 3*sin(5*c + 5*d*x)))/(5*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"
348,1,91,81,0.791017,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(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(5\,\sin\left(c+d\,x\right)+2\,\sin\left(2\,c+2\,d\,x\right)+5\,\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*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(5*sin(c + d*x) + 2*sin(2*c + 2*d*x) + 5*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"
349,0,-1,96,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
350,0,-1,95,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2),x)","\int \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((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2), x)","F"
351,0,-1,140,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/2), x)","F"
352,0,-1,180,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(3/2), x)","F"
353,1,306,201,4.847653,"\text{Not used}","int((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{192\,a^2\,{\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)}}{5\,d}-\frac{16\,a^2\,{\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{1168\,a^2\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{35\,d}+\frac{2336\,a^2\,{\mathrm{e}}^{\frac{c\,9{}\mathrm{i}}{2}+\frac{d\,x\,9{}\mathrm{i}}{2}}\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}}{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)*((192*a^2*exp((c*9i)/2 + (d*x*9i)/2)*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2))/(5*d) - (16*a^2*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) + (1168*a^2*exp((c*9i)/2 + (d*x*9i)/2)*sin((5*c)/2 + (5*d*x)/2)*(a + a*cos(c + d*x))^(1/2))/(35*d) + (2336*a^2*exp((c*9i)/2 + (d*x*9i)/2)*sin((9*c)/2 + (9*d*x)/2)*(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"
354,1,227,161,4.205324,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(5/2),x)","\frac{-\frac{35\,a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}}{2}+35\,a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}+\frac{23\,a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\sqrt{a+a\,\cos\left(c+d\,x\right)}\,\sqrt{\frac{2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1}}}{2}}{\frac{63\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{63\,d\,\cos\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)}{8}+\frac{21\,d\,\cos\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)}{8}+\frac{21\,d\,\cos\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)}{8}}","Not used",1,"(35*a^2*sin((3*c)/2 + (3*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2) - (35*a^2*sin(c/2 + (d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2))/2 + (23*a^2*sin((7*c)/2 + (7*d*x)/2)*(a + a*cos(c + d*x))^(1/2)*((2*exp(c*1i + d*x*1i))/(exp(c*2i + d*x*2i) + 1))^(1/2))/2)/((63*d*cos(c/2 + (d*x)/2))/8 + (63*d*cos((3*c)/2 + (3*d*x)/2))/8 + (21*d*cos((5*c)/2 + (5*d*x)/2))/8 + (21*d*cos((7*c)/2 + (7*d*x)/2))/8)","B"
355,1,137,121,1.623233,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2),x)","\frac{2\,a^2\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(98\,\sin\left(c+d\,x\right)+56\,\sin\left(2\,c+2\,d\,x\right)+141\,\sin\left(3\,c+3\,d\,x\right)+28\,\sin\left(4\,c+4\,d\,x\right)+43\,\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^2*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/2)*(98*sin(c + d*x) + 56*sin(2*c + 2*d*x) + 141*sin(3*c + 3*d*x) + 28*sin(4*c + 4*d*x) + 43*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"
356,0,-1,138,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
357,0,-1,134,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
358,0,-1,140,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2),x)","\int \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((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2), x)","F"
359,0,-1,180,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(1/2), x)","F"
360,0,-1,220,0.000000,"\text{Not used}","int((a + a*cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\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 + a*cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(3/2), x)","F"
361,0,-1,154,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)/(cos(c + d*x) + 1)^(1/2), x)","F"
362,0,-1,118,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)/(cos(c + d*x) + 1)^(1/2), x)","F"
363,0,-1,82,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)/(cos(c + d*x) + 1)^(1/2), x)","F"
364,0,-1,47,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(cos(c + d*x) + 1)^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{\cos\left(c+d\,x\right)+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)/(cos(c + d*x) + 1)^(1/2), x)","F"
365,0,-1,94,0.000000,"\text{Not used}","int(1/((cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)+1}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
366,0,-1,125,0.000000,"\text{Not used}","int(1/((cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)+1}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/((cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
367,0,-1,189,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\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((1/cos(c + d*x))^(7/2)/(a + a*cos(c + d*x))^(1/2), x)","F"
368,0,-1,151,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(1/2), x)","F"
369,0,-1,113,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(1/2), x)","F"
370,0,-1,56,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\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))^(1/2), x)","F"
371,0,-1,105,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+a\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
372,0,-1,168,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(1/2)), x)","F"
373,0,-1,197,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(3/2), x)","F"
374,0,-1,157,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(3/2), x)","F"
375,0,-1,117,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^(3/2),x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^(3/2), x)","F"
376,0,-1,117,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
377,0,-1,174,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
378,0,-1,214,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(3/2)), x)","F"
379,0,-1,237,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(5/2), x)","F"
380,0,-1,197,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(5/2), x)","F"
381,0,-1,157,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^(5/2),x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^(5/2), x)","F"
382,0,-1,157,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
383,0,-1,157,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
384,0,-1,214,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
385,0,-1,254,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(5/2)), x)","F"
386,0,-1,277,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + a*cos(c + d*x))^(7/2), x)","F"
387,0,-1,237,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + a*cos(c + d*x))^(7/2), x)","F"
388,0,-1,197,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^(7/2),x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + a*cos(c + d*x))^(7/2), x)","F"
389,0,-1,197,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
390,0,-1,197,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
391,0,-1,197,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
392,0,-1,254,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
393,0,-1,294,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(7/2)),x)","\int \frac{1}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(1/((1/cos(c + d*x))^(9/2)*(a + a*cos(c + d*x))^(7/2)), x)","F"
394,0,-1,237,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(9/2)),x)","\int \frac{1}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(1/((1/cos(c + d*x))^(5/2)*(a + a*cos(c + d*x))^(9/2)), x)","F"
395,0,-1,237,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(9/2)),x)","\int \frac{1}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{9/2}} \,d x","Not used",1,"int(1/((1/cos(c + d*x))^(7/2)*(a + a*cos(c + d*x))^(9/2)), x)","F"
396,1,44,38,0.736293,"\text{Not used}","int((1/cos(c + d*x))^(5/4)*(a + a*cos(c + d*x))^(3/2),x)","\frac{4\,a\,\sin\left(c+d\,x\right)\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/4}}{d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(4*a*sin(c + d*x)*(a*(cos(c + d*x) + 1))^(1/2)*(1/cos(c + d*x))^(1/4))/(d*(cos(c + d*x) + 1))","B"
397,0,-1,302,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + a*cos(c + d*x))^4,x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int(cos(c + d*x)^m*(a + a*cos(c + d*x))^4, x)","F"
398,0,-1,232,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + a*cos(c + d*x))^3,x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int(cos(c + d*x)^m*(a + a*cos(c + d*x))^3, x)","F"
399,0,-1,173,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + a*cos(c + d*x))^2,x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(c + d*x)^m*(a + a*cos(c + d*x))^2, x)","F"
400,0,-1,131,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + a*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^m\,\left(a+a\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(a + a*cos(c + d*x)), x)","F"
401,0,-1,156,0.000000,"\text{Not used}","int(cos(c + d*x)^m/(a + a*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^m}{a+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^m/(a + a*cos(c + d*x)), x)","F"
402,0,-1,229,0.000000,"\text{Not used}","int(cos(c + d*x)^m/(a + a*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^m}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^m/(a + a*cos(c + d*x))^2, x)","F"
403,1,175,150,3.228703,"\text{Not used}","int(cos(c + d*x)^7*(a + b*cos(c + d*x)),x)","\frac{35\,b\,x}{128}+\frac{\left(2\,a-\frac{93\,b}{64}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+\left(6\,a-\frac{91\,b}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{106\,a}{5}-\frac{1799\,b}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{1026\,a}{35}+\frac{1085\,b}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{1026\,a}{35}-\frac{1085\,b}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{106\,a}{5}+\frac{1799\,b}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,a+\frac{91\,b}{192}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a+\frac{93\,b}{64}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"(35*b*x)/128 + (tan(c/2 + (d*x)/2)*(2*a + (93*b)/64) + tan(c/2 + (d*x)/2)^15*(2*a - (93*b)/64) + tan(c/2 + (d*x)/2)^3*(6*a + (91*b)/192) + tan(c/2 + (d*x)/2)^13*(6*a - (91*b)/192) + tan(c/2 + (d*x)/2)^5*((106*a)/5 + (1799*b)/192) + tan(c/2 + (d*x)/2)^11*((106*a)/5 - (1799*b)/192) + tan(c/2 + (d*x)/2)^7*((1026*a)/35 - (1085*b)/192) + tan(c/2 + (d*x)/2)^9*((1026*a)/35 + (1085*b)/192))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
404,1,154,128,3.245411,"\text{Not used}","int(cos(c + d*x)^6*(a + b*cos(c + d*x)),x)","\frac{5\,a\,x}{16}+\frac{\left(2\,b-\frac{11\,a}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(4\,b-\frac{7\,a}{6}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{86\,b}{5}-\frac{85\,a}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{424\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{35}+\left(\frac{85\,a}{24}+\frac{86\,b}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{7\,a}{6}+4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,a}{8}+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)}^2+1\right)}^7}","Not used",1,"(5*a*x)/16 + (tan(c/2 + (d*x)/2)*((11*a)/8 + 2*b) + tan(c/2 + (d*x)/2)^3*((7*a)/6 + 4*b) - tan(c/2 + (d*x)/2)^11*((7*a)/6 - 4*b) - tan(c/2 + (d*x)/2)^13*((11*a)/8 - 2*b) + tan(c/2 + (d*x)/2)^5*((85*a)/24 + (86*b)/5) - tan(c/2 + (d*x)/2)^9*((85*a)/24 - (86*b)/5) + (424*b*tan(c/2 + (d*x)/2)^7)/35)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
405,1,115,114,0.659251,"\text{Not used}","int(cos(c + d*x)^5*(a + b*cos(c + d*x)),x)","\frac{5\,b\,x}{16}+\frac{8\,a\,\sin\left(c+d\,x\right)}{15\,d}+\frac{5\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{16\,d}+\frac{4\,a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{15\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{5\,d}+\frac{5\,b\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{24\,d}+\frac{b\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{6\,d}","Not used",1,"(5*b*x)/16 + (8*a*sin(c + d*x))/(15*d) + (5*b*cos(c + d*x)*sin(c + d*x))/(16*d) + (4*a*cos(c + d*x)^2*sin(c + d*x))/(15*d) + (a*cos(c + d*x)^4*sin(c + d*x))/(5*d) + (5*b*cos(c + d*x)^3*sin(c + d*x))/(24*d) + (b*cos(c + d*x)^5*sin(c + d*x))/(6*d)","B"
406,1,115,92,4.255346,"\text{Not used}","int(cos(c + d*x)^4*(a + b*cos(c + d*x)),x)","\frac{3\,a\,x}{8}+\frac{\left(2\,b-\frac{5\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,b}{3}-\frac{a}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{116\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\left(\frac{a}{2}+\frac{8\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,a}{4}+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)}^2+1\right)}^5}","Not used",1,"(3*a*x)/8 + (tan(c/2 + (d*x)/2)*((5*a)/4 + 2*b) + tan(c/2 + (d*x)/2)^3*(a/2 + (8*b)/3) - tan(c/2 + (d*x)/2)^9*((5*a)/4 - 2*b) - tan(c/2 + (d*x)/2)^7*(a/2 - (8*b)/3) + (116*b*tan(c/2 + (d*x)/2)^5)/15)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
407,1,75,76,0.577888,"\text{Not used}","int(cos(c + d*x)^3*(a + b*cos(c + d*x)),x)","\frac{3\,b\,x}{8}+\frac{2\,a\,\sin\left(c+d\,x\right)}{3\,d}+\frac{3\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{b\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(3*b*x)/8 + (2*a*sin(c + d*x))/(3*d) + (3*b*cos(c + d*x)*sin(c + d*x))/(8*d) + (a*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (b*cos(c + d*x)^3*sin(c + d*x))/(4*d)","B"
408,1,55,54,0.579688,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x)),x)","\frac{a\,x}{2}+\frac{2\,b\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(a*x)/2 + (2*b*sin(c + d*x))/(3*d) + (a*cos(c + d*x)*sin(c + d*x))/(2*d) + (b*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
409,1,31,38,0.524728,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x)),x)","\frac{b\,x}{2}+\frac{b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(b*x)/2 + (b*sin(2*c + 2*d*x))/(4*d) + (a*sin(c + d*x))/d","B"
410,1,17,15,0.465664,"\text{Not used}","int(a + b*cos(c + d*x),x)","\frac{b\,\sin\left(c+d\,x\right)+a\,d\,x}{d}","Not used",1,"(b*sin(c + d*x) + a*d*x)/d","B"
411,1,57,16,0.535315,"\text{Not used}","int((a + b*cos(c + d*x))/cos(c + d*x),x)","\frac{2\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(2*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
412,1,47,24,0.513987,"\text{Not used}","int((a + b*cos(c + d*x))/cos(c + d*x)^2,x)","\frac{2\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*b*atanh(tan(c/2 + (d*x)/2)))/d - (2*a*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
413,1,81,47,1.131685,"\text{Not used}","int((a + b*cos(c + d*x))/cos(c + d*x)^3,x)","\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{\left(a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(a+2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(a*atanh(tan(c/2 + (d*x)/2)))/d + (tan(c/2 + (d*x)/2)^3*(a - 2*b) + tan(c/2 + (d*x)/2)*(a + 2*b))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
414,1,111,63,2.337038,"\text{Not used}","int((a + b*cos(c + d*x))/cos(c + d*x)^4,x)","\frac{b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\left(2\,a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\left(2\,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,"(b*atanh(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)^5*(2*a - b) + tan(c/2 + (d*x)/2)*(2*a + b) - (4*a*tan(c/2 + (d*x)/2)^3)/3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
415,1,150,85,3.075701,"\text{Not used}","int((a + b*cos(c + d*x))/cos(c + d*x)^5,x)","\frac{\left(\frac{5\,a}{4}-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,a}{4}+\frac{10\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,a}{4}-\frac{10\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,a}{4}+2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*((5*a)/4 + 2*b) + tan(c/2 + (d*x)/2)^7*((5*a)/4 - 2*b) + tan(c/2 + (d*x)/2)^3*((3*a)/4 - (10*b)/3) + tan(c/2 + (d*x)/2)^5*((3*a)/4 + (10*b)/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)) + (3*a*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
416,1,180,101,3.120988,"\text{Not used}","int((a + b*cos(c + d*x))/cos(c + d*x)^6,x)","\frac{3\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\left(2\,a-\frac{5\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{b}{2}-\frac{8\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{116\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\left(-\frac{8\,a}{3}-\frac{b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a+\frac{5\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(3*b*atanh(tan(c/2 + (d*x)/2)))/(4*d) - (tan(c/2 + (d*x)/2)*(2*a + (5*b)/4) - tan(c/2 + (d*x)/2)^3*((8*a)/3 + b/2) + tan(c/2 + (d*x)/2)^9*(2*a - (5*b)/4) - tan(c/2 + (d*x)/2)^7*((8*a)/3 - b/2) + (116*a*tan(c/2 + (d*x)/2)^5)/15)/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
417,1,143,150,0.668364,"\text{Not used}","int(cos(c + d*x)^4*(a + b*cos(c + d*x))^2,x)","\frac{3\,a^2\,x}{8}+\frac{5\,b^2\,x}{16}+\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{15\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{b^2\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{5\,a\,b\,\sin\left(c+d\,x\right)}{4\,d}+\frac{5\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{24\,d}+\frac{a\,b\,\sin\left(5\,c+5\,d\,x\right)}{40\,d}","Not used",1,"(3*a^2*x)/8 + (5*b^2*x)/16 + (a^2*sin(2*c + 2*d*x))/(4*d) + (a^2*sin(4*c + 4*d*x))/(32*d) + (15*b^2*sin(2*c + 2*d*x))/(64*d) + (3*b^2*sin(4*c + 4*d*x))/(64*d) + (b^2*sin(6*c + 6*d*x))/(192*d) + (5*a*b*sin(c + d*x))/(4*d) + (5*a*b*sin(3*c + 3*d*x))/(24*d) + (a*b*sin(5*c + 5*d*x))/(40*d)","B"
418,1,117,111,0.609100,"\text{Not used}","int(cos(c + d*x)^3*(a + b*cos(c + d*x))^2,x)","\frac{3\,a^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{5\,b^2\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,a\,b\,x}{4}+\frac{a^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{5\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{b^2\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{a\,b\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}","Not used",1,"(3*a^2*sin(c + d*x))/(4*d) + (5*b^2*sin(c + d*x))/(8*d) + (3*a*b*x)/4 + (a^2*sin(3*c + 3*d*x))/(12*d) + (5*b^2*sin(3*c + 3*d*x))/(48*d) + (b^2*sin(5*c + 5*d*x))/(80*d) + (a*b*sin(2*c + 2*d*x))/(2*d) + (a*b*sin(4*c + 4*d*x))/(16*d)","B"
419,1,93,101,0.598522,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))^2,x)","\frac{a^2\,x}{2}+\frac{3\,b^2\,x}{8}+\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{b^2\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{3\,a\,b\,\sin\left(c+d\,x\right)}{2\,d}+\frac{a\,b\,\sin\left(3\,c+3\,d\,x\right)}{6\,d}","Not used",1,"(a^2*x)/2 + (3*b^2*x)/8 + (a^2*sin(2*c + 2*d*x))/(4*d) + (b^2*sin(2*c + 2*d*x))/(4*d) + (b^2*sin(4*c + 4*d*x))/(32*d) + (3*a*b*sin(c + d*x))/(2*d) + (a*b*sin(3*c + 3*d*x))/(6*d)","B"
420,1,72,71,0.552372,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^2,x)","\frac{a^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,b^2\,\sin\left(c+d\,x\right)}{3\,d}+a\,b\,x+\frac{b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^2*sin(c + d*x))/d + (2*b^2*sin(c + d*x))/(3*d) + a*b*x + (b^2*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (a*b*cos(c + d*x)*sin(c + d*x))/d","B"
421,1,42,50,0.532527,"\text{Not used}","int((a + b*cos(c + d*x))^2,x)","a^2\,x+\frac{b^2\,x}{2}+\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{2\,a\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"a^2*x + (b^2*x)/2 + (b^2*sin(2*c + 2*d*x))/(4*d) + (2*a*b*sin(c + d*x))/d","B"
422,1,73,33,0.553154,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x),x)","\frac{b^2\,\sin\left(c+d\,x\right)}{d}+\frac{2\,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\,a\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(b^2*sin(c + d*x))/d + (2*a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
423,1,181,33,0.570358,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^2,x)","\frac{2\,b^2\,\mathrm{atan}\left(\frac{64\,b^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,a^2\,b^4+64\,b^6}+\frac{256\,a^2\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{256\,a^2\,b^4+64\,b^6}\right)}{d}-\frac{2\,a^2\,\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)}+\frac{4\,a\,b\,\mathrm{atanh}\left(\frac{128\,a\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^3\,b^3+128\,a\,b^5}+\frac{512\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{512\,a^3\,b^3+128\,a\,b^5}\right)}{d}","Not used",1,"(2*b^2*atan((64*b^6*tan(c/2 + (d*x)/2))/(64*b^6 + 256*a^2*b^4) + (256*a^2*b^4*tan(c/2 + (d*x)/2))/(64*b^6 + 256*a^2*b^4)))/d - (2*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1)) + (4*a*b*atanh((128*a*b^5*tan(c/2 + (d*x)/2))/(128*a*b^5 + 512*a^3*b^3) + (512*a^3*b^3*tan(c/2 + (d*x)/2))/(128*a*b^5 + 512*a^3*b^3)))/d","B"
424,1,99,59,1.165764,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^3,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+2\,b^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a\,b-a^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,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)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(a^2 + 2*b^2))/d - (tan(c/2 + (d*x)/2)^3*(4*a*b - a^2) - tan(c/2 + (d*x)/2)*(4*a*b + a^2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
425,1,141,80,2.592424,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^4,x)","\frac{2\,a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\left(2\,a^2-2\,a\,b+2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,a^2}{3}-4\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^2+2\,a\,b+2\,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)}^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*b*atanh(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)^5*(2*a^2 - 2*a*b + 2*b^2) - tan(c/2 + (d*x)/2)^3*((4*a^2)/3 + 4*b^2) + tan(c/2 + (d*x)/2)*(2*a*b + 2*a^2 + 2*b^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"
426,1,184,110,3.103371,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^5,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{3\,a^2}{4}+b^2\right)}{d}+\frac{\left(\frac{5\,a^2}{4}-4\,a\,b+b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,a^2}{4}+\frac{20\,a\,b}{3}-b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,a^2}{4}-\frac{20\,a\,b}{3}-b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,a^2}{4}+4\,a\,b+b^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((3*a^2)/4 + b^2))/d + (tan(c/2 + (d*x)/2)^5*((20*a*b)/3 + (3*a^2)/4 - b^2) + tan(c/2 + (d*x)/2)*(4*a*b + (5*a^2)/4 + b^2) + tan(c/2 + (d*x)/2)^7*((5*a^2)/4 - 4*a*b + b^2) - tan(c/2 + (d*x)/2)^3*((20*a*b)/3 - (3*a^2)/4 + b^2))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
427,1,221,135,3.229546,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^6,x)","\frac{3\,a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{\left(2\,a^2-\frac{5\,a\,b}{2}+2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{8\,a^2}{3}+a\,b-\frac{16\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,a^2}{15}+\frac{20\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,a^2}{3}-a\,b-\frac{16\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^2+\frac{5\,a\,b}{2}+2\,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,"(3*a*b*atanh(tan(c/2 + (d*x)/2)))/(2*d) - (tan(c/2 + (d*x)/2)^5*((116*a^2)/15 + (20*b^2)/3) + tan(c/2 + (d*x)/2)^9*(2*a^2 - (5*a*b)/2 + 2*b^2) - tan(c/2 + (d*x)/2)^3*(a*b + (8*a^2)/3 + (16*b^2)/3) - tan(c/2 + (d*x)/2)^7*((8*a^2)/3 - a*b + (16*b^2)/3) + tan(c/2 + (d*x)/2)*((5*a*b)/2 + 2*a^2 + 2*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"
428,1,380,170,2.104361,"\text{Not used}","int(cos(c + d*x)^3*(a + b*cos(c + d*x))^3,x)","\frac{\left(2\,a^3-\frac{15\,a^2\,b}{4}+6\,a\,b^2-\frac{11\,b^3}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{22\,a^3}{3}-\frac{21\,a^2\,b}{4}+14\,a\,b^2+\frac{5\,b^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(12\,a^3-\frac{3\,a^2\,b}{2}+\frac{156\,a\,b^2}{5}-\frac{15\,b^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,a^3+\frac{3\,a^2\,b}{2}+\frac{156\,a\,b^2}{5}+\frac{15\,b^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{22\,a^3}{3}+\frac{21\,a^2\,b}{4}+14\,a\,b^2-\frac{5\,b^3}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^3+\frac{15\,a^2\,b}{4}+6\,a\,b^2+\frac{11\,b^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{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^2+5\,b^2\right)}{8\,\left(\frac{9\,a^2\,b}{4}+\frac{5\,b^3}{8}\right)}\right)\,\left(18\,a^2+5\,b^2\right)}{8\,d}-\frac{b\,\left(18\,a^2+5\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^11*(6*a*b^2 - (15*a^2*b)/4 + 2*a^3 - (11*b^3)/8) + tan(c/2 + (d*x)/2)^3*(14*a*b^2 + (21*a^2*b)/4 + (22*a^3)/3 - (5*b^3)/24) + tan(c/2 + (d*x)/2)^9*(14*a*b^2 - (21*a^2*b)/4 + (22*a^3)/3 + (5*b^3)/24) + tan(c/2 + (d*x)/2)^5*((156*a*b^2)/5 + (3*a^2*b)/2 + 12*a^3 + (15*b^3)/4) + tan(c/2 + (d*x)/2)^7*((156*a*b^2)/5 - (3*a^2*b)/2 + 12*a^3 - (15*b^3)/4) + tan(c/2 + (d*x)/2)*(6*a*b^2 + (15*a^2*b)/4 + 2*a^3 + (11*b^3)/8))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (b*atan((b*tan(c/2 + (d*x)/2)*(18*a^2 + 5*b^2))/(8*((9*a^2*b)/4 + (5*b^3)/8)))*(18*a^2 + 5*b^2))/(8*d) - (b*(18*a^2 + 5*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(8*d)","B"
429,1,319,180,2.045481,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))^3,x)","\frac{\left(-a^3+6\,a^2\,b-\frac{15\,a\,b^2}{4}+2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-2\,a^3+16\,a^2\,b-\frac{3\,a\,b^2}{2}+\frac{8\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(20\,a^2\,b+\frac{116\,b^3}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(2\,a^3+16\,a^2\,b+\frac{3\,a\,b^2}{2}+\frac{8\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(a^3+6\,a^2\,b+\frac{15\,a\,b^2}{4}+2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+9\,b^2\right)}{4\,\left(a^3+\frac{9\,a\,b^2}{4}\right)}\right)\,\left(4\,a^2+9\,b^2\right)}{4\,d}-\frac{a\,\left(4\,a^2+9\,b^2\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*((3*a*b^2)/2 + 16*a^2*b + 2*a^3 + (8*b^3)/3) - tan(c/2 + (d*x)/2)^7*((3*a*b^2)/2 - 16*a^2*b + 2*a^3 - (8*b^3)/3) + tan(c/2 + (d*x)/2)*((15*a*b^2)/4 + 6*a^2*b + a^3 + 2*b^3) + tan(c/2 + (d*x)/2)^5*(20*a^2*b + (116*b^3)/15) - tan(c/2 + (d*x)/2)^9*((15*a*b^2)/4 - 6*a^2*b + a^3 - 2*b^3))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(4*a^2 + 9*b^2))/(4*((9*a*b^2)/4 + a^3)))*(4*a^2 + 9*b^2))/(4*d) - (a*(4*a^2 + 9*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
430,1,279,121,1.952114,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^3,x)","\frac{\left(2\,a^3-3\,a^2\,b+6\,a\,b^2-\frac{5\,b^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,a^3-3\,a^2\,b+10\,a\,b^2+\frac{3\,b^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,a^3+3\,a^2\,b+10\,a\,b^2-\frac{3\,b^3}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^3+3\,a^2\,b+6\,a\,b^2+\frac{5\,b^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)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,b\,\mathrm{atan}\left(\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)}{4\,\left(3\,a^2\,b+\frac{3\,b^3}{4}\right)}\right)\,\left(4\,a^2+b^2\right)}{4\,d}-\frac{3\,b\,\left(4\,a^2+b^2\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)^7*(6*a*b^2 - 3*a^2*b + 2*a^3 - (5*b^3)/4) + tan(c/2 + (d*x)/2)^3*(10*a*b^2 + 3*a^2*b + 6*a^3 - (3*b^3)/4) + tan(c/2 + (d*x)/2)^5*(10*a*b^2 - 3*a^2*b + 6*a^3 + (3*b^3)/4) + tan(c/2 + (d*x)/2)*(6*a*b^2 + 3*a^2*b + 2*a^3 + (5*b^3)/4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (3*b*atan((3*b*tan(c/2 + (d*x)/2)*(4*a^2 + b^2))/(4*(3*a^2*b + (3*b^3)/4)))*(4*a^2 + b^2))/(4*d) - (3*b*(4*a^2 + b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(4*d)","B"
431,1,77,76,0.602242,"\text{Not used}","int((a + b*cos(c + d*x))^3,x)","a^3\,x+\frac{3\,b^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,a\,b^2\,x}{2}+\frac{3\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,a^2\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"a^3*x + (3*b^3*sin(c + d*x))/(4*d) + (b^3*sin(3*c + 3*d*x))/(12*d) + (3*a*b^2*x)/2 + (3*a*b^2*sin(2*c + 2*d*x))/(4*d) + (3*a^2*b*sin(c + d*x))/d","B"
432,1,123,73,0.717877,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x),x)","\frac{2\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{6\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(2*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^3*sin(2*c + 2*d*x))/(4*d) + (3*a*b^2*sin(c + d*x))/d + (6*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
433,1,97,68,0.624046,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^2,x)","\frac{b^3\,\sin\left(c+d\,x\right)}{d}+\frac{a^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{6\,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{6\,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)}{d}","Not used",1,"(b^3*sin(c + d*x))/d + (a^3*sin(c + d*x))/(d*cos(c + d*x)) + (6*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
434,1,136,79,0.670323,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^3,x)","\frac{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^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^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{6\,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)}{d}+\frac{3\,a^2\,b\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (6*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*a^2*b*sin(c + d*x))/(d*cos(c + d*x))","B"
435,1,157,109,2.633868,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^4,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^2\,b+2\,b^3\right)}{d}-\frac{\left(2\,a^3-3\,a^2\,b+6\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{4\,a^3}{3}-12\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^3+3\,a^2\,b+6\,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)}^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))*(3*a^2*b + 2*b^3))/d - (tan(c/2 + (d*x)/2)^5*(6*a*b^2 - 3*a^2*b + 2*a^3) - tan(c/2 + (d*x)/2)^3*(12*a*b^2 + (4*a^3)/3) + tan(c/2 + (d*x)/2)*(6*a*b^2 + 3*a^2*b + 2*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"
436,1,224,133,4.221463,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^5,x)","\frac{\left(\frac{5\,a^3}{4}-6\,a^2\,b+3\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,a^3}{4}+10\,a^2\,b-3\,a\,b^2+6\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,a^3}{4}-10\,a^2\,b-3\,a\,b^2-6\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,a^3}{4}+6\,a^2\,b+3\,a\,b^2+2\,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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+4\,b^2\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(3*a*b^2 - 6*a^2*b + (5*a^3)/4 - 2*b^3) - tan(c/2 + (d*x)/2)^3*(3*a*b^2 + 10*a^2*b - (3*a^3)/4 + 6*b^3) + tan(c/2 + (d*x)/2)^5*(10*a^2*b - 3*a*b^2 + (3*a^3)/4 + 6*b^3) + tan(c/2 + (d*x)/2)*(3*a*b^2 + 6*a^2*b + (5*a^3)/4 + 2*b^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)) + (3*a*atanh(tan(c/2 + (d*x)/2))*(a^2 + 4*b^2))/(4*d)","B"
437,1,260,169,4.222902,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{9\,a^2\,b}{4}+b^3\right)}{d}-\frac{\left(2\,a^3-\frac{15\,a^2\,b}{4}+6\,a\,b^2-b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{8\,a^3}{3}+\frac{3\,a^2\,b}{2}-16\,a\,b^2+2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,a^3}{15}+20\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,a^3}{3}-\frac{3\,a^2\,b}{2}-16\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^3+\frac{15\,a^2\,b}{4}+6\,a\,b^2+b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-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(tan(c/2 + (d*x)/2))*((9*a^2*b)/4 + b^3))/d - (tan(c/2 + (d*x)/2)^9*(6*a*b^2 - (15*a^2*b)/4 + 2*a^3 - b^3) - tan(c/2 + (d*x)/2)^3*(16*a*b^2 + (3*a^2*b)/2 + (8*a^3)/3 + 2*b^3) - tan(c/2 + (d*x)/2)^7*(16*a*b^2 - (3*a^2*b)/2 + (8*a^3)/3 - 2*b^3) + tan(c/2 + (d*x)/2)*(6*a*b^2 + (15*a^2*b)/4 + 2*a^3 + b^3) + tan(c/2 + (d*x)/2)^5*(20*a*b^2 + (116*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))","B"
438,1,476,247,2.074291,"\text{Not used}","int(cos(c + d*x)^3*(a + b*cos(c + d*x))^4,x)","\frac{\left(2\,a^4-5\,a^3\,b+12\,a^2\,b^2-\frac{11\,a\,b^3}{2}+2\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{28\,a^4}{3}-12\,a^3\,b+40\,a^2\,b^2-\frac{14\,a\,b^3}{3}+4\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{58\,a^4}{3}-9\,a^3\,b+\frac{452\,a^2\,b^2}{5}-\frac{85\,a\,b^3}{6}+\frac{86\,b^4}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(24\,a^4+\frac{624\,a^2\,b^2}{5}+\frac{424\,b^4}{35}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{58\,a^4}{3}+9\,a^3\,b+\frac{452\,a^2\,b^2}{5}+\frac{85\,a\,b^3}{6}+\frac{86\,b^4}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{28\,a^4}{3}+12\,a^3\,b+40\,a^2\,b^2+\frac{14\,a\,b^3}{3}+4\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^4+5\,a^3\,b+12\,a^2\,b^2+\frac{11\,a\,b^3}{2}+2\,b^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2+5\,b^2\right)}{2\,\left(3\,a^3\,b+\frac{5\,a\,b^3}{2}\right)}\right)\,\left(6\,a^2+5\,b^2\right)}{2\,d}-\frac{a\,b\,\left(6\,a^2+5\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*(24*a^4 + (424*b^4)/35 + (624*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^13*(2*a^4 - 5*a^3*b - (11*a*b^3)/2 + 2*b^4 + 12*a^2*b^2) + tan(c/2 + (d*x)/2)^3*((14*a*b^3)/3 + 12*a^3*b + (28*a^4)/3 + 4*b^4 + 40*a^2*b^2) + tan(c/2 + (d*x)/2)^11*((28*a^4)/3 - 12*a^3*b - (14*a*b^3)/3 + 4*b^4 + 40*a^2*b^2) + tan(c/2 + (d*x)/2)^5*((85*a*b^3)/6 + 9*a^3*b + (58*a^4)/3 + (86*b^4)/5 + (452*a^2*b^2)/5) + tan(c/2 + (d*x)/2)^9*((58*a^4)/3 - 9*a^3*b - (85*a*b^3)/6 + (86*b^4)/5 + (452*a^2*b^2)/5) + tan(c/2 + (d*x)/2)*((11*a*b^3)/2 + 5*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2))/(d*(7*tan(c/2 + (d*x)/2)^2 + 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 + 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 + 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 + 1)) + (a*b*atan((a*b*tan(c/2 + (d*x)/2)*(6*a^2 + 5*b^2))/(2*((5*a*b^3)/2 + 3*a^3*b)))*(6*a^2 + 5*b^2))/(2*d) - (a*b*(6*a^2 + 5*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/(2*d)","B"
439,1,214,235,0.835194,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))^4,x)","\frac{a^4\,x}{2}+\frac{5\,b^4\,x}{16}+\frac{9\,a^2\,b^2\,x}{4}+\frac{a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{15\,b^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,b^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{b^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{5\,a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{a\,b^3\,\sin\left(5\,c+5\,d\,x\right)}{20\,d}+\frac{3\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,a^2\,b^2\,\sin\left(4\,c+4\,d\,x\right)}{16\,d}+\frac{5\,a\,b^3\,\sin\left(c+d\,x\right)}{2\,d}+\frac{3\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a^4*x)/2 + (5*b^4*x)/16 + (9*a^2*b^2*x)/4 + (a^4*sin(2*c + 2*d*x))/(4*d) + (15*b^4*sin(2*c + 2*d*x))/(64*d) + (3*b^4*sin(4*c + 4*d*x))/(64*d) + (b^4*sin(6*c + 6*d*x))/(192*d) + (5*a*b^3*sin(3*c + 3*d*x))/(12*d) + (a^3*b*sin(3*c + 3*d*x))/(3*d) + (a*b^3*sin(5*c + 5*d*x))/(20*d) + (3*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*a^2*b^2*sin(4*c + 4*d*x))/(16*d) + (5*a*b^3*sin(c + d*x))/(2*d) + (3*a^3*b*sin(c + d*x))/d","B"
440,1,363,170,2.037058,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^4,x)","\frac{\left(2\,a^4-4\,a^3\,b+12\,a^2\,b^2-5\,a\,b^3+2\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(8\,a^4-8\,a^3\,b+32\,a^2\,b^2-2\,a\,b^3+\frac{8\,b^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(12\,a^4+40\,a^2\,b^2+\frac{116\,b^4}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(8\,a^4+8\,a^3\,b+32\,a^2\,b^2+2\,a\,b^3+\frac{8\,b^4}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^4+4\,a^3\,b+12\,a^2\,b^2+5\,a\,b^3+2\,b^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+3\,b^2\right)}{4\,a^3\,b+3\,a\,b^3}\right)\,\left(4\,a^2+3\,b^2\right)}{d}-\frac{a\,b\,\left(4\,a^2+3\,b^2\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(12*a^4 + (116*b^4)/15 + 40*a^2*b^2) + tan(c/2 + (d*x)/2)^9*(2*a^4 - 4*a^3*b - 5*a*b^3 + 2*b^4 + 12*a^2*b^2) + tan(c/2 + (d*x)/2)^3*(2*a*b^3 + 8*a^3*b + 8*a^4 + (8*b^4)/3 + 32*a^2*b^2) + tan(c/2 + (d*x)/2)^7*(8*a^4 - 8*a^3*b - 2*a*b^3 + (8*b^4)/3 + 32*a^2*b^2) + tan(c/2 + (d*x)/2)*(5*a*b^3 + 4*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*b^2))/(d*(5*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 + 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) + (a*b*atan((a*b*tan(c/2 + (d*x)/2)*(4*a^2 + 3*b^2))/(3*a*b^3 + 4*a^3*b))*(4*a^2 + 3*b^2))/d - (a*b*(4*a^2 + 3*b^2)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/d","B"
441,1,123,137,0.657066,"\text{Not used}","int((a + b*cos(c + d*x))^4,x)","a^4\,x+\frac{3\,b^4\,x}{8}+3\,a^2\,b^2\,x+\frac{b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{b^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{3\,a^2\,b^2\,\sin\left(2\,c+2\,d\,x\right)}{2\,d}+\frac{3\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{4\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"a^4*x + (3*b^4*x)/8 + 3*a^2*b^2*x + (b^4*sin(2*c + 2*d*x))/(4*d) + (b^4*sin(4*c + 4*d*x))/(32*d) + (a*b^3*sin(3*c + 3*d*x))/(3*d) + (3*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (3*a*b^3*sin(c + d*x))/d + (4*a^3*b*sin(c + d*x))/d","B"
442,1,158,107,0.823680,"\text{Not used}","int((a + b*cos(c + d*x))^4/cos(c + d*x),x)","\frac{3\,b^4\,\sin\left(c+d\,x\right)}{4\,d}+\frac{2\,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{b^4\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{a\,b^3\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{6\,a^2\,b^2\,\sin\left(c+d\,x\right)}{d}+\frac{4\,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^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}","Not used",1,"(3*b^4*sin(c + d*x))/(4*d) + (2*a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^4*sin(3*c + 3*d*x))/(12*d) + (a*b^3*sin(2*c + 2*d*x))/d + (6*a^2*b^2*sin(c + d*x))/d + (4*a*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*a^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
443,1,150,114,0.714518,"\text{Not used}","int((a + b*cos(c + d*x))^4/cos(c + d*x)^2,x)","\frac{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)}{d}+\frac{a^4\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{12\,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{4\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{b^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{8\,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)}{d}","Not used",1,"(b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^4*sin(c + d*x))/(d*cos(c + d*x)) + (12*a^2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a*b^3*sin(c + d*x))/d + (b^4*cos(c + d*x)*sin(c + d*x))/(2*d) + (8*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
444,1,152,108,0.719607,"\text{Not used}","int((a + b*cos(c + d*x))^4/cos(c + d*x)^3,x)","\frac{b^4\,\sin\left(c+d\,x\right)}{d}+\frac{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^4\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{12\,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)}{d}+\frac{8\,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{4\,a^3\,b\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(b^4*sin(c + d*x))/d + (a^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^4*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (12*a^2*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*a*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a^3*b*sin(c + d*x))/(d*cos(c + d*x))","B"
445,1,185,115,0.775024,"\text{Not used}","int((a + b*cos(c + d*x))^4/cos(c + d*x)^4,x)","\frac{2\,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)}{d}+\frac{2\,a^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{a^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{8\,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)}{d}+\frac{4\,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)}{d}+\frac{2\,a^3\,b\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}+\frac{6\,a^2\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*a^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (a^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (8*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*a^3*b*sin(c + d*x))/(d*cos(c + d*x)^2) + (6*a^2*b^2*sin(c + d*x))/(d*cos(c + d*x))","B"
446,1,245,154,4.293418,"\text{Not used}","int((a + b*cos(c + d*x))^4/cos(c + d*x)^5,x)","\frac{\left(\frac{5\,a^4}{4}-8\,a^3\,b+6\,a^2\,b^2-8\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{3\,a^4}{4}+\frac{40\,a^3\,b}{3}-6\,a^2\,b^2+24\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,a^4}{4}-\frac{40\,a^3\,b}{3}-6\,a^2\,b^2-24\,a\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,a^4}{4}+8\,a^3\,b+6\,a^2\,b^2+8\,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)}^8-4\,{\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^4}{4}+6\,a^2\,b^2+2\,b^4\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(8*a*b^3 + 8*a^3*b + (5*a^4)/4 + 6*a^2*b^2) - tan(c/2 + (d*x)/2)^7*(8*a*b^3 + 8*a^3*b - (5*a^4)/4 - 6*a^2*b^2) - tan(c/2 + (d*x)/2)^3*(24*a*b^3 + (40*a^3*b)/3 - (3*a^4)/4 + 6*a^2*b^2) + tan(c/2 + (d*x)/2)^5*(24*a*b^3 + (40*a^3*b)/3 + (3*a^4)/4 - 6*a^2*b^2))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) + (atanh(tan(c/2 + (d*x)/2))*((3*a^4)/4 + 2*b^4 + 6*a^2*b^2))/d","B"
447,1,304,188,4.455992,"\text{Not used}","int((a + b*cos(c + d*x))^4/cos(c + d*x)^6,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^3\,b+4\,a\,b^3\right)}{d}-\frac{\left(2\,a^4-5\,a^3\,b+12\,a^2\,b^2-4\,a\,b^3+2\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{8\,a^4}{3}+2\,a^3\,b-32\,a^2\,b^2+8\,a\,b^3-8\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{116\,a^4}{15}+40\,a^2\,b^2+12\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{8\,a^4}{3}-2\,a^3\,b-32\,a^2\,b^2-8\,a\,b^3-8\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^4+5\,a^3\,b+12\,a^2\,b^2+4\,a\,b^3+2\,b^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{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(tan(c/2 + (d*x)/2))*(4*a*b^3 + 3*a^3*b))/d - (tan(c/2 + (d*x)/2)^5*((116*a^4)/15 + 12*b^4 + 40*a^2*b^2) + tan(c/2 + (d*x)/2)^9*(2*a^4 - 5*a^3*b - 4*a*b^3 + 2*b^4 + 12*a^2*b^2) - tan(c/2 + (d*x)/2)^3*(8*a*b^3 + 2*a^3*b + (8*a^4)/3 + 8*b^4 + 32*a^2*b^2) - tan(c/2 + (d*x)/2)^7*((8*a^4)/3 - 2*a^3*b - 8*a*b^3 + 8*b^4 + 32*a^2*b^2) + tan(c/2 + (d*x)/2)*(4*a*b^3 + 5*a^3*b + 2*a^4 + 2*b^4 + 12*a^2*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"
448,1,370,222,4.307772,"\text{Not used}","int((a + b*cos(c + d*x))^4/cos(c + d*x)^7,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{5\,a^4}{8}+\frac{9\,a^2\,b^2}{2}+b^4\right)}{d}+\frac{\left(\frac{11\,a^4}{8}-8\,a^3\,b+\frac{15\,a^2\,b^2}{2}-8\,a\,b^3+b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{5\,a^4}{24}+\frac{56\,a^3\,b}{3}-\frac{21\,a^2\,b^2}{2}+\frac{88\,a\,b^3}{3}-3\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{15\,a^4}{4}-\frac{208\,a^3\,b}{5}+3\,a^2\,b^2-48\,a\,b^3+2\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{15\,a^4}{4}+\frac{208\,a^3\,b}{5}+3\,a^2\,b^2+48\,a\,b^3+2\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{5\,a^4}{24}-\frac{56\,a^3\,b}{3}-\frac{21\,a^2\,b^2}{2}-\frac{88\,a\,b^3}{3}-3\,b^4\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,a^4}{8}+8\,a^3\,b+\frac{15\,a^2\,b^2}{2}+8\,a\,b^3+b^4\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((5*a^4)/8 + b^4 + (9*a^2*b^2)/2))/d + (tan(c/2 + (d*x)/2)^9*((88*a*b^3)/3 + (56*a^3*b)/3 + (5*a^4)/24 - 3*b^4 - (21*a^2*b^2)/2) - tan(c/2 + (d*x)/2)^3*((88*a*b^3)/3 + (56*a^3*b)/3 - (5*a^4)/24 + 3*b^4 + (21*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^5*(48*a*b^3 + (208*a^3*b)/5 + (15*a^4)/4 + 2*b^4 + 3*a^2*b^2) + tan(c/2 + (d*x)/2)^7*((15*a^4)/4 - (208*a^3*b)/5 - 48*a*b^3 + 2*b^4 + 3*a^2*b^2) + tan(c/2 + (d*x)/2)*(8*a*b^3 + 8*a^3*b + (11*a^4)/8 + b^4 + (15*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^11*((11*a^4)/8 - 8*a^3*b - 8*a*b^3 + b^4 + (15*a^2*b^2)/2))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
449,1,474,193,1.719740,"\text{Not used}","int(cos(c + d*x)^5/(a + b*cos(c + d*x)),x)","\frac{\sin\left(2\,c+2\,d\,x\right)}{4\,b\,d}+\frac{\sin\left(4\,c+4\,d\,x\right)}{32\,b\,d}+\frac{3\,\mathrm{atan}\left(\frac{40\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^6+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^8+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{10}}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(40\,a^4\,b^5+15\,a^2\,b^7+9\,b^9\right)}\right)}{4\,b\,d}-\frac{a\,\sin\left(3\,c+3\,d\,x\right)}{12\,b^2\,d}-\frac{a^3\,\sin\left(c+d\,x\right)}{b^4\,d}+\frac{a^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,b^3\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{40\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^6+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^8+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{10}}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(40\,a^4\,b^5+15\,a^2\,b^7+9\,b^9\right)}\right)}{b^3\,d}+\frac{2\,a^4\,\mathrm{atan}\left(\frac{40\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^6+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^8+9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^{10}}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(40\,a^4\,b^5+15\,a^2\,b^7+9\,b^9\right)}\right)}{b^5\,d}-\frac{3\,a\,\sin\left(c+d\,x\right)}{4\,b^2\,d}-\frac{a^5\,\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^5\,d\,\sqrt{b^2-a^2}}","Not used",1,"sin(2*c + 2*d*x)/(4*b*d) + sin(4*c + 4*d*x)/(32*b*d) + (3*atan((9*b^10*sin(c/2 + (d*x)/2) + 15*a^2*b^8*sin(c/2 + (d*x)/2) + 40*a^4*b^6*sin(c/2 + (d*x)/2))/(b*cos(c/2 + (d*x)/2)*(9*b^9 + 15*a^2*b^7 + 40*a^4*b^5))))/(4*b*d) - (a*sin(3*c + 3*d*x))/(12*b^2*d) - (a^3*sin(c + d*x))/(b^4*d) + (a^2*sin(2*c + 2*d*x))/(4*b^3*d) + (a^2*atan((9*b^10*sin(c/2 + (d*x)/2) + 15*a^2*b^8*sin(c/2 + (d*x)/2) + 40*a^4*b^6*sin(c/2 + (d*x)/2))/(b*cos(c/2 + (d*x)/2)*(9*b^9 + 15*a^2*b^7 + 40*a^4*b^5))))/(b^3*d) + (2*a^4*atan((9*b^10*sin(c/2 + (d*x)/2) + 15*a^2*b^8*sin(c/2 + (d*x)/2) + 40*a^4*b^6*sin(c/2 + (d*x)/2))/(b*cos(c/2 + (d*x)/2)*(9*b^9 + 15*a^2*b^7 + 40*a^4*b^5))))/(b^5*d) - (3*a*sin(c + d*x))/(4*b^2*d) - (a^5*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^5*d*(b^2 - a^2)^(1/2))","B"
450,1,203,148,1.177879,"\text{Not used}","int(cos(c + d*x)^4/(a + b*cos(c + d*x)),x)","\frac{3\,\sin\left(c+d\,x\right)}{4\,b\,d}+\frac{\sin\left(3\,c+3\,d\,x\right)}{12\,b\,d}-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4\,b^2\,d}+\frac{a^2\,\sin\left(c+d\,x\right)}{b^3\,d}-\frac{2\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^4\,d}-\frac{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{a^4\,\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^4\,d\,\sqrt{b^2-a^2}}","Not used",1,"(3*sin(c + d*x))/(4*b*d) + sin(3*c + 3*d*x)/(12*b*d) - (a*sin(2*c + 2*d*x))/(4*b^2*d) + (a^2*sin(c + d*x))/(b^3*d) - (2*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^4*d) - (a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d) + (a^4*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^4*d*(b^2 - a^2)^(1/2))","B"
451,1,168,110,1.069102,"\text{Not used}","int(cos(c + d*x)^3/(a + b*cos(c + d*x)),x)","\frac{\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d}+\frac{\sin\left(2\,c+2\,d\,x\right)}{4\,b\,d}+\frac{2\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^3\,d}-\frac{a\,\sin\left(c+d\,x\right)}{b^2\,d}-\frac{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,"atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(b*d) + sin(2*c + 2*d*x)/(4*b*d) + (2*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^3*d) - (a*sin(c + d*x))/(b^2*d) - (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"
452,1,190,76,0.905158,"\text{Not used}","int(cos(c + d*x)^2/(a + b*cos(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)}{b\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b^2\,d}-\frac{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,"sin(c + d*x)/(b*d) - (2*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d) - (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"
453,1,99,59,0.776478,"\text{Not used}","int(cos(c + d*x)/(a + b*cos(c + d*x)),x)","\frac{2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{b\,d}+\frac{2\,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*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d) + (2*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"
454,1,43,49,0.516937,"\text{Not used}","int(1/(a + b*cos(c + d*x)),x)","\frac{2\,\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*atan((tan(c/2 + (d*x)/2)*(a - b))/(a^2 - b^2)^(1/2)))/(d*(a^2 - b^2)^(1/2))","B"
455,1,99,68,0.836500,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*cos(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a\,d}+\frac{2\,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*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) + (2*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"
456,1,324,85,1.045103,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))),x)","\frac{a^3\,\sin\left(c+d\,x\right)-a\,b^2\,\sin\left(c+d\,x\right)}{a^2\,d\,\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)}-\frac{2\,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)-2\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,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}}{a^2\,d\,\left(a^2-b^2\right)}","Not used",1,"(a^3*sin(c + d*x) - a*b^2*sin(c + d*x))/(a^2*d*cos(c + d*x)*(a^2 - b^2)) - (2*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - 2*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 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"
457,1,1087,119,1.764025,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*cos(c + d*x))),x)","\frac{a\,\left(\frac{\sin\left(c+d\,x\right)}{2}+\frac{\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\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{\frac{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^2\,\sin\left(c+d\,x\right)}{2}+\frac{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{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^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^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^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^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^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,"(a*(sin(c + d*x)/2 + atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/2 + (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^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 - (b^2*sin(c + d*x))/2 + (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)) - (b*sin(2*c + 2*d*x))/(2*d*(a^2 - b^2)*(cos(2*c + 2*d*x)/2 + 1/2)) - (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^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^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^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^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"
458,1,991,157,2.676097,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*cos(c + d*x))),x)","\frac{a^5\,\left(\frac{\sin\left(c+d\,x\right)}{2}+\frac{\sin\left(3\,c+3\,d\,x\right)}{6}\right)-a^4\,\left(\frac{b\,\sin\left(2\,c+2\,d\,x\right)}{4}+\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(3\,c+3\,d\,x\right)}{4}+\frac{3\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}\right)-a^2\,\left(\frac{3\,b^3\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}-\frac{b^3\,\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{4}\right)-a^3\,\left(\frac{b^2\,\sin\left(c+d\,x\right)}{4}-\frac{b^2\,\sin\left(3\,c+3\,d\,x\right)}{12}\right)-a\,\left(\frac{b^4\,\sin\left(c+d\,x\right)}{4}+\frac{b^4\,\sin\left(3\,c+3\,d\,x\right)}{4}\right)+\frac{3\,b^5\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{b^5\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,b^4\,\mathrm{atanh}\left(\frac{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}}{\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(c+d\,x\right)\,\sqrt{b^2-a^2}}{2}+\frac{b^4\,\mathrm{atanh}\left(\frac{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}}{\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(3\,c+3\,d\,x\right)\,\sqrt{b^2-a^2}}{2}}{a^4\,d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\left(a^2-b^2\right)}","Not used",1,"(a^5*(sin(c + d*x)/2 + sin(3*c + 3*d*x)/6) - a^4*((b*sin(2*c + 2*d*x))/4 + (b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4 + (3*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4) - a^2*((3*b^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - (b^3*sin(2*c + 2*d*x))/4 + (b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/4) - a^3*((b^2*sin(c + d*x))/4 - (b^2*sin(3*c + 3*d*x))/12) - a*((b^4*sin(c + d*x))/4 + (b^4*sin(3*c + 3*d*x))/4) + (3*b^5*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (b^5*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 + (3*b^4*atanh((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))/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(a^7 - 3*a^3*b^4 + 2*a^5*b^2)))*cos(c + d*x)*(b^2 - a^2)^(1/2))/2 + (b^4*atanh((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))/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(a^7 - 3*a^3*b^4 + 2*a^5*b^2)))*cos(3*c + 3*d*x)*(b^2 - a^2)^(1/2))/2)/(a^4*d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^2 - b^2))","B"
459,1,3852,266,7.205211,"\text{Not used}","int(cos(c + d*x)^5/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-36\,a^5-6\,a^4\,b+19\,a^3\,b^2+7\,a^2\,b^3+8\,a\,b^4-b^5\right)}{3\,b^4\,\left(a+b\right)\,\left(a-b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(4\,a^5-2\,a^4\,b-3\,a^3\,b^2+a^2\,b^3+b^5\right)}{b^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-36\,a^5+6\,a^4\,b+19\,a^3\,b^2-7\,a^2\,b^3+8\,a\,b^4+b^5\right)}{3\,b^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-4\,a^5-2\,a^4\,b+3\,a^3\,b^2+a^2\,b^3+b^5\right)}{b^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(4\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(4\,a+2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^5}\right)}{b^5}+\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^5}\right)}{b^5}}{\frac{64\,\left(64\,a^{14}-32\,a^{13}\,b-112\,a^{12}\,b^2+48\,a^{11}\,b^3+12\,a^{10}\,b^4-6\,a^9\,b^5+31\,a^8\,b^6-5\,a^7\,b^7+5\,a^6\,b^8\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}+\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(4\,a^2+b^2\right)\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,1{}\mathrm{i}}{b^5}\right)\,1{}\mathrm{i}}{b^5}}\right)\,\left(4\,a^2+b^2\right)}{b^5\,d}-\frac{a^4\,\mathrm{atan}\left(\frac{\frac{a^4\,\left(4\,a^2-5\,b^2\right)\,\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(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a^4\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{32\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,1{}\mathrm{i}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}+\frac{a^4\,\left(4\,a^2-5\,b^2\right)\,\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(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^4\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{32\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)\,1{}\mathrm{i}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}{\frac{64\,\left(64\,a^{14}-32\,a^{13}\,b-112\,a^{12}\,b^2+48\,a^{11}\,b^3+12\,a^{10}\,b^4-6\,a^9\,b^5+31\,a^8\,b^6-5\,a^7\,b^7+5\,a^6\,b^8\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{a^4\,\left(4\,a^2-5\,b^2\right)\,\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(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a^4\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}-\frac{32\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}+\frac{a^4\,\left(4\,a^2-5\,b^2\right)\,\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(32\,a^{12}-32\,a^{11}\,b-48\,a^{10}\,b^2+48\,a^9\,b^3+2\,a^8\,b^4-2\,a^7\,b^5+7\,a^6\,b^6-12\,a^5\,b^7+7\,a^4\,b^8-2\,a^3\,b^9+a^2\,b^{10}\right)}{-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a^4\,\left(\frac{32\,\left(-4\,a^8\,b^{10}+2\,a^7\,b^{11}+9\,a^6\,b^{12}-4\,a^5\,b^{13}-5\,a^4\,b^{14}+a^3\,b^{15}+a\,b^{17}\right)}{-a^3\,b^{12}-a^2\,b^{13}+a\,b^{14}+b^{15}}+\frac{32\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^6\,b^{10}+2\,a^5\,b^{11}+4\,a^4\,b^{12}-4\,a^3\,b^{13}-2\,a^2\,b^{14}+2\,a\,b^{15}\right)}{\left(-a^3\,b^8-a^2\,b^9+a\,b^{10}+b^{11}\right)\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}\right)}{-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}}}\right)\,\left(4\,a^2-5\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(-a^6\,b^5+3\,a^4\,b^7-3\,a^2\,b^9+b^{11}\right)}","Not used",1,"- ((2*tan(c/2 + (d*x)/2)^3*(8*a*b^4 - 6*a^4*b - 36*a^5 - b^5 + 7*a^2*b^3 + 19*a^3*b^2))/(3*b^4*(a + b)*(a - b)) - (2*tan(c/2 + (d*x)/2)^7*(4*a^5 - 2*a^4*b + b^5 + a^2*b^3 - 3*a^3*b^2))/(b^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^5*(8*a*b^4 + 6*a^4*b - 36*a^5 + b^5 - 7*a^2*b^3 + 19*a^3*b^2))/(3*b^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(b^5 - 4*a^5 - 2*a^4*b + a^2*b^3 + 3*a^3*b^2))/(b^4*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^8*(a - b) + tan(c/2 + (d*x)/2)^2*(4*a + 2*b) + tan(c/2 + (d*x)/2)^6*(4*a - 2*b) + 6*a*tan(c/2 + (d*x)/2)^4)) - (2*a*atan(((a*(4*a^2 + b^2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a*(4*a^2 + b^2)*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (a*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10)*32i)/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*1i)/b^5))/b^5 + (a*(4*a^2 + b^2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a*(4*a^2 + b^2)*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (a*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10)*32i)/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*1i)/b^5))/b^5)/((64*(64*a^14 - 32*a^13*b + 5*a^6*b^8 - 5*a^7*b^7 + 31*a^8*b^6 - 6*a^9*b^5 + 12*a^10*b^4 + 48*a^11*b^3 - 112*a^12*b^2))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (a*(4*a^2 + b^2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a*(4*a^2 + b^2)*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (a*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10)*32i)/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*1i)/b^5)*1i)/b^5 + (a*(4*a^2 + b^2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a*(4*a^2 + b^2)*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (a*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10)*32i)/(b^5*(a*b^10 + b^11 - a^2*b^9 - a^3*b^8)))*1i)/b^5)*1i)/b^5))*(4*a^2 + b^2))/(b^5*d) - (a^4*atan(((a^4*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^4*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (32*a^4*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) + (a^4*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^4*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (32*a^4*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))*1i)/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))/((64*(64*a^14 - 32*a^13*b + 5*a^6*b^8 - 5*a^7*b^7 + 31*a^8*b^6 - 6*a^9*b^5 + 12*a^10*b^4 + 48*a^11*b^3 - 112*a^12*b^2))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (a^4*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) + (a^4*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) - (32*a^4*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5) + (a^4*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*a^12 - 32*a^11*b + a^2*b^10 - 2*a^3*b^9 + 7*a^4*b^8 - 12*a^5*b^7 + 7*a^6*b^6 - 2*a^7*b^5 + 2*a^8*b^4 + 48*a^9*b^3 - 48*a^10*b^2))/(a*b^10 + b^11 - a^2*b^9 - a^3*b^8) - (a^4*((32*(a*b^17 + a^3*b^15 - 5*a^4*b^14 - 4*a^5*b^13 + 9*a^6*b^12 + 2*a^7*b^11 - 4*a^8*b^10))/(a*b^14 + b^15 - a^2*b^13 - a^3*b^12) + (32*a^4*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^15 - 2*a^2*b^14 - 4*a^3*b^13 + 4*a^4*b^12 + 2*a^5*b^11 - 2*a^6*b^10))/((a*b^10 + b^11 - a^2*b^9 - a^3*b^8)*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))/(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5)))*(4*a^2 - 5*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(b^11 - 3*a^2*b^9 + 3*a^4*b^7 - a^6*b^5))","B"
460,1,3751,166,7.039469,"\text{Not used}","int(cos(c + d*x)^4/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^4+3\,a^3\,b-5\,a^2\,b^2-3\,a\,b^3+b^4\right)}{\left(a\,b^3-b^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^4-3\,a^3\,b-5\,a^2\,b^2+3\,a\,b^3+b^4\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\,a^4+3\,a^2\,b^2+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(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\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(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\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)}{2\,b^4}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\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(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\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)}{2\,b^4}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,b^4}}{\frac{16\,\left(108\,a^{11}-54\,a^{10}\,b-216\,a^9\,b^2+81\,a^8\,b^3+63\,a^7\,b^4-9\,a^6\,b^5+41\,a^5\,b^6-4\,a^4\,b^7+4\,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(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\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(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\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)}{2\,b^4}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\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(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\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)}{2\,b^4}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^4}}\right)\,\left(a^2\,6{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^4\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a^3\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a^3\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)\,1{}\mathrm{i}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}{\frac{16\,\left(108\,a^{11}-54\,a^{10}\,b-216\,a^9\,b^2+81\,a^8\,b^3+63\,a^7\,b^4-9\,a^6\,b^5+41\,a^5\,b^6-4\,a^4\,b^7+4\,a^3\,b^8\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a^3\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}-\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}+\frac{a^3\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{10}-72\,a^9\,b-120\,a^8\,b^2+120\,a^7\,b^3+17\,a^6\,b^4-26\,a^5\,b^5+23\,a^4\,b^6-20\,a^3\,b^7+11\,a^2\,b^8-2\,a\,b^9+b^{10}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a^3\,\left(\frac{8\,\left(-12\,a^7\,b^8+6\,a^6\,b^9+28\,a^5\,b^{10}-14\,a^4\,b^{11}-16\,a^3\,b^{12}+6\,a^2\,b^{13}+2\,b^{15}\right)}{-a^3\,b^9-a^2\,b^{10}+a\,b^{11}+b^{12}}+\frac{8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}\right)}{-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}}}\right)\,\left(3\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(-a^6\,b^4+3\,a^4\,b^6-3\,a^2\,b^8+b^{10}\right)}","Not used",1,"(atan(((((8*tan(c/2 + (d*x)/2)*(72*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + ((a^2*6i + b^2*1i)*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(a^2*6i + b^2*1i)*(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))))/(2*b^4))*(a^2*6i + b^2*1i)*1i)/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - ((a^2*6i + b^2*1i)*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(a^2*6i + b^2*1i)*(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))))/(2*b^4))*(a^2*6i + b^2*1i)*1i)/(2*b^4))/((16*(108*a^11 - 54*a^10*b + 4*a^3*b^8 - 4*a^4*b^7 + 41*a^5*b^6 - 9*a^6*b^5 + 63*a^7*b^4 + 81*a^8*b^3 - 216*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*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + ((a^2*6i + b^2*1i)*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (4*tan(c/2 + (d*x)/2)*(a^2*6i + b^2*1i)*(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))))/(2*b^4))*(a^2*6i + b^2*1i))/(2*b^4) + (((8*tan(c/2 + (d*x)/2)*(72*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - ((a^2*6i + b^2*1i)*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (4*tan(c/2 + (d*x)/2)*(a^2*6i + b^2*1i)*(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))))/(2*b^4))*(a^2*6i + b^2*1i))/(2*b^4)))*(a^2*6i + b^2*1i)*1i)/(b^4*d) - ((tan(c/2 + (d*x)/2)*(3*a^3*b - 3*a*b^3 + 6*a^4 + b^4 - 5*a^2*b^2))/((a*b^3 - b^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(3*a*b^3 - 3*a^3*b + 6*a^4 + b^4 - 5*a^2*b^2))/((a*b^3 - b^4)*(a + b)) - (2*tan(c/2 + (d*x)/2)^3*(b^4 - 6*a^4 + 3*a^2*b^2))/(b*(a*b^2 - b^3)*(a + b)))/(d*(a + b + tan(c/2 + (d*x)/2)^2*(3*a + b) + tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) + (a^3*atan(((a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^3*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a^3*tan(c/2 + (d*x)/2)*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((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)))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^3*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a^3*tan(c/2 + (d*x)/2)*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((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)))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))*1i)/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))/((16*(108*a^11 - 54*a^10*b + 4*a^3*b^8 - 4*a^4*b^7 + 41*a^5*b^6 - 9*a^6*b^5 + 63*a^7*b^4 + 81*a^8*b^3 - 216*a^9*b^2))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a^3*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) - (8*a^3*tan(c/2 + (d*x)/2)*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((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)))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4) + (a^3*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^10 - 72*a^9*b - 2*a*b^9 + b^10 + 11*a^2*b^8 - 20*a^3*b^7 + 23*a^4*b^6 - 26*a^5*b^5 + 17*a^6*b^4 + 120*a^7*b^3 - 120*a^8*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^3*((8*(2*b^15 + 6*a^2*b^13 - 16*a^3*b^12 - 14*a^4*b^11 + 28*a^5*b^10 + 6*a^6*b^9 - 12*a^7*b^8))/(a*b^11 + b^12 - a^2*b^10 - a^3*b^9) + (8*a^3*tan(c/2 + (d*x)/2)*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/((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)))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))/(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4)))*(3*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(b^10 - 3*a^2*b^8 + 3*a^4*b^6 - a^6*b^4))","B"
461,1,3180,155,6.123634,"\text{Not used}","int(cos(c + d*x)^3/(a + b*cos(c + d*x))^2,x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-2\,a^3+a^2\,b+a\,b^2-b^3\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^3-a^2\,b+a\,b^2+b^3\right)}{b^2\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{4\,a\,\mathrm{atan}\left(\frac{\frac{2\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)}{b^3}+\frac{2\,a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)}{b^3}}{\frac{64\,\left(8\,a^8-4\,a^7\,b-20\,a^6\,b^2+6\,a^5\,b^3+12\,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(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)\,2{}\mathrm{i}}{b^3}+\frac{a\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^6\,b^6+2\,a^5\,b^7+4\,a^4\,b^8-4\,a^3\,b^9-2\,a^2\,b^{10}+2\,a\,b^{11}\right)\,64{}\mathrm{i}}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)\,2{}\mathrm{i}}{b^3}\right)\,2{}\mathrm{i}}{b^3}}\right)}{b^3\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-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}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-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}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}{\frac{64\,\left(8\,a^8-4\,a^7\,b-20\,a^6\,b^2+6\,a^5\,b^3+12\,a^4\,b^4\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{a^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}+\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}-\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-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}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}+\frac{a^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^8-8\,a^7\,b-16\,a^6\,b^2+16\,a^5\,b^3+5\,a^4\,b^4-8\,a^3\,b^5+4\,a^2\,b^6\right)}{-a^3\,b^4-a^2\,b^5+a\,b^6+b^7}-\frac{a^2\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{32\,\left(-2\,a^6\,b^6+a^5\,b^7+5\,a^4\,b^8-3\,a^3\,b^9-3\,a^2\,b^{10}+2\,a\,b^{11}\right)}{-a^3\,b^6-a^2\,b^7+a\,b^8+b^9}+\frac{32\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-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}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9}}\right)\,\left(2\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(-a^6\,b^3+3\,a^4\,b^5-3\,a^2\,b^7+b^9\right)}","Not used",1,"- ((2*tan(c/2 + (d*x)/2)^3*(a*b^2 + a^2*b - 2*a^3 - b^3))/(b^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(a*b^2 - a^2*b - 2*a^3 + b^3))/(b^2*(a + b)*(a - b)))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) + 2*a*tan(c/2 + (d*x)/2)^2)) - (4*a*atan(((2*a*((32*tan(c/2 + (d*x)/2)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3))/b^3 + (2*a*((32*tan(c/2 + (d*x)/2)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3))/b^3)/((64*(8*a^8 - 4*a^7*b + 12*a^4*b^4 + 6*a^5*b^3 - 20*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)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3)*2i)/b^3 + (a*((32*tan(c/2 + (d*x)/2)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (a*tan(c/2 + (d*x)/2)*(2*a*b^11 - 2*a^2*b^10 - 4*a^3*b^9 + 4*a^4*b^8 + 2*a^5*b^7 - 2*a^6*b^6)*64i)/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4)))*2i)/b^3)*2i)/b^3)))/(b^3*d) - (a^2*atan(((a^2*((32*tan(c/2 + (d*x)/2)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a^2*(2*a^2 - 3*b^2)*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*a^2*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a^2*((32*tan(c/2 + (d*x)/2)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a^2*(2*a^2 - 3*b^2)*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*a^2*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))/((64*(8*a^8 - 4*a^7*b + 12*a^4*b^4 + 6*a^5*b^3 - 20*a^6*b^2))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (a^2*((32*tan(c/2 + (d*x)/2)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) + (a^2*(2*a^2 - 3*b^2)*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) - (32*a^2*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3) + (a^2*((32*tan(c/2 + (d*x)/2)*(8*a^8 - 8*a^7*b + 4*a^2*b^6 - 8*a^3*b^5 + 5*a^4*b^4 + 16*a^5*b^3 - 16*a^6*b^2))/(a*b^6 + b^7 - a^2*b^5 - a^3*b^4) - (a^2*(2*a^2 - 3*b^2)*((32*(2*a*b^11 - 3*a^2*b^10 - 3*a^3*b^9 + 5*a^4*b^8 + a^5*b^7 - 2*a^6*b^6))/(a*b^8 + b^9 - a^2*b^7 - a^3*b^6) + (32*a^2*tan(c/2 + (d*x)/2)*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3)))*(2*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(b^9 - 3*a^2*b^7 + 3*a^4*b^5 - a^6*b^3))","B"
462,1,2872,108,6.207873,"\text{Not used}","int(cos(c + d*x)^2/(a + b*cos(c + d*x))^2,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{\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}}{b^2}-\frac{-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{\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}}{b^2}}{\frac{64\,\left(a^5-a^4\,b-3\,a^3\,b^2+2\,a^2\,b^3+2\,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(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{\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{\left(-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{\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\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a+b\right)\,\left(a\,b-b^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}+\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)\,1{}\mathrm{i}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}{\frac{64\,\left(a^5-a^4\,b-3\,a^3\,b^2+2\,a^2\,b^3+2\,a\,b^4\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}+\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}-\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}-\frac{a\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-2\,a^5\,b-5\,a^4\,b^2+4\,a^3\,b^3+3\,a^2\,b^4-2\,a\,b^5+b^6\right)}{-a^3\,b^2-a^2\,b^3+a\,b^4+b^5}-\frac{a\,\left(a^2-2\,b^2\right)\,\left(\frac{32\,\left(a^5\,b^4-3\,a^3\,b^6+a^2\,b^7+2\,a\,b^8-b^9\right)}{-a^3\,b^3-a^2\,b^4+a\,b^5+b^6}+\frac{32\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}\right)}{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}}\right)\,\left(a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8\right)}","Not used",1,"(2*atan((((((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 + (32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))/b^2 - ((((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 - (32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))/b^2)/((64*(2*a*b^4 - a^4*b + a^5 + 2*a^2*b^3 - 3*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (((((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 + (32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2 + (((((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (tan(c/2 + (d*x)/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4)*32i)/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))*1i)/b^2 - (32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2))*1i)/b^2)))/(b^2*d) + (a*atan(((a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (a*(a^2 - 2*b^2)*((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*a*tan(c/2 + (d*x)/2)*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) + (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (a*(a^2 - 2*b^2)*((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*a*tan(c/2 + (d*x)/2)*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))*1i)/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2))/((64*(2*a*b^4 - a^4*b + a^5 + 2*a^2*b^3 - 3*a^3*b^2))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) + (a*(a^2 - 2*b^2)*((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) - (32*a*tan(c/2 + (d*x)/2)*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2) - (a*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(2*a^6 - 2*a^5*b - 2*a*b^5 + b^6 + 3*a^2*b^4 + 4*a^3*b^3 - 5*a^4*b^2))/(a*b^4 + b^5 - a^2*b^3 - a^3*b^2) - (a*(a^2 - 2*b^2)*((32*(2*a*b^8 - b^9 + a^2*b^7 - 3*a^3*b^6 + a^5*b^4))/(a*b^5 + b^6 - a^2*b^4 - a^3*b^3) + (32*a*tan(c/2 + (d*x)/2)*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a*b^9 - 2*a^2*b^8 - 4*a^3*b^7 + 4*a^4*b^6 + 2*a^5*b^5 - 2*a^6*b^4))/((a*b^4 + b^5 - a^2*b^3 - a^3*b^2)*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))/(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)))*(a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)) - (2*a^2*tan(c/2 + (d*x)/2))/(d*(a + b)*(a*b - b^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
463,1,99,85,0.738195,"\text{Not used}","int(cos(c + d*x)/(a + b*cos(c + d*x))^2,x)","\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a+b\right)\,\left(a-b\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{2\,b\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a+b}\,\sqrt{a-b}}\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"(2*a*tan(c/2 + (d*x)/2))/(d*(a + b)*(a - b)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b))) - (2*b*atan((tan(c/2 + (d*x)/2)*(2*a - 2*b))/(2*(a + b)^(1/2)*(a - b)^(1/2))))/(d*(a + b)^(3/2)*(a - b)^(3/2))","B"
464,1,99,86,0.706781,"\text{Not used}","int(1/(a + b*cos(c + d*x))^2,x)","\frac{2\,a\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)}{2\,\sqrt{a+b}\,\sqrt{a-b}}\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a+b\right)\,\left(a-b\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*a*atan((tan(c/2 + (d*x)/2)*(2*a - 2*b))/(2*(a + b)^(1/2)*(a - b)^(1/2))))/(d*(a + b)^(3/2)*(a - b)^(3/2)) - (2*b*tan(c/2 + (d*x)/2))/(d*(a + b)*(a - b)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
465,1,2886,118,5.977427,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*cos(c + d*x))^2),x)","-\frac{2\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a+b\right)\,\left(a\,b-a^2\right)\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\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)\,\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)}}{a^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)\,1{}\mathrm{i}}{a^2}-\frac{\left(\frac{\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\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)\,\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)}}{a^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}\right)\,1{}\mathrm{i}}{a^2}}{\frac{\frac{\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\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)\,\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)}}{a^2}-\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}}{a^2}-\frac{64\,\left(2\,a^4\,b+2\,a^3\,b^2-3\,a^2\,b^3-a\,b^4+b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{\frac{\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\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)\,\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)}}{a^2}+\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}}{a^2}}\right)\,2{}\mathrm{i}}{a^2\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(2\,a^2-b^2\right)\,\left(\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(2\,a^2-b^2\right)\,\left(\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}{\frac{64\,\left(2\,a^4\,b+2\,a^3\,b^2-3\,a^2\,b^3-a\,b^4+b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}+\frac{b\,\left(2\,a^2-b^2\right)\,\left(\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^6-2\,a^5\,b+3\,a^4\,b^2+4\,a^3\,b^3-5\,a^2\,b^4-2\,a\,b^5+2\,b^6\right)}{a^5+a^4\,b-a^3\,b^2-a^2\,b^3}-\frac{b\,\left(2\,a^2-b^2\right)\,\left(\frac{32\,\left(-a^9+2\,a^8\,b+a^7\,b^2-3\,a^6\,b^3+a^4\,b^5\right)}{a^6+a^5\,b-a^4\,b^2-a^3\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\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}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6}}\right)\,\left(2\,a^2-b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(a^8-3\,a^6\,b^2+3\,a^4\,b^4-a^2\,b^6\right)}","Not used",1,"- (atan((((((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*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^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2 - ((((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*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^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))*1i)/a^2)/((((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*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^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))/a^2 - (64*(2*a^4*b - a*b^4 + b^5 - 3*a^2*b^3 + 2*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*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^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2))/a^2))*2i)/(a^2*d) - (b*atan(((b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*(2*a^2 - b^2)*((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*(2*a^2 - b^2)*((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))/((64*(2*a^4*b - a*b^4 + b^5 - 3*a^2*b^3 + 2*a^3*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) + (b*(2*a^2 - b^2)*((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) + (32*b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2) + (b*((32*tan(c/2 + (d*x)/2)*(a^6 - 2*a^5*b - 2*a*b^5 + 2*b^6 - 5*a^2*b^4 + 4*a^3*b^3 + 3*a^4*b^2))/(a^4*b + a^5 - a^2*b^3 - a^3*b^2) - (b*(2*a^2 - b^2)*((32*(2*a^8*b - a^9 + a^4*b^5 - 3*a^6*b^3 + a^7*b^2))/(a^5*b + a^6 - a^3*b^3 - a^4*b^2) - (32*b*tan(c/2 + (d*x)/2)*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^9*b - 2*a^4*b^6 + 2*a^5*b^5 + 4*a^6*b^4 - 4*a^7*b^3 - 2*a^8*b^2))/((a^4*b + a^5 - a^2*b^3 - a^3*b^2)*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)))*(2*a^2 - b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(a^8 - a^2*b^6 + 3*a^4*b^4 - 3*a^6*b^2)) - (2*b^2*tan(c/2 + (d*x)/2))/(d*(a + b)*(a*b - a^2)*(a + b + tan(c/2 + (d*x)/2)^2*(a - b)))","B"
466,1,3176,155,5.919795,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^2),x)","-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-a^3+a^2\,b+a\,b^2-2\,b^3\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^3-a^2\,b+a\,b^2+2\,b^3\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{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{2\,b\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{64\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)\,2{}\mathrm{i}}{a^3}+\frac{b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{2\,b\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{64\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)\,2{}\mathrm{i}}{a^3}}{\frac{64\,\left(12\,a^4\,b^4+6\,a^3\,b^5-20\,a^2\,b^6-4\,a\,b^7+8\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{2\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{2\,b\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{64\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)}{a^3}+\frac{2\,b\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{2\,b\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{64\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^{11}\,b-2\,a^{10}\,b^2-4\,a^9\,b^3+4\,a^8\,b^4+2\,a^7\,b^5-2\,a^6\,b^6\right)}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)}{a^3}\right)}{a^3}}\right)\,4{}\mathrm{i}}{a^3\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(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}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}+\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(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}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}{\frac{64\,\left(12\,a^4\,b^4+6\,a^3\,b^5-20\,a^2\,b^6-4\,a\,b^7+8\,b^8\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}+\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(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}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}-\frac{b^2\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6\,b^2-8\,a^5\,b^3+5\,a^4\,b^4+16\,a^3\,b^5-16\,a^2\,b^6-8\,a\,b^7+8\,b^8\right)}{a^7+a^6\,b-a^5\,b^2-a^4\,b^3}-\frac{b^2\,\left(3\,a^2-2\,b^2\right)\,\left(\frac{32\,\left(2\,a^{11}\,b-3\,a^{10}\,b^2-3\,a^9\,b^3+5\,a^8\,b^4+a^7\,b^5-2\,a^6\,b^6\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{32\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(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}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6}}\right)\,\left(3\,a^2-2\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(a^9-3\,a^7\,b^2+3\,a^5\,b^4-a^3\,b^6\right)}","Not used",1,"(b*atan(((b*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (2*b*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (64*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3)*2i)/a^3 + (b*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (2*b*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (64*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3)*2i)/a^3)/((64*(8*b^8 - 4*a*b^7 - 20*a^2*b^6 + 6*a^3*b^5 + 12*a^4*b^4))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (2*b*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (2*b*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (64*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3))/a^3 + (2*b*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (2*b*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (64*b*tan(c/2 + (d*x)/2)*(2*a^11*b - 2*a^6*b^6 + 2*a^7*b^5 + 4*a^8*b^4 - 4*a^9*b^3 - 2*a^10*b^2))/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2))))/a^3))/a^3))*4i)/(a^3*d) - ((2*tan(c/2 + (d*x)/2)^3*(a*b^2 + a^2*b - a^3 - 2*b^3))/(a^2*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(a*b^2 - a^2*b - a^3 + 2*b^3))/(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^2*atan(((b^2*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b^2*(3*a^2 - 2*b^2)*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*b^2*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) + (b^2*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b^2*(3*a^2 - 2*b^2)*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*b^2*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*1i)/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))/((64*(8*b^8 - 4*a*b^7 - 20*a^2*b^6 + 6*a^3*b^5 + 12*a^4*b^4))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^2*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) + (b^2*(3*a^2 - 2*b^2)*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (32*b^2*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2) - (b^2*((32*tan(c/2 + (d*x)/2)*(8*b^8 - 8*a*b^7 - 16*a^2*b^6 + 16*a^3*b^5 + 5*a^4*b^4 - 8*a^5*b^3 + 4*a^6*b^2))/(a^6*b + a^7 - a^4*b^3 - a^5*b^2) - (b^2*(3*a^2 - 2*b^2)*((32*(2*a^11*b - 2*a^6*b^6 + a^7*b^5 + 5*a^8*b^4 - 3*a^9*b^3 - 3*a^10*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (32*b^2*tan(c/2 + (d*x)/2)*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(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))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2)))*(3*a^2 - 2*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(a^9 - a^3*b^6 + 3*a^5*b^4 - 3*a^7*b^2))","B"
467,1,3699,217,6.927031,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*cos(c + d*x))^2),x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-3\,a^3\,b-5\,a^2\,b^2+3\,a\,b^3+6\,b^4\right)}{\left(a^3\,b-a^4\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^4+3\,a^3\,b-5\,a^2\,b^2-3\,a\,b^3+6\,b^4\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^4+3\,a^2\,b^2-6\,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(a^2+6\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(a^2+6\,b^2\right)\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\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^2+6\,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)}{2\,a^4}\right)\,1{}\mathrm{i}}{2\,a^4}+\frac{\left(a^2+6\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(a^2+6\,b^2\right)\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\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^2+6\,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)}{2\,a^4}\right)\,1{}\mathrm{i}}{2\,a^4}}{\frac{16\,\left(4\,a^8\,b^3-4\,a^7\,b^4+41\,a^6\,b^5-9\,a^5\,b^6+63\,a^4\,b^7+81\,a^3\,b^8-216\,a^2\,b^9-54\,a\,b^{10}+108\,b^{11}\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{\left(a^2+6\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{\left(a^2+6\,b^2\right)\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\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^2+6\,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)}{2\,a^4}\right)}{2\,a^4}+\frac{\left(a^2+6\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{\left(a^2+6\,b^2\right)\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\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^2+6\,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)}{2\,a^4}\right)}{2\,a^4}}\right)\,\left(a^2+6\,b^2\right)\,1{}\mathrm{i}}{a^4\,d}-\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^3\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^3\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{16\,\left(4\,a^8\,b^3-4\,a^7\,b^4+41\,a^6\,b^5-9\,a^5\,b^6+63\,a^4\,b^7+81\,a^3\,b^8-216\,a^2\,b^9-54\,a\,b^{10}+108\,b^{11}\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}+\frac{b^3\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}+\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}-\frac{b^3\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,a^7\,b^3+23\,a^6\,b^4-26\,a^5\,b^5+17\,a^4\,b^6+120\,a^3\,b^7-120\,a^2\,b^8-72\,a\,b^9+72\,b^{10}\right)}{a^9+a^8\,b-a^7\,b^2-a^6\,b^3}-\frac{b^3\,\left(\frac{8\,\left(2\,a^{15}+6\,a^{13}\,b^2-16\,a^{12}\,b^3-14\,a^{11}\,b^4+28\,a^{10}\,b^5+6\,a^9\,b^6-12\,a^8\,b^7\right)}{a^{12}+a^{11}\,b-a^{10}\,b^2-a^9\,b^3}-\frac{8\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(8\,a^{13}\,b-8\,a^{12}\,b^2-16\,a^{11}\,b^3+16\,a^{10}\,b^4+8\,a^9\,b^5-8\,a^8\,b^6\right)}{\left(a^9+a^8\,b-a^7\,b^2-a^6\,b^3\right)\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\left(4\,a^2-3\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)*(3*a*b^3 - 3*a^3*b + a^4 + 6*b^4 - 5*a^2*b^2))/((a^3*b - a^4)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(3*a^3*b - 3*a*b^3 + a^4 + 6*b^4 - 5*a^2*b^2))/((a^3*b - a^4)*(a + b)) + (2*tan(c/2 + (d*x)/2)^3*(a^4 - 6*b^4 + 3*a^2*b^2))/(a*(a^2*b - a^3)*(a + b)))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) + tan(c/2 + (d*x)/2)^6*(a - b))) - (atan((((a^2 + 6*b^2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - ((a^2 + 6*b^2)*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2 + 6*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^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/(2*a^4))*1i)/(2*a^4) + ((a^2 + 6*b^2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + ((a^2 + 6*b^2)*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2 + 6*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^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/(2*a^4))*1i)/(2*a^4))/((16*(108*b^11 - 54*a*b^10 - 216*a^2*b^9 + 81*a^3*b^8 + 63*a^4*b^7 - 9*a^5*b^6 + 41*a^6*b^5 - 4*a^7*b^4 + 4*a^8*b^3))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - ((a^2 + 6*b^2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - ((a^2 + 6*b^2)*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2 + 6*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^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/(2*a^4)))/(2*a^4) + ((a^2 + 6*b^2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + ((a^2 + 6*b^2)*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2 + 6*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^4*(a^8*b + a^9 - a^6*b^3 - a^7*b^2))))/(2*a^4)))/(2*a^4)))*(a^2 + 6*b^2)*1i)/(a^4*d) - (b^3*atan(((b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^3*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b^3*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((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)))*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^3*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b^3*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((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)))*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((16*(108*b^11 - 54*a*b^10 - 216*a^2*b^9 + 81*a^3*b^8 + 63*a^4*b^7 - 9*a^5*b^6 + 41*a^6*b^5 - 4*a^7*b^4 + 4*a^8*b^3))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) + (b^3*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) + (8*b^3*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((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)))*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) - (b^3*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 72*a*b^9 + 72*b^10 - 120*a^2*b^8 + 120*a^3*b^7 + 17*a^4*b^6 - 26*a^5*b^5 + 23*a^6*b^4 - 20*a^7*b^3 + 11*a^8*b^2))/(a^8*b + a^9 - a^6*b^3 - a^7*b^2) - (b^3*((8*(2*a^15 - 12*a^8*b^7 + 6*a^9*b^6 + 28*a^10*b^5 - 14*a^11*b^4 - 16*a^12*b^3 + 6*a^13*b^2))/(a^11*b + a^12 - a^9*b^3 - a^10*b^2) - (8*b^3*tan(c/2 + (d*x)/2)*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(8*a^13*b - 8*a^8*b^6 + 8*a^9*b^5 + 16*a^10*b^4 - 16*a^11*b^3 - 8*a^12*b^2))/((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)))*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(4*a^2 - 3*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
468,1,3843,270,7.092915,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b*cos(c + d*x))^2),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^5+a^3\,b^2-3\,a^2\,b^3-2\,a\,b^4+4\,b^5\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^5-8\,a^4\,b-7\,a^3\,b^2-19\,a^2\,b^3+6\,a\,b^4+36\,b^5\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^5+8\,a^4\,b-7\,a^3\,b^2+19\,a^2\,b^3+6\,a\,b^4-36\,b^5\right)}{3\,a^4\,\left(a+b\right)\,\left(a-b\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^5+a^3\,b^2+3\,a^2\,b^3-2\,a\,b^4-4\,b^5\right)}{a^4\,\left(a+b\right)\,\left(a-b\right)}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-2\,a-4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}+\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}}{\frac{64\,\left(5\,a^8\,b^6-5\,a^7\,b^7+31\,a^6\,b^8-6\,a^5\,b^9+12\,a^4\,b^{10}+48\,a^3\,b^{11}-112\,a^2\,b^{12}-32\,a\,b^{13}+64\,b^{14}\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)}{a^5}\right)}{a^5}-\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b\,\left(a^2+4\,b^2\right)\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,b^2\right)\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)}{a^5}\right)}{a^5}}\right)\,\left(a^2+4\,b^2\right)\,2{}\mathrm{i}}{a^5\,d}+\frac{b^4\,\mathrm{atan}\left(\frac{\frac{b^4\,\left(5\,a^2-4\,b^2\right)\,\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^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^4\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}+\frac{b^4\,\left(5\,a^2-4\,b^2\right)\,\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^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^4\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)\,1{}\mathrm{i}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}{\frac{64\,\left(5\,a^8\,b^6-5\,a^7\,b^7+31\,a^6\,b^8-6\,a^5\,b^9+12\,a^4\,b^{10}+48\,a^3\,b^{11}-112\,a^2\,b^{12}-32\,a\,b^{13}+64\,b^{14}\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{b^4\,\left(5\,a^2-4\,b^2\right)\,\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^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b^4\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{32\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}-\frac{b^4\,\left(5\,a^2-4\,b^2\right)\,\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^{10}\,b^2-2\,a^9\,b^3+7\,a^8\,b^4-12\,a^7\,b^5+7\,a^6\,b^6-2\,a^5\,b^7+2\,a^4\,b^8+48\,a^3\,b^9-48\,a^2\,b^{10}-32\,a\,b^{11}+32\,b^{12}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b^4\,\left(\frac{32\,\left(a^{17}\,b+a^{15}\,b^3-5\,a^{14}\,b^4-4\,a^{13}\,b^5+9\,a^{12}\,b^6+2\,a^{11}\,b^7-4\,a^{10}\,b^8\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{32\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(2\,a^{15}\,b-2\,a^{14}\,b^2-4\,a^{13}\,b^3+4\,a^{12}\,b^4+2\,a^{11}\,b^5-2\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}\right)}{a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6}}\right)\,\left(5\,a^2-4\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^7*(a^5 - 2*a*b^4 + 4*b^5 - 3*a^2*b^3 + a^3*b^2))/(a^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(6*a*b^4 - 8*a^4*b + a^5 + 36*b^5 - 19*a^2*b^3 - 7*a^3*b^2))/(3*a^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)^5*(6*a*b^4 + 8*a^4*b + a^5 - 36*b^5 + 19*a^2*b^3 - 7*a^3*b^2))/(3*a^4*(a + b)*(a - b)) + (2*tan(c/2 + (d*x)/2)*(a^5 - 2*a*b^4 - 4*b^5 + 3*a^2*b^3 + a^3*b^2))/(a^4*(a + b)*(a - b)))/(d*(a + b - tan(c/2 + (d*x)/2)^8*(a - b) - tan(c/2 + (d*x)/2)^2*(2*a + 4*b) + tan(c/2 + (d*x)/2)^6*(2*a - 4*b) + 6*b*tan(c/2 + (d*x)/2)^4)) + (b*atan(((b*(a^2 + 4*b^2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b*(a^2 + 4*b^2)*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b*tan(c/2 + (d*x)/2)*(a^2 + 4*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2))))/a^5)*1i)/a^5 + (b*(a^2 + 4*b^2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b*(a^2 + 4*b^2)*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b*tan(c/2 + (d*x)/2)*(a^2 + 4*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2))))/a^5)*1i)/a^5)/((64*(64*b^14 - 32*a*b^13 - 112*a^2*b^12 + 48*a^3*b^11 + 12*a^4*b^10 - 6*a^5*b^9 + 31*a^6*b^8 - 5*a^7*b^7 + 5*a^8*b^6))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (b*(a^2 + 4*b^2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b*(a^2 + 4*b^2)*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b*tan(c/2 + (d*x)/2)*(a^2 + 4*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2))))/a^5))/a^5 - (b*(a^2 + 4*b^2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b*(a^2 + 4*b^2)*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b*tan(c/2 + (d*x)/2)*(a^2 + 4*b^2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2))))/a^5))/a^5))*(a^2 + 4*b^2)*2i)/(a^5*d) + (b^4*atan(((b^4*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^4*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) + (b^4*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^4*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))*1i)/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))/((64*(64*b^14 - 32*a*b^13 - 112*a^2*b^12 + 48*a^3*b^11 + 12*a^4*b^10 - 6*a^5*b^9 + 31*a^6*b^8 - 5*a^7*b^7 + 5*a^8*b^6))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (b^4*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b^4*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (32*b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2) - (b^4*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((32*tan(c/2 + (d*x)/2)*(32*b^12 - 32*a*b^11 - 48*a^2*b^10 + 48*a^3*b^9 + 2*a^4*b^8 - 2*a^5*b^7 + 7*a^6*b^6 - 12*a^7*b^5 + 7*a^8*b^4 - 2*a^9*b^3 + a^10*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b^4*((32*(a^17*b - 4*a^10*b^8 + 2*a^11*b^7 + 9*a^12*b^6 - 4*a^13*b^5 - 5*a^14*b^4 + a^15*b^3))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (32*b^4*tan(c/2 + (d*x)/2)*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*(2*a^15*b - 2*a^10*b^6 + 2*a^11*b^5 + 4*a^12*b^4 - 4*a^13*b^3 - 2*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))/(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*(5*a^2 - 4*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
469,1,5962,300,8.670048,"\text{Not used}","int(cos(c + d*x)^5/(a + b*cos(c + d*x))^3,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^7+18\,a^6\,b-67\,a^5\,b^2-29\,a^4\,b^3+26\,a^3\,b^4+5\,a^2\,b^5-4\,a\,b^6+3\,b^7\right)}{{\left(a+b\right)}^2\,\left(a^2\,b^4-2\,a\,b^5+b^6\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-36\,a^7+18\,a^6\,b+67\,a^5\,b^2-29\,a^4\,b^3-26\,a^3\,b^4+5\,a^2\,b^5+4\,a\,b^6+3\,b^7\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(-12\,a^6+6\,a^5\,b+23\,a^4\,b^2-10\,a^3\,b^3-8\,a^2\,b^4+5\,a\,b^5+b^6\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(12\,a^6+6\,a^5\,b-23\,a^4\,b^2-10\,a^3\,b^3+8\,a^2\,b^4+5\,a\,b^5-b^6\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(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,b^5}}{\frac{8\,\left(1728\,a^{15}-864\,a^{14}\,b-7344\,a^{13}\,b^2+3456\,a^{12}\,b^3+11700\,a^{11}\,b^4-4770\,a^{10}\,b^5-7829\,a^9\,b^6+2326\,a^8\,b^7+1314\,a^7\,b^8-11\,a^6\,b^9+411\,a^5\,b^{10}-20\,a^4\,b^{11}+20\,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(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\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(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)}{2\,b^5}}\right)\,\left(a^2\,12{}\mathrm{i}+b^2\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{b^5\,d}+\frac{a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{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(1728\,a^{15}-864\,a^{14}\,b-7344\,a^{13}\,b^2+3456\,a^{12}\,b^3+11700\,a^{11}\,b^4-4770\,a^{10}\,b^5-7829\,a^9\,b^6+2326\,a^8\,b^7+1314\,a^7\,b^8-11\,a^6\,b^9+411\,a^5\,b^{10}-20\,a^4\,b^{11}+20\,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^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}+\frac{a^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(288\,a^{14}-288\,a^{13}\,b-1104\,a^{12}\,b^2+1104\,a^{11}\,b^3+1538\,a^{10}\,b^4-1538\,a^9\,b^5-827\,a^8\,b^6+872\,a^7\,b^7+18\,a^6\,b^8-108\,a^5\,b^9+74\,a^4\,b^{10}-40\,a^3\,b^{11}+21\,a^2\,b^{12}-2\,a\,b^{13}+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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-48\,a^{11}\,b^{10}+24\,a^{10}\,b^{11}+212\,a^9\,b^{12}-100\,a^8\,b^{13}-360\,a^7\,b^{14}+164\,a^6\,b^{15}+276\,a^5\,b^{16}-120\,a^4\,b^{17}-80\,a^3\,b^{18}+28\,a^2\,b^{19}+4\,b^{21}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,\left(-8\,a^{10}\,b^{10}+8\,a^9\,b^{11}+32\,a^8\,b^{12}-32\,a^7\,b^{13}-48\,a^6\,b^{14}+48\,a^5\,b^{15}+32\,a^4\,b^{16}-32\,a^3\,b^{17}-8\,a^2\,b^{18}+8\,a\,b^{19}\right)}{\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)\,\left(-a^7\,b^8-a^6\,b^9+3\,a^5\,b^{10}+3\,a^4\,b^{11}-3\,a^3\,b^{12}-3\,a^2\,b^{13}+a\,b^{14}+b^{15}\right)}\right)\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)}{2\,\left(-a^{10}\,b^5+5\,a^8\,b^7-10\,a^6\,b^9+10\,a^4\,b^{11}-5\,a^2\,b^{13}+b^{15}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(12\,a^4-29\,a^2\,b^2+20\,b^4\right)\,1{}\mathrm{i}}{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,"(atan(((((8*tan(c/2 + (d*x)/2)*(288*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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)*(a^2*12i + b^2*1i)*(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)))*(a^2*12i + b^2*1i))/(2*b^5))*(a^2*12i + b^2*1i)*1i)/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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)*(a^2*12i + b^2*1i)*(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)))*(a^2*12i + b^2*1i))/(2*b^5))*(a^2*12i + b^2*1i)*1i)/(2*b^5))/((8*(1728*a^15 - 864*a^14*b + 20*a^3*b^12 - 20*a^4*b^11 + 411*a^5*b^10 - 11*a^6*b^9 + 1314*a^7*b^8 + 2326*a^8*b^7 - 7829*a^9*b^6 - 4770*a^10*b^5 + 11700*a^11*b^4 + 3456*a^12*b^3 - 7344*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*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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)*(a^2*12i + b^2*1i)*(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)))*(a^2*12i + b^2*1i))/(2*b^5))*(a^2*12i + b^2*1i))/(2*b^5) + (((8*tan(c/2 + (d*x)/2)*(288*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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)*(a^2*12i + b^2*1i)*(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)))*(a^2*12i + b^2*1i))/(2*b^5))*(a^2*12i + b^2*1i))/(2*b^5)))*(a^2*12i + b^2*1i)*1i)/(b^5*d) - ((tan(c/2 + (d*x)/2)^3*(18*a^6*b - 4*a*b^6 + 36*a^7 + 3*b^7 + 5*a^2*b^5 + 26*a^3*b^4 - 29*a^4*b^3 - 67*a^5*b^2))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^5*(4*a*b^6 + 18*a^6*b - 36*a^7 + 3*b^7 + 5*a^2*b^5 - 26*a^3*b^4 - 29*a^4*b^3 + 67*a^5*b^2))/((a + b)^2*(b^6 - 2*a*b^5 + a^2*b^4)) - (tan(c/2 + (d*x)/2)^7*(5*a*b^5 + 6*a^5*b - 12*a^6 + b^6 - 8*a^2*b^4 - 10*a^3*b^3 + 23*a^4*b^2))/((a*b^4 - b^5)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(5*a*b^5 + 6*a^5*b + 12*a^6 - b^6 + 8*a^2*b^4 - 10*a^3*b^3 - 23*a^4*b^2))/((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)) + (a^3*atan(((a^3*((8*tan(c/2 + (d*x)/2)*(288*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*b^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*1i)/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a^3*((8*tan(c/2 + (d*x)/2)*(288*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*b^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*1i)/(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*a^15 - 864*a^14*b + 20*a^3*b^12 - 20*a^4*b^11 + 411*a^5*b^10 - 11*a^6*b^9 + 1314*a^7*b^8 + 2326*a^8*b^7 - 7829*a^9*b^6 - 4770*a^10*b^5 + 11700*a^11*b^4 + 3456*a^12*b^3 - 7344*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^3*((8*tan(c/2 + (d*x)/2)*(288*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*b^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)) + (a^3*((8*tan(c/2 + (d*x)/2)*(288*a^14 - 288*a^13*b - 2*a*b^13 + b^14 + 21*a^2*b^12 - 40*a^3*b^11 + 74*a^4*b^10 - 108*a^5*b^9 + 18*a^6*b^8 + 872*a^7*b^7 - 827*a^8*b^6 - 1538*a^9*b^5 + 1538*a^10*b^4 + 1104*a^11*b^3 - 1104*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*b^21 + 28*a^2*b^19 - 80*a^3*b^18 - 120*a^4*b^17 + 276*a^5*b^16 + 164*a^6*b^15 - 360*a^7*b^14 - 100*a^8*b^13 + 212*a^9*b^12 + 24*a^10*b^11 - 48*a^11*b^10))/(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^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*(8*a*b^19 - 8*a^2*b^18 - 32*a^3*b^17 + 32*a^4*b^16 + 48*a^5*b^15 - 48*a^6*b^14 - 32*a^7*b^13 + 32*a^8*b^12 + 8*a^9*b^11 - 8*a^10*b^10))/((b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)*(a*b^14 + b^15 - 3*a^2*b^13 - 3*a^3*b^12 + 3*a^4*b^11 + 3*a^5*b^10 - a^6*b^9 - a^7*b^8)))*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5)))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2))/(2*(b^15 - 5*a^2*b^13 + 10*a^4*b^11 - 10*a^6*b^9 + 5*a^8*b^7 - a^10*b^5))))*(-(a + b)^5*(a - b)^5)^(1/2)*(12*a^4 + 20*b^4 - 29*a^2*b^2)*1i)/(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"
470,1,5350,221,8.232203,"\text{Not used}","int(cos(c + d*x)^4/(a + b*cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^5-3\,a^4\,b-12\,a^3\,b^2+4\,a^2\,b^3+2\,a\,b^4-2\,b^5\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\,a^5+3\,a^4\,b-12\,a^3\,b^2-4\,a^2\,b^3+2\,a\,b^4+2\,b^5\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\,a^6-13\,a^4\,b^2+6\,a^2\,b^4-2\,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{6\,a\,\mathrm{atan}\left(\frac{\frac{3\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}+\frac{3\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)}{b^4}}{\frac{48\,\left(36\,a^{12}-18\,a^{11}\,b-162\,a^{10}\,b^2+81\,a^9\,b^3+288\,a^8\,b^4-126\,a^7\,b^5-234\,a^6\,b^6+72\,a^5\,b^7+72\,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(72\,a^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)\,24{}\mathrm{i}}{b^4\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,3{}\mathrm{i}}{b^4}\right)\,3{}\mathrm{i}}{b^4}}\right)}{b^4\,d}-\frac{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^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{3\,a^2\,\left(\frac{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{12\,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(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,3{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{a^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(72\,a^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{3\,a^2\,\left(\frac{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{12\,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(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,3{}\mathrm{i}}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}{\frac{48\,\left(36\,a^{12}-18\,a^{11}\,b-162\,a^{10}\,b^2+81\,a^9\,b^3+288\,a^8\,b^4-126\,a^7\,b^5-234\,a^6\,b^6+72\,a^5\,b^7+72\,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{3\,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^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{3\,a^2\,\left(\frac{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{12\,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(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}+\frac{3\,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^{12}-72\,a^{11}\,b-288\,a^{10}\,b^2+288\,a^9\,b^3+441\,a^8\,b^4-432\,a^7\,b^5-288\,a^6\,b^6+288\,a^5\,b^7+36\,a^4\,b^8-72\,a^3\,b^9+36\,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{3\,a^2\,\left(\frac{24\,\left(-4\,a^{10}\,b^8+2\,a^9\,b^9+18\,a^8\,b^{10}-8\,a^7\,b^{11}-32\,a^6\,b^{12}+14\,a^5\,b^{13}+26\,a^4\,b^{14}-12\,a^3\,b^{15}-8\,a^2\,b^{16}+4\,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{12\,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(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,\left(-8\,a^{10}\,b^8+8\,a^9\,b^9+32\,a^8\,b^{10}-32\,a^7\,b^{11}-48\,a^6\,b^{12}+48\,a^5\,b^{13}+32\,a^4\,b^{14}-32\,a^3\,b^{15}-8\,a^2\,b^{16}+8\,a\,b^{17}\right)}{\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)\,\left(-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}\right)\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)}{2\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+4\,b^4\right)\,3{}\mathrm{i}}{d\,\left(-a^{10}\,b^4+5\,a^8\,b^6-10\,a^6\,b^8+10\,a^4\,b^{10}-5\,a^2\,b^{12}+b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(2*a*b^4 - 3*a^4*b + 6*a^5 - 2*b^5 + 4*a^2*b^3 - 12*a^3*b^2))/((a*b^3 - b^4)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(2*a*b^4 + 3*a^4*b + 6*a^5 + 2*b^5 - 4*a^2*b^3 - 12*a^3*b^2))/((a + b)*(b^5 - 2*a*b^4 + a^2*b^3)) + (2*tan(c/2 + (d*x)/2)^3*(6*a^6 - 2*b^6 + 6*a^2*b^4 - 13*a^4*b^2))/(b*(a*b^2 - b^3)*(a + b)^2*(a - b)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a*b + 3*a^2 - b^2) + tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b - 3*a^2 + b^2))) - (6*a*atan(((3*a*((8*tan(c/2 + (d*x)/2)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4))/b^4 + (3*a*((8*tan(c/2 + (d*x)/2)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4))/b^4)/((48*(36*a^12 - 18*a^11*b + 72*a^4*b^8 + 72*a^5*b^7 - 234*a^6*b^6 - 126*a^7*b^5 + 288*a^8*b^4 + 81*a^9*b^3 - 162*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)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4)*3i)/b^4 + (a*((8*tan(c/2 + (d*x)/2)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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*tan(c/2 + (d*x)/2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8)*24i)/(b^4*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*3i)/b^4)*3i)/b^4)))/(b^4*d) - (a^2*atan(((a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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) + (3*a^2*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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) - (12*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2)*3i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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) - (3*a^2*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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) + (12*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2)*3i)/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))/((48*(36*a^12 - 18*a^11*b + 72*a^4*b^8 + 72*a^5*b^7 - 234*a^6*b^6 - 126*a^7*b^5 + 288*a^8*b^4 + 81*a^9*b^3 - 162*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) - (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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) + (3*a^2*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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) - (12*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)) + (3*a^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*a^12 - 72*a^11*b + 36*a^2*b^10 - 72*a^3*b^9 + 36*a^4*b^8 + 288*a^5*b^7 - 288*a^6*b^6 - 432*a^7*b^5 + 441*a^8*b^4 + 288*a^9*b^3 - 288*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) - (3*a^2*((24*(4*a*b^17 - 8*a^2*b^16 - 12*a^3*b^15 + 26*a^4*b^14 + 14*a^5*b^13 - 32*a^6*b^12 - 8*a^7*b^11 + 18*a^8*b^10 + 2*a^9*b^9 - 4*a^10*b^8))/(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) + (12*a^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*(8*a*b^17 - 8*a^2*b^16 - 32*a^3*b^15 + 32*a^4*b^14 + 48*a^5*b^13 - 48*a^6*b^12 - 32*a^7*b^11 + 32*a^8*b^10 + 8*a^9*b^9 - 8*a^10*b^8))/((b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)*(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4)))*(2*a^4 + 4*b^4 - 5*a^2*b^2))/(2*(b^14 - 5*a^2*b^12 + 10*a^4*b^10 - 10*a^6*b^8 + 5*a^8*b^6 - a^10*b^4))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 4*b^4 - 5*a^2*b^2)*3i)/(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"
471,1,5102,179,8.800873,"\text{Not used}","int(cos(c + d*x)^3/(a + b*cos(c + d*x))^3,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\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{\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}}{b^3}-\frac{-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\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{\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}}{b^3}}{\frac{16\,\left(4\,a^9-2\,a^8\,b-18\,a^7\,b^2+13\,a^6\,b^3+36\,a^5\,b^4-26\,a^4\,b^5-34\,a^3\,b^6+24\,a^2\,b^7+12\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\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{\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{\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\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{\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{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-2\,a^4+a^3\,b+6\,a^2\,b^2\right)}{\left(a\,b^2-b^3\right)\,{\left(a+b\right)}^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4+a^3\,b-6\,a^2\,b^2\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{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{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(4\,a^9-2\,a^8\,b-18\,a^7\,b^2+13\,a^6\,b^3+36\,a^5\,b^4-26\,a^4\,b^5-34\,a^3\,b^6+24\,a^2\,b^7+12\,a\,b^8\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}+\frac{a\,\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-8\,a^9\,b-32\,a^8\,b^2+32\,a^7\,b^3+57\,a^6\,b^4-48\,a^5\,b^5-52\,a^4\,b^6+32\,a^3\,b^7+24\,a^2\,b^8-8\,a\,b^9+4\,b^{10}\right)}{-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}}-\frac{a\,\left(\frac{8\,\left(4\,a^9\,b^6-2\,a^8\,b^7-18\,a^7\,b^8+4\,a^6\,b^9+36\,a^5\,b^{10}-6\,a^4\,b^{11}-34\,a^3\,b^{12}+8\,a^2\,b^{13}+12\,a\,b^{14}-4\,b^{15}\right)}{-a^7\,b^6-a^6\,b^7+3\,a^5\,b^8+3\,a^4\,b^9-3\,a^3\,b^{10}-3\,a^2\,b^{11}+a\,b^{12}+b^{13}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,\left(-8\,a^{10}\,b^6+8\,a^9\,b^7+32\,a^8\,b^8-32\,a^7\,b^9-48\,a^6\,b^{10}+48\,a^5\,b^{11}+32\,a^4\,b^{12}-32\,a^3\,b^{13}-8\,a^2\,b^{14}+8\,a\,b^{15}\right)}{\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)\,\left(-a^7\,b^4-a^6\,b^5+3\,a^5\,b^6+3\,a^4\,b^7-3\,a^3\,b^8-3\,a^2\,b^9+a\,b^{10}+b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)}{2\,\left(-a^{10}\,b^3+5\,a^8\,b^5-10\,a^6\,b^7+10\,a^4\,b^9-5\,a^2\,b^{11}+b^{13}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a^4-5\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{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*atan((((((8*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(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 - ((((8*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(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)/((((((8*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 + (8*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(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*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (tan(c/2 + (d*x)/2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6)*8i)/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*1i)/b^3 - (8*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(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*(12*a*b^8 - 2*a^8*b + 4*a^9 + 24*a^2*b^7 - 34*a^3*b^6 - 26*a^4*b^5 + 36*a^5*b^4 + 13*a^6*b^3 - 18*a^7*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))))/(b^3*d) + ((tan(c/2 + (d*x)/2)^3*(a^3*b - 2*a^4 + 6*a^2*b^2))/((a*b^2 - b^3)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(a^3*b + 2*a^4 - 6*a^2*b^2))/((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)) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (a*((8*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*1i)/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) + (a*((8*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (a*((8*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*1i)/(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*(12*a*b^8 - 2*a^8*b + 4*a^9 + 24*a^2*b^7 - 34*a^3*b^6 - 26*a^4*b^5 + 36*a^5*b^4 + 13*a^6*b^3 - 18*a^7*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*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) + (a*((8*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)) - (a*((8*tan(c/2 + (d*x)/2)*(8*a^10 - 8*a^9*b - 8*a*b^9 + 4*b^10 + 24*a^2*b^8 + 32*a^3*b^7 - 52*a^4*b^6 - 48*a^5*b^5 + 57*a^6*b^4 + 32*a^7*b^3 - 32*a^8*b^2))/(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4) - (a*((8*(12*a*b^14 - 4*b^15 + 8*a^2*b^13 - 34*a^3*b^12 - 6*a^4*b^11 + 36*a^5*b^10 + 4*a^6*b^9 - 18*a^7*b^8 - 2*a^8*b^7 + 4*a^9*b^6))/(a*b^12 + b^13 - 3*a^2*b^11 - 3*a^3*b^10 + 3*a^4*b^9 + 3*a^5*b^8 - a^6*b^7 - a^7*b^6) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*(8*a*b^15 - 8*a^2*b^14 - 32*a^3*b^13 + 32*a^4*b^12 + 48*a^5*b^11 - 48*a^6*b^10 - 32*a^7*b^9 + 32*a^8*b^8 + 8*a^9*b^7 - 8*a^10*b^6))/((b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3)))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2))/(2*(b^13 - 5*a^2*b^11 + 10*a^4*b^9 - 10*a^6*b^7 + 5*a^8*b^5 - a^10*b^3))))*(-(a + b)^5*(a - b)^5)^(1/2)*(2*a^4 + 6*b^4 - 5*a^2*b^2)*1i)/(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"
472,1,203,149,2.987403,"\text{Not used}","int(cos(c + d*x)^2/(a + b*cos(c + d*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(a^2+2\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+4\,b\,a\right)}{{\left(a+b\right)}^2\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a\,b-a^2\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"(atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(a^2 + 2*b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((tan(c/2 + (d*x)/2)^3*(4*a*b + a^2))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(4*a*b - a^2))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
473,1,207,134,3.150731,"\text{Not used}","int(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^2+a\,b+2\,b^2\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^2-a\,b+2\,b^2\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{3\,a\,b\,\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)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(a*b + 2*a^2 + 2*b^2))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(2*a^2 - a*b + 2*b^2))/((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)) - (3*a*b*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))))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
474,1,203,133,2.879555,"\text{Not used}","int(1/(a + b*cos(c + d*x))^3,x)","\frac{\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a-2\,b\right)\,\left(a^2-2\,a\,b+b^2\right)}{2\,\sqrt{a+b}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,a^2+b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(b^2+4\,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(4\,a\,b-b^2\right)}{\left(a+b\right)\,\left(a^2-2\,a\,b+b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}","Not used",1,"(atan((tan(c/2 + (d*x)/2)*(2*a - 2*b)*(a^2 - 2*a*b + b^2))/(2*(a + b)^(1/2)*(a - b)^(5/2)))*(2*a^2 + b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2)) - ((tan(c/2 + (d*x)/2)^3*(4*a*b + b^2))/((a + b)^2*(a - b)) + (tan(c/2 + (d*x)/2)*(4*a*b - b^2))/((a + b)*(a^2 - 2*a*b + b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2))","B"
475,1,5090,182,9.058319,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*cos(c + d*x))^3),x)","-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\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\,\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)}}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)\,1{}\mathrm{i}}{a^3}-\frac{\left(\frac{\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\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\,\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)}}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}\right)\,1{}\mathrm{i}}{a^3}}{\frac{\frac{\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\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\,\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)}}{a^3}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\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}}{a^3}+\frac{\frac{\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\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\,\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)}}{a^3}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\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}}{a^3}-\frac{16\,\left(12\,a^8\,b+24\,a^7\,b^2-34\,a^6\,b^3-26\,a^5\,b^4+36\,a^4\,b^5+13\,a^3\,b^6-18\,a^2\,b^7-2\,a\,b^8+4\,b^9\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}}\right)\,2{}\mathrm{i}}{a^3\,d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^2\,b^2+a\,b^3-2\,b^4\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(-6\,a^2\,b^2+a\,b^3+2\,b^4\right)}{\left(a+b\right)\,\left(a^4-2\,a^3\,b+a^2\,b^2\right)}}{d\,\left(2\,a\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,1{}\mathrm{i}}{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^8\,b+24\,a^7\,b^2-34\,a^6\,b^3-26\,a^5\,b^4+36\,a^4\,b^5+13\,a^3\,b^6-18\,a^2\,b^7-2\,a\,b^8+4\,b^9\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}-\frac{b\,\left(\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{10}-8\,a^9\,b+24\,a^8\,b^2+32\,a^7\,b^3-52\,a^6\,b^4-48\,a^5\,b^5+57\,a^4\,b^6+32\,a^3\,b^7-32\,a^2\,b^8-8\,a\,b^9+8\,b^{10}\right)}{a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7}+\frac{b\,\left(\frac{8\,\left(-4\,a^{15}+12\,a^{14}\,b+8\,a^{13}\,b^2-34\,a^{12}\,b^3-6\,a^{11}\,b^4+36\,a^{10}\,b^5+4\,a^9\,b^6-18\,a^8\,b^7-2\,a^7\,b^8+4\,a^6\,b^9\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-32\,a^{13}\,b^3+32\,a^{12}\,b^4+48\,a^{11}\,b^5-48\,a^{10}\,b^6-32\,a^9\,b^7+32\,a^8\,b^8+8\,a^7\,b^9-8\,a^6\,b^{10}\right)}{\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{13}-5\,a^{11}\,b^2+10\,a^9\,b^4-10\,a^7\,b^6+5\,a^5\,b^8-a^3\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(6\,a^4-5\,a^2\,b^2+2\,b^4\right)\,1{}\mathrm{i}}{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,"- (atan((((((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3 - ((((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))*1i)/a^3)/((((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (8*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 - (8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))/a^3 + (((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (8*tan(c/2 + (d*x)/2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/(a^3*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))/a^3 + (8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2))/a^3 - (16*(12*a^8*b - 2*a*b^8 + 4*b^9 - 18*a^2*b^7 + 13*a^3*b^6 + 36*a^4*b^5 - 26*a^5*b^4 - 34*a^6*b^3 + 24*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)))*2i)/(a^3*d) - ((tan(c/2 + (d*x)/2)^3*(a*b^3 - 2*b^4 + 6*a^2*b^2))/((a^2*b - a^3)*(a + b)^2) + (tan(c/2 + (d*x)/2)*(a*b^3 + 2*b^4 - 6*a^2*b^2))/((a + b)*(a^4 - 2*a^3*b + a^2*b^2)))/(d*(2*a*b + tan(c/2 + (d*x)/2)^2*(2*a^2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 - 2*a*b + b^2) + a^2 + b^2)) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*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) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*1i)/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*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) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*1i)/(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*(12*a^8*b - 2*a*b^8 + 4*b^9 - 18*a^2*b^7 + 13*a^3*b^6 + 36*a^4*b^5 - 26*a^5*b^4 - 34*a^6*b^3 + 24*a^7*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) - (b*((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*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) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)) - (b*((8*tan(c/2 + (d*x)/2)*(4*a^10 - 8*a^9*b - 8*a*b^9 + 8*b^10 - 32*a^2*b^8 + 32*a^3*b^7 + 57*a^4*b^6 - 48*a^5*b^5 - 52*a^6*b^4 + 32*a^7*b^3 + 24*a^8*b^2))/(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2) + (b*((8*(12*a^14*b - 4*a^15 + 4*a^6*b^9 - 2*a^7*b^8 - 18*a^8*b^7 + 4*a^9*b^6 + 36*a^10*b^5 - 6*a^11*b^4 - 34*a^12*b^3 + 8*a^13*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) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^15*b - 8*a^6*b^10 + 8*a^7*b^9 + 32*a^8*b^8 - 32*a^9*b^7 - 48*a^10*b^6 + 48*a^11*b^5 + 32*a^12*b^4 - 32*a^13*b^3 - 8*a^14*b^2))/((a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)*(a^10*b + a^11 - a^4*b^7 - a^5*b^6 + 3*a^6*b^5 + 3*a^7*b^4 - 3*a^8*b^3 - 3*a^9*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^13 - a^3*b^10 + 5*a^5*b^8 - 10*a^7*b^6 + 10*a^9*b^4 - 5*a^11*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(6*a^4 + 2*b^4 - 5*a^2*b^2)*1i)/(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"
476,1,5347,232,8.453136,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^3),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^5-2\,a^4\,b-4\,a^3\,b^2+12\,a^2\,b^3+3\,a\,b^4-6\,b^5\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^5+2\,a^4\,b-4\,a^3\,b^2-12\,a^2\,b^3+3\,a\,b^4+6\,b^5\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^6-6\,a^4\,b^2+13\,a^2\,b^4-6\,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{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{3\,b\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)\,3{}\mathrm{i}}{a^4}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{3\,b\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)\,3{}\mathrm{i}}{a^4}}{\frac{48\,\left(72\,a^8\,b^4+72\,a^7\,b^5-234\,a^6\,b^6-126\,a^5\,b^7+288\,a^4\,b^8+81\,a^3\,b^9-162\,a^2\,b^{10}-18\,a\,b^{11}+36\,b^{12}\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{3\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{3\,b\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)}{a^4}+\frac{3\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{3\,b\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}+\frac{24\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{17}\,b-8\,a^{16}\,b^2-32\,a^{15}\,b^3+32\,a^{14}\,b^4+48\,a^{13}\,b^5-48\,a^{12}\,b^6-32\,a^{11}\,b^7+32\,a^{10}\,b^8+8\,a^9\,b^9-8\,a^8\,b^{10}\right)}{a^4\,\left(a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7\right)}\right)}{a^4}\right)}{a^4}}\right)\,6{}\mathrm{i}}{a^4\,d}+\frac{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(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{3\,b^2\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\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{12\,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(4\,a^4-5\,a^2\,b^2+2\,b^4\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(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,3{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{b^2\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{3\,b^2\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\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{12\,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(4\,a^4-5\,a^2\,b^2+2\,b^4\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(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,3{}\mathrm{i}}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}{\frac{48\,\left(72\,a^8\,b^4+72\,a^7\,b^5-234\,a^6\,b^6-126\,a^5\,b^7+288\,a^4\,b^8+81\,a^3\,b^9-162\,a^2\,b^{10}-18\,a\,b^{11}+36\,b^{12}\right)}{a^{16}+a^{15}\,b-3\,a^{14}\,b^2-3\,a^{13}\,b^3+3\,a^{12}\,b^4+3\,a^{11}\,b^5-a^{10}\,b^6-a^9\,b^7}-\frac{3\,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(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}-\frac{3\,b^2\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\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{12\,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(4\,a^4-5\,a^2\,b^2+2\,b^4\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(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}+\frac{3\,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(36\,a^{10}\,b^2-72\,a^9\,b^3+36\,a^8\,b^4+288\,a^7\,b^5-288\,a^6\,b^6-432\,a^5\,b^7+441\,a^4\,b^8+288\,a^3\,b^9-288\,a^2\,b^{10}-72\,a\,b^{11}+72\,b^{12}\right)}{a^{13}+a^{12}\,b-3\,a^{11}\,b^2-3\,a^{10}\,b^3+3\,a^9\,b^4+3\,a^8\,b^5-a^7\,b^6-a^6\,b^7}+\frac{3\,b^2\,\left(\frac{24\,\left(4\,a^{17}\,b-8\,a^{16}\,b^2-12\,a^{15}\,b^3+26\,a^{14}\,b^4+14\,a^{13}\,b^5-32\,a^{12}\,b^6-8\,a^{11}\,b^7+18\,a^{10}\,b^8+2\,a^9\,b^9-4\,a^8\,b^{10}\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{12\,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(4\,a^4-5\,a^2\,b^2+2\,b^4\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(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}\right)\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)}{2\,\left(a^{14}-5\,a^{12}\,b^2+10\,a^{10}\,b^4-10\,a^8\,b^6+5\,a^6\,b^8-a^4\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(4\,a^4-5\,a^2\,b^2+2\,b^4\right)\,3{}\mathrm{i}}{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,"(b*atan(((b*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (3*b*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (24*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4)*3i)/a^4 + (b*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (3*b*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (24*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4)*3i)/a^4)/((48*(36*b^12 - 18*a*b^11 - 162*a^2*b^10 + 81*a^3*b^9 + 288*a^4*b^8 - 126*a^5*b^7 - 234*a^6*b^6 + 72*a^7*b^5 + 72*a^8*b^4))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (3*b*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (3*b*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (24*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4))/a^4 + (3*b*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (3*b*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (24*b*tan(c/2 + (d*x)/2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/(a^4*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2))))/a^4))/a^4))*6i)/(a^4*d) - ((tan(c/2 + (d*x)/2)^5*(3*a*b^4 - 2*a^4*b + 2*a^5 - 6*b^5 + 12*a^2*b^3 - 4*a^3*b^2))/((a^3*b - a^4)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(3*a*b^4 + 2*a^4*b + 2*a^5 + 6*b^5 - 12*a^2*b^3 - 4*a^3*b^2))/((a + b)*(a^5 - 2*a^4*b + a^3*b^2)) + (2*tan(c/2 + (d*x)/2)^3*(2*a^6 - 6*b^6 + 13*a^2*b^4 - 6*a^4*b^2))/(a*(a^2*b - a^3)*(a + b)^2*(a - b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^2*(2*a*b - a^2 + 3*b^2) - tan(c/2 + (d*x)/2)^6*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^4*(2*a*b + a^2 - 3*b^2))) + (b^2*atan(((b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (3*b^2*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (12*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(4*a^4 + 2*b^4 - 5*a^2*b^2)*3i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + (b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (3*b^2*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (12*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(4*a^4 + 2*b^4 - 5*a^2*b^2)*3i)/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))/((48*(36*b^12 - 18*a*b^11 - 162*a^2*b^10 + 81*a^3*b^9 + 288*a^4*b^8 - 126*a^5*b^7 - 234*a^6*b^6 + 72*a^7*b^5 + 72*a^8*b^4))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (3*b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) - (3*b^2*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) - (12*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)) + (3*b^2*(-(a + b)^5*(a - b)^5)^(1/2)*((8*tan(c/2 + (d*x)/2)*(72*b^12 - 72*a*b^11 - 288*a^2*b^10 + 288*a^3*b^9 + 441*a^4*b^8 - 432*a^5*b^7 - 288*a^6*b^6 + 288*a^7*b^5 + 36*a^8*b^4 - 72*a^9*b^3 + 36*a^10*b^2))/(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2) + (3*b^2*((24*(4*a^17*b - 4*a^8*b^10 + 2*a^9*b^9 + 18*a^10*b^8 - 8*a^11*b^7 - 32*a^12*b^6 + 14*a^13*b^5 + 26*a^14*b^4 - 12*a^15*b^3 - 8*a^16*b^2))/(a^15*b + a^16 - a^9*b^7 - a^10*b^6 + 3*a^11*b^5 + 3*a^12*b^4 - 3*a^13*b^3 - 3*a^14*b^2) + (12*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*(8*a^17*b - 8*a^8*b^10 + 8*a^9*b^9 + 32*a^10*b^8 - 32*a^11*b^7 - 48*a^12*b^6 + 48*a^13*b^5 + 32*a^14*b^4 - 32*a^15*b^3 - 8*a^16*b^2))/((a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)*(a^12*b + a^13 - a^6*b^7 - a^7*b^6 + 3*a^8*b^5 + 3*a^9*b^4 - 3*a^10*b^3 - 3*a^11*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2)))*(4*a^4 + 2*b^4 - 5*a^2*b^2))/(2*(a^14 - a^4*b^10 + 5*a^6*b^8 - 10*a^8*b^6 + 10*a^10*b^4 - 5*a^12*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(4*a^4 + 2*b^4 - 5*a^2*b^2)*3i)/(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"
477,1,5910,305,9.160208,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^7-4\,a^6\,b+5\,a^5\,b^2+26\,a^4\,b^3-29\,a^3\,b^4-67\,a^2\,b^5+18\,a\,b^6+36\,b^7\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^7+4\,a^6\,b+5\,a^5\,b^2-26\,a^4\,b^3-29\,a^3\,b^4+67\,a^2\,b^5+18\,a\,b^6-36\,b^7\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^6+5\,a^5\,b-8\,a^4\,b^2-10\,a^3\,b^3+23\,a^2\,b^4+6\,a\,b^5-12\,b^6\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^6+5\,a^5\,b+8\,a^4\,b^2-10\,a^3\,b^3-23\,a^2\,b^4+6\,a\,b^5+12\,b^6\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(a^2+12\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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(a^2+12\,b^2\right)\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^2+12\,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)}{2\,a^5}\right)\,1{}\mathrm{i}}{2\,a^5}+\frac{\left(a^2+12\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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(a^2+12\,b^2\right)\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^2+12\,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)}{2\,a^5}\right)\,1{}\mathrm{i}}{2\,a^5}}{\frac{8\,\left(20\,a^{12}\,b^3-20\,a^{11}\,b^4+411\,a^{10}\,b^5-11\,a^9\,b^6+1314\,a^8\,b^7+2326\,a^7\,b^8-7829\,a^6\,b^9-4770\,a^5\,b^{10}+11700\,a^4\,b^{11}+3456\,a^3\,b^{12}-7344\,a^2\,b^{13}-864\,a\,b^{14}+1728\,b^{15}\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(a^2+12\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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(a^2+12\,b^2\right)\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^2+12\,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)}{2\,a^5}\right)}{2\,a^5}+\frac{\left(a^2+12\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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(a^2+12\,b^2\right)\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^2+12\,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)}{2\,a^5}\right)}{2\,a^5}}\right)\,\left(a^2+12\,b^2\right)\,1{}\mathrm{i}}{a^5\,d}-\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{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^{12}\,b^3-20\,a^{11}\,b^4+411\,a^{10}\,b^5-11\,a^9\,b^6+1314\,a^8\,b^7+2326\,a^7\,b^8-7829\,a^6\,b^9-4770\,a^5\,b^{10}+11700\,a^4\,b^{11}+3456\,a^3\,b^{12}-7344\,a^2\,b^{13}-864\,a\,b^{14}+1728\,b^{15}\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^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}+\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{14}-2\,a^{13}\,b+21\,a^{12}\,b^2-40\,a^{11}\,b^3+74\,a^{10}\,b^4-108\,a^9\,b^5+18\,a^8\,b^6+872\,a^7\,b^7-827\,a^6\,b^8-1538\,a^5\,b^9+1538\,a^4\,b^{10}+1104\,a^3\,b^{11}-1104\,a^2\,b^{12}-288\,a\,b^{13}+288\,b^{14}\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^3\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(4\,a^{21}+28\,a^{19}\,b^2-80\,a^{18}\,b^3-120\,a^{17}\,b^4+276\,a^{16}\,b^5+164\,a^{15}\,b^6-360\,a^{14}\,b^7-100\,a^{13}\,b^8+212\,a^{12}\,b^9+24\,a^{11}\,b^{10}-48\,a^{10}\,b^{11}\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^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{19}\,b-8\,a^{18}\,b^2-32\,a^{17}\,b^3+32\,a^{16}\,b^4+48\,a^{15}\,b^5-48\,a^{14}\,b^6-32\,a^{13}\,b^7+32\,a^{12}\,b^8+8\,a^{11}\,b^9-8\,a^{10}\,b^{10}\right)}{\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)\,\left(a^{15}+a^{14}\,b-3\,a^{13}\,b^2-3\,a^{12}\,b^3+3\,a^{11}\,b^4+3\,a^{10}\,b^5-a^9\,b^6-a^8\,b^7\right)}\right)\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{15}-5\,a^{13}\,b^2+10\,a^{11}\,b^4-10\,a^9\,b^6+5\,a^7\,b^8-a^5\,b^{10}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(20\,a^4-29\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{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*(18*a*b^6 - 4*a^6*b + 3*a^7 + 36*b^7 - 67*a^2*b^5 - 29*a^3*b^4 + 26*a^4*b^3 + 5*a^5*b^2))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) + (tan(c/2 + (d*x)/2)^5*(18*a*b^6 + 4*a^6*b + 3*a^7 - 36*b^7 + 67*a^2*b^5 - 29*a^3*b^4 - 26*a^4*b^3 + 5*a^5*b^2))/((a + b)^2*(a^6 - 2*a^5*b + a^4*b^2)) - (tan(c/2 + (d*x)/2)^7*(6*a*b^5 + 5*a^5*b + a^6 - 12*b^6 + 23*a^2*b^4 - 10*a^3*b^3 - 8*a^4*b^2))/((a^4*b - a^5)*(a + b)^2) - (tan(c/2 + (d*x)/2)*(6*a*b^5 + 5*a^5*b - a^6 + 12*b^6 - 23*a^2*b^4 - 10*a^3*b^3 + 8*a^4*b^2))/((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((((a^2 + 12*b^2)*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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) - ((a^2 + 12*b^2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2 + 12*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^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))))/(2*a^5))*1i)/(2*a^5) + ((a^2 + 12*b^2)*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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) + ((a^2 + 12*b^2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2 + 12*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^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))))/(2*a^5))*1i)/(2*a^5))/((8*(1728*b^15 - 864*a*b^14 - 7344*a^2*b^13 + 3456*a^3*b^12 + 11700*a^4*b^11 - 4770*a^5*b^10 - 7829*a^6*b^9 + 2326*a^7*b^8 + 1314*a^8*b^7 - 11*a^9*b^6 + 411*a^10*b^5 - 20*a^11*b^4 + 20*a^12*b^3))/(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) - ((a^2 + 12*b^2)*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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) - ((a^2 + 12*b^2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2 + 12*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^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))))/(2*a^5)))/(2*a^5) + ((a^2 + 12*b^2)*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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) + ((a^2 + 12*b^2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2 + 12*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/(a^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))))/(2*a^5)))/(2*a^5)))*(a^2 + 12*b^2)*1i)/(a^5*d) - (b^3*atan(((b^3*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b^3*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*1i)/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))/((8*(1728*b^15 - 864*a*b^14 - 7344*a^2*b^13 + 3456*a^3*b^12 + 11700*a^4*b^11 - 4770*a^5*b^10 - 7829*a^6*b^9 + 2326*a^7*b^8 + 1314*a^8*b^7 - 11*a^9*b^6 + 411*a^10*b^5 - 20*a^11*b^4 + 20*a^12*b^3))/(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^3*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) - (4*b^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)) + (b^3*((8*tan(c/2 + (d*x)/2)*(a^14 - 2*a^13*b - 288*a*b^13 + 288*b^14 - 1104*a^2*b^12 + 1104*a^3*b^11 + 1538*a^4*b^10 - 1538*a^5*b^9 - 827*a^6*b^8 + 872*a^7*b^7 + 18*a^8*b^6 - 108*a^9*b^5 + 74*a^10*b^4 - 40*a^11*b^3 + 21*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^3*(-(a + b)^5*(a - b)^5)^(1/2)*((4*(4*a^21 - 48*a^10*b^11 + 24*a^11*b^10 + 212*a^12*b^9 - 100*a^13*b^8 - 360*a^14*b^7 + 164*a^15*b^6 + 276*a^16*b^5 - 120*a^17*b^4 - 80*a^18*b^3 + 28*a^19*b^2))/(a^18*b + a^19 - a^12*b^7 - a^13*b^6 + 3*a^14*b^5 + 3*a^15*b^4 - 3*a^16*b^3 - 3*a^17*b^2) + (4*b^3*tan(c/2 + (d*x)/2)*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*(8*a^19*b - 8*a^10*b^10 + 8*a^11*b^9 + 32*a^12*b^8 - 32*a^13*b^7 - 48*a^14*b^6 + 48*a^15*b^5 + 32*a^16*b^4 - 32*a^17*b^3 - 8*a^18*b^2))/((a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)*(a^14*b + a^15 - a^8*b^7 - a^9*b^6 + 3*a^10*b^5 + 3*a^11*b^4 - 3*a^12*b^3 - 3*a^13*b^2)))*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2)))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2))/(2*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))))*(-(a + b)^5*(a - b)^5)^(1/2)*(20*a^4 + 12*b^4 - 29*a^2*b^2)*1i)/(d*(a^15 - a^5*b^10 + 5*a^7*b^8 - 10*a^9*b^6 + 10*a^11*b^4 - 5*a^13*b^2))","B"
478,1,7494,307,9.895110,"\text{Not used}","int(cos(c + d*x)^5/(a + b*cos(c + d*x))^4,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-72\,a^8+12\,a^7\,b+236\,a^6\,b^2-47\,a^5\,b^3-273\,a^4\,b^4+60\,a^3\,b^5+72\,a^2\,b^6-18\,b^8\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\,a^8+12\,a^7\,b-236\,a^6\,b^2-47\,a^5\,b^3+273\,a^4\,b^4+60\,a^3\,b^5-72\,a^2\,b^6+18\,b^8\right)}{3\,b^4\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^7-4\,a^6\,b+24\,a^5\,b^2+11\,a^4\,b^3-26\,a^3\,b^4-6\,a^2\,b^5+2\,a\,b^6+2\,b^7\right)}{b^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-8\,a^7+4\,a^6\,b+24\,a^5\,b^2-11\,a^4\,b^3-26\,a^3\,b^4+6\,a^2\,b^5+2\,a\,b^6-2\,b^7\right)}{b^4\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a\,b^2-6\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^3+6\,a^2\,b-2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^3-6\,a^2\,b+2\,b^3\right)+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{8\,a\,\mathrm{atan}\left(\frac{\frac{4\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)}{b^5}+\frac{4\,a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)}{b^5}}{\frac{32\,\left(128\,a^{16}-64\,a^{15}\,b-832\,a^{14}\,b^2+400\,a^{13}\,b^3+2288\,a^{12}\,b^4-1088\,a^{11}\,b^5-3472\,a^{10}\,b^6+1602\,a^9\,b^7+3088\,a^8\,b^8-1280\,a^7\,b^9-1520\,a^6\,b^{10}+480\,a^5\,b^{11}+320\,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(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)\,4{}\mathrm{i}}{b^5}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)\,32{}\mathrm{i}}{b^5\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,4{}\mathrm{i}}{b^5}\right)\,4{}\mathrm{i}}{b^5}}\right)}{b^5\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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^2\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\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\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\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^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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^2\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\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\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}}{\frac{32\,\left(128\,a^{16}-64\,a^{15}\,b-832\,a^{14}\,b^2+400\,a^{13}\,b^3+2288\,a^{12}\,b^4-1088\,a^{11}\,b^5-3472\,a^{10}\,b^6+1602\,a^9\,b^7+3088\,a^8\,b^8-1280\,a^7\,b^9-1520\,a^6\,b^{10}+480\,a^5\,b^{11}+320\,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^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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^2\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\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\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\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^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{16}-128\,a^{15}\,b-768\,a^{14}\,b^2+768\,a^{13}\,b^3+1920\,a^{12}\,b^4-1920\,a^{11}\,b^5-2600\,a^{10}\,b^6+2560\,a^9\,b^7+2025\,a^8\,b^8-1920\,a^7\,b^9-824\,a^6\,b^{10}+768\,a^5\,b^{11}+80\,a^4\,b^{12}-128\,a^3\,b^{13}+64\,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^2\,\left(\frac{16\,\left(-8\,a^{14}\,b^{10}+4\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}-25\,a^{11}\,b^{13}-143\,a^{10}\,b^{14}+63\,a^9\,b^{15}+217\,a^8\,b^{16}-87\,a^7\,b^{17}-193\,a^6\,b^{18}+73\,a^5\,b^{19}+95\,a^4\,b^{20}-36\,a^3\,b^{21}-20\,a^2\,b^{22}+8\,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^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\right)\,\left(-8\,a^{14}\,b^{10}+8\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}-48\,a^{11}\,b^{13}-120\,a^{10}\,b^{14}+120\,a^9\,b^{15}+160\,a^8\,b^{16}-160\,a^7\,b^{17}-120\,a^6\,b^{18}+120\,a^5\,b^{19}+48\,a^4\,b^{20}-48\,a^3\,b^{21}-8\,a^2\,b^{22}+8\,a\,b^{23}\right)}{\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)\,\left(-a^{11}\,b^8-a^{10}\,b^9+5\,a^9\,b^{10}+5\,a^8\,b^{11}-10\,a^7\,b^{12}-10\,a^6\,b^{13}+10\,a^5\,b^{14}+10\,a^4\,b^{15}-5\,a^3\,b^{16}-5\,a^2\,b^{17}+a\,b^{18}+b^{19}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\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\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\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\,a^6-28\,a^4\,b^2+35\,a^2\,b^4-20\,b^6\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^5+7\,a^{12}\,b^7-21\,a^{10}\,b^9+35\,a^8\,b^{11}-35\,a^6\,b^{13}+21\,a^4\,b^{15}-7\,a^2\,b^{17}+b^{19}\right)}","Not used",1,"- ((tan(c/2 + (d*x)/2)^3*(12*a^7*b - 72*a^8 - 18*b^8 + 72*a^2*b^6 + 60*a^3*b^5 - 273*a^4*b^4 - 47*a^5*b^3 + 236*a^6*b^2))/(3*b^4*(a + b)^2*(a - b)^3) - (tan(c/2 + (d*x)/2)^5*(12*a^7*b + 72*a^8 + 18*b^8 - 72*a^2*b^6 + 60*a^3*b^5 + 273*a^4*b^4 - 47*a^5*b^3 - 236*a^6*b^2))/(3*b^4*(a + b)^3*(a - b)^2) + (tan(c/2 + (d*x)/2)*(2*a*b^6 - 4*a^6*b - 8*a^7 + 2*b^7 - 6*a^2*b^5 - 26*a^3*b^4 + 11*a^4*b^3 + 24*a^5*b^2))/(b^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^7*(2*a*b^6 + 4*a^6*b - 8*a^7 - 2*b^7 + 6*a^2*b^5 - 26*a^3*b^4 - 11*a^4*b^3 + 24*a^5*b^2))/(b^4*(a + b)^3*(a - b)))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^3) + tan(c/2 + (d*x)/2)^2*(6*a^2*b + 4*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)^6*(4*a^3 - 6*a^2*b + 2*b^3) + a^3 + b^3 + tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (8*a*atan(((4*a*((8*tan(c/2 + (d*x)/2)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5))/b^5 + (4*a*((8*tan(c/2 + (d*x)/2)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5))/b^5)/((32*(128*a^16 - 64*a^15*b + 320*a^4*b^12 + 480*a^5*b^11 - 1520*a^6*b^10 - 1280*a^7*b^9 + 3088*a^8*b^8 + 1602*a^9*b^7 - 3472*a^10*b^6 - 1088*a^11*b^5 + 2288*a^12*b^4 + 400*a^13*b^3 - 832*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)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5)*4i)/b^5 + (a*((8*tan(c/2 + (d*x)/2)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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*tan(c/2 + (d*x)/2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10)*32i)/(b^5*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*4i)/b^5)*4i)/b^5)))/(b^5*d) - (a^2*atan(((a^2*((8*tan(c/2 + (d*x)/2)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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^2*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) + (a^2*((8*tan(c/2 + (d*x)/2)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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^2*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2)*1i)/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))/((32*(128*a^16 - 64*a^15*b + 320*a^4*b^12 + 480*a^5*b^11 - 1520*a^6*b^10 - 1280*a^7*b^9 + 3088*a^8*b^8 + 1602*a^9*b^7 - 3472*a^10*b^6 - 1088*a^11*b^5 + 2288*a^12*b^4 + 400*a^13*b^3 - 832*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^2*((8*tan(c/2 + (d*x)/2)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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^2*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)) + (a^2*((8*tan(c/2 + (d*x)/2)*(128*a^16 - 128*a^15*b + 64*a^2*b^14 - 128*a^3*b^13 + 80*a^4*b^12 + 768*a^5*b^11 - 824*a^6*b^10 - 1920*a^7*b^9 + 2025*a^8*b^8 + 2560*a^9*b^7 - 2600*a^10*b^6 - 1920*a^11*b^5 + 1920*a^12*b^4 + 768*a^13*b^3 - 768*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^2*((16*(8*a*b^23 - 20*a^2*b^22 - 36*a^3*b^21 + 95*a^4*b^20 + 73*a^5*b^19 - 193*a^6*b^18 - 87*a^7*b^17 + 217*a^8*b^16 + 63*a^9*b^15 - 143*a^10*b^14 - 25*a^11*b^13 + 52*a^12*b^12 + 4*a^13*b^11 - 8*a^14*b^10))/(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^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2)*(8*a*b^23 - 8*a^2*b^22 - 48*a^3*b^21 + 48*a^4*b^20 + 120*a^5*b^19 - 120*a^6*b^18 - 160*a^7*b^17 + 160*a^8*b^16 + 120*a^9*b^15 - 120*a^10*b^14 - 48*a^11*b^13 + 48*a^12*b^12 + 8*a^13*b^11 - 8*a^14*b^10))/((b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)*(a*b^18 + b^19 - 5*a^2*b^17 - 5*a^3*b^16 + 10*a^4*b^15 + 10*a^5*b^14 - 10*a^6*b^13 - 10*a^7*b^12 + 5*a^8*b^11 + 5*a^9*b^10 - a^10*b^9 - a^11*b^8)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2))/(2*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 20*b^6 + 35*a^2*b^4 - 28*a^4*b^2)*1i)/(d*(b^19 - 7*a^2*b^17 + 21*a^4*b^15 - 35*a^6*b^13 + 35*a^8*b^11 - 21*a^10*b^9 + 7*a^12*b^7 - a^14*b^5))","B"
479,1,7247,250,12.371045,"\text{Not used}","int(cos(c + d*x)^4/(a + b*cos(c + d*x))^4,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^6-a^5\,b-6\,a^4\,b^2+4\,a^3\,b^3+12\,a^2\,b^4\right)}{\left(a\,b^3-b^4\right)\,{\left(a+b\right)}^3}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^6-11\,a^4\,b^2+18\,a^2\,b^4\right)}{3\,{\left(a+b\right)}^2\,\left(a^2\,b^3-2\,a\,b^4+b^5\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6+a^5\,b-6\,a^4\,b^2-4\,a^3\,b^3+12\,a^2\,b^4\right)}{\left(a+b\right)\,\left(a^3\,b^3-3\,a^2\,b^4+3\,a\,b^5-b^6\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\,\mathrm{atan}\left(\frac{\frac{\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,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^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\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{\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}}{b^4}-\frac{-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,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^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\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{\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}}{b^4}}{\frac{16\,\left(4\,a^{13}-2\,a^{12}\,b-26\,a^{11}\,b^2+11\,a^{10}\,b^3+70\,a^9\,b^4-34\,a^8\,b^5-110\,a^7\,b^6+66\,a^6\,b^7+110\,a^5\,b^8-64\,a^4\,b^9-64\,a^3\,b^{10}+48\,a^2\,b^{11}+16\,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(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,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^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\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{\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{\left(-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,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^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\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{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)\,8{}\mathrm{i}}{b^4\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,1{}\mathrm{i}}{b^4}\right)\,1{}\mathrm{i}}{b^4}}\right)}{b^4\,d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,a^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,a^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)\,1{}\mathrm{i}}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}{\frac{16\,\left(4\,a^{13}-2\,a^{12}\,b-26\,a^{11}\,b^2+11\,a^{10}\,b^3+70\,a^9\,b^4-34\,a^8\,b^5-110\,a^7\,b^6+66\,a^6\,b^7+110\,a^5\,b^8-64\,a^4\,b^9-64\,a^3\,b^{10}+48\,a^2\,b^{11}+16\,a\,b^{12}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}+\frac{a\,\left(\frac{8\,\left(4\,a^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}-\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}-\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{14}-8\,a^{13}\,b-48\,a^{12}\,b^2+48\,a^{11}\,b^3+117\,a^{10}\,b^4-120\,a^9\,b^5-164\,a^8\,b^6+160\,a^7\,b^7+156\,a^6\,b^8-120\,a^5\,b^9-92\,a^4\,b^{10}+48\,a^3\,b^{11}+44\,a^2\,b^{12}-8\,a\,b^{13}+4\,b^{14}\right)}{-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}}-\frac{a\,\left(\frac{8\,\left(4\,a^{13}\,b^8-2\,a^{12}\,b^9-26\,a^{11}\,b^{10}+14\,a^{10}\,b^{11}+70\,a^9\,b^{12}-30\,a^8\,b^{13}-110\,a^7\,b^{14}+30\,a^6\,b^{15}+110\,a^5\,b^{16}-20\,a^4\,b^{17}-64\,a^3\,b^{18}+12\,a^2\,b^{19}+16\,a\,b^{20}-4\,b^{21}\right)}{-a^{11}\,b^9-a^{10}\,b^{10}+5\,a^9\,b^{11}+5\,a^8\,b^{12}-10\,a^7\,b^{13}-10\,a^6\,b^{14}+10\,a^5\,b^{15}+10\,a^4\,b^{16}-5\,a^3\,b^{17}-5\,a^2\,b^{18}+a\,b^{19}+b^{20}}+\frac{4\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)\,\left(-8\,a^{14}\,b^8+8\,a^{13}\,b^9+48\,a^{12}\,b^{10}-48\,a^{11}\,b^{11}-120\,a^{10}\,b^{12}+120\,a^9\,b^{13}+160\,a^8\,b^{14}-160\,a^7\,b^{15}-120\,a^6\,b^{16}+120\,a^5\,b^{17}+48\,a^4\,b^{18}-48\,a^3\,b^{19}-8\,a^2\,b^{20}+8\,a\,b^{21}\right)}{\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)\,\left(-a^{11}\,b^6-a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-10\,a^7\,b^{10}-10\,a^6\,b^{11}+10\,a^5\,b^{12}+10\,a^4\,b^{13}-5\,a^3\,b^{14}-5\,a^2\,b^{15}+a\,b^{16}+b^{17}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)}{2\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(2\,a^6-7\,a^4\,b^2+8\,a^2\,b^4-8\,b^6\right)\,1{}\mathrm{i}}{d\,\left(-a^{14}\,b^4+7\,a^{12}\,b^6-21\,a^{10}\,b^8+35\,a^8\,b^{10}-35\,a^6\,b^{12}+21\,a^4\,b^{14}-7\,a^2\,b^{16}+b^{18}\right)}","Not used",1,"(2*atan((((((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (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 + (8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(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^4 - ((((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (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 - (8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(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^4)/((((((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (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 + (8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(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 + (((((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (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 - (8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(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 + (16*(16*a*b^12 - 2*a^12*b + 4*a^13 + 48*a^2*b^11 - 64*a^3*b^10 - 64*a^4*b^9 + 110*a^5*b^8 + 66*a^6*b^7 - 110*a^7*b^6 - 34*a^8*b^5 + 70*a^9*b^4 + 11*a^10*b^3 - 26*a^11*b^2))/(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^4*d) - ((tan(c/2 + (d*x)/2)^5*(2*a^6 - a^5*b + 12*a^2*b^4 + 4*a^3*b^3 - 6*a^4*b^2))/((a*b^3 - b^4)*(a + b)^3) + (4*tan(c/2 + (d*x)/2)^3*(3*a^6 + 18*a^2*b^4 - 11*a^4*b^2))/(3*(a + b)^2*(b^5 - 2*a*b^4 + a^2*b^3)) + (tan(c/2 + (d*x)/2)*(a^5*b + 2*a^6 + 12*a^2*b^4 - 4*a^3*b^3 - 6*a^4*b^2))/((a + b)*(3*a*b^5 - b^6 - 3*a^2*b^4 + 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))) + (a*atan(((a*((8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (a*((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) + (a*((8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (a*((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2)*1i)/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))/((16*(16*a*b^12 - 2*a^12*b + 4*a^13 + 48*a^2*b^11 - 64*a^3*b^10 - 64*a^4*b^9 + 110*a^5*b^8 + 66*a^6*b^7 - 110*a^7*b^6 - 34*a^8*b^5 + 70*a^9*b^4 + 11*a^10*b^3 - 26*a^11*b^2))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (a*((8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) + (a*((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) - (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)) - (a*((8*tan(c/2 + (d*x)/2)*(8*a^14 - 8*a^13*b - 8*a*b^13 + 4*b^14 + 44*a^2*b^12 + 48*a^3*b^11 - 92*a^4*b^10 - 120*a^5*b^9 + 156*a^6*b^8 + 160*a^7*b^7 - 164*a^8*b^6 - 120*a^9*b^5 + 117*a^10*b^4 + 48*a^11*b^3 - 48*a^12*b^2))/(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6) - (a*((8*(16*a*b^20 - 4*b^21 + 12*a^2*b^19 - 64*a^3*b^18 - 20*a^4*b^17 + 110*a^5*b^16 + 30*a^6*b^15 - 110*a^7*b^14 - 30*a^8*b^13 + 70*a^9*b^12 + 14*a^10*b^11 - 26*a^11*b^10 - 2*a^12*b^9 + 4*a^13*b^8))/(a*b^19 + b^20 - 5*a^2*b^18 - 5*a^3*b^17 + 10*a^4*b^16 + 10*a^5*b^15 - 10*a^6*b^14 - 10*a^7*b^13 + 5*a^8*b^12 + 5*a^9*b^11 - a^10*b^10 - a^11*b^9) + (4*a*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2)*(8*a*b^21 - 8*a^2*b^20 - 48*a^3*b^19 + 48*a^4*b^18 + 120*a^5*b^17 - 120*a^6*b^16 - 160*a^7*b^15 + 160*a^8*b^14 + 120*a^9*b^13 - 120*a^10*b^12 - 48*a^11*b^11 + 48*a^12*b^10 + 8*a^13*b^9 - 8*a^14*b^8))/((b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)*(a*b^16 + b^17 - 5*a^2*b^15 - 5*a^3*b^14 + 10*a^4*b^13 + 10*a^5*b^12 - 10*a^6*b^11 - 10*a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - a^10*b^7 - a^11*b^6)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4)))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2))/(2*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))))*(-(a + b)^7*(a - b)^7)^(1/2)*(2*a^6 - 8*b^6 + 8*a^2*b^4 - 7*a^4*b^2)*1i)/(d*(b^18 - 7*a^2*b^16 + 21*a^4*b^14 - 35*a^6*b^12 + 35*a^8*b^10 - 21*a^10*b^8 + 7*a^12*b^6 - a^14*b^4))","B"
480,1,378,222,4.211235,"\text{Not used}","int(cos(c + d*x)^3/(a + b*cos(c + d*x))^4,x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^3+9\,a\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^3+3\,a^2\,b+6\,a\,b^2\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^3-3\,a^2\,b+6\,a\,b^2\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2+2\,b^2\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\left(3\,a^2\,b+2\,b^3\right)\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(3\,a^2+2\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((4*tan(c/2 + (d*x)/2)^3*(9*a*b^2 + a^3))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(6*a*b^2 + 3*a^2*b + 2*a^3))/((a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(6*a*b^2 - 3*a^2*b + 2*a^3))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (b*atan((b*tan(c/2 + (d*x)/2)*(3*a^2 + 2*b^2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(3*a^2*b + 2*b^3)*(a + b)^(1/2)*(a - b)^(7/2)))*(3*a^2 + 2*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
481,1,381,206,4.148627,"\text{Not used}","int(cos(c + d*x)^2/(a + b*cos(c + d*x))^4,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,b^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}\,\left(a^3+4\,a\,b^2\right)}\right)\,\left(a^2+4\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^3+6\,a^2\,b+2\,a\,b^2+2\,b^3\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(7\,a^2\,b+3\,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(a^3-6\,a^2\,b+2\,a\,b^2-2\,b^3\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(a^2 + 4*b^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)*(4*a*b^2 + a^3)))*(a^2 + 4*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((tan(c/2 + (d*x)/2)^5*(2*a*b^2 + 6*a^2*b + a^3 + 2*b^3))/((a + b)^3*(a - b)) + (4*tan(c/2 + (d*x)/2)^3*(7*a^2*b + 3*b^3))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) - (tan(c/2 + (d*x)/2)*(2*a*b^2 - 6*a^2*b + a^3 - 2*b^3))/((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"
482,1,382,192,4.253266,"\text{Not used}","int(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(2\,a^3+2\,a^2\,b+6\,a\,b^2+b^3\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^3+7\,a\,b^2\right)}{3\,{\left(a+b\right)}^2\,\left(a^2-2\,a\,b+b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^3-2\,a^2\,b+6\,a\,b^2-b^3\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^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}\,\left(4\,a^2\,b+b^3\right)}\right)\,\left(4\,a^2+b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(6*a*b^2 + 2*a^2*b + 2*a^3 + b^3))/((a + b)^3*(a - b)) + (4*tan(c/2 + (d*x)/2)^3*(7*a*b^2 + 3*a^3))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)*(6*a*b^2 - 2*a^2*b + 2*a^3 - b^3))/((a + b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3)))/(d*(3*a*b^2 - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) - tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (b*atan((b*tan(c/2 + (d*x)/2)*(4*a^2 + b^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)*(4*a^2*b + b^3)))*(4*a^2 + b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
483,1,378,184,4.122620,"\text{Not used}","int(1/(a + b*cos(c + d*x))^4,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+3\,b^2\right)\,\left(2\,a-2\,b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}{2\,\left(2\,a^3+3\,a\,b^2\right)\,\sqrt{a+b}\,{\left(a-b\right)}^{7/2}}\right)\,\left(2\,a^2+3\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}-\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,a^2\,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)}^5\,\left(6\,a^2\,b+3\,a\,b^2+2\,b^3\right)}{{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2\,b-3\,a\,b^2+2\,b^3\right)}{\left(a+b\right)\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(2*a^2 + 3*b^2)*(2*a - 2*b)*(3*a*b^2 - 3*a^2*b + a^3 - b^3))/(2*(3*a*b^2 + 2*a^3)*(a + b)^(1/2)*(a - b)^(7/2)))*(2*a^2 + 3*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2)) - ((4*tan(c/2 + (d*x)/2)^3*(9*a^2*b + b^3))/(3*(a + b)^2*(a^2 - 2*a*b + b^2)) + (tan(c/2 + (d*x)/2)^5*(3*a*b^2 + 6*a^2*b + 2*b^3))/((a + b)^3*(a - b)) + (tan(c/2 + (d*x)/2)*(6*a^2*b - 3*a*b^2 + 2*b^3))/((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"
484,1,7235,251,12.506186,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*cos(c + d*x))^4),x)","-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\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\,\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)}}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\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}}\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(\frac{\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\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\,\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)}}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\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}}\right)\,1{}\mathrm{i}}{a^4}}{\frac{\frac{\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\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\,\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)}}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\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}}}{a^4}+\frac{\frac{\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\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\,\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)}}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\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}}}{a^4}-\frac{16\,\left(16\,a^{12}\,b+48\,a^{11}\,b^2-64\,a^{10}\,b^3-64\,a^9\,b^4+110\,a^8\,b^5+66\,a^7\,b^6-110\,a^6\,b^7-34\,a^5\,b^8+70\,a^4\,b^9+11\,a^3\,b^{10}-26\,a^2\,b^{11}-2\,a\,b^{12}+4\,b^{13}\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}}}\right)\,2{}\mathrm{i}}{a^4\,d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,a^4\,b^2+4\,a^3\,b^3-6\,a^2\,b^4-a\,b^5+2\,b^6\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(18\,a^4\,b^2-11\,a^2\,b^4+3\,b^6\right)}{3\,{\left(a+b\right)}^2\,\left(a^5-2\,a^4\,b+a^3\,b^2\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^4\,b^2-4\,a^3\,b^3-6\,a^2\,b^4+a\,b^5+2\,b^6\right)}{\left(a+b\right)\,\left(-a^6+3\,a^5\,b-3\,a^4\,b^2+a^3\,b^3\right)}}{d\,\left(3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-3\,a^3+3\,a^2\,b+3\,a\,b^2-3\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3-3\,a^2\,b+3\,a\,b^2+3\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)\,1{}\mathrm{i}}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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^{12}\,b+48\,a^{11}\,b^2-64\,a^{10}\,b^3-64\,a^9\,b^4+110\,a^8\,b^5+66\,a^7\,b^6-110\,a^6\,b^7-34\,a^5\,b^8+70\,a^4\,b^9+11\,a^3\,b^{10}-26\,a^2\,b^{11}-2\,a\,b^{12}+4\,b^{13}\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}-\frac{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{14}-8\,a^{13}\,b+44\,a^{12}\,b^2+48\,a^{11}\,b^3-92\,a^{10}\,b^4-120\,a^9\,b^5+156\,a^8\,b^6+160\,a^7\,b^7-164\,a^6\,b^8-120\,a^5\,b^9+117\,a^4\,b^{10}+48\,a^3\,b^{11}-48\,a^2\,b^{12}-8\,a\,b^{13}+8\,b^{14}\right)}{a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}}+\frac{b\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(\frac{8\,\left(-4\,a^{21}+16\,a^{20}\,b+12\,a^{19}\,b^2-64\,a^{18}\,b^3-20\,a^{17}\,b^4+110\,a^{16}\,b^5+30\,a^{15}\,b^6-110\,a^{14}\,b^7-30\,a^{13}\,b^8+70\,a^{12}\,b^9+14\,a^{11}\,b^{10}-26\,a^{10}\,b^{11}-2\,a^9\,b^{12}+4\,a^8\,b^{13}\right)}{a^{20}+a^{19}\,b-5\,a^{18}\,b^2-5\,a^{17}\,b^3+10\,a^{16}\,b^4+10\,a^{15}\,b^5-10\,a^{14}\,b^6-10\,a^{13}\,b^7+5\,a^{12}\,b^8+5\,a^{11}\,b^9-a^{10}\,b^{10}-a^9\,b^{11}}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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)\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\right)}{2\,\left(a^{18}-7\,a^{16}\,b^2+21\,a^{14}\,b^4-35\,a^{12}\,b^6+35\,a^{10}\,b^8-21\,a^8\,b^{10}+7\,a^6\,b^{12}-a^4\,b^{14}\right)}}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(8\,a^6-8\,a^4\,b^2+7\,a^2\,b^4-2\,b^6\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,"- (atan((((((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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)*(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 - (8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))*1i)/a^4 - ((((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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)*(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 + (8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))*1i)/a^4)/((((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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)*(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 - (8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))/a^4 + (((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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)*(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 + (8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2))/a^4 - (16*(16*a^12*b - 2*a*b^12 + 4*b^13 - 26*a^2*b^11 + 11*a^3*b^10 + 70*a^4*b^9 - 34*a^5*b^8 - 110*a^6*b^7 + 66*a^7*b^6 + 110*a^8*b^5 - 64*a^9*b^4 - 64*a^10*b^3 + 48*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)))*2i)/(a^4*d) - ((tan(c/2 + (d*x)/2)^5*(2*b^6 - a*b^5 - 6*a^2*b^4 + 4*a^3*b^3 + 12*a^4*b^2))/((a^3*b - a^4)*(a + b)^3) - (4*tan(c/2 + (d*x)/2)^3*(3*b^6 - 11*a^2*b^4 + 18*a^4*b^2))/(3*(a + b)^2*(a^5 - 2*a^4*b + a^3*b^2)) + (tan(c/2 + (d*x)/2)*(a*b^5 + 2*b^6 - 6*a^2*b^4 - 4*a^3*b^3 + 12*a^4*b^2))/((a + b)*(3*a^5*b - a^6 + a^3*b^3 - 3*a^4*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))) - (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*1i)/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))/((16*(16*a^12*b - 2*a*b^12 + 4*b^13 - 26*a^2*b^11 + 11*a^3*b^10 + 70*a^4*b^9 - 34*a^5*b^8 - 110*a^6*b^7 + 66*a^7*b^6 + 110*a^8*b^5 - 64*a^9*b^4 - 64*a^10*b^3 + 48*a^11*b^2))/(a^19*b + a^20 - a^9*b^11 - a^10*b^10 + 5*a^11*b^9 + 5*a^12*b^8 - 10*a^13*b^7 - 10*a^14*b^6 + 10*a^15*b^5 + 10*a^16*b^4 - 5*a^17*b^3 - 5*a^18*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) - (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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) - (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)) - (b*((8*tan(c/2 + (d*x)/2)*(4*a^14 - 8*a^13*b - 8*a*b^13 + 8*b^14 - 48*a^2*b^12 + 48*a^3*b^11 + 117*a^4*b^10 - 120*a^5*b^9 - 164*a^6*b^8 + 160*a^7*b^7 + 156*a^8*b^6 - 120*a^9*b^5 - 92*a^10*b^4 + 48*a^11*b^3 + 44*a^12*b^2))/(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2) + (b*(-(a + b)^7*(a - b)^7)^(1/2)*((8*(16*a^20*b - 4*a^21 + 4*a^8*b^13 - 2*a^9*b^12 - 26*a^10*b^11 + 14*a^11*b^10 + 70*a^12*b^9 - 30*a^13*b^8 - 110*a^14*b^7 + 30*a^15*b^6 + 110*a^16*b^5 - 20*a^17*b^4 - 64*a^18*b^3 + 12*a^19*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) + (4*b*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*(8*a^21*b - 8*a^8*b^14 + 8*a^9*b^13 + 48*a^10*b^12 - 48*a^11*b^11 - 120*a^12*b^10 + 120*a^13*b^9 + 160*a^14*b^8 - 160*a^15*b^7 - 120*a^16*b^6 + 120*a^17*b^5 + 48*a^18*b^4 - 48*a^19*b^3 - 8*a^20*b^2))/((a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)*(a^16*b + a^17 - a^6*b^11 - a^7*b^10 + 5*a^8*b^9 + 5*a^9*b^8 - 10*a^10*b^7 - 10*a^11*b^6 + 10*a^12*b^5 + 10*a^13*b^4 - 5*a^14*b^3 - 5*a^15*b^2)))*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2))/(2*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(8*a^6 - 2*b^6 + 7*a^2*b^4 - 8*a^4*b^2)*1i)/(d*(a^18 - a^4*b^14 + 7*a^6*b^12 - 21*a^8*b^10 + 35*a^10*b^8 - 35*a^12*b^6 + 21*a^14*b^4 - 7*a^16*b^2))","B"
485,1,7490,308,9.946464,"\text{Not used}","int(1/(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^8+72\,a^6\,b^2+60\,a^5\,b^3-273\,a^4\,b^4-47\,a^3\,b^5+236\,a^2\,b^6+12\,a\,b^7-72\,b^8\right)}{3\,a^4\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(18\,a^8-72\,a^6\,b^2+60\,a^5\,b^3+273\,a^4\,b^4-47\,a^3\,b^5-236\,a^2\,b^6+12\,a\,b^7+72\,b^8\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^7-2\,a^6\,b+6\,a^5\,b^2+26\,a^4\,b^3-11\,a^3\,b^4-24\,a^2\,b^5+4\,a\,b^6+8\,b^7\right)}{a^4\,\left(a+b\right)\,{\left(a-b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-2\,a^7+2\,a^6\,b+6\,a^5\,b^2-26\,a^4\,b^3-11\,a^3\,b^4+24\,a^2\,b^5+4\,a\,b^6-8\,b^7\right)}{a^4\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left(3\,a\,b^2+3\,a^2\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(6\,a^2\,b-6\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^3+6\,a\,b^2+4\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^3-6\,a\,b^2+4\,b^3\right)+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{4\,b\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)\,4{}\mathrm{i}}{a^5}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{4\,b\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)\,4{}\mathrm{i}}{a^5}}{\frac{32\,\left(320\,a^{12}\,b^4+480\,a^{11}\,b^5-1520\,a^{10}\,b^6-1280\,a^9\,b^7+3088\,a^8\,b^8+1602\,a^7\,b^9-3472\,a^6\,b^{10}-1088\,a^5\,b^{11}+2288\,a^4\,b^{12}+400\,a^3\,b^{13}-832\,a^2\,b^{14}-64\,a\,b^{15}+128\,b^{16}\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\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}-\frac{4\,b\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}-\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)}{a^5}+\frac{4\,b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\right)}{a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}}+\frac{4\,b\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^{23}+a^{22}\,b-5\,a^{21}\,b^2-5\,a^{20}\,b^3+10\,a^{19}\,b^4+10\,a^{18}\,b^5-10\,a^{17}\,b^6-10\,a^{16}\,b^7+5\,a^{15}\,b^8+5\,a^{14}\,b^9-a^{13}\,b^{10}-a^{12}\,b^{11}}+\frac{32\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{a^5\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)}{a^5}\right)}{a^5}}\right)\,8{}\mathrm{i}}{a^5\,d}+\frac{b^2\,\mathrm{atan}\left(\frac{\frac{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\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^2\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\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^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\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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{b^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\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^2\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\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^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\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\right)\,1{}\mathrm{i}}{2\,\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)}}{\frac{32\,\left(320\,a^{12}\,b^4+480\,a^{11}\,b^5-1520\,a^{10}\,b^6-1280\,a^9\,b^7+3088\,a^8\,b^8+1602\,a^7\,b^9-3472\,a^6\,b^{10}-1088\,a^5\,b^{11}+2288\,a^4\,b^{12}+400\,a^3\,b^{13}-832\,a^2\,b^{14}-64\,a\,b^{15}+128\,b^{16}\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^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\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^2\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\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^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\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{14}\,b^2-128\,a^{13}\,b^3+80\,a^{12}\,b^4+768\,a^{11}\,b^5-824\,a^{10}\,b^6-1920\,a^9\,b^7+2025\,a^8\,b^8+2560\,a^7\,b^9-2600\,a^6\,b^{10}-1920\,a^5\,b^{11}+1920\,a^4\,b^{12}+768\,a^3\,b^{13}-768\,a^2\,b^{14}-128\,a\,b^{15}+128\,b^{16}\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^2\,\left(\frac{16\,\left(8\,a^{23}\,b-20\,a^{22}\,b^2-36\,a^{21}\,b^3+95\,a^{20}\,b^4+73\,a^{19}\,b^5-193\,a^{18}\,b^6-87\,a^{17}\,b^7+217\,a^{16}\,b^8+63\,a^{15}\,b^9-143\,a^{14}\,b^{10}-25\,a^{13}\,b^{11}+52\,a^{12}\,b^{12}+4\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\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^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\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\right)\,\left(8\,a^{23}\,b-8\,a^{22}\,b^2-48\,a^{21}\,b^3+48\,a^{20}\,b^4+120\,a^{19}\,b^5-120\,a^{18}\,b^6-160\,a^{17}\,b^7+160\,a^{16}\,b^8+120\,a^{15}\,b^9-120\,a^{14}\,b^{10}-48\,a^{13}\,b^{11}+48\,a^{12}\,b^{12}+8\,a^{11}\,b^{13}-8\,a^{10}\,b^{14}\right)}{\left(a^{19}-7\,a^{17}\,b^2+21\,a^{15}\,b^4-35\,a^{13}\,b^6+35\,a^{11}\,b^8-21\,a^9\,b^{10}+7\,a^7\,b^{12}-a^5\,b^{14}\right)\,\left(a^{19}+a^{18}\,b-5\,a^{17}\,b^2-5\,a^{16}\,b^3+10\,a^{15}\,b^4+10\,a^{14}\,b^5-10\,a^{13}\,b^6-10\,a^{12}\,b^7+5\,a^{11}\,b^8+5\,a^{10}\,b^9-a^9\,b^{10}-a^8\,b^{11}\right)}\right)\,\sqrt{-{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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(20\,a^6-35\,a^4\,b^2+28\,a^2\,b^4-8\,b^6\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,"(b*atan(((b*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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*b*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (32*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5)*4i)/a^5 + (b*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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*b*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (32*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5)*4i)/a^5)/((32*(128*b^16 - 64*a*b^15 - 832*a^2*b^14 + 400*a^3*b^13 + 2288*a^4*b^12 - 1088*a^5*b^11 - 3472*a^6*b^10 + 1602*a^7*b^9 + 3088*a^8*b^8 - 1280*a^9*b^7 - 1520*a^10*b^6 + 480*a^11*b^5 + 320*a^12*b^4))/(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*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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*b*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (32*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5))/a^5 + (4*b*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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*b*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (32*b*tan(c/2 + (d*x)/2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/(a^5*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2))))/a^5))/a^5))*8i)/(a^5*d) - ((tan(c/2 + (d*x)/2)^3*(12*a*b^7 - 18*a^8 - 72*b^8 + 236*a^2*b^6 - 47*a^3*b^5 - 273*a^4*b^4 + 60*a^5*b^3 + 72*a^6*b^2))/(3*a^4*(a + b)^2*(a - b)^3) - (tan(c/2 + (d*x)/2)^5*(12*a*b^7 + 18*a^8 + 72*b^8 - 236*a^2*b^6 - 47*a^3*b^5 + 273*a^4*b^4 + 60*a^5*b^3 - 72*a^6*b^2))/(3*a^4*(a + b)^3*(a - b)^2) + (tan(c/2 + (d*x)/2)*(4*a*b^6 - 2*a^6*b - 2*a^7 + 8*b^7 - 24*a^2*b^5 - 11*a^3*b^4 + 26*a^4*b^3 + 6*a^5*b^2))/(a^4*(a + b)*(a - b)^3) + (tan(c/2 + (d*x)/2)^7*(4*a*b^6 + 2*a^6*b - 2*a^7 - 8*b^7 + 24*a^2*b^5 - 11*a^3*b^4 - 26*a^4*b^3 + 6*a^5*b^2))/(a^4*(a + b)^3*(a - b)))/(d*(3*a*b^2 + 3*a^2*b - tan(c/2 + (d*x)/2)^4*(6*a^2*b - 6*b^3) - tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 2*a^3 + 4*b^3) - tan(c/2 + (d*x)/2)^6*(2*a^3 - 6*a*b^2 + 4*b^3) + a^3 + b^3 - tan(c/2 + (d*x)/2)^8*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) + (b^2*atan(((b^2*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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^2*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (b^2*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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^2*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2)*1i)/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))/((32*(128*b^16 - 64*a*b^15 - 832*a^2*b^14 + 400*a^3*b^13 + 2288*a^4*b^12 - 1088*a^5*b^11 - 3472*a^6*b^10 + 1602*a^7*b^9 + 3088*a^8*b^8 - 1280*a^9*b^7 - 1520*a^10*b^6 + 480*a^11*b^5 + 320*a^12*b^4))/(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^2*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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^2*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) - (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)) + (b^2*((8*tan(c/2 + (d*x)/2)*(128*b^16 - 128*a*b^15 - 768*a^2*b^14 + 768*a^3*b^13 + 1920*a^4*b^12 - 1920*a^5*b^11 - 2600*a^6*b^10 + 2560*a^7*b^9 + 2025*a^8*b^8 - 1920*a^9*b^7 - 824*a^10*b^6 + 768*a^11*b^5 + 80*a^12*b^4 - 128*a^13*b^3 + 64*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^2*((16*(8*a^23*b - 8*a^10*b^14 + 4*a^11*b^13 + 52*a^12*b^12 - 25*a^13*b^11 - 143*a^14*b^10 + 63*a^15*b^9 + 217*a^16*b^8 - 87*a^17*b^7 - 193*a^18*b^6 + 73*a^19*b^5 + 95*a^20*b^4 - 36*a^21*b^3 - 20*a^22*b^2))/(a^22*b + a^23 - a^12*b^11 - a^13*b^10 + 5*a^14*b^9 + 5*a^15*b^8 - 10*a^16*b^7 - 10*a^17*b^6 + 10*a^18*b^5 + 10*a^19*b^4 - 5*a^20*b^3 - 5*a^21*b^2) + (4*b^2*tan(c/2 + (d*x)/2)*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2)*(8*a^23*b - 8*a^10*b^14 + 8*a^11*b^13 + 48*a^12*b^12 - 48*a^13*b^11 - 120*a^14*b^10 + 120*a^15*b^9 + 160*a^16*b^8 - 160*a^17*b^7 - 120*a^18*b^6 + 120*a^19*b^5 + 48*a^20*b^4 - 48*a^21*b^3 - 8*a^22*b^2))/((a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)*(a^18*b + a^19 - a^8*b^11 - a^9*b^10 + 5*a^10*b^9 + 5*a^11*b^8 - 10*a^12*b^7 - 10*a^13*b^6 + 10*a^14*b^5 + 10*a^15*b^4 - 5*a^16*b^3 - 5*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2)))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2))/(2*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))))*(-(a + b)^7*(a - b)^7)^(1/2)*(20*a^6 - 8*b^6 + 28*a^2*b^4 - 35*a^4*b^2)*1i)/(d*(a^19 - a^5*b^14 + 7*a^7*b^12 - 21*a^9*b^10 + 35*a^11*b^8 - 35*a^13*b^6 + 21*a^15*b^4 - 7*a^17*b^2))","B"
486,0,-1,264,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\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))^(1/2), x)","F"
487,0,-1,207,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\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))^(1/2), x)","F"
488,0,-1,162,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\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))^(1/2), x)","F"
489,0,-1,57,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2),x)","\int \sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(1/2), x)","F"
490,0,-1,118,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x),x)","\int \frac{\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))^(1/2)/cos(c + d*x), x)","F"
491,0,-1,197,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x)^2,x)","\int \frac{\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))^(1/2)/cos(c + d*x)^2, x)","F"
492,0,-1,262,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x)^3,x)","\int \frac{\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))^(1/2)/cos(c + d*x)^3, x)","F"
493,0,-1,314,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b*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)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2), x)","F"
494,0,-1,258,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(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)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2), x)","F"
495,0,-1,199,0.000000,"\text{Not used}","int(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)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2), x)","F"
496,0,-1,157,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(3/2),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2), x)","F"
497,0,-1,179,0.000000,"\text{Not used}","int((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)}^{3/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x), x)","F"
498,0,-1,209,0.000000,"\text{Not used}","int((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)}^{3/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^2, x)","F"
499,0,-1,255,0.000000,"\text{Not used}","int((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)}^{3/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^3, x)","F"
500,0,-1,371,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2),x)","\int {\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(cos(c + d*x)^3*(a + b*cos(c + d*x))^(5/2), x)","F"
501,0,-1,308,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(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)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2), x)","F"
502,0,-1,249,0.000000,"\text{Not used}","int(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)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2), x)","F"
503,0,-1,197,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(5/2),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2), x)","F"
504,0,-1,222,0.000000,"\text{Not used}","int((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)}^{5/2}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x), x)","F"
505,0,-1,222,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^2, x)","F"
506,0,-1,270,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^3, x)","F"
507,0,-1,323,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^4, x)","F"
508,0,-1,246,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(7/2),x)","\int {\left(a+b\,\cos\left(c+d\,x\right)\right)}^{7/2} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(7/2), x)","F"
509,0,-1,138,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(4*cos(c + d*x) + 3)^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{4\,\cos\left(c+d\,x\right)+3} \,d x","Not used",1,"int(cos(c + d*x)^3*(4*cos(c + d*x) + 3)^(1/2), x)","F"
510,0,-1,105,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(4*cos(c + d*x) + 3)^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{4\,\cos\left(c+d\,x\right)+3} \,d x","Not used",1,"int(cos(c + d*x)^2*(4*cos(c + d*x) + 3)^(1/2), x)","F"
511,0,-1,78,0.000000,"\text{Not used}","int(cos(c + d*x)*(4*cos(c + d*x) + 3)^(1/2),x)","\int \cos\left(c+d\,x\right)\,\sqrt{4\,\cos\left(c+d\,x\right)+3} \,d x","Not used",1,"int(cos(c + d*x)*(4*cos(c + d*x) + 3)^(1/2), x)","F"
512,0,-1,23,0.000000,"\text{Not used}","int((4*cos(c + d*x) + 3)^(1/2),x)","\int \sqrt{4\,\cos\left(c+d\,x\right)+3} \,d x","Not used",1,"int((4*cos(c + d*x) + 3)^(1/2), x)","F"
513,0,-1,48,0.000000,"\text{Not used}","int((4*cos(c + d*x) + 3)^(1/2)/cos(c + d*x),x)","\int \frac{\sqrt{4\,\cos\left(c+d\,x\right)+3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((4*cos(c + d*x) + 3)^(1/2)/cos(c + d*x), x)","F"
514,0,-1,95,0.000000,"\text{Not used}","int((4*cos(c + d*x) + 3)^(1/2)/cos(c + d*x)^2,x)","\int \frac{\sqrt{4\,\cos\left(c+d\,x\right)+3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((4*cos(c + d*x) + 3)^(1/2)/cos(c + d*x)^2, x)","F"
515,0,-1,135,0.000000,"\text{Not used}","int((4*cos(c + d*x) + 3)^(1/2)/cos(c + d*x)^3,x)","\int \frac{\sqrt{4\,\cos\left(c+d\,x\right)+3}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((4*cos(c + d*x) + 3)^(1/2)/cos(c + d*x)^3, x)","F"
516,0,-1,140,0.000000,"\text{Not used}","int(cos(c + d*x)^3*(3 - 4*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^3\,\sqrt{3-4\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^3*(3 - 4*cos(c + d*x))^(1/2), x)","F"
517,0,-1,107,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(3 - 4*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{3-4\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^2*(3 - 4*cos(c + d*x))^(1/2), x)","F"
518,0,-1,80,0.000000,"\text{Not used}","int(cos(c + d*x)*(3 - 4*cos(c + d*x))^(1/2),x)","\int \cos\left(c+d\,x\right)\,\sqrt{3-4\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)*(3 - 4*cos(c + d*x))^(1/2), x)","F"
519,0,-1,24,0.000000,"\text{Not used}","int((3 - 4*cos(c + d*x))^(1/2),x)","\int \sqrt{3-4\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((3 - 4*cos(c + d*x))^(1/2), x)","F"
520,0,-1,50,0.000000,"\text{Not used}","int((3 - 4*cos(c + d*x))^(1/2)/cos(c + d*x),x)","\int \frac{\sqrt{3-4\,\cos\left(c+d\,x\right)}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((3 - 4*cos(c + d*x))^(1/2)/cos(c + d*x), x)","F"
521,0,-1,98,0.000000,"\text{Not used}","int((3 - 4*cos(c + d*x))^(1/2)/cos(c + d*x)^2,x)","\int \frac{\sqrt{3-4\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((3 - 4*cos(c + d*x))^(1/2)/cos(c + d*x)^2, x)","F"
522,0,-1,138,0.000000,"\text{Not used}","int((3 - 4*cos(c + d*x))^(1/2)/cos(c + d*x)^3,x)","\int \frac{\sqrt{3-4\,\cos\left(c+d\,x\right)}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((3 - 4*cos(c + d*x))^(1/2)/cos(c + d*x)^3, x)","F"
523,0,-1,215,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{\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))^(1/2), x)","F"
524,1,116,165,0.564063,"\text{Not used}","int(cos(c + d*x)^2/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,\sin\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}{3\,b\,d}+\frac{2\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}\,\left(\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(2\,a^2+b^2\right)-2\,a\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)\right)}{3\,b^2\,d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*sin(c + d*x)*(a + b*cos(c + d*x))^(1/2))/(3*b*d) + (2*((a + b*cos(c + d*x))/(a + b))^(1/2)*(ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*(2*a^2 + b^2) - 2*a*ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b)))/(3*b^2*d*(a + b*cos(c + d*x))^(1/2))","B"
525,1,80,122,0.660158,"\text{Not used}","int(cos(c + d*x)/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,\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*(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"
526,1,52,57,0.599335,"\text{Not used}","int(1/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*ellipticF(c/2 + (d*x)/2, (2*b)/(a + b))*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2))","B"
527,0,-1,58,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b*cos(c + d*x))^(1/2)), x)","F"
528,0,-1,206,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(1/2)), x)","F"
529,0,-1,268,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(1/2)), x)","F"
530,0,-1,326,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(a + b*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)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + b*cos(c + d*x))^(3/2), x)","F"
531,0,-1,257,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(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)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + b*cos(c + d*x))^(3/2), x)","F"
532,0,-1,186,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(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)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + b*cos(c + d*x))^(3/2), x)","F"
533,0,-1,170,0.000000,"\text{Not used}","int(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)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)/(a + b*cos(c + d*x))^(3/2), x)","F"
534,0,-1,106,0.000000,"\text{Not used}","int(1/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*cos(c + d*x))^(3/2), x)","F"
535,0,-1,176,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)),x)","\int \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(1/(cos(c + d*x)*(a + b*cos(c + d*x))^(3/2)), x)","F"
536,0,-1,277,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(3/2)), x)","F"
537,0,-1,345,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^3*(a + b*cos(c + d*x))^(3/2)), x)","F"
538,0,-1,436,0.000000,"\text{Not used}","int(cos(c + d*x)^5/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^5/(a + b*cos(c + d*x))^(5/2), x)","F"
539,0,-1,345,0.000000,"\text{Not used}","int(cos(c + d*x)^4/(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)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^4/(a + b*cos(c + d*x))^(5/2), x)","F"
540,0,-1,281,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(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)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^3/(a + b*cos(c + d*x))^(5/2), x)","F"
541,0,-1,263,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(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)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^2/(a + b*cos(c + d*x))^(5/2), x)","F"
542,0,-1,243,0.000000,"\text{Not used}","int(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)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)/(a + b*cos(c + d*x))^(5/2), x)","F"
543,0,-1,221,0.000000,"\text{Not used}","int(1/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b*cos(c + d*x))^(5/2), x)","F"
544,0,-1,320,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)),x)","\int \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(1/(cos(c + d*x)*(a + b*cos(c + d*x))^(5/2)), x)","F"
545,0,-1,380,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^2*(a + b*cos(c + d*x))^(5/2)), x)","F"
546,0,-1,282,0.000000,"\text{Not used}","int(1/(a + b*cos(c + d*x))^(7/2),x)","\int \frac{1}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int(1/(a + b*cos(c + d*x))^(7/2), x)","F"
547,0,-1,111,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(4*cos(c + d*x) + 3)^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{\sqrt{4\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int(cos(c + d*x)^3/(4*cos(c + d*x) + 3)^(1/2), x)","F"
548,1,78,78,0.089636,"\text{Not used}","int(cos(c + d*x)^2/(4*cos(c + d*x) + 3)^(1/2),x)","\frac{\sin\left(c+d\,x\right)\,\sqrt{4\,\cos\left(c+d\,x\right)+3}}{6\,d}-\frac{\sqrt{\frac{4\,\cos\left(c+d\,x\right)}{7}+\frac{3}{7}}\,\left(42\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{8}{7}\right)-34\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{8}{7}\right)\right)}{24\,d\,\sqrt{4\,\cos\left(c+d\,x\right)+3}}","Not used",1,"(sin(c + d*x)*(4*cos(c + d*x) + 3)^(1/2))/(6*d) - (((4*cos(c + d*x))/7 + 3/7)^(1/2)*(42*ellipticE(c/2 + (d*x)/2, 8/7) - 34*ellipticF(c/2 + (d*x)/2, 8/7)))/(24*d*(4*cos(c + d*x) + 3)^(1/2))","B"
549,1,54,51,0.627946,"\text{Not used}","int(cos(c + d*x)/(4*cos(c + d*x) + 3)^(1/2),x)","\frac{\sqrt{\frac{4\,\cos\left(c+d\,x\right)}{7}+\frac{3}{7}}\,\left(7\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{8}{7}\right)-3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{8}{7}\right)\right)}{2\,d\,\sqrt{4\,\cos\left(c+d\,x\right)+3}}","Not used",1,"(((4*cos(c + d*x))/7 + 3/7)^(1/2)*(7*ellipticE(c/2 + (d*x)/2, 8/7) - 3*ellipticF(c/2 + (d*x)/2, 8/7)))/(2*d*(4*cos(c + d*x) + 3)^(1/2))","B"
550,1,39,23,0.573181,"\text{Not used}","int(1/(4*cos(c + d*x) + 3)^(1/2),x)","\frac{2\,\sqrt{\frac{4\,\cos\left(c+d\,x\right)}{7}+\frac{3}{7}}\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{8}{7}\right)}{d\,\sqrt{4\,\cos\left(c+d\,x\right)+3}}","Not used",1,"(2*((4*cos(c + d*x))/7 + 3/7)^(1/2)*ellipticF(c/2 + (d*x)/2, 8/7))/(d*(4*cos(c + d*x) + 3)^(1/2))","B"
551,0,-1,24,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(4*cos(c + d*x) + 3)^(1/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,\sqrt{4\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(4*cos(c + d*x) + 3)^(1/2)), x)","F"
552,0,-1,101,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(4*cos(c + d*x) + 3)^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,\sqrt{4\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(4*cos(c + d*x) + 3)^(1/2)), x)","F"
553,0,-1,137,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(4*cos(c + d*x) + 3)^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,\sqrt{4\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(4*cos(c + d*x) + 3)^(1/2)), x)","F"
554,0,-1,113,0.000000,"\text{Not used}","int(cos(c + d*x)^3/(3 - 4*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^3}{\sqrt{3-4\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^3/(3 - 4*cos(c + d*x))^(1/2), x)","F"
555,1,78,80,0.089416,"\text{Not used}","int(cos(c + d*x)^2/(3 - 4*cos(c + d*x))^(1/2),x)","\frac{\sqrt{4\,\cos\left(c+d\,x\right)-3}\,\left(6\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|8\right)+34\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|8\right)\right)}{24\,d\,\sqrt{3-4\,\cos\left(c+d\,x\right)}}-\frac{\sin\left(c+d\,x\right)\,\sqrt{3-4\,\cos\left(c+d\,x\right)}}{6\,d}","Not used",1,"((4*cos(c + d*x) - 3)^(1/2)*(6*ellipticE(c/2 + (d*x)/2, 8) + 34*ellipticF(c/2 + (d*x)/2, 8)))/(24*d*(3 - 4*cos(c + d*x))^(1/2)) - (sin(c + d*x)*(3 - 4*cos(c + d*x))^(1/2))/(6*d)","B"
556,1,52,53,0.139721,"\text{Not used}","int(cos(c + d*x)/(3 - 4*cos(c + d*x))^(1/2),x)","\frac{\sqrt{4\,\cos\left(c+d\,x\right)-3}\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|8\right)+3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|8\right)\right)}{2\,d\,\sqrt{3-4\,\cos\left(c+d\,x\right)}}","Not used",1,"((4*cos(c + d*x) - 3)^(1/2)*(ellipticE(c/2 + (d*x)/2, 8) + 3*ellipticF(c/2 + (d*x)/2, 8)))/(2*d*(3 - 4*cos(c + d*x))^(1/2))","B"
557,1,39,24,0.570434,"\text{Not used}","int(1/(3 - 4*cos(c + d*x))^(1/2),x)","\frac{2\,\sqrt{4\,\cos\left(c+d\,x\right)-3}\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|8\right)}{d\,\sqrt{3-4\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*(4*cos(c + d*x) - 3)^(1/2)*ellipticF(c/2 + (d*x)/2, 8))/(d*(3 - 4*cos(c + d*x))^(1/2))","B"
558,0,-1,25,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(3 - 4*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,\sqrt{3-4\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(3 - 4*cos(c + d*x))^(1/2)), x)","F"
559,0,-1,104,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(3 - 4*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,\sqrt{3-4\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(3 - 4*cos(c + d*x))^(1/2)), x)","F"
560,0,-1,140,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(3 - 4*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,\sqrt{3-4\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(3 - 4*cos(c + d*x))^(1/2)), x)","F"
561,1,87,111,0.962213,"\text{Not used}","int(cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)),x)","-\frac{2\,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\,{\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*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*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"
562,1,80,87,0.739809,"\text{Not used}","int(cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,A\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,B\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*A*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*B*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
563,1,53,61,0.653326,"\text{Not used}","int(cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)),x)","\frac{2\,A\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,B\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*A*ellipticE(c/2 + (d*x)/2, 2))/d + (2*B*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*B*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
564,1,33,35,0.260055,"\text{Not used}","int((A + B*cos(c + d*x))/cos(c + d*x)^(1/2),x)","\frac{2\,A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}","Not used",1,"(2*A*ellipticF(c/2 + (d*x)/2, 2))/d + (2*B*ellipticE(c/2 + (d*x)/2, 2))/d","B"
565,1,60,57,0.973276,"\text{Not used}","int((A + B*cos(c + d*x))/cos(c + d*x)^(3/2),x)","\frac{2\,B\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,A\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*B*ellipticF(c/2 + (d*x)/2, 2))/d + (2*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"
566,1,87,83,1.230783,"\text{Not used}","int((A + B*cos(c + d*x))/cos(c + d*x)^(5/2),x)","\frac{2\,A\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{2\,B\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*A*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (2*B*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
567,1,87,111,1.461135,"\text{Not used}","int((A + B*cos(c + d*x))/cos(c + d*x)^(7/2),x)","\frac{2\,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\,\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*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*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"
568,1,135,160,1.043597,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2,x)","-\frac{2\,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^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\,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^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^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*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"
569,1,128,135,0.890354,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2,x)","\frac{2\,\left(a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}-\frac{2\,b^2\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{9\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{4\,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*(a^2*ellipticF(c/2 + (d*x)/2, 2) + a^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) - (2*b^2*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (4*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"
570,1,102,101,1.006329,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{4\,a\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*a*b*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (4*a*b*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2))","B"
571,1,76,72,0.940650,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^(1/2),x)","\frac{2\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}+\frac{4\,a\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}","Not used",1,"(2*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*b^2*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*b^2*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) + (4*a*b*ellipticE(c/2 + (d*x)/2, 2))/d","B"
572,1,81,68,1.133920,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^(3/2),x)","\frac{2\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{4\,a\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,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^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*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"
573,1,108,95,1.239882,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^(5/2),x)","\frac{2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}+\frac{4\,a\,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^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*a^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(3*d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2)) + (4*a*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"
574,1,113,135,1.384904,"\text{Not used}","int((a + b*cos(c + d*x))^2/cos(c + d*x)^(7/2),x)","\frac{6\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,b^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\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{15\,d\,{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(6*a^2*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 30*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*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(15*d*cos(c + d*x)^(5/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
575,1,178,194,1.045715,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3,x)","\frac{2\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,a^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,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^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\,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^3*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*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^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*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"
576,1,146,159,0.938368,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3,x)","\frac{2\,\left(a^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a^2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{d}-\frac{2\,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\,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*(a^3*ellipticE(c/2 + (d*x)/2, 2) + a^2*b*ellipticF(c/2 + (d*x)/2, 2) + a^2*b*cos(c + d*x)^(1/2)*sin(c + d*x)))/d - (2*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*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"
577,1,125,116,0.876300,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^(1/2),x)","\frac{2\,a^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{d}-\frac{2\,b^3\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*a*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*a*b^2*cos(c + d*x)^(1/2)*sin(c + d*x))/d - (2*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"
578,1,124,124,0.929638,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^(3/2),x)","\frac{2\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{6\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,b^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}+\frac{2\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*b^3*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (6*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (6*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*b^3*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) + (2*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"
579,1,128,120,1.638290,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^(5/2),x)","\frac{2\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^3+3\,a\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,b^2\right)}{d}+\frac{2\,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^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^3*ellipticE(c/2 + (d*x)/2, 2) + 3*a*b^2*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*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^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"
580,1,156,149,1.738152,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^(7/2),x)","\frac{2\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,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\,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^2\,b\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*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*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^2*b*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
581,1,147,194,2.001456,"\text{Not used}","int((a + b*cos(c + d*x))^3/cos(c + d*x)^(9/2),x)","\frac{\frac{2\,a^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,b^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)+\frac{6\,a^2\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,a\,b^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"((2*a^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*b^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + (6*a^2*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*a*b^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
582,0,-1,112,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{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)), x)","F"
583,0,-1,75,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}}{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)), x)","F"
584,0,-1,53,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\cos\left(c+d\,x\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)), x)","F"
585,0,-1,29,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))), x)","F"
586,0,-1,77,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{3/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))), x)","F"
587,0,-1,128,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/2}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))), x)","F"
588,0,-1,245,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + b*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)}^2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)/(a + b*cos(c + d*x))^2, x)","F"
589,0,-1,185,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(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)}^2} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(a + b*cos(c + d*x))^2, x)","F"
590,0,-1,163,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(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)}^2} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(a + b*cos(c + d*x))^2, x)","F"
591,0,-1,148,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(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)}^2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(a + b*cos(c + d*x))^2, x)","F"
592,0,-1,157,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
593,0,-1,217,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
594,0,-1,281,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
595,0,-1,346,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)/(a + b*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)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)/(a + b*cos(c + d*x))^3, x)","F"
596,0,-1,282,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)/(a + b*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)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)/(a + b*cos(c + d*x))^3, x)","F"
597,0,-1,264,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(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)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(a + b*cos(c + d*x))^3, x)","F"
598,0,-1,244,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(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)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(a + b*cos(c + d*x))^3, x)","F"
599,0,-1,250,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(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)}^3} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(a + b*cos(c + d*x))^3, x)","F"
600,0,-1,261,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
601,0,-1,328,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
602,0,-1,395,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
603,0,-1,438,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,\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))^(1/2), x)","F"
604,0,-1,371,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \sqrt{\cos\left(c+d\,x\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))^(1/2), x)","F"
605,0,-1,135,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2),x)","\int \frac{\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))^(1/2)/cos(c + d*x)^(1/2), x)","F"
606,0,-1,229,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x)^(3/2),x)","\int \frac{\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))^(1/2)/cos(c + d*x)^(3/2), x)","F"
607,0,-1,271,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x)^(5/2),x)","\int \frac{\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))^(1/2)/cos(c + d*x)^(5/2), x)","F"
608,0,-1,329,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x)^(7/2),x)","\int \frac{\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))^(1/2)/cos(c + d*x)^(7/2), x)","F"
609,0,-1,389,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/cos(c + d*x)^(9/2),x)","\int \frac{\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))^(1/2)/cos(c + d*x)^(9/2), x)","F"
610,0,-1,508,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(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)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
611,0,-1,433,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(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)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
612,0,-1,375,0.000000,"\text{Not used}","int((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)}^{3/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^(1/2), x)","F"
613,0,-1,337,0.000000,"\text{Not used}","int((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)}^{3/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^(3/2), x)","F"
614,0,-1,277,0.000000,"\text{Not used}","int((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)}^{3/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^(5/2), x)","F"
615,0,-1,325,0.000000,"\text{Not used}","int((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)}^{3/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^(7/2), x)","F"
616,0,-1,387,0.000000,"\text{Not used}","int((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)}^{3/2}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^(9/2), x)","F"
617,0,-1,454,0.000000,"\text{Not used}","int((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)}^{3/2}}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/cos(c + d*x)^(11/2), x)","F"
618,0,-1,506,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(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)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
619,0,-1,443,0.000000,"\text{Not used}","int((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)}^{5/2}}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^(1/2), x)","F"
620,0,-1,445,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^(3/2), x)","F"
621,0,-1,392,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^(5/2), x)","F"
622,0,-1,338,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^(7/2), x)","F"
623,0,-1,387,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^(9/2), x)","F"
624,0,-1,454,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^(11/2), x)","F"
625,0,-1,522,0.000000,"\text{Not used}","int((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)}^{5/2}}{{\cos\left(c+d\,x\right)}^{13/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/cos(c + d*x)^(13/2), x)","F"
626,0,-1,379,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{3/2}}{\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))^(1/2), x)","F"
627,0,-1,116,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\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))^(1/2), x)","F"
628,0,-1,109,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
629,0,-1,224,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
630,0,-1,274,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
631,0,-1,465,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\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(cos(c + d*x)^(5/2)/(a + b*cos(c + d*x))^(3/2), x)","F"
632,0,-1,387,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(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)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(a + b*cos(c + d*x))^(3/2), x)","F"
633,0,-1,266,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(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)}^{3/2}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(a + b*cos(c + d*x))^(3/2), x)","F"
634,0,-1,267,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{\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(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
635,0,-1,285,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
636,0,-1,357,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
637,0,-1,433,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(7/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
638,0,-1,497,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(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)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^(5/2)/(a + b*cos(c + d*x))^(5/2), x)","F"
639,0,-1,342,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)/(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)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^(3/2)/(a + b*cos(c + d*x))^(5/2), x)","F"
640,0,-1,359,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(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)}^{5/2}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(a + b*cos(c + d*x))^(5/2), x)","F"
641,0,-1,381,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{1}{\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(1/(cos(c + d*x)^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
642,0,-1,398,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
643,0,-1,473,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/(cos(c + d*x)^(5/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
644,0,-1,32,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(3*cos(c + d*x) + 2)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{3\,\cos\left(c+d\,x\right)+2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(3*cos(c + d*x) + 2)^(1/2)), x)","F"
645,0,-1,25,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(3*cos(c + d*x) - 2)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(3*cos(c + d*x) - 2)^(1/2)), x)","F"
646,0,-1,56,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(2 - 3*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{2-3\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(2 - 3*cos(c + d*x))^(1/2)), x)","F"
647,0,-1,49,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(- 3*cos(c + d*x) - 2)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{-3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(- 3*cos(c + d*x) - 2)^(1/2)), x)","F"
648,0,-1,58,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(2*cos(c + d*x) + 3)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{2\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(2*cos(c + d*x) + 3)^(1/2)), x)","F"
649,0,-1,60,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(3 - 2*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{3-2\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(3 - 2*cos(c + d*x))^(1/2)), x)","F"
650,0,-1,84,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(2*cos(c + d*x) - 3)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(2*cos(c + d*x) - 3)^(1/2)), x)","F"
651,0,-1,82,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/2)*(- 2*cos(c + d*x) - 3)^(1/2)),x)","\int \frac{1}{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{-2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/2)*(- 2*cos(c + d*x) - 3)^(1/2)), x)","F"
652,0,-1,54,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(3*cos(c + d*x) + 2)^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{3\,\cos\left(c+d\,x\right)+2}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(3*cos(c + d*x) + 2)^(1/2)), x)","F"
653,0,-1,47,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(3*cos(c + d*x) - 2)^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(3*cos(c + d*x) - 2)^(1/2)), x)","F"
654,0,-1,34,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(2 - 3*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{2-3\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(2 - 3*cos(c + d*x))^(1/2)), x)","F"
655,0,-1,27,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(- 3*cos(c + d*x) - 2)^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{-3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(- 3*cos(c + d*x) - 2)^(1/2)), x)","F"
656,0,-1,80,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(2*cos(c + d*x) + 3)^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{2\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(2*cos(c + d*x) + 3)^(1/2)), x)","F"
657,0,-1,82,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(3 - 2*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{3-2\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(3 - 2*cos(c + d*x))^(1/2)), x)","F"
658,0,-1,62,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(2*cos(c + d*x) - 3)^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(2*cos(c + d*x) - 3)^(1/2)), x)","F"
659,0,-1,60,0.000000,"\text{Not used}","int(1/((-cos(c + d*x))^(1/2)*(- 2*cos(c + d*x) - 3)^(1/2)),x)","\int \frac{1}{\sqrt{-\cos\left(c+d\,x\right)}\,\sqrt{-2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int(1/((-cos(c + d*x))^(1/2)*(- 2*cos(c + d*x) - 3)^(1/2)), x)","F"
660,0,-1,77,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(3*cos(c + d*x) + 2)^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{3\,\cos\left(c+d\,x\right)+2}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(3*cos(c + d*x) + 2)^(1/2), x)","F"
661,0,-1,75,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(3*cos(c + d*x) - 2)^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(3*cos(c + d*x) - 2)^(1/2), x)","F"
662,0,-1,99,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(2 - 3*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{2-3\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(2 - 3*cos(c + d*x))^(1/2), x)","F"
663,0,-1,101,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(- 3*cos(c + d*x) - 2)^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{-3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(- 3*cos(c + d*x) - 2)^(1/2), x)","F"
664,0,-1,73,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(2*cos(c + d*x) + 3)^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{2\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(2*cos(c + d*x) + 3)^(1/2), x)","F"
665,0,-1,75,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(3 - 2*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{3-2\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(3 - 2*cos(c + d*x))^(1/2), x)","F"
666,0,-1,99,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(2*cos(c + d*x) - 3)^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(2*cos(c + d*x) - 3)^(1/2), x)","F"
667,0,-1,97,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)/(- 2*cos(c + d*x) - 3)^(1/2),x)","\int \frac{\sqrt{\cos\left(c+d\,x\right)}}{\sqrt{-2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int(cos(c + d*x)^(1/2)/(- 2*cos(c + d*x) - 3)^(1/2), x)","F"
668,0,-1,99,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(3*cos(c + d*x) + 2)^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{3\,\cos\left(c+d\,x\right)+2}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(3*cos(c + d*x) + 2)^(1/2), x)","F"
669,0,-1,97,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(3*cos(c + d*x) - 2)^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(3*cos(c + d*x) - 2)^(1/2), x)","F"
670,0,-1,77,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(2 - 3*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{2-3\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(2 - 3*cos(c + d*x))^(1/2), x)","F"
671,0,-1,79,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(- 3*cos(c + d*x) - 2)^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{-3\,\cos\left(c+d\,x\right)-2}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(- 3*cos(c + d*x) - 2)^(1/2), x)","F"
672,0,-1,95,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(2*cos(c + d*x) + 3)^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{2\,\cos\left(c+d\,x\right)+3}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(2*cos(c + d*x) + 3)^(1/2), x)","F"
673,0,-1,97,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(3 - 2*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{3-2\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(3 - 2*cos(c + d*x))^(1/2), x)","F"
674,0,-1,77,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(2*cos(c + d*x) - 3)^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(2*cos(c + d*x) - 3)^(1/2), x)","F"
675,0,-1,75,0.000000,"\text{Not used}","int((-cos(c + d*x))^(1/2)/(- 2*cos(c + d*x) - 3)^(1/2),x)","\int \frac{\sqrt{-\cos\left(c+d\,x\right)}}{\sqrt{-2\,\cos\left(c+d\,x\right)-3}} \,d x","Not used",1,"int((-cos(c + d*x))^(1/2)/(- 2*cos(c + d*x) - 3)^(1/2), x)","F"
676,0,-1,176,0.000000,"\text{Not used}","int(cos(c + d*x)^(2/3)/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{2/3}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(2/3)/(a + b*cos(c + d*x)), x)","F"
677,0,-1,176,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/3)/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^{1/3}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^(1/3)/(a + b*cos(c + d*x)), x)","F"
678,0,-1,176,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/3)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{1/3}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(1/3)*(a + b*cos(c + d*x))), x)","F"
679,0,-1,176,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(2/3)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{2/3}\,\left(a+b\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(2/3)*(a + b*cos(c + d*x))), x)","F"
680,0,-1,28,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/3)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{7/3}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(cos(c + d*x)^(7/3)/(a + b*cos(c + d*x))^(1/2), x)","F"
681,0,-1,28,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/3)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/3}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(cos(c + d*x)^(5/3)/(a + b*cos(c + d*x))^(1/2), x)","F"
682,0,-1,28,0.000000,"\text{Not used}","int(cos(c + d*x)^(4/3)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{4/3}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(cos(c + d*x)^(4/3)/(a + b*cos(c + d*x))^(1/2), x)","F"
683,0,-1,28,0.000000,"\text{Not used}","int(cos(c + d*x)^(2/3)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{2/3}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(cos(c + d*x)^(2/3)/(a + b*cos(c + d*x))^(1/2), x)","F"
684,0,-1,28,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/3)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{1/3}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(cos(c + d*x)^(1/3)/(a + b*cos(c + d*x))^(1/2), x)","F"
685,0,-1,28,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(1/3)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{1/3}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(1/(cos(c + d*x)^(1/3)*(a + b*cos(c + d*x))^(1/2)), x)","F"
686,0,-1,28,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(2/3)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{2/3}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(1/(cos(c + d*x)^(2/3)*(a + b*cos(c + d*x))^(1/2)), x)","F"
687,0,-1,28,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(4/3)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{4/3}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(1/(cos(c + d*x)^(4/3)*(a + b*cos(c + d*x))^(1/2)), x)","F"
688,0,-1,28,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(5/3)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{5/3}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(1/(cos(c + d*x)^(5/3)*(a + b*cos(c + d*x))^(1/2)), x)","F"
689,0,-1,28,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/3)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/3}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int(1/(cos(c + d*x)^(7/3)*(a + b*cos(c + d*x))^(1/2)), x)","F"
690,0,-1,151,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(7/2), x)","F"
691,0,-1,123,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/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} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(5/2), x)","F"
692,0,-1,97,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/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} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(3/2), x)","F"
693,0,-1,75,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(1/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)}} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(1/cos(c + d*x))^(1/2), x)","F"
694,0,-1,101,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(1/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)}}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(1/cos(c + d*x))^(1/2), x)","F"
695,0,-1,127,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(1/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}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(1/cos(c + d*x))^(3/2), x)","F"
696,0,-1,151,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(1/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}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(1/cos(c + d*x))^(5/2), x)","F"
697,0,-1,200,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^2, x)","F"
698,0,-1,175,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^2, x)","F"
699,0,-1,135,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2, x)","F"
700,0,-1,108,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2, x)","F"
701,0,-1,112,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2,x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2, x)","F"
702,0,-1,141,0.000000,"\text{Not used}","int((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)}^2}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^2/(1/cos(c + d*x))^(1/2), x)","F"
703,0,-1,175,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^2/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^2/(1/cos(c + d*x))^(3/2), x)","F"
704,0,-1,200,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^2/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^2/(1/cos(c + d*x))^(5/2), x)","F"
705,0,-1,234,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^3, x)","F"
706,0,-1,189,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^3, x)","F"
707,0,-1,160,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3, x)","F"
708,0,-1,166,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3, x)","F"
709,0,-1,156,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3,x)","\int \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((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3, x)","F"
710,0,-1,199,0.000000,"\text{Not used}","int((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)}^3}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^3/(1/cos(c + d*x))^(1/2), x)","F"
711,0,-1,234,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^3/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^3/(1/cos(c + d*x))^(3/2), x)","F"
712,0,-1,188,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x)), x)","F"
713,0,-1,117,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x)),x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x)), x)","F"
714,0,-1,49,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x)), x)","F"
715,0,-1,93,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))), x)","F"
716,0,-1,135,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))), x)","F"
717,0,-1,172,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))), x)","F"
718,0,-1,341,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^2, x)","F"
719,0,-1,277,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^2, x)","F"
720,0,-1,217,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^2,x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^2, x)","F"
721,0,-1,208,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^2), x)","F"
722,0,-1,223,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^2), x)","F"
723,0,-1,245,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^2), x)","F"
724,0,-1,455,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^3, x)","F"
725,0,-1,388,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^3, x)","F"
726,0,-1,321,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^3,x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^3, x)","F"
727,0,-1,317,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^3), x)","F"
728,0,-1,302,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^3), x)","F"
729,0,-1,319,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^3), x)","F"
730,0,-1,369,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2),x)","\int {\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((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
731,0,-1,311,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2),x)","\int {\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((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
732,0,-1,269,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2),x)","\int {\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((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
733,0,-1,155,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2),x)","\int \sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2), x)","F"
734,0,-1,431,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\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))^(1/2)/(1/cos(c + d*x))^(1/2), x)","F"
735,0,-1,498,0.000000,"\text{Not used}","int((a + b*cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\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))^(1/2)/(1/cos(c + d*x))^(3/2), x)","F"
736,0,-1,427,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
737,0,-1,365,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
738,0,-1,317,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
739,0,-1,397,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
740,0,-1,435,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2),x)","\int \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((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2), x)","F"
741,0,-1,493,0.000000,"\text{Not used}","int((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)}^{3/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/2), x)","F"
742,0,-1,568,0.000000,"\text{Not used}","int((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)}^{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))^(3/2)/(1/cos(c + d*x))^(3/2), x)","F"
743,0,-1,494,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
744,0,-1,427,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
745,0,-1,378,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
746,0,-1,452,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
747,0,-1,505,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
748,0,-1,503,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2),x)","\int \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((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2), x)","F"
749,0,-1,566,0.000000,"\text{Not used}","int((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)}^{5/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + b*cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(1/2), x)","F"
750,0,-1,638,0.000000,"\text{Not used}","int((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)}^{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))^(5/2)/(1/cos(c + d*x))^(3/2), x)","F"
751,0,-1,314,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\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((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^(1/2), x)","F"
752,0,-1,264,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{{\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((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^(1/2), x)","F"
753,0,-1,129,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^(1/2), x)","F"
754,0,-1,136,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{a+b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
755,0,-1,474,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
756,0,-1,505,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(1/2)), x)","F"
757,0,-1,397,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^(3/2), x)","F"
758,0,-1,325,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^(3/2), x)","F"
759,0,-1,307,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^(3/2),x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^(3/2), x)","F"
760,0,-1,306,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
761,0,-1,447,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
762,0,-1,525,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(3/2)), x)","F"
763,0,-1,513,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)/(a + b*cos(c + d*x))^(5/2), x)","F"
764,0,-1,438,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)/(a + b*cos(c + d*x))^(5/2), x)","F"
765,0,-1,421,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^(5/2),x)","\int \frac{\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((1/cos(c + d*x))^(1/2)/(a + b*cos(c + d*x))^(5/2), x)","F"
766,0,-1,399,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{1}{\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(1/((1/cos(c + d*x))^(1/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
767,0,-1,382,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(3/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
768,0,-1,557,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\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(1/((1/cos(c + d*x))^(5/2)*(a + b*cos(c + d*x))^(5/2)), x)","F"
769,0,-1,330,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + b*cos(c + d*x))^4,x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^4 \,d x","Not used",1,"int(cos(c + d*x)^m*(a + b*cos(c + d*x))^4, x)","F"
770,0,-1,250,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + b*cos(c + d*x))^3,x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int(cos(c + d*x)^m*(a + b*cos(c + d*x))^3, x)","F"
771,0,-1,179,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + b*cos(c + d*x))^2,x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int(cos(c + d*x)^m*(a + b*cos(c + d*x))^2, x)","F"
772,0,-1,131,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(a + b*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^m\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(a + b*cos(c + d*x)), x)","F"
773,0,-1,190,0.000000,"\text{Not used}","int(cos(c + d*x)^m/(a + b*cos(c + d*x)),x)","\int \frac{{\cos\left(c+d\,x\right)}^m}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(cos(c + d*x)^m/(a + b*cos(c + d*x)), x)","F"
774,0,-1,294,0.000000,"\text{Not used}","int(cos(c + d*x)^m/(a + b*cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^m}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^m/(a + b*cos(c + d*x))^2, x)","F"
775,0,-1,282,0.000000,"\text{Not used}","int((1/cos(c + d*x))^m*(a + b*cos(c + d*x))^3,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((1/cos(c + d*x))^m*(a + b*cos(c + d*x))^3, x)","F"
776,0,-1,200,0.000000,"\text{Not used}","int((1/cos(c + d*x))^m*(a + b*cos(c + d*x))^2,x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((1/cos(c + d*x))^m*(a + b*cos(c + d*x))^2, x)","F"
777,0,-1,143,0.000000,"\text{Not used}","int((1/cos(c + d*x))^m*(a + b*cos(c + d*x)),x)","\int {\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^m\,\left(a+b\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((1/cos(c + d*x))^m*(a + b*cos(c + d*x)), x)","F"
778,0,-1,26,0.000000,"\text{Not used}","int((1 - cos(x))^(1/2)/(a - cos(x))^(1/2),x)","\int \frac{\sqrt{1-\cos\left(x\right)}}{\sqrt{a-\cos\left(x\right)}} \,d x","Not used",1,"int((1 - cos(x))^(1/2)/(a - cos(x))^(1/2), x)","F"
779,0,-1,65,0.000000,"\text{Not used}","int((-(cos(x) - 1)/(a - cos(x)))^(1/2),x)","\int \sqrt{-\frac{\cos\left(x\right)-1}{a-\cos\left(x\right)}} \,d x","Not used",1,"int((-(cos(x) - 1)/(a - cos(x)))^(1/2), x)","F"
780,1,25,37,0.630050,"\text{Not used}","int(-(B/2 - B*cos(c + d*x))*(a + a*cos(c + d*x)),x)","\frac{B\,a\,\left(2\,\sin\left(c+d\,x\right)+\sin\left(2\,c+2\,d\,x\right)\right)}{4\,d}","Not used",1,"(B*a*(2*sin(c + d*x) + sin(2*c + 2*d*x)))/(4*d)","B"
781,1,29,26,0.677292,"\text{Not used}","int(-((4*B)/5 - B*cos(c + d*x))*(a + a*cos(c + d*x))^4,x)","\frac{32\,B\,a^4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5\,d}","Not used",1,"(32*B*a^4*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2))/(5*d)","B"
782,1,28,28,0.892247,"\text{Not used}","int((B*cos(c + d*x) - (B*n)/(n + 1))*(a + a*cos(c + d*x))^n,x)","\frac{B\,\sin\left(c+d\,x\right)\,{\left(a\,\left(\cos\left(c+d\,x\right)+1\right)\right)}^n}{d\,\left(n+1\right)}","Not used",1,"(B*sin(c + d*x)*(a*(cos(c + d*x) + 1))^n)/(d*(n + 1))","B"
783,1,33,26,0.640484,"\text{Not used}","int(-((3*B)/2 - B*cos(c + d*x))/(a + a*cos(c + d*x))^3,x)","-\frac{B\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}{8\,a^3\,d}","Not used",1,"-(B*tan(c/2 + (d*x)/2)*(tan(c/2 + (d*x)/2)^2 + 1)^2)/(8*a^3*d)","B"
784,0,-1,28,0.000000,"\text{Not used}","int(-((3*B)/5 - B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2),x)","\int -\left(\frac{3\,B}{5}-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(-((3*B)/5 - B*cos(c + d*x))*(a + a*cos(c + d*x))^(3/2), x)","F"
785,1,37,26,0.742256,"\text{Not used}","int((B + B*cos(c + d*x))/(a + a*cos(c + d*x))^(1/2),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,\sqrt{a\,\left(\cos\left(c+d\,x\right)+1\right)}}{a\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(2*B*sin(c + d*x)*(a*(cos(c + d*x) + 1))^(1/2))/(a*d*(cos(c + d*x) + 1))","B"
786,1,85,28,5.331213,"\text{Not used}","int(-((5*B)/3 - B*cos(c + d*x))/(a + a*cos(c + d*x))^(5/2),x)","\frac{8\,B\,{\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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,1{}\mathrm{i}-\mathrm{i}\right)}{3\,a^3\,d\,{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}^5}","Not used",1,"(8*B*exp(c*2i + d*x*2i)*(a + a*(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*1i - 1i))/(3*a^3*d*(exp(c*1i + d*x*1i) + 1)^5)","B"
787,0,-1,104,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(2/3),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(2/3), x)","F"
788,0,-1,102,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/3),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{1/3} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(a + a*cos(c + d*x))^(1/3), x)","F"
789,0,-1,101,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(1/3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(1/3), x)","F"
790,0,-1,105,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(2/3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(a+a\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(a + a*cos(c + d*x))^(2/3), x)","F"
791,1,93,63,0.936747,"\text{Not used}","int((B*cos(c + d*x) + (B*b)/a)/(a + b*cos(c + d*x)),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\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)}\right)\,\sqrt{b^2-a^2}}{a\,b\,d}","Not used",1,"(2*B*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d) + (2*B*atanh((sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a + b)))*(b^2 - a^2)^(1/2))/(a*b*d)","B"
792,1,37,22,0.845113,"\text{Not used}","int((a + b*cos(c + d*x))/(b + a*cos(c + d*x))^2,x)","\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*tan(c/2 + (d*x)/2))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
793,1,74,47,0.667494,"\text{Not used}","int(-(cos(c + d*x) + 3)/(cos(c + d*x) - 2),x)","\frac{\left(\frac{\pi -\frac{5\,\pi \,\sqrt{3}}{3}}{d}-\frac{\pi +\frac{5\,\pi \,\sqrt{3}}{3}}{d}\right)\,\left(\mathrm{atan}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\frac{d\,x}{2}\right)}{\pi }-\frac{d\,x-\frac{10\,\sqrt{3}\,\mathrm{atan}\left(\sqrt{3}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{3}}{d}","Not used",1,"(((pi - (5*3^(1/2)*pi)/3)/d - (pi + (5*3^(1/2)*pi)/3)/d)*(atan(tan(c/2 + (d*x)/2)) - (d*x)/2))/pi - (d*x - (10*3^(1/2)*atan(3^(1/2)*tan(c/2 + (d*x)/2)))/3)/d","B"
794,1,56,58,1.034688,"\text{Not used}","int((B*a + B*b*cos(c + d*x))/(a + b*cos(c + d*x))^(1/2),x)","\frac{2\,B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|\frac{2\,b}{a+b}\right)\,\left(a+b\right)\,\sqrt{\frac{a+b\,\cos\left(c+d\,x\right)}{a+b}}}{d\,\sqrt{a+b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*B*ellipticE(c/2 + (d*x)/2, (2*b)/(a + b))*(a + b)*((a + b*cos(c + d*x))/(a + b))^(1/2))/(d*(a + b*cos(c + d*x))^(1/2))","B"
795,0,-1,229,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(2/3),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{2/3} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(2/3), x)","F"
796,0,-1,229,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/3),x)","\int \left(A+B\,\cos\left(c+d\,x\right)\right)\,{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{1/3} \,d x","Not used",1,"int((A + B*cos(c + d*x))*(a + b*cos(c + d*x))^(1/3), x)","F"
797,0,-1,226,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(1/3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(1/3), x)","F"
798,0,-1,226,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(2/3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(a+b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(a + b*cos(c + d*x))^(2/3), x)","F"
799,0,-1,168,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^2\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)), x)","F"
800,0,-1,139,0.000000,"\text{Not used}","int(cos(c + d*x)*(b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)),x)","\int \cos\left(c+d\,x\right)\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)*(b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)), x)","F"
801,0,-1,108,0.000000,"\text{Not used}","int((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)),x)","\int \sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)), x)","F"
802,0,-1,80,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x),x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x), x)","F"
803,0,-1,105,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^2,x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^2, x)","F"
804,0,-1,136,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^3,x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^3, x)","F"
805,0,-1,169,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^4,x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^4, x)","F"
806,0,-1,169,0.000000,"\text{Not used}","int(cos(c + d*x)*(b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)),x)","\int \cos\left(c+d\,x\right)\,{\left(b\,\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(cos(c + d*x)*(b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)), x)","F"
807,0,-1,140,0.000000,"\text{Not used}","int((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)),x)","\int {\left(b\,\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*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)), x)","F"
808,0,-1,112,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x), x)","F"
809,0,-1,83,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^2,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^2, x)","F"
810,0,-1,110,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^3,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^3, x)","F"
811,0,-1,141,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^4,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^4, x)","F"
812,0,-1,174,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^5,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^5, x)","F"
813,0,-1,171,0.000000,"\text{Not used}","int((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)),x)","\int {\left(b\,\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*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)), x)","F"
814,0,-1,145,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x), x)","F"
815,0,-1,116,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^2,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^2, x)","F"
816,0,-1,85,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^3,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^3, x)","F"
817,0,-1,112,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^4,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^4, x)","F"
818,0,-1,143,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^5,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^5} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^5, x)","F"
819,0,-1,176,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^6,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^6} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^6, x)","F"
820,0,-1,173,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(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{b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/2), x)","F"
821,0,-1,144,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(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{b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/2), x)","F"
822,1,94,113,0.282092,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/2),x)","\frac{2\,B\,\sin\left(c+d\,x\right)\,\sqrt{b\,\cos\left(c+d\,x\right)}}{3\,b\,d}+\frac{2\,A\,\sqrt{\cos\left(c+d\,x\right)}\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d\,\sqrt{b\,\cos\left(c+d\,x\right)}}+\frac{2\,B\,\sqrt{\cos\left(c+d\,x\right)}\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d\,\sqrt{b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*B*sin(c + d*x)*(b*cos(c + d*x))^(1/2))/(3*b*d) + (2*A*cos(c + d*x)^(1/2)*ellipticE(c/2 + (d*x)/2, 2))/(d*(b*cos(c + d*x))^(1/2)) + (2*B*cos(c + d*x)^(1/2)*ellipticF(c/2 + (d*x)/2, 2))/(3*d*(b*cos(c + d*x))^(1/2))","B"
823,1,48,82,0.342239,"\text{Not used}","int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(1/2),x)","\frac{2\,\sqrt{\cos\left(c+d\,x\right)}\,\left(A\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+B\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\right)}{d\,\sqrt{b\,\cos\left(c+d\,x\right)}}","Not used",1,"(2*cos(c + d*x)^(1/2)*(A*ellipticF(c/2 + (d*x)/2, 2) + B*ellipticE(c/2 + (d*x)/2, 2)))/(d*(b*cos(c + d*x))^(1/2))","B"
824,0,-1,106,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(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{b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)*(b*cos(c + d*x))^(1/2)), x)","F"
825,0,-1,135,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(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{b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(b*cos(c + d*x))^(1/2)), x)","F"
826,0,-1,168,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(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{b\,\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(b*cos(c + d*x))^(1/2)), x)","F"
827,0,-1,176,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(b*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(b\,\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)))/(b*cos(c + d*x))^(3/2), x)","F"
828,0,-1,147,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(3/2), x)","F"
829,0,-1,116,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(3/2), x)","F"
830,0,-1,85,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(3/2), x)","F"
831,0,-1,112,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(3/2),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(3/2), x)","F"
832,0,-1,140,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(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(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)*(b*cos(c + d*x))^(3/2)), x)","F"
833,0,-1,171,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(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(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*(b*cos(c + d*x))^(3/2)), x)","F"
834,0,-1,176,0.000000,"\text{Not used}","int((cos(c + d*x)^5*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(5/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^5\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((cos(c + d*x)^5*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(5/2), x)","F"
835,0,-1,147,0.000000,"\text{Not used}","int((cos(c + d*x)^4*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(5/2), x)","F"
836,0,-1,116,0.000000,"\text{Not used}","int((cos(c + d*x)^3*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(5/2), x)","F"
837,0,-1,85,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(5/2), x)","F"
838,0,-1,112,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(5/2), x)","F"
839,0,-1,143,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(5/2),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(5/2), x)","F"
840,0,-1,173,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(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(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)*(b*cos(c + d*x))^(5/2)), x)","F"
841,0,-1,176,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(7/2),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(7/2), x)","F"
842,1,105,172,2.297047,"\text{Not used}","int(cos(c + d*x)^(5/2)*(b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(24\,B\,\sin\left(c+d\,x\right)+80\,A\,\sin\left(2\,c+2\,d\,x\right)+8\,A\,\sin\left(4\,c+4\,d\,x\right)+27\,B\,\sin\left(3\,c+3\,d\,x\right)+3\,B\,\sin\left(5\,c+5\,d\,x\right)+72\,B\,d\,x\,\cos\left(c+d\,x\right)\right)}{96\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(24*B*sin(c + d*x) + 80*A*sin(2*c + 2*d*x) + 8*A*sin(4*c + 4*d*x) + 27*B*sin(3*c + 3*d*x) + 3*B*sin(5*c + 5*d*x) + 72*B*d*x*cos(c + d*x)))/(96*d*(cos(2*c + 2*d*x) + 1))","B"
843,1,92,136,1.245186,"\text{Not used}","int(cos(c + d*x)^(3/2)*(b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(3\,A\,\sin\left(c+d\,x\right)+3\,A\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(4\,c+4\,d\,x\right)+12\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{12\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(3*A*sin(c + d*x) + 3*A*sin(3*c + 3*d*x) + 10*B*sin(2*c + 2*d*x) + B*sin(4*c + 4*d*x) + 12*A*d*x*cos(c + d*x)))/(12*d*(cos(2*c + 2*d*x) + 1))","B"
844,1,79,98,0.822468,"\text{Not used}","int(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(c+d\,x\right)+4\,A\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(3\,c+3\,d\,x\right)+4\,B\,d\,x\,\cos\left(c+d\,x\right)\right)}{4\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(B*sin(c + d*x) + 4*A*sin(2*c + 2*d*x) + B*sin(3*c + 3*d*x) + 4*B*d*x*cos(c + d*x)))/(4*d*(cos(2*c + 2*d*x) + 1))","B"
845,1,35,59,0.290526,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(c+d\,x\right)+A\,d\,x\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}}","Not used",1,"((b*cos(c + d*x))^(1/2)*(B*sin(c + d*x) + A*d*x))/(d*cos(c + d*x)^(1/2))","B"
846,0,-1,60,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(3/2), x)","F"
847,0,-1,68,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(5/2),x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(5/2), x)","F"
848,0,-1,107,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2), x)","F"
849,0,-1,145,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2),x)","\int \frac{\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2), x)","F"
850,1,106,177,1.909699,"\text{Not used}","int(cos(c + d*x)^(3/2)*(b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)),x)","\frac{b\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(24\,B\,\sin\left(c+d\,x\right)+80\,A\,\sin\left(2\,c+2\,d\,x\right)+8\,A\,\sin\left(4\,c+4\,d\,x\right)+27\,B\,\sin\left(3\,c+3\,d\,x\right)+3\,B\,\sin\left(5\,c+5\,d\,x\right)+72\,B\,d\,x\,\cos\left(c+d\,x\right)\right)}{96\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(b*cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(24*B*sin(c + d*x) + 80*A*sin(2*c + 2*d*x) + 8*A*sin(4*c + 4*d*x) + 27*B*sin(3*c + 3*d*x) + 3*B*sin(5*c + 5*d*x) + 72*B*d*x*cos(c + d*x)))/(96*d*(cos(2*c + 2*d*x) + 1))","B"
851,1,93,140,1.226353,"\text{Not used}","int(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)),x)","\frac{b\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(3\,A\,\sin\left(c+d\,x\right)+3\,A\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(4\,c+4\,d\,x\right)+12\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{12\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(b*cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(3*A*sin(c + d*x) + 3*A*sin(3*c + 3*d*x) + 10*B*sin(2*c + 2*d*x) + B*sin(4*c + 4*d*x) + 12*A*d*x*cos(c + d*x)))/(12*d*(cos(2*c + 2*d*x) + 1))","B"
852,1,50,101,0.517404,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\frac{b\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(4\,A\,\sin\left(c+d\,x\right)+B\,\sin\left(2\,c+2\,d\,x\right)+2\,B\,d\,x\right)}{4\,d\,\sqrt{\cos\left(c+d\,x\right)}}","Not used",1,"(b*(b*cos(c + d*x))^(1/2)*(4*A*sin(c + d*x) + B*sin(2*c + 2*d*x) + 2*B*d*x))/(4*d*cos(c + d*x)^(1/2))","B"
853,1,36,61,0.854127,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\frac{b\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(c+d\,x\right)+A\,d\,x\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}}","Not used",1,"(b*(b*cos(c + d*x))^(1/2)*(B*sin(c + d*x) + A*d*x))/(d*cos(c + d*x)^(1/2))","B"
854,0,-1,62,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(5/2), x)","F"
855,0,-1,70,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2), x)","F"
856,0,-1,110,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2), x)","F"
857,0,-1,149,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(11/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{3/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(3/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(11/2), x)","F"
858,1,108,187,2.192162,"\text{Not used}","int(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)),x)","\frac{b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(24\,B\,\sin\left(c+d\,x\right)+80\,A\,\sin\left(2\,c+2\,d\,x\right)+8\,A\,\sin\left(4\,c+4\,d\,x\right)+27\,B\,\sin\left(3\,c+3\,d\,x\right)+3\,B\,\sin\left(5\,c+5\,d\,x\right)+72\,B\,d\,x\,\cos\left(c+d\,x\right)\right)}{96\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(b^2*cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(24*B*sin(c + d*x) + 80*A*sin(2*c + 2*d*x) + 8*A*sin(4*c + 4*d*x) + 27*B*sin(3*c + 3*d*x) + 3*B*sin(5*c + 5*d*x) + 72*B*d*x*cos(c + d*x)))/(96*d*(cos(2*c + 2*d*x) + 1))","B"
859,1,64,148,0.712624,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\frac{b^2\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(9\,B\,\sin\left(c+d\,x\right)+3\,A\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(3\,c+3\,d\,x\right)+6\,A\,d\,x\right)}{12\,d\,\sqrt{\cos\left(c+d\,x\right)}}","Not used",1,"(b^2*(b*cos(c + d*x))^(1/2)*(9*B*sin(c + d*x) + 3*A*sin(2*c + 2*d*x) + B*sin(3*c + 3*d*x) + 6*A*d*x))/(12*d*cos(c + d*x)^(1/2))","B"
860,1,52,107,1.045240,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\frac{b^2\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(4\,A\,\sin\left(c+d\,x\right)+B\,\sin\left(2\,c+2\,d\,x\right)+2\,B\,d\,x\right)}{4\,d\,\sqrt{\cos\left(c+d\,x\right)}}","Not used",1,"(b^2*(b*cos(c + d*x))^(1/2)*(4*A*sin(c + d*x) + B*sin(2*c + 2*d*x) + 2*B*d*x))/(4*d*cos(c + d*x)^(1/2))","B"
861,1,38,65,1.040717,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(5/2),x)","\frac{b^2\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(c+d\,x\right)+A\,d\,x\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}}","Not used",1,"(b^2*(b*cos(c + d*x))^(1/2)*(B*sin(c + d*x) + A*d*x))/(d*cos(c + d*x)^(1/2))","B"
862,0,-1,66,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2), x)","F"
863,0,-1,74,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2), x)","F"
864,0,-1,116,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(11/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{11/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(11/2), x)","F"
865,0,-1,157,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(13/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{5/2}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{13/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^(5/2)*(A + B*cos(c + d*x)))/cos(c + d*x)^(13/2), x)","F"
866,1,95,136,1.821724,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(3\,A\,\sin\left(c+d\,x\right)+3\,A\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(4\,c+4\,d\,x\right)+12\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{12\,b\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(3*A*sin(c + d*x) + 3*A*sin(3*c + 3*d*x) + 10*B*sin(2*c + 2*d*x) + B*sin(4*c + 4*d*x) + 12*A*d*x*cos(c + d*x)))/(12*b*d*(cos(2*c + 2*d*x) + 1))","B"
867,1,82,98,1.368730,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(c+d\,x\right)+4\,A\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(3\,c+3\,d\,x\right)+4\,B\,d\,x\,\cos\left(c+d\,x\right)\right)}{4\,b\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(B*sin(c + d*x) + 4*A*sin(2*c + 2*d*x) + B*sin(3*c + 3*d*x) + 4*B*d*x*cos(c + d*x)))/(4*b*d*(cos(2*c + 2*d*x) + 1))","B"
868,1,61,59,0.537346,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(2\,c+2\,d\,x\right)+2\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{b\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(B*sin(2*c + 2*d*x) + 2*A*d*x*cos(c + d*x)))/(b*d*(cos(2*c + 2*d*x) + 1))","B"
869,0,-1,60,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(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{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)*(b*cos(c + d*x))^(1/2)), x)","F"
870,0,-1,68,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(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{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)*(b*cos(c + d*x))^(1/2)), x)","F"
871,0,-1,107,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(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{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)*(b*cos(c + d*x))^(1/2)), x)","F"
872,0,-1,145,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(7/2)*(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{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)*(b*cos(c + d*x))^(1/2)), x)","F"
873,1,95,148,1.565712,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(3/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(3\,A\,\sin\left(c+d\,x\right)+3\,A\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(4\,c+4\,d\,x\right)+12\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{12\,b^2\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(3*A*sin(c + d*x) + 3*A*sin(3*c + 3*d*x) + 10*B*sin(2*c + 2*d*x) + B*sin(4*c + 4*d*x) + 12*A*d*x*cos(c + d*x)))/(12*b^2*d*(cos(2*c + 2*d*x) + 1))","B"
874,1,82,107,0.687823,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(3/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(c+d\,x\right)+4\,A\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(3\,c+3\,d\,x\right)+4\,B\,d\,x\,\cos\left(c+d\,x\right)\right)}{4\,b^2\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(B*sin(c + d*x) + 4*A*sin(2*c + 2*d*x) + B*sin(3*c + 3*d*x) + 4*B*d*x*cos(c + d*x)))/(4*b^2*d*(cos(2*c + 2*d*x) + 1))","B"
875,1,61,65,1.020578,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(3/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(2\,c+2\,d\,x\right)+2\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{b^2\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(B*sin(2*c + 2*d*x) + 2*A*d*x*cos(c + d*x)))/(b^2*d*(cos(2*c + 2*d*x) + 1))","B"
876,0,-1,66,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(3/2), x)","F"
877,0,-1,74,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(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(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)*(b*cos(c + d*x))^(3/2)), x)","F"
878,0,-1,116,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(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(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)*(b*cos(c + d*x))^(3/2)), x)","F"
879,0,-1,157,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(5/2)*(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(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)*(b*cos(c + d*x))^(3/2)), x)","F"
880,1,95,148,1.558760,"\text{Not used}","int((cos(c + d*x)^(9/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(5/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(3\,A\,\sin\left(c+d\,x\right)+3\,A\,\sin\left(3\,c+3\,d\,x\right)+10\,B\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(4\,c+4\,d\,x\right)+12\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{12\,b^3\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(3*A*sin(c + d*x) + 3*A*sin(3*c + 3*d*x) + 10*B*sin(2*c + 2*d*x) + B*sin(4*c + 4*d*x) + 12*A*d*x*cos(c + d*x)))/(12*b^3*d*(cos(2*c + 2*d*x) + 1))","B"
881,1,82,107,0.700160,"\text{Not used}","int((cos(c + d*x)^(7/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(5/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(c+d\,x\right)+4\,A\,\sin\left(2\,c+2\,d\,x\right)+B\,\sin\left(3\,c+3\,d\,x\right)+4\,B\,d\,x\,\cos\left(c+d\,x\right)\right)}{4\,b^3\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(B*sin(c + d*x) + 4*A*sin(2*c + 2*d*x) + B*sin(3*c + 3*d*x) + 4*B*d*x*cos(c + d*x)))/(4*b^3*d*(cos(2*c + 2*d*x) + 1))","B"
882,1,61,65,0.481203,"\text{Not used}","int((cos(c + d*x)^(5/2)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(5/2),x)","\frac{\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{b\,\cos\left(c+d\,x\right)}\,\left(B\,\sin\left(2\,c+2\,d\,x\right)+2\,A\,d\,x\,\cos\left(c+d\,x\right)\right)}{b^3\,d\,\left(\cos\left(2\,c+2\,d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^(1/2)*(B*sin(2*c + 2*d*x) + 2*A*d*x*cos(c + d*x)))/(b^3*d*(cos(2*c + 2*d*x) + 1))","B"
883,0,-1,66,0.000000,"\text{Not used}","int((cos(c + d*x)^(3/2)*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(5/2), x)","F"
884,0,-1,74,0.000000,"\text{Not used}","int((cos(c + d*x)^(1/2)*(A + B*cos(c + d*x)))/(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(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)))/(b*cos(c + d*x))^(5/2), x)","F"
885,0,-1,116,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(1/2)*(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(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)*(b*cos(c + d*x))^(5/2)), x)","F"
886,0,-1,157,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^(3/2)*(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(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)*(b*cos(c + d*x))^(5/2)), x)","F"
887,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)), x)","F"
888,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)*(b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)),x)","\int \cos\left(c+d\,x\right)\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)*(b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)), x)","F"
889,0,-1,119,0.000000,"\text{Not used}","int((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)),x)","\int {\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)), x)","F"
890,0,-1,114,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)))/cos(c + d*x),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)))/cos(c + d*x), x)","F"
891,0,-1,112,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^2,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^2, x)","F"
892,0,-1,117,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^3,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^3, x)","F"
893,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)), x)","F"
894,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)*(b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)),x)","\int \cos\left(c+d\,x\right)\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)*(b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)), x)","F"
895,0,-1,119,0.000000,"\text{Not used}","int((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)),x)","\int {\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)), x)","F"
896,0,-1,116,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)))/cos(c + d*x),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)))/cos(c + d*x), x)","F"
897,0,-1,112,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^2,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^2, x)","F"
898,0,-1,115,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^3,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)))/cos(c + d*x)^3, x)","F"
899,0,-1,119,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(2/3),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(2/3), x)","F"
900,0,-1,119,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(2/3),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(2/3), x)","F"
901,0,-1,117,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(2/3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(2/3), x)","F"
902,0,-1,114,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(b*cos(c + d*x))^(2/3)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)*(b*cos(c + d*x))^(2/3)), x)","F"
903,0,-1,114,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(b*cos(c + d*x))^(2/3)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^2\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(b*cos(c + d*x))^(2/3)), x)","F"
904,0,-1,117,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(b*cos(c + d*x))^(2/3)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^3\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(b*cos(c + d*x))^(2/3)), x)","F"
905,0,-1,119,0.000000,"\text{Not used}","int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(4/3),x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((cos(c + d*x)^2*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(4/3), x)","F"
906,0,-1,119,0.000000,"\text{Not used}","int((cos(c + d*x)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(4/3),x)","\int \frac{\cos\left(c+d\,x\right)\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((cos(c + d*x)*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(4/3), x)","F"
907,0,-1,117,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(4/3),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(b*cos(c + d*x))^(4/3), x)","F"
908,0,-1,114,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)*(b*cos(c + d*x))^(4/3)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{\cos\left(c+d\,x\right)\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)*(b*cos(c + d*x))^(4/3)), x)","F"
909,0,-1,114,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(b*cos(c + d*x))^(4/3)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^2\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^2*(b*cos(c + d*x))^(4/3)), x)","F"
910,0,-1,117,0.000000,"\text{Not used}","int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(b*cos(c + d*x))^(4/3)),x)","\int \frac{A+B\,\cos\left(c+d\,x\right)}{{\cos\left(c+d\,x\right)}^3\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((A + B*cos(c + d*x))/(cos(c + d*x)^3*(b*cos(c + d*x))^(4/3)), x)","F"
911,0,-1,157,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)), x)","F"
912,0,-1,141,0.000000,"\text{Not used}","int(cos(c + d*x)^2*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^2\,{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^2*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)), x)","F"
913,0,-1,141,0.000000,"\text{Not used}","int(cos(c + d*x)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)),x)","\int \cos\left(c+d\,x\right)\,{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)), x)","F"
914,0,-1,141,0.000000,"\text{Not used}","int((b*cos(c + d*x))^n*(A + B*cos(c + d*x)),x)","\int {\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int((b*cos(c + d*x))^n*(A + B*cos(c + d*x)), x)","F"
915,0,-1,132,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x), x)","F"
916,0,-1,131,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^2,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^2, x)","F"
917,0,-1,139,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^3,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^3, x)","F"
918,0,-1,141,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^4,x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^4, x)","F"
919,0,-1,163,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^(5/2)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)), x)","F"
920,0,-1,163,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^(3/2)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)), x)","F"
921,0,-1,163,0.000000,"\text{Not used}","int(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)),x)","\int \sqrt{\cos\left(c+d\,x\right)}\,{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^(1/2)*(b*cos(c + d*x))^n*(A + B*cos(c + d*x)), x)","F"
922,0,-1,163,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(1/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{\sqrt{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(1/2), x)","F"
923,0,-1,163,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(3/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(3/2), x)","F"
924,0,-1,163,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(5/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(5/2), x)","F"
925,0,-1,163,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{7/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(7/2), x)","F"
926,0,-1,163,0.000000,"\text{Not used}","int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2),x)","\int \frac{{\left(b\,\cos\left(c+d\,x\right)\right)}^n\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\cos\left(c+d\,x\right)}^{9/2}} \,d x","Not used",1,"int(((b*cos(c + d*x))^n*(A + B*cos(c + d*x)))/cos(c + d*x)^(9/2), x)","F"
927,0,-1,169,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(b*cos(c + d*x))^(4/3)*(A + B*cos(c + d*x)), x)","F"
928,0,-1,167,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(b*cos(c + d*x))^(2/3)*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(b*cos(c + d*x))^(2/3)*(A + B*cos(c + d*x)), x)","F"
929,0,-1,167,0.000000,"\text{Not used}","int(cos(c + d*x)^m*(b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)),x)","\int {\cos\left(c+d\,x\right)}^m\,{\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}\,\left(A+B\,\cos\left(c+d\,x\right)\right) \,d x","Not used",1,"int(cos(c + d*x)^m*(b*cos(c + d*x))^(1/3)*(A + B*cos(c + d*x)), x)","F"
930,0,-1,167,0.000000,"\text{Not used}","int((cos(c + d*x)^m*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/3),x)","\int \frac{{\cos\left(c+d\,x\right)}^m\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int((cos(c + d*x)^m*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(1/3), x)","F"
931,0,-1,167,0.000000,"\text{Not used}","int((cos(c + d*x)^m*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(2/3),x)","\int \frac{{\cos\left(c+d\,x\right)}^m\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{2/3}} \,d x","Not used",1,"int((cos(c + d*x)^m*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(2/3), x)","F"
932,0,-1,171,0.000000,"\text{Not used}","int((cos(c + d*x)^m*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(4/3),x)","\int \frac{{\cos\left(c+d\,x\right)}^m\,\left(A+B\,\cos\left(c+d\,x\right)\right)}{{\left(b\,\cos\left(c+d\,x\right)\right)}^{4/3}} \,d x","Not used",1,"int((cos(c + d*x)^m*(A + B*cos(c + d*x)))/(b*cos(c + d*x))^(4/3), x)","F"