1,1,130,85,3.941498,"\text{Not used}","int((a + a/cos(c + d*x))/cos(c + d*x)^4,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"
2,1,102,63,2.510771,"\text{Not used}","int((a + a/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{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"
3,1,75,47,1.057134,"\text{Not used}","int((a + a/cos(c + d*x))/cos(c + d*x)^2,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"
4,1,47,24,0.684553,"\text{Not used}","int((a + a/cos(c + d*x))/cos(c + d*x),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"
5,1,20,16,0.609810,"\text{Not used}","int(a + a/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"
6,1,15,15,0.599754,"\text{Not used}","int(cos(c + d*x)*(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"
7,1,50,38,1.062549,"\text{Not used}","int(cos(c + d*x)^2*(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"
8,1,55,54,0.654197,"\text{Not used}","int(cos(c + d*x)^3*(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"
9,1,79,76,4.170230,"\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)}^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"
10,1,170,122,5.700436,"\text{Not used}","int((a + a/cos(c + d*x))^2/cos(c + d*x)^4,x)","\frac{3\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\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)}^{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^2*atanh(tan(c/2 + (d*x)/2)))/(2*d) - ((72*a^2*tan(c/2 + (d*x)/2)^5)/5 - 9*a^2*tan(c/2 + (d*x)/2)^3 - 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*(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"
11,1,141,96,3.959760,"\text{Not used}","int((a + a/cos(c + d*x))^2/cos(c + d*x)^3,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"
12,1,112,74,2.465919,"\text{Not used}","int((a + a/cos(c + d*x))^2/cos(c + d*x)^2,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"
13,1,83,54,1.175302,"\text{Not used}","int((a + a/cos(c + d*x))^2/cos(c + d*x),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"
14,1,56,34,0.710183,"\text{Not used}","int((a + a/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"
15,1,33,34,0.700497,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^2,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"
16,1,57,45,1.073715,"\text{Not used}","int(cos(c + d*x)^2*(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"
17,1,61,57,0.655744,"\text{Not used}","int(cos(c + d*x)^3*(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"
18,1,89,87,4.192582,"\text{Not used}","int(cos(c + d*x)^4*(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"
19,1,105,103,4.418772,"\text{Not used}","int(cos(c + d*x)^5*(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"
20,1,170,114,5.482327,"\text{Not used}","int((a + a/cos(c + d*x))^3/cos(c + d*x)^3,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"
21,1,141,93,4.052919,"\text{Not used}","int((a + a/cos(c + d*x))^3/cos(c + d*x)^2,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"
22,1,112,72,2.574332,"\text{Not used}","int((a + a/cos(c + d*x))^3/cos(c + d*x),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"
23,1,88,66,0.737210,"\text{Not used}","int((a + a/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"
24,1,57,48,0.700136,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^3,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"
25,1,88,59,0.725036,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^3,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"
26,1,63,63,0.669719,"\text{Not used}","int(cos(c + d*x)^3*(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"
27,1,89,85,4.173031,"\text{Not used}","int(cos(c + d*x)^4*(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"
28,1,105,105,4.376944,"\text{Not used}","int(cos(c + d*x)^5*(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"
29,1,121,129,3.491757,"\text{Not used}","int(cos(c + d*x)^6*(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"
30,1,199,136,4.648883,"\text{Not used}","int((a + a/cos(c + d*x))^4/cos(c + d*x)^3,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"
31,1,170,111,5.470394,"\text{Not used}","int((a + a/cos(c + d*x))^4/cos(c + d*x)^2,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"
32,1,141,96,3.989257,"\text{Not used}","int((a + a/cos(c + d*x))^4/cos(c + d*x),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"
33,1,117,91,0.878349,"\text{Not used}","int((a + a/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"
34,1,115,73,0.905305,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^4,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"
35,1,117,73,0.890703,"\text{Not used}","int(cos(c + d*x)^2*(a + a/cos(c + d*x))^4,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"
36,1,93,73,0.686838,"\text{Not used}","int(cos(c + d*x)^3*(a + a/cos(c + d*x))^4,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"
37,1,89,87,4.124943,"\text{Not used}","int(cos(c + d*x)^4*(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"
38,1,105,102,4.428461,"\text{Not used}","int(cos(c + d*x)^5*(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"
39,1,121,127,3.418477,"\text{Not used}","int(cos(c + d*x)^6*(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"
40,1,137,147,3.636042,"\text{Not used}","int(cos(c + d*x)^7*(a + a/cos(c + d*x))^4,x)","\frac{11\,a^4\,x}{4}+\frac{\frac{11\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{2}+\frac{110\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}+\frac{3113\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{30}+\frac{5632\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{35}+\frac{1501\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{10}+70\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{53\,a^4\,\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)}^7}","Not used",1,"(11*a^4*x)/4 + (70*a^4*tan(c/2 + (d*x)/2)^3 + (1501*a^4*tan(c/2 + (d*x)/2)^5)/10 + (5632*a^4*tan(c/2 + (d*x)/2)^7)/35 + (3113*a^4*tan(c/2 + (d*x)/2)^9)/30 + (110*a^4*tan(c/2 + (d*x)/2)^11)/3 + (11*a^4*tan(c/2 + (d*x)/2)^13)/2 + (53*a^4*tan(c/2 + (d*x)/2))/2)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^7)","B"
41,1,228,156,4.843347,"\text{Not used}","int((a + a/cos(c + d*x))^5/cos(c + d*x)^3,x)","\frac{93\,a^5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{\frac{93\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}-\frac{155\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{2}+\frac{8773\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{40}-\frac{11904\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{35}+\frac{37169\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{120}-\frac{943\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{419\,a^5\,\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)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(93*a^5*atanh(tan(c/2 + (d*x)/2)))/(8*d) - ((37169*a^5*tan(c/2 + (d*x)/2)^5)/120 - (943*a^5*tan(c/2 + (d*x)/2)^3)/6 - (11904*a^5*tan(c/2 + (d*x)/2)^7)/35 + (8773*a^5*tan(c/2 + (d*x)/2)^9)/40 - (155*a^5*tan(c/2 + (d*x)/2)^11)/2 + (93*a^5*tan(c/2 + (d*x)/2)^13)/8 + (419*a^5*tan(c/2 + (d*x)/2))/8)/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
42,1,96,103,0.932653,"\text{Not used}","int(1/(cos(c + d*x)^5*(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"
43,1,95,85,0.727183,"\text{Not used}","int(1/(cos(c + d*x)^4*(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"
44,1,67,51,0.678510,"\text{Not used}","int(1/(cos(c + d*x)^3*(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"
45,1,31,38,0.646592,"\text{Not used}","int(1/(cos(c + d*x)^2*(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"
46,1,16,22,0.589034,"\text{Not used}","int(1/(cos(c + d*x)*(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"
47,1,23,29,0.637707,"\text{Not used}","int(1/(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"
48,1,66,44,0.661686,"\text{Not used}","int(cos(c + d*x)/(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"
49,1,89,74,0.724564,"\text{Not used}","int(cos(c + d*x)^2/(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"
50,1,70,94,0.906995,"\text{Not used}","int(cos(c + d*x)^3/(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"
51,1,98,118,2.454282,"\text{Not used}","int(cos(c + d*x)^4/(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"
52,1,122,123,0.735013,"\text{Not used}","int(1/(cos(c + d*x)^5*(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"
53,1,92,89,0.687757,"\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{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"
54,1,43,66,0.642775,"\text{Not used}","int(1/(cos(c + d*x)^3*(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"
55,1,30,55,0.596415,"\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)\,\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"
56,1,30,55,0.596676,"\text{Not used}","int(1/(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"
57,1,35,57,0.629998,"\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)}^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"
58,1,91,72,0.698139,"\text{Not used}","int(cos(c + d*x)/(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"
59,1,113,110,0.734913,"\text{Not used}","int(cos(c + d*x)^2/(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"
60,1,135,124,0.782172,"\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)-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"
61,1,141,162,0.678504,"\text{Not used}","int(1/(cos(c + d*x)^6*(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"
62,1,111,128,0.682168,"\text{Not used}","int(1/(cos(c + d*x)^5*(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"
63,1,58,105,0.687817,"\text{Not used}","int(1/(cos(c + d*x)^4*(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"
64,1,45,83,0.616167,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a/cos(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\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"
65,1,30,83,0.596549,"\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)\,\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"
66,1,45,83,0.618742,"\text{Not used}","int(1/(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(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"
67,1,81,88,0.691653,"\text{Not used}","int(1/(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"
68,1,113,103,0.727878,"\text{Not used}","int(cos(c + d*x)/(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"
69,1,137,147,0.758032,"\text{Not used}","int(cos(c + d*x)^2/(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"
70,1,160,193,0.754210,"\text{Not used}","int(1/(cos(c + d*x)^7*(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"
71,1,130,159,0.702244,"\text{Not used}","int(1/(cos(c + d*x)^6*(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"
72,1,83,136,0.667549,"\text{Not used}","int(1/(cos(c + d*x)^5*(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"
73,1,58,120,0.672593,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^4),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(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"
74,1,58,112,0.661861,"\text{Not used}","int(1/(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(-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"
75,1,58,112,0.674807,"\text{Not used}","int(1/(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"
76,1,58,112,0.669497,"\text{Not used}","int(1/(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(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"
77,1,102,111,0.724727,"\text{Not used}","int(1/(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"
78,1,137,126,0.754883,"\text{Not used}","int(cos(c + d*x)/(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"
79,1,159,176,0.810575,"\text{Not used}","int(cos(c + d*x)^2/(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"
80,1,149,200,0.715028,"\text{Not used}","int(1/(cos(c + d*x)^7*(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"
81,1,99,177,0.691491,"\text{Not used}","int(1/(cos(c + d*x)^6*(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"
82,1,127,159,0.763543,"\text{Not used}","int(1/(cos(c + d*x)^5*(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"
83,1,58,159,0.719886,"\text{Not used}","int(1/(cos(c + d*x)^4*(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"
84,1,45,139,0.656184,"\text{Not used}","int(1/(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(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"
85,1,58,143,0.689056,"\text{Not used}","int(1/(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(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"
86,1,127,143,0.762674,"\text{Not used}","int(1/(cos(c + d*x)*(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"
87,1,125,144,0.798302,"\text{Not used}","int(1/(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"
88,1,159,159,0.831835,"\text{Not used}","int(cos(c + d*x)/(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"
89,1,181,215,0.949621,"\text{Not used}","int(cos(c + d*x)^2/(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"
90,1,331,122,5.925214,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^4,x)","-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,32{}\mathrm{i}}{35\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{\left(\frac{16{}\mathrm{i}}{7\,d}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,16{}\mathrm{i}}{7\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\left(\frac{16{}\mathrm{i}}{5\,d}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,128{}\mathrm{i}}{35\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,16{}\mathrm{i}}{35\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((16i/(5*d) + (exp(c*1i + d*x*1i)*128i)/(35*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((16i/(7*d) + (exp(c*1i + d*x*1i)*16i)/(7*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*32i)/(35*d*(exp(c*1i + d*x*1i) + 1)) - (exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*16i)/(35*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
91,1,115,86,4.458307,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^3,x)","\frac{8\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,5{}\mathrm{i}-{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,5{}\mathrm{i}-{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,2{}\mathrm{i}+2{}\mathrm{i}\right)}{15\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"(8*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*2i + d*x*2i)*5i - exp(c*3i + d*x*3i)*5i - exp(c*5i + d*x*5i)*2i + 2i))/(15*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
92,1,108,56,1.389010,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^2,x)","\frac{4\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(3\,\sin\left(c+d\,x\right)+4\,\sin\left(2\,c+2\,d\,x\right)+3\,\sin\left(3\,c+3\,d\,x\right)+\sin\left(4\,c+4\,d\,x\right)\right)}{3\,d\,\left(12\,\cos\left(c+d\,x\right)+8\,\cos\left(2\,c+2\,d\,x\right)+4\,\cos\left(3\,c+3\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)+7\right)}","Not used",1,"(4*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(3*sin(c + d*x) + 4*sin(2*c + 2*d*x) + 3*sin(3*c + 3*d*x) + sin(4*c + 4*d*x)))/(3*d*(12*cos(c + d*x) + 8*cos(2*c + 2*d*x) + 4*cos(3*c + 3*d*x) + cos(4*c + 4*d*x) + 7))","B"
93,1,41,26,0.190562,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x),x)","\frac{2\,\sin\left(c+d\,x\right)\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\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))/cos(c + d*x))^(1/2))/(d*(cos(c + d*x) + 1))","B"
94,0,-1,37,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2), x)","F"
95,0,-1,62,0.000000,"\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+\frac{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"
96,0,-1,102,0.000000,"\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+\frac{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"
97,0,-1,138,0.000000,"\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+\frac{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"
98,0,-1,174,0.000000,"\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+\frac{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"
99,1,429,162,6.700945,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x)^4,x)","\frac{\left(\frac{a\,32{}\mathrm{i}}{9\,d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,32{}\mathrm{i}}{9\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{\left(\frac{a\,80{}\mathrm{i}}{7\,d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,176{}\mathrm{i}}{63\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\left(\frac{a\,48{}\mathrm{i}}{5\,d}+\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,352{}\mathrm{i}}{105\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,544{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,272{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"(((a*32i)/(9*d) - (a*exp(c*1i + d*x*1i)*32i)/(9*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - (((a*80i)/(7*d) - (a*exp(c*1i + d*x*1i)*176i)/(63*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + (((a*48i)/(5*d) + (a*exp(c*1i + d*x*1i)*352i)/(105*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*544i)/(315*d*(exp(c*1i + d*x*1i) + 1)) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*272i)/(315*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
100,1,346,116,5.084242,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x)^3,x)","-\frac{\left(\frac{a\,16{}\mathrm{i}}{7\,d}+\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,16{}\mathrm{i}}{7\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\left(\frac{a\,8{}\mathrm{i}}{3\,d}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,104{}\mathrm{i}}{105\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\left(\frac{a\,8{}\mathrm{i}}{5\,d}+\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,184{}\mathrm{i}}{35\,d}\right)\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{a\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,208{}\mathrm{i}}{105\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"(((a*8i)/(3*d) - (a*exp(c*1i + d*x*1i)*104i)/(105*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - (((a*16i)/(7*d) + (a*exp(c*1i + d*x*1i)*16i)/(7*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + (((a*8i)/(5*d) + (a*exp(c*1i + d*x*1i)*184i)/(35*d))*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (a*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*208i)/(105*d*(exp(c*1i + d*x*1i) + 1))","B"
101,1,116,86,4.364073,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x)^2,x)","\frac{4\,a\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,5{}\mathrm{i}-{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,5{}\mathrm{i}-{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,3{}\mathrm{i}+3{}\mathrm{i}\right)}{5\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"(4*a*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*2i + d*x*2i)*5i - exp(c*3i + d*x*3i)*5i - exp(c*5i + d*x*5i)*3i + 3i))/(5*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
102,1,111,59,1.236982,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x),x)","\frac{2\,a\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(12\,\sin\left(c+d\,x\right)+14\,\sin\left(2\,c+2\,d\,x\right)+12\,\sin\left(3\,c+3\,d\,x\right)+5\,\sin\left(4\,c+4\,d\,x\right)\right)}{3\,d\,\left(12\,\cos\left(c+d\,x\right)+8\,\cos\left(2\,c+2\,d\,x\right)+4\,\cos\left(3\,c+3\,d\,x\right)+\cos\left(4\,c+4\,d\,x\right)+7\right)}","Not used",1,"(2*a*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(12*sin(c + d*x) + 14*sin(2*c + 2*d*x) + 12*sin(3*c + 3*d*x) + 5*sin(4*c + 4*d*x)))/(3*d*(12*cos(c + d*x) + 8*cos(2*c + 2*d*x) + 4*cos(3*c + 3*d*x) + cos(4*c + 4*d*x) + 7))","B"
103,0,-1,66,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
104,0,-1,65,0.000000,"\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+\frac{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"
105,0,-1,106,0.000000,"\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+\frac{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,-1,144,0.000000,"\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+\frac{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"
107,1,542,203,9.324526,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/cos(c + d*x)^4,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,64{}\mathrm{i}}{11\,d}+\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,64{}\mathrm{i}}{11\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^5}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,16{}\mathrm{i}}{d}+\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,640{}\mathrm{i}}{231\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,64{}\mathrm{i}}{9\,d}+\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,2176{}\mathrm{i}}{99\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,80{}\mathrm{i}}{7\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,12688{}\mathrm{i}}{693\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,2272{}\mathrm{i}}{693\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,1136{}\mathrm{i}}{693\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*64i)/(11*d) + (a^2*exp(c*1i + d*x*1i)*64i)/(11*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^5) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*16i)/d + (a^2*exp(c*1i + d*x*1i)*640i)/(231*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*64i)/(9*d) + (a^2*exp(c*1i + d*x*1i)*2176i)/(99*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*80i)/(7*d) - (a^2*exp(c*1i + d*x*1i)*12688i)/(693*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*2272i)/(693*d*(exp(c*1i + d*x*1i) + 1)) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*1136i)/(693*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1))","B"
108,1,456,146,8.176408,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/cos(c + d*x)^3,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,32{}\mathrm{i}}{9\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,32{}\mathrm{i}}{9\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^4}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,96{}\mathrm{i}}{7\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,32{}\mathrm{i}}{63\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,8{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,584{}\mathrm{i}}{315\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}+\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,56{}\mathrm{i}}{5\,d}+\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,904{}\mathrm{i}}{105\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,1168{}\mathrm{i}}{315\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*32i)/(9*d) - (a^2*exp(c*1i + d*x*1i)*32i)/(9*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^4) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*96i)/(7*d) - (a^2*exp(c*1i + d*x*1i)*32i)/(63*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*8i)/(3*d) - (a^2*exp(c*1i + d*x*1i)*584i)/(315*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) + ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*56i)/(5*d) + (a^2*exp(c*1i + d*x*1i)*904i)/(105*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*1168i)/(315*d*(exp(c*1i + d*x*1i) + 1))","B"
109,1,349,116,4.579939,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/cos(c + d*x)^2,x)","\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,20{}\mathrm{i}}{3\,d}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,4{}\mathrm{i}}{21\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}-\frac{\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,\left(\frac{a^2\,16{}\mathrm{i}}{7\,d}+\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,16{}\mathrm{i}}{7\,d}\right)}{\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^3}-\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,92{}\mathrm{i}}{21\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)}+\frac{a^2\,{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,\sqrt{a+\frac{a}{\frac{{\mathrm{e}}^{-c\,1{}\mathrm{i}-d\,x\,1{}\mathrm{i}}}{2}+\frac{{\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}}{2}}}\,48{}\mathrm{i}}{7\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*20i)/(3*d) - (a^2*exp(c*1i + d*x*1i)*4i)/(21*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)) - ((a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*((a^2*16i)/(7*d) + (a^2*exp(c*1i + d*x*1i)*16i)/(7*d)))/((exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^3) - (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*92i)/(21*d*(exp(c*1i + d*x*1i) + 1)) + (a^2*exp(c*1i + d*x*1i)*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*48i)/(7*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
110,1,146,89,4.505604,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/cos(c + d*x),x)","-\frac{2\,a^2\,\sqrt{a+\frac{a}{\frac{{\mathrm{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({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}\,15{}\mathrm{i}-{\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}\,70{}\mathrm{i}+{\mathrm{e}}^{c\,3{}\mathrm{i}+d\,x\,3{}\mathrm{i}}\,70{}\mathrm{i}-{\mathrm{e}}^{c\,4{}\mathrm{i}+d\,x\,4{}\mathrm{i}}\,15{}\mathrm{i}+{\mathrm{e}}^{c\,5{}\mathrm{i}+d\,x\,5{}\mathrm{i}}\,43{}\mathrm{i}-43{}\mathrm{i}\right)}{15\,d\,\left({\mathrm{e}}^{c\,1{}\mathrm{i}+d\,x\,1{}\mathrm{i}}+1\right)\,{\left({\mathrm{e}}^{c\,2{}\mathrm{i}+d\,x\,2{}\mathrm{i}}+1\right)}^2}","Not used",1,"-(2*a^2*(a + a/(exp(- c*1i - d*x*1i)/2 + exp(c*1i + d*x*1i)/2))^(1/2)*(exp(c*1i + d*x*1i)*15i - exp(c*2i + d*x*2i)*70i + exp(c*3i + d*x*3i)*70i - exp(c*4i + d*x*4i)*15i + exp(c*5i + d*x*5i)*43i - 43i))/(15*d*(exp(c*1i + d*x*1i) + 1)*(exp(c*2i + d*x*2i) + 1)^2)","B"
111,0,-1,98,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2),x)","\int {\left(a+\frac{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"
112,0,-1,94,0.000000,"\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+\frac{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"
113,0,-1,106,0.000000,"\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+\frac{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,-1,144,0.000000,"\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+\frac{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"
115,0,-1,182,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{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"
116,1,36,27,0.786866,"\text{Not used}","int((a - a/cos(c + d*x))^(1/2)/cos(c + d*x),x)","\frac{\sin\left(c+d\,x\right)\,\sqrt{a-\frac{a}{\cos\left(c+d\,x\right)}}}{d\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}","Not used",1,"(sin(c + d*x)*(a - a/cos(c + d*x))^(1/2))/(d*sin(c/2 + (d*x)/2)^2)","B"
117,0,-1,38,0.000000,"\text{Not used}","int((a - a/cos(c + d*x))^(1/2),x)","\int \sqrt{a-\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a - a/cos(c + d*x))^(1/2), x)","F"
118,0,-1,65,0.000000,"\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-\frac{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"
119,0,-1,140,0.000000,"\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+\frac{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"
120,0,-1,104,0.000000,"\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+\frac{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"
121,0,-1,73,0.000000,"\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+\frac{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"
122,0,-1,46,0.000000,"\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+\frac{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"
123,0,-1,85,0.000000,"\text{Not used}","int(1/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{1}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/(a + a/cos(c + d*x))^(1/2), x)","F"
124,0,-1,108,0.000000,"\text{Not used}","int(cos(c + d*x)/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)}{\sqrt{a+\frac{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"
125,0,-1,147,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{\sqrt{a+\frac{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"
126,0,-1,183,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + a/cos(c + d*x))^(3/2)), x)","F"
127,0,-1,145,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(3/2)), x)","F"
128,0,-1,105,0.000000,"\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+\frac{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"
129,0,-1,77,0.000000,"\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+\frac{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"
130,0,-1,77,0.000000,"\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+\frac{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"
131,0,-1,114,0.000000,"\text{Not used}","int(1/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{1}{{\left(a+\frac{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"
132,0,-1,144,0.000000,"\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+\frac{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"
133,0,-1,185,0.000000,"\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+\frac{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,-1,183,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + a/cos(c + d*x))^(5/2)), x)","F"
135,0,-1,145,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/2)), x)","F"
136,0,-1,107,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/2)), x)","F"
137,0,-1,107,0.000000,"\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+\frac{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"
138,0,-1,107,0.000000,"\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+\frac{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"
139,0,-1,144,0.000000,"\text{Not used}","int(1/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{1}{{\left(a+\frac{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"
140,0,-1,174,0.000000,"\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+\frac{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"
141,0,-1,48,0.000000,"\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-\frac{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"
142,0,-1,87,0.000000,"\text{Not used}","int(1/(a - a/cos(c + d*x))^(1/2),x)","\int \frac{1}{\sqrt{a-\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/(a - a/cos(c + d*x))^(1/2), x)","F"
143,0,-1,383,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(2/3)/cos(c + d*x)^3,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(2/3)/cos(c + d*x)^3, x)","F"
144,0,-1,353,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(2/3)/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(2/3)/cos(c + d*x)^2, x)","F"
145,0,-1,326,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(2/3)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(2/3)/cos(c + d*x), x)","F"
146,0,-1,77,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(2/3),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(2/3), x)","F"
147,0,-1,77,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^(2/3),x)","\int \cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int(cos(c + d*x)*(a + a/cos(c + d*x))^(2/3), x)","F"
148,0,-1,413,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/3)/cos(c + d*x)^3,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/3)/cos(c + d*x)^3, x)","F"
149,0,-1,383,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/3)/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/3)/cos(c + d*x)^2, x)","F"
150,0,-1,356,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/3)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/3)/cos(c + d*x), x)","F"
151,0,-1,86,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/3),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/3), x)","F"
152,0,-1,86,0.000000,"\text{Not used}","int(cos(c + d*x)*(a + a/cos(c + d*x))^(5/3),x)","\int \cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",1,"int(cos(c + d*x)*(a + a/cos(c + d*x))^(5/3), x)","F"
153,0,-1,371,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(1/3)), x)","F"
154,0,-1,336,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(1/3)), x)","F"
155,0,-1,306,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(1/3)), x)","F"
156,0,-1,276,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/3)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + a/cos(c + d*x))^(1/3)), x)","F"
157,0,-1,75,0.000000,"\text{Not used}","int(1/(a + a/cos(c + d*x))^(1/3),x)","\int \frac{1}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(a + a/cos(c + d*x))^(1/3), x)","F"
158,0,-1,75,0.000000,"\text{Not used}","int(cos(c + d*x)/(a + a/cos(c + d*x))^(1/3),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(cos(c + d*x)/(a + a/cos(c + d*x))^(1/3), x)","F"
159,0,-1,766,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + a/cos(c + d*x))^(5/3)), x)","F"
160,0,-1,731,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + a/cos(c + d*x))^(5/3)), x)","F"
161,0,-1,731,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + a/cos(c + d*x))^(5/3)), x)","F"
162,0,-1,744,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/3)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + a/cos(c + d*x))^(5/3)), x)","F"
163,0,-1,90,0.000000,"\text{Not used}","int(1/(a + a/cos(c + d*x))^(5/3),x)","\int \frac{1}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(a + a/cos(c + d*x))^(5/3), x)","F"
164,0,-1,90,0.000000,"\text{Not used}","int(cos(c + d*x)/(a + a/cos(c + d*x))^(5/3),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(cos(c + d*x)/(a + a/cos(c + d*x))^(5/3), x)","F"
165,0,-1,151,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2),x)","\int \left(a+\frac{a}{\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 + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2), x)","F"
166,0,-1,123,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2),x)","\int \left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2), x)","F"
167,0,-1,97,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2),x)","\int \left(a+\frac{a}{\cos\left(c+d\,x\right)}\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"
168,0,-1,75,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(1/cos(c + d*x))^(1/2),x)","\int \frac{a+\frac{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"
169,0,-1,101,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(1/cos(c + d*x))^(3/2),x)","\int \frac{a+\frac{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"
170,0,-1,127,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(1/cos(c + d*x))^(5/2),x)","\int \frac{a+\frac{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"
171,0,-1,151,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(1/cos(c + d*x))^(7/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(1/cos(c + d*x))^(7/2), x)","F"
172,0,-1,187,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2),x)","\int {\left(a+\frac{a}{\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 + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2), x)","F"
173,0,-1,161,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
174,0,-1,131,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
175,0,-1,64,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
176,0,-1,107,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{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"
177,0,-1,135,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\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 + a/cos(c + d*x))^2/(1/cos(c + d*x))^(5/2), x)","F"
178,0,-1,161,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(1/cos(c + d*x))^(7/2), x)","F"
179,0,-1,187,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
180,0,-1,157,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
181,0,-1,131,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
182,0,-1,131,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{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"
183,0,-1,131,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(5/2), x)","F"
184,0,-1,161,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(7/2), x)","F"
185,0,-1,187,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^3/(1/cos(c + d*x))^(9/2), x)","F"
186,0,-1,213,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^4*(1/cos(c + d*x))^(3/2), x)","F"
187,0,-1,187,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
188,0,-1,161,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
189,0,-1,118,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(3/2), x)","F"
190,0,-1,159,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(5/2), x)","F"
191,0,-1,161,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(7/2), x)","F"
192,0,-1,187,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(9/2), x)","F"
193,0,-1,213,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^4/(1/cos(c + d*x))^(11/2), x)","F"
194,0,-1,164,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + a/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{a+\frac{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)), x)","F"
195,0,-1,136,0.000000,"\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+\frac{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"
196,0,-1,110,0.000000,"\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+\frac{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"
197,0,-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+\frac{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"
198,0,-1,112,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
199,0,-1,140,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(3/2)), x)","F"
200,0,-1,168,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{\left(a+\frac{a}{\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(1/((a + a/cos(c + d*x))*(1/cos(c + d*x))^(5/2)), x)","F"
201,0,-1,202,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)/(a + a/cos(c + d*x))^2, x)","F"
202,0,-1,176,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{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"
203,0,-1,149,0.000000,"\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+\frac{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"
204,0,-1,77,0.000000,"\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+\frac{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"
205,0,-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+\frac{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"
206,0,-1,152,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)), x)","F"
207,0,-1,178,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)), x)","F"
208,0,-1,200,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\left(a+\frac{a}{\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(1/((a + a/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2)), x)","F"
209,0,-1,247,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(11/2)/(a + a/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int((1/cos(c + d*x))^(11/2)/(a + a/cos(c + d*x))^3, x)","F"
210,0,-1,221,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)/(a + a/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{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"
211,0,-1,195,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + a/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{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"
212,0,-1,195,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(a + a/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(a+\frac{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"
213,0,-1,195,0.000000,"\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+\frac{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"
214,0,-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+\frac{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"
215,0,-1,195,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)), x)","F"
216,0,-1,221,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)), x)","F"
217,0,-1,247,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))^3*(1/cos(c + d*x))^(5/2)), x)","F"
218,0,-1,116,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2),x)","\int \sqrt{a+\frac{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))^(1/2)*(1/cos(c + d*x))^(5/2), x)","F"
219,0,-1,72,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2),x)","\int \sqrt{a+\frac{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"
220,0,-1,37,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2),x)","\int \sqrt{a+\frac{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"
221,1,53,36,0.537010,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(1/2),x)","\frac{\sin\left(2\,c+2\,d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}}{d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(sin(2*c + 2*d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2))/(d*(cos(c + d*x) + 1))","B"
222,1,69,77,1.296843,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(3/2),x)","\frac{\cos\left(c+d\,x\right)\,\left(4\,\sin\left(c+d\,x\right)+\sin\left(2\,c+2\,d\,x\right)\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}}{3\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(4*sin(c + d*x) + sin(2*c + 2*d*x))*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2))/(3*d*(cos(c + d*x) + 1))","B"
223,1,82,115,1.667901,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(5/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(35\,\sin\left(c+d\,x\right)+8\,\sin\left(2\,c+2\,d\,x\right)+3\,\sin\left(3\,c+3\,d\,x\right)\right)}{30\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(35*sin(c + d*x) + 8*sin(2*c + 2*d*x) + 3*sin(3*c + 3*d*x)))/(30*d*(cos(c + d*x) + 1))","B"
224,1,93,153,2.202155,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(7/2),x)","\frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(140\,\sin\left(c+d\,x\right)+42\,\sin\left(2\,c+2\,d\,x\right)+12\,\sin\left(3\,c+3\,d\,x\right)+5\,\sin\left(4\,c+4\,d\,x\right)\right)}{140\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(140*sin(c + d*x) + 42*sin(2*c + 2*d*x) + 12*sin(3*c + 3*d*x) + 5*sin(4*c + 4*d*x)))/(140*d*(cos(c + d*x) + 1))","B"
225,0,-1,160,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2), x)","F"
226,0,-1,120,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
227,0,-1,75,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
228,0,-1,76,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
229,1,70,79,1.406179,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(3/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\left(10\,\sin\left(c+d\,x\right)+\sin\left(2\,c+2\,d\,x\right)\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}}{3\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(10*sin(c + d*x) + sin(2*c + 2*d*x))*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2))/(3*d*(cos(c + d*x) + 1))","B"
230,1,81,116,1.772919,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(5/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\left(25\,\sin\left(c+d\,x\right)+6\,\sin\left(2\,c+2\,d\,x\right)+\sin\left(3\,c+3\,d\,x\right)\right)\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}}{10\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*(25*sin(c + d*x) + 6*sin(2*c + 2*d*x) + sin(3*c + 3*d*x))*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2))/(10*d*(cos(c + d*x) + 1))","B"
231,1,94,161,2.325213,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(7/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(910\,\sin\left(c+d\,x\right)+238\,\sin\left(2\,c+2\,d\,x\right)+78\,\sin\left(3\,c+3\,d\,x\right)+15\,\sin\left(4\,c+4\,d\,x\right)\right)}{420\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(910*sin(c + d*x) + 238*sin(2*c + 2*d*x) + 78*sin(3*c + 3*d*x) + 15*sin(4*c + 4*d*x)))/(420*d*(cos(c + d*x) + 1))","B"
232,1,105,201,3.021738,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(9/2),x)","\frac{a\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(4830\,\sin\left(c+d\,x\right)+1428\,\sin\left(2\,c+2\,d\,x\right)+513\,\sin\left(3\,c+3\,d\,x\right)+170\,\sin\left(4\,c+4\,d\,x\right)+35\,\sin\left(5\,c+5\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(4830*sin(c + d*x) + 1428*sin(2*c + 2*d*x) + 513*sin(3*c + 3*d*x) + 170*sin(4*c + 4*d*x) + 35*sin(5*c + 5*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
233,0,-1,200,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2), x)","F"
234,0,-1,160,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
235,0,-1,120,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
236,0,-1,112,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
237,0,-1,118,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{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"
238,1,85,119,1.834958,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(5/2),x)","\frac{a^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(175\,\sin\left(c+d\,x\right)+28\,\sin\left(2\,c+2\,d\,x\right)+3\,\sin\left(3\,c+3\,d\,x\right)\right)}{30\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a^2*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(175*sin(c + d*x) + 28*sin(2*c + 2*d*x) + 3*sin(3*c + 3*d*x)))/(30*d*(cos(c + d*x) + 1))","B"
239,1,96,156,2.316018,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(7/2),x)","\frac{a^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(392\,\sin\left(c+d\,x\right)+98\,\sin\left(2\,c+2\,d\,x\right)+24\,\sin\left(3\,c+3\,d\,x\right)+3\,\sin\left(4\,c+4\,d\,x\right)\right)}{84\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a^2*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(392*sin(c + d*x) + 98*sin(2*c + 2*d*x) + 24*sin(3*c + 3*d*x) + 3*sin(4*c + 4*d*x)))/(84*d*(cos(c + d*x) + 1))","B"
240,1,107,201,2.957788,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(9/2),x)","\frac{a^2\,\cos\left(c+d\,x\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}\,\left(10290\,\sin\left(c+d\,x\right)+2856\,\sin\left(2\,c+2\,d\,x\right)+981\,\sin\left(3\,c+3\,d\,x\right)+260\,\sin\left(4\,c+4\,d\,x\right)+35\,\sin\left(5\,c+5\,d\,x\right)\right)}{2520\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(a^2*cos(c + d*x)*(1/cos(c + d*x))^(1/2)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2)*(10290*sin(c + d*x) + 2856*sin(2*c + 2*d*x) + 981*sin(3*c + 3*d*x) + 260*sin(4*c + 4*d*x) + 35*sin(5*c + 5*d*x)))/(2520*d*(cos(c + d*x) + 1))","B"
241,1,356,241,6.925461,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(11/2),x)","\frac{\sqrt{a-\frac{a}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}-1\right)\,\left(\frac{23\,a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{4\,d}+\frac{19\,a^2\,\sin\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{12\,d}+\frac{5\,a^2\,\sin\left(\frac{5\,c}{2}+\frac{5\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{8\,d}+\frac{13\,a^2\,\sin\left(\frac{7\,c}{2}+\frac{7\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{56\,d}+\frac{5\,a^2\,\sin\left(\frac{9\,c}{2}+\frac{9\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{72\,d}+\frac{a^2\,\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,\left(-2\,{\sin\left(\frac{11\,c}{4}+\frac{11\,d\,x}{4}\right)}^2+\sin\left(\frac{11\,c}{2}+\frac{11\,d\,x}{2}\right)\,1{}\mathrm{i}+1\right)}{88\,d}\right)}{2\,\sqrt{-\frac{1}{2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1}}\,\left(2\,{\sin\left(\frac{c}{4}+\frac{d\,x}{4}\right)}^2-1\right)}","Not used",1,"((a - a/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(sin((11*c)/2 + (11*d*x)/2)*1i + 2*sin((11*c)/4 + (11*d*x)/4)^2 - 1)*((23*a^2*sin(c/2 + (d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(4*d) + (19*a^2*sin((3*c)/2 + (3*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(12*d) + (5*a^2*sin((5*c)/2 + (5*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(8*d) + (13*a^2*sin((7*c)/2 + (7*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(56*d) + (5*a^2*sin((9*c)/2 + (9*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(72*d) + (a^2*sin((11*c)/2 + (11*d*x)/2)*(sin((11*c)/2 + (11*d*x)/2)*1i - 2*sin((11*c)/4 + (11*d*x)/4)^2 + 1))/(88*d)))/(2*(-1/(2*sin(c/2 + (d*x)/2)^2 - 1))^(1/2)*(2*sin(c/4 + (d*x)/4)^2 - 1))","B"
242,1,55,38,0.745535,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/4),x)","\frac{2\,a\,\sin\left(2\,c+2\,d\,x\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/4}\,\sqrt{\frac{a\,\left(\cos\left(c+d\,x\right)+1\right)}{\cos\left(c+d\,x\right)}}}{d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(2*a*sin(2*c + 2*d*x)*(1/cos(c + d*x))^(3/4)*((a*(cos(c + d*x) + 1))/cos(c + d*x))^(1/2))/(d*(cos(c + d*x) + 1))","B"
243,0,-1,37,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(1/2)*(1/cos(e + f*x))^(1/2),x)","\int \sqrt{a+\frac{a}{\cos\left(e+f\,x\right)}}\,\sqrt{\frac{1}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a/cos(e + f*x))^(1/2)*(1/cos(e + f*x))^(1/2), x)","F"
244,0,-1,38,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(1/2)*(-1/cos(e + f*x))^(1/2),x)","\int \sqrt{a-\frac{a}{\cos\left(e+f\,x\right)}}\,\sqrt{-\frac{1}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((a - a/cos(e + f*x))^(1/2)*(-1/cos(e + f*x))^(1/2), x)","F"
245,0,-1,128,0.000000,"\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+\frac{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"
246,0,-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{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{a+\frac{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"
247,0,-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+\frac{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"
248,0,-1,93,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
249,0,-1,131,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{\sqrt{a+\frac{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(1/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
250,0,-1,169,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{\sqrt{a+\frac{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(1/((a + a/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
251,0,-1,174,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)/(a + a/cos(c + d*x))^(3/2), x)","F"
252,0,-1,134,0.000000,"\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+\frac{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"
253,0,-1,97,0.000000,"\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+\frac{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"
254,0,-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{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+\frac{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"
255,0,-1,137,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)), x)","F"
256,0,-1,177,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)), x)","F"
257,0,-1,217,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)), x)","F"
258,0,-1,214,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(9/2)/(a + a/cos(c + d*x))^(5/2), x)","F"
259,0,-1,174,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)/(a + a/cos(c + d*x))^(5/2), x)","F"
260,0,-1,137,0.000000,"\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+\frac{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"
261,0,-1,137,0.000000,"\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+\frac{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"
262,0,-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{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{{\left(a+\frac{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"
263,0,-1,177,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)), x)","F"
264,0,-1,217,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + a/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)), x)","F"
265,0,-1,126,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(1/cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(7/2)/(1/cos(c + d*x) + 1)^(1/2), x)","F"
266,0,-1,85,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/2)/(1/cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(5/2)/(1/cos(c + d*x) + 1)^(1/2), x)","F"
267,0,-1,54,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(3/2)/(1/cos(c + d*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(3/2)/(1/cos(c + d*x) + 1)^(1/2), x)","F"
268,0,-1,27,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(1/cos(c + d*x) + 1)^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}+1}} \,d x","Not used",1,"int((1/cos(c + d*x))^(1/2)/(1/cos(c + d*x) + 1)^(1/2), x)","F"
269,0,-1,62,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}+1}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((1/cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
270,0,-1,98,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{\sqrt{\frac{1}{\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/((1/cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
271,0,-1,134,0.000000,"\text{Not used}","int(1/((1/cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}+1}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/((1/cos(c + d*x) + 1)^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
272,0,-1,325,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(4/3),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(4/3), x)","F"
273,0,-1,280,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(1/3),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(1/3), x)","F"
274,0,-1,326,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/(e/cos(c + d*x))^(2/3),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)/(e/cos(c + d*x))^(2/3), x)","F"
275,0,-1,716,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(8/3),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{8/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(8/3), x)","F"
276,0,-1,673,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(5/3),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(5/3), x)","F"
277,0,-1,624,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(2/3),x)","\int \sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(2/3), x)","F"
278,0,-1,662,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/(e/cos(c + d*x))^(1/3),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)/(e/cos(c + d*x))^(1/3), x)","F"
279,0,-1,715,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/(e/cos(c + d*x))^(4/3),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)/(e/cos(c + d*x))^(4/3), x)","F"
280,0,-1,78,0.000000,"\text{Not used}","int((e/cos(c + d*x))^(2/3)/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((e/cos(c + d*x))^(2/3)/(a + a/cos(c + d*x))^(1/2), x)","F"
281,0,-1,76,0.000000,"\text{Not used}","int((e/cos(c + d*x))^(1/3)/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((e/cos(c + d*x))^(1/3)/(a + a/cos(c + d*x))^(1/2), x)","F"
282,0,-1,76,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(1/3)),x)","\int \frac{1}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(1/3)), x)","F"
283,0,-1,78,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(2/3)),x)","\int \frac{1}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,{\left(\frac{e}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int(1/((a + a/cos(c + d*x))^(1/2)*(e/cos(c + d*x))^(2/3)), x)","F"
284,0,-1,78,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^(4/3),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{1/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/3)*(1/cos(c + d*x))^(4/3), x)","F"
285,0,-1,79,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^(4/3),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^(4/3), x)","F"
286,0,-1,327,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^(5/3),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{2/3}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(2/3)*(1/cos(c + d*x))^(5/3), x)","F"
287,0,-1,80,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(4/3)/(1/cos(c + d*x))^(1/3),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{4/3}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(4/3)/(1/cos(c + d*x))^(1/3), x)","F"
288,0,-1,304,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^4*(1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^4\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^4*(1/cos(e + f*x))^n, x)","F"
289,0,-1,230,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^3*(1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^3\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^3*(1/cos(e + f*x))^n, x)","F"
290,0,-1,172,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^2*(1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^2\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^2*(1/cos(e + f*x))^n, x)","F"
291,0,-1,132,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))*(1/cos(e + f*x))^n,x)","\int \left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))*(1/cos(e + f*x))^n, x)","F"
292,0,-1,174,0.000000,"\text{Not used}","int((1/cos(e + f*x))^n/(a + a/cos(e + f*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{a+\frac{a}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((1/cos(e + f*x))^n/(a + a/cos(e + f*x)), x)","F"
293,0,-1,217,0.000000,"\text{Not used}","int((1/cos(e + f*x))^n/(a + a/cos(e + f*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^2} \,d x","Not used",1,"int((1/cos(e + f*x))^n/(a + a/cos(e + f*x))^2, x)","F"
294,0,-1,162,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^(5/2)*(1/cos(e + f*x))^n,x)","\int {\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^{5/2}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^(5/2)*(1/cos(e + f*x))^n, x)","F"
295,0,-1,98,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^(3/2)*(1/cos(e + f*x))^n,x)","\int {\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^{3/2}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^(3/2)*(1/cos(e + f*x))^n, x)","F"
296,0,-1,45,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^(1/2)*(1/cos(e + f*x))^n,x)","\int \sqrt{\frac{1}{\cos\left(e+f\,x\right)}+1}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^(1/2)*(1/cos(e + f*x))^n, x)","F"
297,0,-1,59,0.000000,"\text{Not used}","int((1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{\frac{1}{\cos\left(e+f\,x\right)}+1}} \,d x","Not used",1,"int((1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(1/2), x)","F"
298,0,-1,62,0.000000,"\text{Not used}","int((1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(3/2), x)","F"
299,0,-1,117,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^(3/2)*(-1/cos(e + f*x))^n,x)","\int {\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^{3/2}\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^(3/2)*(-1/cos(e + f*x))^n, x)","F"
300,0,-1,64,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^(1/2)*(-1/cos(e + f*x))^n,x)","\int \sqrt{\frac{1}{\cos\left(e+f\,x\right)}+1}\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^(1/2)*(-1/cos(e + f*x))^n, x)","F"
301,0,-1,73,0.000000,"\text{Not used}","int((-1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(1/2),x)","\int \frac{{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{\frac{1}{\cos\left(e+f\,x\right)}+1}} \,d x","Not used",1,"int((-1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(1/2), x)","F"
302,0,-1,73,0.000000,"\text{Not used}","int((-1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(3/2),x)","\int \frac{{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^{3/2}} \,d x","Not used",1,"int((-1/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(3/2), x)","F"
303,0,-1,117,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^(3/2)*(d/cos(e + f*x))^n,x)","\int {\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^{3/2}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^(3/2)*(d/cos(e + f*x))^n, x)","F"
304,0,-1,64,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^(1/2)*(d/cos(e + f*x))^n,x)","\int \sqrt{\frac{1}{\cos\left(e+f\,x\right)}+1}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^(1/2)*(d/cos(e + f*x))^n, x)","F"
305,0,-1,73,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(1/2),x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{\frac{1}{\cos\left(e+f\,x\right)}+1}} \,d x","Not used",1,"int((d/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(1/2), x)","F"
306,0,-1,73,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(3/2),x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^{3/2}} \,d x","Not used",1,"int((d/cos(e + f*x))^n/(1/cos(e + f*x) + 1)^(3/2), x)","F"
307,0,-1,177,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(5/2)*(1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^(5/2)*(1/cos(e + f*x))^n, x)","F"
308,0,-1,108,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(3/2)*(1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^(3/2)*(1/cos(e + f*x))^n, x)","F"
309,0,-1,48,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(1/2)*(1/cos(e + f*x))^n,x)","\int \sqrt{a+\frac{a}{\cos\left(e+f\,x\right)}}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^(1/2)*(1/cos(e + f*x))^n, x)","F"
310,0,-1,61,0.000000,"\text{Not used}","int((1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{a+\frac{a}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int((1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(1/2), x)","F"
311,0,-1,67,0.000000,"\text{Not used}","int((1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(3/2), x)","F"
312,0,-1,130,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(3/2)*(-1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^(3/2)*(-1/cos(e + f*x))^n, x)","F"
313,0,-1,70,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(1/2)*(-1/cos(e + f*x))^n,x)","\int \sqrt{a+\frac{a}{\cos\left(e+f\,x\right)}}\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^(1/2)*(-1/cos(e + f*x))^n, x)","F"
314,0,-1,75,0.000000,"\text{Not used}","int((-1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(1/2),x)","\int \frac{{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{a+\frac{a}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int((-1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(1/2), x)","F"
315,0,-1,78,0.000000,"\text{Not used}","int((-1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(3/2),x)","\int \frac{{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((-1/cos(e + f*x))^n/(a + a/cos(e + f*x))^(3/2), x)","F"
316,0,-1,130,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(3/2)*(d/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^(3/2)*(d/cos(e + f*x))^n, x)","F"
317,0,-1,70,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^(1/2)*(d/cos(e + f*x))^n,x)","\int \sqrt{a+\frac{a}{\cos\left(e+f\,x\right)}}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^(1/2)*(d/cos(e + f*x))^n, x)","F"
318,0,-1,75,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(a + a/cos(e + f*x))^(1/2),x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{a+\frac{a}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int((d/cos(e + f*x))^n/(a + a/cos(e + f*x))^(1/2), x)","F"
319,0,-1,78,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(a + a/cos(e + f*x))^(3/2),x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((d/cos(e + f*x))^n/(a + a/cos(e + f*x))^(3/2), x)","F"
320,0,-1,178,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(5/2)*(-1/cos(e + f*x))^n,x)","\int {\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^{5/2}\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^(5/2)*(-1/cos(e + f*x))^n, x)","F"
321,0,-1,108,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(3/2)*(-1/cos(e + f*x))^n,x)","\int {\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^(3/2)*(-1/cos(e + f*x))^n, x)","F"
322,0,-1,47,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(1/2)*(-1/cos(e + f*x))^n,x)","\int \sqrt{a-\frac{a}{\cos\left(e+f\,x\right)}}\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^(1/2)*(-1/cos(e + f*x))^n, x)","F"
323,0,-1,58,0.000000,"\text{Not used}","int((-1/cos(e + f*x))^n/(a - a/cos(e + f*x))^(1/2),x)","\int \frac{{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{a-\frac{a}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int((-1/cos(e + f*x))^n/(a - a/cos(e + f*x))^(1/2), x)","F"
324,0,-1,64,0.000000,"\text{Not used}","int((-1/cos(e + f*x))^n/(a - a/cos(e + f*x))^(3/2),x)","\int \frac{{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((-1/cos(e + f*x))^n/(a - a/cos(e + f*x))^(3/2), x)","F"
325,0,-1,130,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(3/2)*(1/cos(e + f*x))^n,x)","\int {\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^(3/2)*(1/cos(e + f*x))^n, x)","F"
326,0,-1,69,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(1/2)*(1/cos(e + f*x))^n,x)","\int \sqrt{a-\frac{a}{\cos\left(e+f\,x\right)}}\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^(1/2)*(1/cos(e + f*x))^n, x)","F"
327,0,-1,130,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(3/2)*(d/cos(e + f*x))^n,x)","\int {\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^{3/2}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^(3/2)*(d/cos(e + f*x))^n, x)","F"
328,0,-1,69,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^(1/2)*(d/cos(e + f*x))^n,x)","\int \sqrt{a-\frac{a}{\cos\left(e+f\,x\right)}}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^(1/2)*(d/cos(e + f*x))^n, x)","F"
329,0,-1,72,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^m*(1/cos(e + f*x))^n,x)","\int {\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^m\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^m*(1/cos(e + f*x))^n, x)","F"
330,0,-1,89,0.000000,"\text{Not used}","int((1 - 1/cos(e + f*x))^m*(1/cos(e + f*x))^n,x)","\int {\left(1-\frac{1}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1 - 1/cos(e + f*x))^m*(1/cos(e + f*x))^n, x)","F"
331,0,-1,88,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m*(1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^m*(1/cos(e + f*x))^n, x)","F"
332,0,-1,90,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^m*(1/cos(e + f*x))^n,x)","\int {\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^m*(1/cos(e + f*x))^n, x)","F"
333,0,-1,85,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^m*(-1/cos(e + f*x))^n,x)","\int {\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^m\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^m*(-1/cos(e + f*x))^n, x)","F"
334,0,-1,70,0.000000,"\text{Not used}","int((1 - 1/cos(e + f*x))^m*(-1/cos(e + f*x))^n,x)","\int {\left(1-\frac{1}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1 - 1/cos(e + f*x))^m*(-1/cos(e + f*x))^n, x)","F"
335,0,-1,87,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m*(-1/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^m*(-1/cos(e + f*x))^n, x)","F"
336,0,-1,87,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^m*(-1/cos(e + f*x))^n,x)","\int {\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(-\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^m*(-1/cos(e + f*x))^n, x)","F"
337,0,-1,79,0.000000,"\text{Not used}","int((1/cos(e + f*x) + 1)^m*(d/cos(e + f*x))^n,x)","\int {\left(\frac{1}{\cos\left(e+f\,x\right)}+1\right)}^m\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1/cos(e + f*x) + 1)^m*(d/cos(e + f*x))^n, x)","F"
338,0,-1,79,0.000000,"\text{Not used}","int((1 - 1/cos(e + f*x))^m*(d/cos(e + f*x))^n,x)","\int {\left(1-\frac{1}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((1 - 1/cos(e + f*x))^m*(d/cos(e + f*x))^n, x)","F"
339,0,-1,95,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m*(d/cos(e + f*x))^n,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + a/cos(e + f*x))^m*(d/cos(e + f*x))^n, x)","F"
340,0,-1,96,0.000000,"\text{Not used}","int((a - a/cos(e + f*x))^m*(d/cos(e + f*x))^n,x)","\int {\left(a-\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a - a/cos(e + f*x))^m*(d/cos(e + f*x))^n, x)","F"
341,0,-1,211,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m/cos(e + f*x)^4,x)","\int \frac{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m}{{\cos\left(e+f\,x\right)}^4} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m/cos(e + f*x)^4, x)","F"
342,0,-1,155,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m/cos(e + f*x)^3,x)","\int \frac{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m/cos(e + f*x)^3, x)","F"
343,0,-1,107,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m/cos(e + f*x)^2,x)","\int \frac{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m/cos(e + f*x)^2, x)","F"
344,0,-1,73,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m/cos(e + f*x),x)","\int \frac{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m}{\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m/cos(e + f*x), x)","F"
345,0,-1,83,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m,x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m \,d x","Not used",1,"int((a + a/cos(e + f*x))^m, x)","F"
346,0,-1,84,0.000000,"\text{Not used}","int(cos(e + f*x)*(a + a/cos(e + f*x))^m,x)","\int \cos\left(e+f\,x\right)\,{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m \,d x","Not used",1,"int(cos(e + f*x)*(a + a/cos(e + f*x))^m, x)","F"
347,0,-1,98,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m*(d/cos(e + f*x))^(3/2),x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m*(d/cos(e + f*x))^(3/2), x)","F"
348,0,-1,96,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m*(d/cos(e + f*x))^(1/2),x)","\int {\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m\,\sqrt{\frac{d}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m*(d/cos(e + f*x))^(1/2), x)","F"
349,0,-1,96,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m/(d/cos(e + f*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m}{\sqrt{\frac{d}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m/(d/cos(e + f*x))^(1/2), x)","F"
350,0,-1,98,0.000000,"\text{Not used}","int((a + a/cos(e + f*x))^m/(d/cos(e + f*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^m}{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(e + f*x))^m/(d/cos(e + f*x))^(3/2), x)","F"
351,1,87,111,1.177730,"\text{Not used}","int(cos(c + d*x)^(7/2)*(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"
352,1,80,87,0.783493,"\text{Not used}","int(cos(c + d*x)^(5/2)*(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"
353,1,53,61,0.762903,"\text{Not used}","int(cos(c + d*x)^(3/2)*(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"
354,1,27,35,0.195972,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + a/cos(c + d*x)),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"
355,1,60,57,1.032315,"\text{Not used}","int((a + a/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\,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"
356,1,87,83,1.171149,"\text{Not used}","int((a + a/cos(c + d*x))/cos(c + d*x)^(3/2),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"
357,1,87,111,1.281756,"\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{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"
358,1,87,135,1.377493,"\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{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\,\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*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*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"
359,1,136,147,1.183862,"\text{Not used}","int(cos(c + d*x)^(9/2)*(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"
360,1,129,121,1.038503,"\text{Not used}","int(cos(c + d*x)^(7/2)*(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"
361,1,104,95,0.918656,"\text{Not used}","int(cos(c + d*x)^(5/2)*(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"
362,1,59,67,0.884923,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^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"
363,1,82,44,1.214163,"\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)}{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"
364,1,109,91,1.271949,"\text{Not used}","int((a + a/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{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"
365,1,114,121,1.377897,"\text{Not used}","int((a + a/cos(c + d*x))^2/cos(c + d*x)^(3/2),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"
366,1,114,147,1.456046,"\text{Not used}","int((a + a/cos(c + d*x))^2/cos(c + d*x)^(5/2),x)","\frac{30\,a^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(30*a^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 84*a^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2) + 70*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
367,1,206,147,1.150336,"\text{Not used}","int(cos(c + d*x)^(9/2)*(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"
368,1,143,121,1.025761,"\text{Not used}","int(cos(c + d*x)^(7/2)*(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"
369,1,104,91,0.974514,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^3,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"
370,1,104,91,1.015975,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + a/cos(c + d*x))^3,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"
371,1,126,91,1.639854,"\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)+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"
372,1,154,117,1.584981,"\text{Not used}","int((a + a/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^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"
373,1,145,147,1.642119,"\text{Not used}","int((a + a/cos(c + d*x))^3/cos(c + d*x)^(3/2),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"
374,0,-1,128,0.000000,"\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+\frac{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"
375,0,-1,100,0.000000,"\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+\frac{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"
376,0,-1,72,0.000000,"\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+\frac{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"
377,0,-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+\frac{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"
378,0,-1,70,0.000000,"\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+\frac{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"
379,0,-1,96,0.000000,"\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+\frac{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"
380,0,-1,124,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+\frac{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"
381,0,-1,160,0.000000,"\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+\frac{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"
382,0,-1,138,0.000000,"\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+\frac{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"
383,0,-1,112,0.000000,"\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+\frac{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"
384,0,-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+\frac{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"
385,0,-1,57,0.000000,"\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+\frac{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"
386,0,-1,109,0.000000,"\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+\frac{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"
387,0,-1,136,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{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"
388,0,-1,162,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2} \,d x","Not used",1,"int(1/(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^2), x)","F"
389,0,-1,207,0.000000,"\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+\frac{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"
390,0,-1,181,0.000000,"\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+\frac{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"
391,0,-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+\frac{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"
392,0,-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+\frac{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"
393,0,-1,155,0.000000,"\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+\frac{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"
394,0,-1,155,0.000000,"\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+\frac{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"
395,0,-1,155,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{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"
396,0,-1,181,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{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"
397,0,-1,207,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^3),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{11/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3} \,d x","Not used",1,"int(1/(cos(c + d*x)^(11/2)*(a + a/cos(c + d*x))^3), x)","F"
398,0,-1,153,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+\frac{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))^(1/2), x)","F"
399,0,-1,115,0.000000,"\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+\frac{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"
400,0,-1,77,0.000000,"\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+\frac{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"
401,0,-1,36,0.000000,"\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+\frac{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"
402,0,-1,57,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a+\frac{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"
403,0,-1,92,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^(3/2),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^(3/2), x)","F"
404,0,-1,136,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^(5/2),x)","\int \frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(1/2)/cos(c + d*x)^(5/2), x)","F"
405,0,-1,161,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2), x)","F"
406,0,-1,116,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{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"
407,0,-1,79,0.000000,"\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+\frac{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"
408,0,-1,96,0.000000,"\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+\frac{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"
409,0,-1,95,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{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"
410,0,-1,140,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{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"
411,0,-1,180,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^(3/2)/cos(c + d*x)^(5/2), x)","F"
412,0,-1,201,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(5/2), x)","F"
413,0,-1,156,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{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"
414,0,-1,119,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + a/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{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"
415,0,-1,138,0.000000,"\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+\frac{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"
416,0,-1,132,0.000000,"\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+\frac{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"
417,0,-1,140,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{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"
418,0,-1,180,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{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"
419,0,-1,220,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^(5/2)/cos(c + d*x)^(5/2),x)","\int \frac{{\left(a+\frac{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"
420,0,-1,189,0.000000,"\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+\frac{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"
421,0,-1,151,0.000000,"\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+\frac{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"
422,0,-1,113,0.000000,"\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+\frac{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"
423,0,-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+\frac{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"
424,0,-1,135,0.000000,"\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+\frac{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"
425,0,-1,168,0.000000,"\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+\frac{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"
426,0,-1,211,0.000000,"\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+\frac{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"
427,0,-1,237,0.000000,"\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+\frac{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"
428,0,-1,197,0.000000,"\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+\frac{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"
429,0,-1,157,0.000000,"\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+\frac{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"
430,0,-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{1}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{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"
431,0,-1,117,0.000000,"\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+\frac{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"
432,0,-1,174,0.000000,"\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+\frac{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"
433,0,-1,214,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(3/2)), x)","F"
434,0,-1,237,0.000000,"\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+\frac{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"
435,0,-1,197,0.000000,"\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+\frac{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"
436,0,-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{1}{\sqrt{\cos\left(c+d\,x\right)}\,{\left(a+\frac{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"
437,0,-1,157,0.000000,"\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+\frac{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"
438,0,-1,157,0.000000,"\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+\frac{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"
439,0,-1,214,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(7/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
440,0,-1,254,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^(9/2)*(a + a/cos(c + d*x))^(5/2)), x)","F"
441,0,-1,244,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n*(a + a/cos(e + f*x))^3,x)","\int {\left(d\,\cos\left(e+f\,x\right)\right)}^n\,{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^3 \,d x","Not used",1,"int((d*cos(e + f*x))^n*(a + a/cos(e + f*x))^3, x)","F"
442,0,-1,179,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n*(a + a/cos(e + f*x))^2,x)","\int {\left(d\,\cos\left(e+f\,x\right)\right)}^n\,{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^2 \,d x","Not used",1,"int((d*cos(e + f*x))^n*(a + a/cos(e + f*x))^2, x)","F"
443,0,-1,132,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n*(a + a/cos(e + f*x)),x)","\int {\left(d\,\cos\left(e+f\,x\right)\right)}^n\,\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right) \,d x","Not used",1,"int((d*cos(e + f*x))^n*(a + a/cos(e + f*x)), x)","F"
444,0,-1,178,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n/(a + a/cos(e + f*x)),x)","\int \frac{{\left(d\,\cos\left(e+f\,x\right)\right)}^n}{a+\frac{a}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((d*cos(e + f*x))^n/(a + a/cos(e + f*x)), x)","F"
445,0,-1,215,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n/(a + a/cos(e + f*x))^2,x)","\int \frac{{\left(d\,\cos\left(e+f\,x\right)\right)}^n}{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^2} \,d x","Not used",1,"int((d*cos(e + f*x))^n/(a + a/cos(e + f*x))^2, x)","F"
446,1,152,85,3.574050,"\text{Not used}","int((a + b/cos(c + d*x))/cos(c + d*x)^4,x)","\frac{\left(\frac{5\,b}{4}-2\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{10\,a}{3}+\frac{3\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{3\,b}{4}-\frac{10\,a}{3}\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)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{3\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*a + (5*b)/4) - tan(c/2 + (d*x)/2)^7*(2*a - (5*b)/4) - tan(c/2 + (d*x)/2)^3*((10*a)/3 - (3*b)/4) + tan(c/2 + (d*x)/2)^5*((10*a)/3 + (3*b)/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*b*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
447,1,109,63,2.808867,"\text{Not used}","int((a + b/cos(c + d*x))/cos(c + d*x)^3,x)","\frac{\left(a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\left(-a-2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(a - 2*b) - tan(c/2 + (d*x)/2)*(a + 2*b) + (4*b*tan(c/2 + (d*x)/2)^3)/3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1)) + (a*atanh(tan(c/2 + (d*x)/2)))/d","B"
448,1,85,47,1.475878,"\text{Not used}","int((a + b/cos(c + d*x))/cos(c + d*x)^2,x)","\frac{b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a-b\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\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,"(b*atanh(tan(c/2 + (d*x)/2)))/d - (tan(c/2 + (d*x)/2)^3*(2*a - b) - tan(c/2 + (d*x)/2)*(2*a + b))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
449,1,47,24,0.792725,"\text{Not used}","int((a + b/cos(c + d*x))/cos(c + d*x),x)","\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)))/d - (2*b*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
450,1,57,16,0.803324,"\text{Not used}","int(a + b/cos(c + d*x),x)","\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)}{d}+\frac{2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(2*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
451,1,17,15,0.743549,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x)),x)","\frac{a\,\sin\left(c+d\,x\right)+b\,d\,x}{d}","Not used",1,"(a*sin(c + d*x) + b*d*x)/d","B"
452,1,31,38,0.813196,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x)),x)","\frac{a\,x}{2}+\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*x)/2 + (a*sin(2*c + 2*d*x))/(4*d) + (b*sin(c + d*x))/d","B"
453,1,55,54,0.830725,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x)),x)","\frac{b\,x}{2}+\frac{2\,a\,\sin\left(c+d\,x\right)}{3\,d}+\frac{b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(b*x)/2 + (2*a*sin(c + d*x))/(3*d) + (b*cos(c + d*x)*sin(c + d*x))/(2*d) + (a*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
454,1,75,76,0.832488,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x)),x)","\frac{3\,a\,x}{8}+\frac{2\,b\,\sin\left(c+d\,x\right)}{3\,d}+\frac{3\,a\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{a\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(3*a*x)/8 + (2*b*sin(c + d*x))/(3*d) + (3*a*cos(c + d*x)*sin(c + d*x))/(8*d) + (a*cos(c + d*x)^3*sin(c + d*x))/(4*d) + (b*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
455,1,113,92,4.748332,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x)),x)","\frac{3\,b\,x}{8}+\frac{\left(2\,a-\frac{5\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,a}{3}-\frac{b}{2}\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)}^2+1\right)}^5}","Not used",1,"(3*b*x)/8 + (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*(tan(c/2 + (d*x)/2)^2 + 1)^5)","B"
456,1,221,135,3.823207,"\text{Not used}","int((a + b/cos(c + d*x))^2/cos(c + d*x)^4,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{16\,a^2}{3}+a\,b-\frac{8\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{20\,a^2}{3}+\frac{116\,b^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{16\,a^2}{3}-a\,b-\frac{8\,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*((20*a^2)/3 + (116*b^2)/15) + 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 + (16*a^2)/3 + (8*b^2)/3) - tan(c/2 + (d*x)/2)^7*((16*a^2)/3 - a*b + (8*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"
457,1,184,110,3.664031,"\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+\frac{3\,b^2}{4}\right)}{d}+\frac{\left(a^2-4\,a\,b+\frac{5\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-a^2+\frac{20\,a\,b}{3}+\frac{3\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-a^2-\frac{20\,a\,b}{3}+\frac{3\,b^2}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(a^2+4\,a\,b+\frac{5\,b^2}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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))*(a^2 + (3*b^2)/4))/d + (tan(c/2 + (d*x)/2)^5*((20*a*b)/3 - a^2 + (3*b^2)/4) + tan(c/2 + (d*x)/2)*(4*a*b + a^2 + (5*b^2)/4) + tan(c/2 + (d*x)/2)^7*(a^2 - 4*a*b + (5*b^2)/4) - tan(c/2 + (d*x)/2)^3*((20*a*b)/3 + a^2 - (3*b^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"
458,1,141,80,3.066348,"\text{Not used}","int((a + b/cos(c + d*x))^2/cos(c + d*x)^2,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(-4\,a^2-\frac{4\,b^2}{3}\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 + (4*b^2)/3) + 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"
459,1,99,59,1.529141,"\text{Not used}","int((a + b/cos(c + d*x))^2/cos(c + d*x),x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^2+b^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a\,b-b^2\right)-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(b^2+4\,a\,b\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))*(2*a^2 + b^2))/d - (tan(c/2 + (d*x)/2)^3*(4*a*b - b^2) - tan(c/2 + (d*x)/2)*(4*a*b + b^2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
460,1,181,33,0.865810,"\text{Not used}","int((a + b/cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{atan}\left(\frac{64\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^6+256\,a^4\,b^2}+\frac{256\,a^4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^6+256\,a^4\,b^2}\right)}{d}-\frac{2\,b^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^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,a^5\,b+512\,a^3\,b^3}+\frac{512\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,a^5\,b+512\,a^3\,b^3}\right)}{d}","Not used",1,"(2*a^2*atan((64*a^6*tan(c/2 + (d*x)/2))/(64*a^6 + 256*a^4*b^2) + (256*a^4*b^2*tan(c/2 + (d*x)/2))/(64*a^6 + 256*a^4*b^2)))/d - (2*b^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - 1)) + (4*a*b*atanh((128*a^5*b*tan(c/2 + (d*x)/2))/(128*a^5*b + 512*a^3*b^3) + (512*a^3*b^3*tan(c/2 + (d*x)/2))/(128*a^5*b + 512*a^3*b^3)))/d","B"
461,1,73,33,0.845901,"\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\,\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,"(a^2*sin(c + d*x))/d + (2*b^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"
462,1,42,50,0.854376,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^2,x)","\frac{a^2\,x}{2}+b^2\,x+\frac{a^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)/2 + b^2*x + (a^2*sin(2*c + 2*d*x))/(4*d) + (2*a*b*sin(c + d*x))/d","B"
463,1,72,58,0.825345,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^2,x)","\frac{2\,a^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{b^2\,\sin\left(c+d\,x\right)}{d}+a\,b\,x+\frac{a^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,"(2*a^2*sin(c + d*x))/(3*d) + (b^2*sin(c + d*x))/d + a*b*x + (a^2*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (a*b*cos(c + d*x)*sin(c + d*x))/d","B"
464,1,93,101,0.865788,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^2,x)","\frac{3\,a^2\,x}{8}+\frac{b^2\,x}{2}+\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{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4\,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,"(3*a^2*x)/8 + (b^2*x)/2 + (a^2*sin(2*c + 2*d*x))/(4*d) + (a^2*sin(4*c + 4*d*x))/(32*d) + (b^2*sin(2*c + 2*d*x))/(4*d) + (3*a*b*sin(c + d*x))/(2*d) + (a*b*sin(3*c + 3*d*x))/(6*d)","B"
465,1,117,111,0.894381,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))^2,x)","\frac{5\,a^2\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,b^2\,\sin\left(c+d\,x\right)}{4\,d}+\frac{3\,a\,b\,x}{4}+\frac{5\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{a^2\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}+\frac{b^2\,\sin\left(3\,c+3\,d\,x\right)}{12\,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,"(5*a^2*sin(c + d*x))/(8*d) + (3*b^2*sin(c + d*x))/(4*d) + (3*a*b*x)/4 + (5*a^2*sin(3*c + 3*d*x))/(48*d) + (a^2*sin(5*c + 5*d*x))/(80*d) + (b^2*sin(3*c + 3*d*x))/(12*d) + (a*b*sin(2*c + 2*d*x))/(2*d) + (a*b*sin(4*c + 4*d*x))/(16*d)","B"
466,1,258,189,4.765908,"\text{Not used}","int((a + b/cos(c + d*x))^3/cos(c + d*x)^3,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^3+\frac{9\,a\,b^2}{4}\right)}{d}-\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)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*((9*a*b^2)/4 + a^3))/d - (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)^3*((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))","B"
467,1,226,130,4.797593,"\text{Not used}","int((a + b/cos(c + d*x))^3/cos(c + d*x)^2,x)","\frac{3\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,a^2+b^2\right)}{4\,d}-\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)}","Not used",1,"(3*b*atanh(tan(c/2 + (d*x)/2))*(4*a^2 + b^2))/(4*d) - (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*(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"
468,1,157,99,3.150779,"\text{Not used}","int((a + b/cos(c + d*x))^3/cos(c + d*x),x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a^3+3\,a\,b^2\right)}{d}-\frac{\left(6\,a^2\,b-3\,a\,b^2+2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-12\,a^2\,b-\frac{4\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(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)}^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*b^2 + 2*a^3))/d - (tan(c/2 + (d*x)/2)^5*(6*a^2*b - 3*a*b^2 + 2*b^3) - tan(c/2 + (d*x)/2)^3*(12*a^2*b + (4*b^3)/3) + tan(c/2 + (d*x)/2)*(3*a*b^2 + 6*a^2*b + 2*b^3))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
469,1,136,73,0.954874,"\text{Not used}","int((a + b/cos(c + d*x))^3,x)","\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)}{d}+\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)}{d}+\frac{b^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}+\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}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(2*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) + (6*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*a*b^2*sin(c + d*x))/(d*cos(c + d*x))","B"
470,1,97,67,0.923360,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^3,x)","\frac{a^3\,\sin\left(c+d\,x\right)}{d}+\frac{b^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\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}+\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}","Not used",1,"(a^3*sin(c + d*x))/d + (b^3*sin(c + d*x))/(d*cos(c + d*x)) + (6*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
471,1,123,79,1.025378,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^3,x)","\frac{a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^3\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,a^2\,b\,\sin\left(c+d\,x\right)}{d}+\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}","Not used",1,"(a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^3*sin(2*c + 2*d*x))/(4*d) + (3*a^2*b*sin(c + d*x))/d + (6*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
472,1,77,100,0.862008,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^3,x)","b^3\,x+\frac{3\,a^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{a^3\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{3\,a^2\,b\,x}{2}+\frac{3\,a^2\,b\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"b^3*x + (3*a^3*sin(c + d*x))/(4*d) + (a^3*sin(3*c + 3*d*x))/(12*d) + (3*a^2*b*x)/2 + (3*a^2*b*sin(2*c + 2*d*x))/(4*d) + (3*a*b^2*sin(c + d*x))/d","B"
473,1,250,123,3.834139,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^3,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{atan}\left(\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,b^2\right)}{4\,\left(\frac{3\,a^3}{4}+3\,a\,b^2\right)}\right)\,\left(a^2+4\,b^2\right)}{4\,d}","Not used",1,"(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)^7*(3*a*b^2 - 6*a^2*b + (5*a^3)/4 - 2*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*(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*a*atan((3*a*tan(c/2 + (d*x)/2)*(a^2 + 4*b^2))/(4*(3*a*b^2 + (3*a^3)/4)))*(a^2 + 4*b^2))/(4*d)","B"
474,1,287,160,3.925623,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))^3,x)","\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)}+\frac{b\,\mathrm{atan}\left(\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^2+4\,b^2\right)}{4\,\left(\frac{9\,a^2\,b}{4}+b^3\right)}\right)\,\left(9\,a^2+4\,b^2\right)}{4\,d}","Not used",1,"(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)^9*(6*a*b^2 - (15*a^2*b)/4 + 2*a^3 - 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*atan((b*tan(c/2 + (d*x)/2)*(9*a^2 + 4*b^2))/(4*((9*a^2*b)/4 + b^3)))*(9*a^2 + 4*b^2))/(4*d)","B"
475,1,350,185,3.298472,"\text{Not used}","int(cos(c + d*x)^6*(a + b/cos(c + d*x))^3,x)","\frac{\left(-\frac{11\,a^3}{8}+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)}^{11}+\left(\frac{5\,a^3}{24}+14\,a^2\,b-\frac{21\,a\,b^2}{4}+\frac{22\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(-\frac{15\,a^3}{4}+\frac{156\,a^2\,b}{5}-\frac{3\,a\,b^2}{2}+12\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{15\,a^3}{4}+\frac{156\,a^2\,b}{5}+\frac{3\,a\,b^2}{2}+12\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{5\,a^3}{24}+14\,a^2\,b+\frac{21\,a\,b^2}{4}+\frac{22\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{11\,a^3}{8}+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)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^2+18\,b^2\right)}{8\,\left(\frac{5\,a^3}{8}+\frac{9\,a\,b^2}{4}\right)}\right)\,\left(5\,a^2+18\,b^2\right)}{8\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((21*a*b^2)/4 + 14*a^2*b - (5*a^3)/24 + (22*b^3)/3) - tan(c/2 + (d*x)/2)^11*((15*a*b^2)/4 - 6*a^2*b + (11*a^3)/8 - 2*b^3) + tan(c/2 + (d*x)/2)^9*(14*a^2*b - (21*a*b^2)/4 + (5*a^3)/24 + (22*b^3)/3) + tan(c/2 + (d*x)/2)^5*((3*a*b^2)/2 + (156*a^2*b)/5 + (15*a^3)/4 + 12*b^3) - tan(c/2 + (d*x)/2)^7*((3*a*b^2)/2 - (156*a^2*b)/5 + (15*a^3)/4 - 12*b^3) + tan(c/2 + (d*x)/2)*((15*a*b^2)/4 + 6*a^2*b + (11*a^3)/8 + 2*b^3))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (a*atan((a*tan(c/2 + (d*x)/2)*(5*a^2 + 18*b^2))/(8*((9*a*b^2)/4 + (5*a^3)/8)))*(5*a^2 + 18*b^2))/(8*d)","B"
476,1,370,244,4.878264,"\text{Not used}","int((a + b/cos(c + d*x))^4/cos(c + d*x)^3,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4+\frac{9\,a^2\,b^2}{2}+\frac{5\,b^4}{8}\right)}{d}+\frac{\left(a^4-8\,a^3\,b+\frac{15\,a^2\,b^2}{2}-8\,a\,b^3+\frac{11\,b^4}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(-3\,a^4+\frac{88\,a^3\,b}{3}-\frac{21\,a^2\,b^2}{2}+\frac{56\,a\,b^3}{3}+\frac{5\,b^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,a^4-48\,a^3\,b+3\,a^2\,b^2-\frac{208\,a\,b^3}{5}+\frac{15\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(2\,a^4+48\,a^3\,b+3\,a^2\,b^2+\frac{208\,a\,b^3}{5}+\frac{15\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-3\,a^4-\frac{88\,a^3\,b}{3}-\frac{21\,a^2\,b^2}{2}-\frac{56\,a\,b^3}{3}+\frac{5\,b^4}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(a^4+8\,a^3\,b+\frac{15\,a^2\,b^2}{2}+8\,a\,b^3+\frac{11\,b^4}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(a^4 + (5*b^4)/8 + (9*a^2*b^2)/2))/d + (tan(c/2 + (d*x)/2)^9*((56*a*b^3)/3 + (88*a^3*b)/3 - 3*a^4 + (5*b^4)/24 - (21*a^2*b^2)/2) - tan(c/2 + (d*x)/2)^3*((56*a*b^3)/3 + (88*a^3*b)/3 + 3*a^4 - (5*b^4)/24 + (21*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^5*((208*a*b^3)/5 + 48*a^3*b + 2*a^4 + (15*b^4)/4 + 3*a^2*b^2) + tan(c/2 + (d*x)/2)^7*(2*a^4 - 48*a^3*b - (208*a*b^3)/5 + (15*b^4)/4 + 3*a^2*b^2) + tan(c/2 + (d*x)/2)*(8*a*b^3 + 8*a^3*b + a^4 + (11*b^4)/8 + (15*a^2*b^2)/2) + tan(c/2 + (d*x)/2)^11*(a^4 - 8*a^3*b - 8*a*b^3 + (11*b^4)/8 + (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"
477,1,304,179,4.969743,"\text{Not used}","int((a + b/cos(c + d*x))^4/cos(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,a^3\,b+3\,a\,b^3\right)}{d}-\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)}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(3*a*b^3 + 4*a^3*b))/d - (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))","B"
478,1,245,146,4.921959,"\text{Not used}","int((a + b/cos(c + d*x))^4/cos(c + d*x),x)","\frac{\left(-8\,a^3\,b+6\,a^2\,b^2-8\,a\,b^3+\frac{5\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(24\,a^3\,b-6\,a^2\,b^2+\frac{40\,a\,b^3}{3}+\frac{3\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-24\,a^3\,b-6\,a^2\,b^2-\frac{40\,a\,b^3}{3}+\frac{3\,b^4}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(8\,a^3\,b+6\,a^2\,b^2+8\,a\,b^3+\frac{5\,b^4}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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(2\,a^4+6\,a^2\,b^2+\frac{3\,b^4}{4}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(8*a*b^3 + 8*a^3*b + (5*b^4)/4 + 6*a^2*b^2) - tan(c/2 + (d*x)/2)^7*(8*a*b^3 + 8*a^3*b - (5*b^4)/4 - 6*a^2*b^2) - tan(c/2 + (d*x)/2)^3*((40*a*b^3)/3 + 24*a^3*b - (3*b^4)/4 + 6*a^2*b^2) + tan(c/2 + (d*x)/2)^5*((40*a*b^3)/3 + 24*a^3*b + (3*b^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))*(2*a^4 + (3*b^4)/4 + 6*a^2*b^2))/d","B"
479,1,185,107,1.028851,"\text{Not used}","int((a + b/cos(c + d*x))^4,x)","\frac{2\,a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,b^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{b^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{4\,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{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}+\frac{2\,a\,b^3\,\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*a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*b^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (b^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (4*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (8*a^3*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*a*b^3*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"
480,1,152,104,1.039548,"\text{Not used}","int(cos(c + d*x)*(a + b/cos(c + d*x))^4,x)","\frac{a^4\,\sin\left(c+d\,x\right)}{d}+\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)}{d}+\frac{b^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^3\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,a\,b^3\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(a^4*sin(c + d*x))/d + (b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^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^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a*b^3*sin(c + d*x))/(d*cos(c + d*x))","B"
481,1,150,108,1.033819,"\text{Not used}","int(cos(c + d*x)^2*(a + b/cos(c + d*x))^4,x)","\frac{a^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b^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{a^4\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{4\,a^3\,b\,\sin\left(c+d\,x\right)}{d}+\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}","Not used",1,"(a^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^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 + (a^4*cos(c + d*x)*sin(c + d*x))/(2*d) + (4*a^3*b*sin(c + d*x))/d + (8*a*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
482,1,158,115,1.114961,"\text{Not used}","int(cos(c + d*x)^3*(a + b/cos(c + d*x))^4,x)","\frac{3\,a^4\,\sin\left(c+d\,x\right)}{4\,d}+\frac{2\,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)}{d}+\frac{a^4\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{a^3\,b\,\sin\left(2\,c+2\,d\,x\right)}{d}+\frac{6\,a^2\,b^2\,\sin\left(c+d\,x\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\,\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*a^4*sin(c + d*x))/(4*d) + (2*b^4*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^4*sin(3*c + 3*d*x))/(12*d) + (a^3*b*sin(2*c + 2*d*x))/d + (6*a^2*b^2*sin(c + d*x))/d + (8*a*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (4*a^3*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d","B"
483,1,123,145,0.884379,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^4,x)","\frac{3\,a^4\,x}{8}+b^4\,x+3\,a^2\,b^2\,x+\frac{a^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a^4\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}+\frac{a^3\,b\,\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{4\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,a^3\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(3*a^4*x)/8 + b^4*x + 3*a^2*b^2*x + (a^4*sin(2*c + 2*d*x))/(4*d) + (a^4*sin(4*c + 4*d*x))/(32*d) + (a^3*b*sin(3*c + 3*d*x))/(3*d) + (3*a^2*b^2*sin(2*c + 2*d*x))/(2*d) + (4*a*b^3*sin(c + d*x))/d + (3*a^3*b*sin(c + d*x))/d","B"
484,1,330,173,3.821061,"\text{Not used}","int(cos(c + d*x)^5*(a + b/cos(c + d*x))^4,x)","\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)}+\frac{a\,b\,\mathrm{atan}\left(\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^2+4\,b^2\right)}{3\,a^3\,b+4\,a\,b^3}\right)\,\left(3\,a^2+4\,b^2\right)}{d}","Not used",1,"(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)) + (a*b*atan((a*b*tan(c/2 + (d*x)/2)*(3*a^2 + 4*b^2))/(4*a*b^3 + 3*a^3*b))*(3*a^2 + 4*b^2))/d","B"
485,1,214,213,1.093656,"\text{Not used}","int(cos(c + d*x)^6*(a + b/cos(c + d*x))^4,x)","\frac{5\,a^4\,x}{16}+\frac{b^4\,x}{2}+\frac{9\,a^2\,b^2\,x}{4}+\frac{15\,a^4\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{3\,a^4\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}+\frac{a^4\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}+\frac{b^4\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a\,b^3\,\sin\left(3\,c+3\,d\,x\right)}{3\,d}+\frac{5\,a^3\,b\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{a^3\,b\,\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{3\,a\,b^3\,\sin\left(c+d\,x\right)}{d}+\frac{5\,a^3\,b\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(5*a^4*x)/16 + (b^4*x)/2 + (9*a^2*b^2*x)/4 + (15*a^4*sin(2*c + 2*d*x))/(64*d) + (3*a^4*sin(4*c + 4*d*x))/(64*d) + (a^4*sin(6*c + 6*d*x))/(192*d) + (b^4*sin(2*c + 2*d*x))/(4*d) + (a*b^3*sin(3*c + 3*d*x))/(3*d) + (5*a^3*b*sin(3*c + 3*d*x))/(12*d) + (a^3*b*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) + (3*a*b^3*sin(c + d*x))/d + (5*a^3*b*sin(c + d*x))/(2*d)","B"
486,1,274,158,1.364487,"\text{Not used}","int((a + b/cos(c + d*x))^5,x)","\frac{2\,a^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,b^5\,\sin\left(c+d\,x\right)}{8\,d\,{\cos\left(c+d\,x\right)}^2}+\frac{b^5\,\sin\left(c+d\,x\right)}{4\,d\,{\cos\left(c+d\,x\right)}^4}+\frac{10\,a\,b^4\,\sin\left(c+d\,x\right)}{3\,d\,\cos\left(c+d\,x\right)}+\frac{5\,a\,b^4\,\sin\left(c+d\,x\right)}{3\,d\,{\cos\left(c+d\,x\right)}^3}+\frac{10\,a^3\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{5\,a^2\,b^3\,\sin\left(c+d\,x\right)}{d\,{\cos\left(c+d\,x\right)}^2}-\frac{b^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,3{}\mathrm{i}}{4\,d}-\frac{a^2\,b^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,10{}\mathrm{i}}{d}-\frac{a^4\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,10{}\mathrm{i}}{d}","Not used",1,"(2*a^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (b^5*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*3i)/(4*d) + (3*b^5*sin(c + d*x))/(8*d*cos(c + d*x)^2) + (b^5*sin(c + d*x))/(4*d*cos(c + d*x)^4) - (a^2*b^3*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*10i)/d - (a^4*b*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*10i)/d + (10*a*b^4*sin(c + d*x))/(3*d*cos(c + d*x)) + (5*a*b^4*sin(c + d*x))/(3*d*cos(c + d*x)^3) + (10*a^3*b^2*sin(c + d*x))/(d*cos(c + d*x)) + (5*a^2*b^3*sin(c + d*x))/(d*cos(c + d*x)^2)","B"
487,1,1021,157,2.452533,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))),x)","-\frac{\frac{9\,a^4\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{8\,a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^7\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^5\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^3\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(4\,a^4\,\left(a^2-b^2\right)+b^4\,\left(a^2-b^2\right)+2\,a^5\,b-4\,a^6+2\,a^3\,b^3+4\,a^2\,b^2\,\left(a^2-b^2\right)-a\,b^3\,\left(a^2-b^2\right)-2\,a^3\,b\,\left(a^2-b^2\right)\right)}\right)}{2}-\frac{3\,b^3\,\sin\left(c+d\,x\right)\,\sqrt{a^2-b^2}}{2}-\frac{b^3\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a^2-b^2}}{2}+\frac{3\,a^4\,\cos\left(3\,c+3\,d\,x\right)\,\mathrm{atanh}\left(\frac{8\,a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^7\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^5\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^3\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(4\,a^4\,\left(a^2-b^2\right)+b^4\,\left(a^2-b^2\right)+2\,a^5\,b-4\,a^6+2\,a^3\,b^3+4\,a^2\,b^2\,\left(a^2-b^2\right)-a\,b^3\,\left(a^2-b^2\right)-2\,a^3\,b\,\left(a^2-b^2\right)\right)}\right)}{2}+\frac{3\,a^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{a^2-b^2}}{2}-\frac{3\,a^2\,b\,\sin\left(c+d\,x\right)\,\sqrt{a^2-b^2}}{4}+\frac{9\,a^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)\,\sqrt{a^2-b^2}}{2}+\frac{3\,a\,b^2\,\sin\left(2\,c+2\,d\,x\right)\,\sqrt{a^2-b^2}}{4}-\frac{3\,a^2\,b\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a^2-b^2}}{4}+\frac{9\,a\,b^2\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{4}+\frac{3\,a\,b^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)\,\sqrt{a^2-b^2}}{4}}{3\,b^4\,d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)\,\sqrt{a^2-b^2}}","Not used",1,"-((9*a^4*cos(c + d*x)*atanh((8*a^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^8*sin(c/2 + (d*x)/2) + b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^7*b*sin(c/2 + (d*x)/2) - 2*a*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^5*b*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 5*a^2*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^3*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^4*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2))/(b*cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(4*a^4*(a^2 - b^2) + b^4*(a^2 - b^2) + 2*a^5*b - 4*a^6 + 2*a^3*b^3 + 4*a^2*b^2*(a^2 - b^2) - a*b^3*(a^2 - b^2) - 2*a^3*b*(a^2 - b^2)))))/2 - (3*b^3*sin(c + d*x)*(a^2 - b^2)^(1/2))/2 - (b^3*sin(3*c + 3*d*x)*(a^2 - b^2)^(1/2))/2 + (3*a^4*cos(3*c + 3*d*x)*atanh((8*a^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^8*sin(c/2 + (d*x)/2) + b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^7*b*sin(c/2 + (d*x)/2) - 2*a*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^5*b*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 5*a^2*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^3*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^4*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2))/(b*cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(4*a^4*(a^2 - b^2) + b^4*(a^2 - b^2) + 2*a^5*b - 4*a^6 + 2*a^3*b^3 + 4*a^2*b^2*(a^2 - b^2) - a*b^3*(a^2 - b^2) - 2*a^3*b*(a^2 - b^2)))))/2 + (3*a^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*(a^2 - b^2)^(1/2))/2 - (3*a^2*b*sin(c + d*x)*(a^2 - b^2)^(1/2))/4 + (9*a^3*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*(a^2 - b^2)^(1/2))/2 + (3*a*b^2*sin(2*c + 2*d*x)*(a^2 - b^2)^(1/2))/4 - (3*a^2*b*sin(3*c + 3*d*x)*(a^2 - b^2)^(1/2))/4 + (9*a*b^2*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*(a^2 - b^2)^(1/2))/4 + (3*a*b^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x)*(a^2 - b^2)^(1/2))/4)/(3*b^4*d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4)*(a^2 - b^2)^(1/2))","B"
488,1,1002,119,1.645749,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))),x)","\frac{\sin\left(c+d\,x\right)}{2\,b\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\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\,b\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{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)}{b^3\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\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\,b\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{2\,b^2\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{a^3\,\mathrm{atan}\left(\frac{\left(8\,a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^7\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^5\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^3\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)\right)\,1{}\mathrm{i}}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(4\,a^4\,\left(a^2-b^2\right)+b^4\,\left(a^2-b^2\right)+2\,a^5\,b-4\,a^6+2\,a^3\,b^3+4\,a^2\,b^2\,\left(a^2-b^2\right)-a\,b^3\,\left(a^2-b^2\right)-2\,a^3\,b\,\left(a^2-b^2\right)\right)}\right)\,1{}\mathrm{i}}{b^3\,d\,\sqrt{a^2-b^2}\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}+\frac{a^2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)}{b^3\,d\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}-\frac{a^3\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{\left(8\,a^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^7\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^5\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+5\,a^2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-8\,a^3\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+8\,a^4\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)\right)\,1{}\mathrm{i}}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(4\,a^4\,\left(a^2-b^2\right)+b^4\,\left(a^2-b^2\right)+2\,a^5\,b-4\,a^6+2\,a^3\,b^3+4\,a^2\,b^2\,\left(a^2-b^2\right)-a\,b^3\,\left(a^2-b^2\right)-2\,a^3\,b\,\left(a^2-b^2\right)\right)}\right)\,1{}\mathrm{i}}{b^3\,d\,\sqrt{a^2-b^2}\,\left(\frac{\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{1}{2}\right)}","Not used",1,"sin(c + d*x)/(2*b*d*(cos(2*c + 2*d*x)/2 + 1/2)) + atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))/(2*b*d*(cos(2*c + 2*d*x)/2 + 1/2)) + (a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^3*d*(cos(2*c + 2*d*x)/2 + 1/2)) + (atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/(2*b*d*(cos(2*c + 2*d*x)/2 + 1/2)) - (a*sin(2*c + 2*d*x))/(2*b^2*d*(cos(2*c + 2*d*x)/2 + 1/2)) - (a^3*atan(((8*a^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^8*sin(c/2 + (d*x)/2) + b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^7*b*sin(c/2 + (d*x)/2) - 2*a*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^5*b*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 5*a^2*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^3*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^4*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2))*1i)/(b*cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(4*a^4*(a^2 - b^2) + b^4*(a^2 - b^2) + 2*a^5*b - 4*a^6 + 2*a^3*b^3 + 4*a^2*b^2*(a^2 - b^2) - a*b^3*(a^2 - b^2) - 2*a^3*b*(a^2 - b^2))))*1i)/(b^3*d*(a^2 - b^2)^(1/2)*(cos(2*c + 2*d*x)/2 + 1/2)) + (a^2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x))/(b^3*d*(cos(2*c + 2*d*x)/2 + 1/2)) - (a^3*cos(2*c + 2*d*x)*atan(((8*a^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^8*sin(c/2 + (d*x)/2) + b^6*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^7*b*sin(c/2 + (d*x)/2) - 2*a*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^5*b*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 5*a^2*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 8*a^3*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 8*a^4*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2))*1i)/(b*cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(4*a^4*(a^2 - b^2) + b^4*(a^2 - b^2) + 2*a^5*b - 4*a^6 + 2*a^3*b^3 + 4*a^2*b^2*(a^2 - b^2) - a*b^3*(a^2 - b^2) - 2*a^3*b*(a^2 - b^2))))*1i)/(b^3*d*(a^2 - b^2)^(1/2)*(cos(2*c + 2*d*x)/2 + 1/2))","B"
489,1,119,85,1.212574,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))),x)","\frac{\mathrm{tan}\left(c+d\,x\right)}{b\,d}-\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)}{b^2\,d}-\frac{a^2\,\mathrm{atan}\left(\frac{a\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}-b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}\right)\,2{}\mathrm{i}}{b^2\,d\,\sqrt{a^2-b^2}}","Not used",1,"tan(c + d*x)/(b*d) - (2*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b^2*d) - (a^2*atan((a*sin(c/2 + (d*x)/2)*1i - b*sin(c/2 + (d*x)/2)*1i)/(cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)))*2i)/(b^2*d*(a^2 - b^2)^(1/2))","B"
490,1,186,68,1.062984,"\text{Not used}","int(1/(cos(c + d*x)^2*(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)}{b\,d}+\frac{2\,a\,\mathrm{atanh}\left(\frac{2\,a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-2\,a^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+2\,a^3\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(a\,b-b^2\right)}\right)}{b\,d\,\sqrt{a^2-b^2}}","Not used",1,"(2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d) + (2*a*atanh((2*a^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 2*a^4*sin(c/2 + (d*x)/2) + b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 2*a^3*b*sin(c/2 + (d*x)/2) - 2*a*b*sin(c/2 + (d*x)/2)*(a^2 - b^2))/(b*cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(a*b - b^2))))/(b*d*(a^2 - b^2)^(1/2))","B"
491,1,40,49,0.894155,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))),x)","\frac{2\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a-b}}{\sqrt{a+b}}\right)}{d\,\sqrt{a+b}\,\sqrt{a-b}}","Not used",1,"(2*atanh((tan(c/2 + (d*x)/2)*(a - b)^(1/2))/(a + b)^(1/2)))/(d*(a + b)^(1/2)*(a - b)^(1/2))","B"
492,1,186,59,1.089070,"\text{Not used}","int(1/(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)}{a\,d}+\frac{2\,b\,\mathrm{atanh}\left(\frac{2\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)+2\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)-2\,a\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,a\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(a\,b-a^2\right)}\right)}{a\,d\,\sqrt{a^2-b^2}}","Not used",1,"(2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) + (2*b*atanh((2*b^4*sin(c/2 + (d*x)/2) + a^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) + 2*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2) - 2*a*b^3*sin(c/2 + (d*x)/2) - 2*a*b*sin(c/2 + (d*x)/2)*(a^2 - b^2))/(a*cos(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(a*b - a^2))))/(a*d*(a^2 - b^2)^(1/2))","B"
493,1,395,76,1.309565,"\text{Not used}","int(cos(c + d*x)/(a + b/cos(c + d*x)),x)","\frac{a^3\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}+\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\,\left(a^4-a^2\,b^2\right)}-\frac{a\,b^2\,\sin\left(c+d\,x\right)}{d\,\left(a^4-a^2\,b^2\right)}-\frac{2\,a^2\,b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d\,\left(a^4-a^2\,b^2\right)}+\frac{b^2\,\mathrm{atan}\left(\frac{-a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}\,2{}\mathrm{i}+b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}-a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,3{}\mathrm{i}+a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}+a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^2+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^4}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^4-a^2\,b^2\right)}","Not used",1,"(a^3*sin(c + d*x))/(d*(a^4 - a^2*b^2)) + (2*b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2)) - (a*b^2*sin(c + d*x))/(d*(a^4 - a^2*b^2)) + (b^2*atan((b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2)*2i - a^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*2i - a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*3i + a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i + a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*1i)/(a^6*cos(c/2 + (d*x)/2) + a^2*b^4*cos(c/2 + (d*x)/2) - 2*a^4*b^2*cos(c/2 + (d*x)/2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^4 - a^2*b^2)) - (2*a^2*b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(d*(a^4 - a^2*b^2))","B"
494,1,592,110,1.811487,"\text{Not used}","int(cos(c + d*x)^2/(a + b/cos(c + d*x)),x)","\frac{a\,\left(\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{\sin\left(2\,c+2\,d\,x\right)}{4}\right)}{d\,\left(a^2-b^2\right)}-\frac{b\,\sin\left(c+d\,x\right)}{d\,\left(a^2-b^2\right)}+\frac{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)-\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}}{a\,d\,\left(a^2-b^2\right)}+\frac{b^3\,\sin\left(c+d\,x\right)}{a^2\,d\,\left(a^2-b^2\right)}-\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)}{a^3\,d\,\left(a^2-b^2\right)}-\frac{b^3\,\mathrm{atan}\left(\frac{\left(8\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(4\,b^5\,\left(a^2-b^2\right)+2\,a\,b^6-a^7+4\,b^7-2\,a^2\,b^5+a^3\,b^4-2\,a^4\,b^3-2\,a^5\,b^2+2\,a^2\,b^3\,\left(a^2-b^2\right)+2\,a\,b^4\,\left(a^2-b^2\right)\right)}\right)\,2{}\mathrm{i}}{a^3\,d\,\sqrt{a^2-b^2}}","Not used",1,"(a*(atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + sin(2*c + 2*d*x)/4))/(d*(a^2 - b^2)) - (b*sin(c + d*x))/(d*(a^2 - b^2)) + (b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (b^2*sin(2*c + 2*d*x))/4)/(a*d*(a^2 - b^2)) - (b^3*atan(((8*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(4*b^5*(a^2 - b^2) + 2*a*b^6 - a^7 + 4*b^7 - 2*a^2*b^5 + a^3*b^4 - 2*a^4*b^3 - 2*a^5*b^2 + 2*a^2*b^3*(a^2 - b^2) + 2*a*b^4*(a^2 - b^2))))*2i)/(a^3*d*(a^2 - b^2)^(1/2)) + (b^3*sin(c + d*x))/(a^2*d*(a^2 - b^2)) - (2*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^3*d*(a^2 - b^2))","B"
495,1,654,148,2.063829,"\text{Not used}","int(cos(c + d*x)^3/(a + b/cos(c + d*x)),x)","\frac{\frac{b^2\,\sin\left(c+d\,x\right)}{4}-\frac{b^2\,\sin\left(3\,c+3\,d\,x\right)}{12}}{a\,d\,\left(a^2-b^2\right)}-\frac{b\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{b\,\sin\left(2\,c+2\,d\,x\right)}{4}}{d\,\left(a^2-b^2\right)}+\frac{a\,\left(\frac{3\,\sin\left(c+d\,x\right)}{4}+\frac{\sin\left(3\,c+3\,d\,x\right)}{12}\right)}{d\,\left(a^2-b^2\right)}-\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)-\frac{b^3\,\sin\left(2\,c+2\,d\,x\right)}{4}}{a^2\,d\,\left(a^2-b^2\right)}-\frac{b^4\,\sin\left(c+d\,x\right)}{a^3\,d\,\left(a^2-b^2\right)}+\frac{2\,b^5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^4\,d\,\left(a^2-b^2\right)}+\frac{b^4\,\mathrm{atan}\left(\frac{\left(8\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+8\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-8\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+3\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-2\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(4\,b^5\,\left(a^2-b^2\right)+2\,a\,b^6-a^7+4\,b^7-2\,a^2\,b^5+a^3\,b^4-2\,a^4\,b^3-2\,a^5\,b^2+2\,a^2\,b^3\,\left(a^2-b^2\right)+2\,a\,b^4\,\left(a^2-b^2\right)\right)}\right)\,2{}\mathrm{i}}{a^4\,d\,\sqrt{a^2-b^2}}","Not used",1,"((b^2*sin(c + d*x))/4 - (b^2*sin(3*c + 3*d*x))/12)/(a*d*(a^2 - b^2)) - (b*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (b*sin(2*c + 2*d*x))/4)/(d*(a^2 - b^2)) + (a*((3*sin(c + d*x))/4 + sin(3*c + 3*d*x)/12))/(d*(a^2 - b^2)) - (b^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (b^3*sin(2*c + 2*d*x))/4)/(a^2*d*(a^2 - b^2)) + (b^4*atan(((8*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - a^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 8*b^9*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 8*a^2*b^7*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*a^4*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 3*a^5*b^4*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*a^6*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 2*a^7*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + a^8*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))*1i)/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(4*b^5*(a^2 - b^2) + 2*a*b^6 - a^7 + 4*b^7 - 2*a^2*b^5 + a^3*b^4 - 2*a^4*b^3 - 2*a^5*b^2 + 2*a^2*b^3*(a^2 - b^2) + 2*a*b^4*(a^2 - b^2))))*2i)/(a^4*d*(a^2 - b^2)^(1/2)) - (b^4*sin(c + d*x))/(a^3*d*(a^2 - b^2)) + (2*b^5*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^4*d*(a^2 - b^2))","B"
496,1,2678,193,3.424586,"\text{Not used}","int(cos(c + d*x)^4/(a + b/cos(c + d*x)),x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(5\,a^3+8\,a^2\,b+4\,a\,b^2+8\,b^3\right)}{4\,a^4}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^3-8\,a^2\,b+4\,a\,b^2-8\,b^3\right)}{4\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(9\,a^3+40\,a^2\,b-12\,a\,b^2+72\,b^3\right)}{12\,a^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-9\,a^3+40\,a^2\,b+12\,a\,b^2+72\,b^3\right)}{12\,a^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{16\,a^{13}}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^5}-\frac{\left(\frac{\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{16\,a^{13}}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^5}}{-\frac{9\,a^9\,b^5-18\,a^8\,b^6+33\,a^7\,b^7-48\,a^6\,b^8+88\,a^5\,b^9-104\,a^4\,b^{10}+104\,a^3\,b^{11}-96\,a^2\,b^{12}+96\,a\,b^{13}-64\,b^{14}}{a^{12}}+\frac{\left(\frac{\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{16\,a^{13}}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}+\frac{\left(\frac{\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{16\,a^{13}}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)}{8\,a^5}}\right)\,\left(a^4\,3{}\mathrm{i}+a^2\,b^2\,4{}\mathrm{i}+b^4\,8{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,a^5\,d}+\frac{b^5\,\mathrm{atan}\left(\frac{\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}+\frac{b^5\,\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}-\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\sqrt{a^2-b^2}}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}-\frac{b^5\,\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}+\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\sqrt{a^2-b^2}}{a^7-a^5\,b^2}\right)\,1{}\mathrm{i}}{a^7-a^5\,b^2}}{\frac{9\,a^9\,b^5-18\,a^8\,b^6+33\,a^7\,b^7-48\,a^6\,b^8+88\,a^5\,b^9-104\,a^4\,b^{10}+104\,a^3\,b^{11}-96\,a^2\,b^{12}+96\,a\,b^{13}-64\,b^{14}}{a^{12}}-\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}+\frac{b^5\,\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}-\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\sqrt{a^2-b^2}}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}+\frac{b^5\,\sqrt{a^2-b^2}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+51\,a^9\,b^2-81\,a^8\,b^3+136\,a^7\,b^4-216\,a^6\,b^5+256\,a^5\,b^6-256\,a^4\,b^7+256\,a^3\,b^8-256\,a^2\,b^9+256\,a\,b^{10}-128\,b^{11}\right)}{2\,a^8}-\frac{b^5\,\left(\frac{12\,a^{16}-12\,a^{15}\,b+4\,a^{14}\,b^2-4\,a^{13}\,b^3+16\,a^{12}\,b^4-48\,a^{11}\,b^5+32\,a^{10}\,b^6}{a^{12}}+\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(128\,a^{12}\,b-256\,a^{11}\,b^2+128\,a^{10}\,b^3\right)}{2\,a^8\,\left(a^7-a^5\,b^2\right)}\right)\,\sqrt{a^2-b^2}}{a^7-a^5\,b^2}\right)}{a^7-a^5\,b^2}}\right)\,\sqrt{a^2-b^2}\,2{}\mathrm{i}}{d\,\left(a^7-a^5\,b^2\right)}","Not used",1,"(b^5*atan(((b^5*(a^2 - b^2)^(1/2)*((tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8) + (b^5*((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 - (b^5*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(a^2 - b^2)^(1/2))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2) + (b^5*(a^2 - b^2)^(1/2)*((tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8) - (b^5*((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 + (b^5*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(a^2 - b^2)^(1/2))/(a^7 - a^5*b^2))*1i)/(a^7 - a^5*b^2))/((96*a*b^13 - 64*b^14 - 96*a^2*b^12 + 104*a^3*b^11 - 104*a^4*b^10 + 88*a^5*b^9 - 48*a^6*b^8 + 33*a^7*b^7 - 18*a^8*b^6 + 9*a^9*b^5)/a^12 - (b^5*(a^2 - b^2)^(1/2)*((tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8) + (b^5*((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 - (b^5*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(a^2 - b^2)^(1/2))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2) + (b^5*(a^2 - b^2)^(1/2)*((tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8) - (b^5*((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 + (b^5*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(2*a^8*(a^7 - a^5*b^2)))*(a^2 - b^2)^(1/2))/(a^7 - a^5*b^2)))/(a^7 - a^5*b^2)))*(a^2 - b^2)^(1/2)*2i)/(d*(a^7 - a^5*b^2)) - (atan(((((((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 - (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*8i + a^2*b^2*4i)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(16*a^13))*(a^4*3i + b^4*8i + a^2*b^2*4i))/(8*a^5) + (tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8))*(a^4*3i + b^4*8i + a^2*b^2*4i)*1i)/(8*a^5) - (((((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 + (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*8i + a^2*b^2*4i)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(16*a^13))*(a^4*3i + b^4*8i + a^2*b^2*4i))/(8*a^5) - (tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8))*(a^4*3i + b^4*8i + a^2*b^2*4i)*1i)/(8*a^5))/((((((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 - (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*8i + a^2*b^2*4i)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(16*a^13))*(a^4*3i + b^4*8i + a^2*b^2*4i))/(8*a^5) + (tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8))*(a^4*3i + b^4*8i + a^2*b^2*4i))/(8*a^5) - (96*a*b^13 - 64*b^14 - 96*a^2*b^12 + 104*a^3*b^11 - 104*a^4*b^10 + 88*a^5*b^9 - 48*a^6*b^8 + 33*a^7*b^7 - 18*a^8*b^6 + 9*a^9*b^5)/a^12 + (((((12*a^16 - 12*a^15*b + 32*a^10*b^6 - 48*a^11*b^5 + 16*a^12*b^4 - 4*a^13*b^3 + 4*a^14*b^2)/a^12 + (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*8i + a^2*b^2*4i)*(128*a^12*b + 128*a^10*b^3 - 256*a^11*b^2))/(16*a^13))*(a^4*3i + b^4*8i + a^2*b^2*4i))/(8*a^5) - (tan(c/2 + (d*x)/2)*(256*a*b^10 - 27*a^10*b + 9*a^11 - 128*b^11 - 256*a^2*b^9 + 256*a^3*b^8 - 256*a^4*b^7 + 256*a^5*b^6 - 216*a^6*b^5 + 136*a^7*b^4 - 81*a^8*b^3 + 51*a^9*b^2))/(2*a^8))*(a^4*3i + b^4*8i + a^2*b^2*4i))/(8*a^5)))*(a^4*3i + b^4*8i + a^2*b^2*4i)*1i)/(4*a^5*d) - ((tan(c/2 + (d*x)/2)^7*(4*a*b^2 + 8*a^2*b + 5*a^3 + 8*b^3))/(4*a^4) - (tan(c/2 + (d*x)/2)*(4*a*b^2 - 8*a^2*b + 5*a^3 - 8*b^3))/(4*a^4) + (tan(c/2 + (d*x)/2)^3*(40*a^2*b - 12*a*b^2 + 9*a^3 + 72*b^3))/(12*a^4) + (tan(c/2 + (d*x)/2)^5*(12*a*b^2 + 40*a^2*b - 9*a^3 + 72*b^3))/(12*a^4))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
497,1,3685,222,8.010479,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))^2),x)","-\frac{\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)}+\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)}{b^3\,\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)}^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(6\,a^2+b^2\right)\,\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(6\,a^2+b^2\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(6\,a^2+b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{2\,b^4}\right)\,1{}\mathrm{i}}{2\,b^4}+\frac{\left(6\,a^2+b^2\right)\,\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(6\,a^2+b^2\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(6\,a^2+b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{2\,b^4}\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(6\,a^2+b^2\right)\,\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(6\,a^2+b^2\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(6\,a^2+b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{2\,b^4}\right)}{2\,b^4}+\frac{\left(6\,a^2+b^2\right)\,\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(6\,a^2+b^2\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(6\,a^2+b^2\right)\,\left(-8\,a^6\,b^8+8\,a^5\,b^9+16\,a^4\,b^{10}-16\,a^3\,b^{11}-8\,a^2\,b^{12}+8\,a\,b^{13}\right)}{b^4\,\left(-a^3\,b^6-a^2\,b^7+a\,b^8+b^9\right)}\right)}{2\,b^4}\right)}{2\,b^4}}\right)\,\left(6\,a^2+b^2\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,"- ((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)) + (tan(c/2 + (d*x)/2)*(3*a^3*b - 3*a*b^3 + 6*a^4 + b^4 - 5*a^2*b^2))/(b^3*(a + b)*(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))) - (atan((((6*a^2 + b^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) - ((6*a^2 + b^2)*((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)*(6*a^2 + b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/(2*b^4))*1i)/(2*b^4) + ((6*a^2 + b^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) + ((6*a^2 + b^2)*((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)*(6*a^2 + b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/(2*b^4))*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) - ((6*a^2 + b^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) - ((6*a^2 + b^2)*((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)*(6*a^2 + b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/(2*b^4)))/(2*b^4) + ((6*a^2 + b^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) + ((6*a^2 + b^2)*((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)*(6*a^2 + b^2)*(8*a*b^13 - 8*a^2*b^12 - 16*a^3*b^11 + 16*a^4*b^10 + 8*a^5*b^9 - 8*a^6*b^8))/(b^4*(a*b^8 + b^9 - a^2*b^7 - a^3*b^6))))/(2*b^4)))/(2*b^4)))*(6*a^2 + b^2)*1i)/(b^4*d) - (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"
498,1,3159,164,6.810663,"\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)}^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{a\,\mathrm{atan}\left(\frac{\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{2\,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{64\,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)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{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{2\,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{64\,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)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}\right)\,2{}\mathrm{i}}{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{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{2\,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{64\,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)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{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{2\,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{64\,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)}{b^3\,\left(-a^3\,b^4-a^2\,b^5+a\,b^6+b^7\right)}\right)}{b^3}\right)}{b^3}}\right)\,4{}\mathrm{i}}{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)) + (a*atan(((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) - (2*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) - (64*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))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/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) + (2*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) + (64*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))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3)*2i)/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) - (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) - (2*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) - (64*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))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/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) + (2*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) + (64*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))/(b^3*(a*b^6 + b^7 - a^2*b^5 - a^3*b^4))))/b^3))/b^3))*4i)/(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"
499,1,2848,117,6.726622,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))^2),x)","-\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(b-a\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^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\,\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)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}}{b^2}-\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}\right)\,1{}\mathrm{i}}{b^2}-\frac{\left(\frac{\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\,\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)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}}{b^2}+\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}\right)\,1{}\mathrm{i}}{b^2}}{\frac{\frac{\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\,\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)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}}{b^2}-\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}}{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{\frac{\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\,\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)}{b^2\,\left(-a^3\,b^2-a^2\,b^3+a\,b^4+b^5\right)}}{b^2}+\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}}{b^2}}\right)\,2{}\mathrm{i}}{b^2\,d}-\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,"- (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) - (32*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))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/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) + (32*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))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/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) - (32*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))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/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) + (32*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))/(b^2*(a*b^4 + b^5 - a^2*b^3 - a^3*b^2)))/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))*2i)/(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"
500,1,92,85,1.117908,"\text{Not used}","int(1/(cos(c + d*x)^2*(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(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{2\,b\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\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*atanh((tan(c/2 + (d*x)/2)*(a - b)^(1/2))/(a + b)^(1/2)))/(d*(a + b)^(3/2)*(a - b)^(3/2))","B"
501,1,92,86,1.042513,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^2),x)","\frac{2\,a\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\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(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(2*a*atanh((tan(c/2 + (d*x)/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"
502,1,2886,109,6.671968,"\text{Not used}","int(1/(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(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{\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{\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)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}}{a^2}-\frac{-\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{\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{\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)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}}{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{\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{\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{\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)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{\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{\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{\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)\,32{}\mathrm{i}}{a^2\,\left(a^5+a^4\,b-a^3\,b^2-a^2\,b^3\right)}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}-\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(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{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,"(2*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) - (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)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/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 - ((((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) + (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)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/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) - (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)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/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) + (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)*32i)/(a^2*(a^4*b + a^5 - a^2*b^3 - a^3*b^2)))*1i)/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)))/(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"
503,1,3169,146,7.011159,"\text{Not used}","int(cos(c + d*x)/(a + b/cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-a^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{4\,b\,\mathrm{atan}\left(\frac{\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{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{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)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{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{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{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)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{a^3}\right)}{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{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{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{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)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{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{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{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)\,64{}\mathrm{i}}{a^3\,\left(a^7+a^6\,b-a^5\,b^2-a^4\,b^3\right)}\right)\,2{}\mathrm{i}}{a^3}\right)\,2{}\mathrm{i}}{a^3}}\right)}{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,"((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)) - (4*b*atan(((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) + (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) - (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)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/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) - (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) + (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)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/a^3))/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) - (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) + (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) - (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)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/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) - (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) + (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)*64i)/(a^3*(a^6*b + a^7 - a^4*b^3 - a^5*b^2)))*2i)/a^3)*2i)/a^3)))/(a^3*d) - (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"
504,1,3738,208,8.323086,"\text{Not used}","int(cos(c + d*x)^2/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(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(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(a+3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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(\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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\right)}{2\,a^4}+\frac{\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2-20\,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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\right)}{2\,a^4}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,6{}\mathrm{i}\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,"(atan(((((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*1i + b^2*6i)*((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*1i + b^2*6i)*(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))*(a^2*1i + b^2*6i)*1i)/(2*a^4) + (((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*1i + b^2*6i)*((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*1i + b^2*6i)*(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))*(a^2*1i + b^2*6i)*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) - (((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*1i + b^2*6i)*((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*1i + b^2*6i)*(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))*(a^2*1i + b^2*6i))/(2*a^4) + (((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*1i + b^2*6i)*((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*1i + b^2*6i)*(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))*(a^2*1i + b^2*6i))/(2*a^4)))*(a^2*1i + b^2*6i)*1i)/(a^4*d) - ((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))) + (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"
505,1,3839,261,9.084974,"\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)}^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(4\,b-2\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(2\,a+4\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{2\,b\,\mathrm{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{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)\,32{}\mathrm{i}}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,1{}\mathrm{i}}{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{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)\,32{}\mathrm{i}}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,1{}\mathrm{i}}{a^5}\right)}{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{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)\,32{}\mathrm{i}}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,1{}\mathrm{i}}{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{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)\,32{}\mathrm{i}}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,1{}\mathrm{i}}{a^5}\right)\,1{}\mathrm{i}}{a^5}}\right)\,\left(a^2+4\,b^2\right)}{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)) - (2*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) - (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)*32i)/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*1i)/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) + (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)*32i)/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*1i)/a^5))/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) - (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)*32i)/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*1i)/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) + (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)*32i)/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*1i)/a^5)*1i)/a^5))*(a^2 + 4*b^2))/(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"
506,1,5332,230,9.290070,"\text{Not used}","int(1/(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)}^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{a\,\mathrm{atan}\left(\frac{\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{3\,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{24\,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)}{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)}{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{3\,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{24\,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)}{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)}{b^4}\right)\,3{}\mathrm{i}}{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{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{3\,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{24\,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)}{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)}{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{3\,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{24\,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)}{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)}{b^4}\right)}{b^4}}\right)\,6{}\mathrm{i}}{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))) + (a*atan(((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) - (3*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) - (24*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))/(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))))/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) + (3*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) + (24*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))/(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))))/b^4)*3i)/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*((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*((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) - (24*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))/(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))))/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) + (3*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) + (24*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))/(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))))/b^4))/b^4))*6i)/(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"
507,1,5078,188,9.497172,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^3),x)","-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\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{8\,\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)}{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)}}{b^3}-\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}}\right)\,1{}\mathrm{i}}{b^3}-\frac{\left(\frac{\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{8\,\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)}{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)}}{b^3}+\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}}\right)\,1{}\mathrm{i}}{b^3}}{\frac{\frac{\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{8\,\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)}{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)}}{b^3}-\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}}}{b^3}+\frac{\frac{\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{8\,\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)}{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)}}{b^3}+\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}}}{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}}}\right)\,2{}\mathrm{i}}{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,"- (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) - (8*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))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 - (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) + (8*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))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 + (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) - (8*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))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 - (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) + (8*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))/(b^3*(a*b^10 + b^11 - 3*a^2*b^9 - 3*a^3*b^8 + 3*a^4*b^7 + 3*a^5*b^6 - a^6*b^5 - a^7*b^4)))/b^3 + (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 - (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)))*2i)/(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"
508,1,204,149,3.235131,"\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(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)}+\frac{\mathrm{atanh}\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}}","Not used",1,"((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)) + (atanh((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))","B"
509,1,210,134,3.373804,"\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)}^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{atanh}\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*atanh((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"
510,1,204,133,3.183034,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^3),x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^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)}+\frac{\mathrm{atanh}\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}}","Not used",1,"((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)) + (atanh((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))","B"
511,1,5090,173,9.221831,"\text{Not used}","int(1/(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(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{\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{\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)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}}{a^3}-\frac{-\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{\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{\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)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}}{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}+\frac{\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{\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{\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)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}+\frac{\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{\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{\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)\,8{}\mathrm{i}}{a^3\,\left(a^{11}+a^{10}\,b-3\,a^9\,b^2-3\,a^8\,b^3+3\,a^7\,b^4+3\,a^6\,b^5-a^5\,b^6-a^4\,b^7\right)}\right)\,1{}\mathrm{i}}{a^3}\right)\,1{}\mathrm{i}}{a^3}}\right)}{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,"(2*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) - (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)*8i)/(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)))*1i)/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) + (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)*8i)/(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)))*1i)/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) - (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)*8i)/(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)))*1i)/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) + (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)*8i)/(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)))*1i)/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 + (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))))/(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"
512,1,5338,223,8.999351,"\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)\,\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{{\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{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{6\,b\,\mathrm{atan}\left(\frac{\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{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{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)\,24{}\mathrm{i}}{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)\,3{}\mathrm{i}}{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{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{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)\,24{}\mathrm{i}}{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)\,3{}\mathrm{i}}{a^4}\right)}{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{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{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{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)\,24{}\mathrm{i}}{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)\,3{}\mathrm{i}}{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{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{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)\,24{}\mathrm{i}}{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)\,3{}\mathrm{i}}{a^4}\right)\,3{}\mathrm{i}}{a^4}}\right)}{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,"((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)) - (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) + (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))) - (6*b*atan(((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) + (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) - (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)*24i)/(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)))*3i)/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) - (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) + (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)*24i)/(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)))*3i)/a^4))/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) - (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) + (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) - (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)*24i)/(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)))*3i)/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) - (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) + (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)*24i)/(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)))*3i)/a^4)*3i)/a^4)))/(a^4*d) - (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"
513,1,5950,296,9.285321,"\text{Not used}","int(cos(c + d*x)^2/(a + b/cos(c + d*x))^3,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(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(\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,a^5}+\frac{\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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(\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\right)}{2\,a^5}+\frac{\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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)\,\left(a^2\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\right)}{2\,a^5}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,12{}\mathrm{i}\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,"(atan(((((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*1i + b^2*12i)*((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*1i + b^2*12i)*(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))*(a^2*1i + b^2*12i)*1i)/(2*a^5) + (((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*1i + b^2*12i)*((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*1i + b^2*12i)*(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))*(a^2*1i + b^2*12i)*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) - (((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*1i + b^2*12i)*((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*1i + b^2*12i)*(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))*(a^2*1i + b^2*12i))/(2*a^5) + (((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*1i + b^2*12i)*((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*1i + b^2*12i)*(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))*(a^2*1i + b^2*12i))/(2*a^5)))*(a^2*1i + b^2*12i)*1i)/(a^5*d) - ((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)) + (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"
514,1,7476,316,10.357918,"\text{Not used}","int(1/(cos(c + d*x)^6*(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{a\,\mathrm{atan}\left(\frac{\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{4\,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{32\,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)}{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)}{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{4\,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{32\,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)}{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)}{b^5}\right)\,4{}\mathrm{i}}{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{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{4\,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{32\,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)}{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)}{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{4\,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{32\,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)}{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)}{b^5}\right)}{b^5}}\right)\,8{}\mathrm{i}}{b^5\,d}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(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))) + (a*atan(((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) - (4*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) - (32*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))/(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))))/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) + (4*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) + (32*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))/(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))))/b^5)*4i)/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) - (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) - (4*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) - (32*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))/(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))))/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) + (4*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) + (32*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))/(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))))/b^5))/b^5))*8i)/(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"
515,1,7222,259,12.447938,"\text{Not used}","int(1/(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)}^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({\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)-{\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)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\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{8\,\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)}{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)}}{b^4}-\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}}\right)\,1{}\mathrm{i}}{b^4}-\frac{\left(\frac{\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{8\,\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)}{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)}}{b^4}+\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}}\right)\,1{}\mathrm{i}}{b^4}}{\frac{\frac{\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{8\,\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)}{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)}}{b^4}-\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}}}{b^4}+\frac{\frac{\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{8\,\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)}{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)}}{b^4}+\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}}}{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}}}\right)\,2{}\mathrm{i}}{b^4\,d}-\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{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,"- ((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*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^6*(3*a*b^2 - 3*a^2*b + a^3 - b^3))) - (atan((((((8*(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) - (8*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))/(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)))/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) + (8*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))/(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)))/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) - (8*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))/(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)))/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) + (8*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))/(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)))/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 - (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)))*2i)/(b^4*d) - (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"
516,1,378,222,4.412532,"\text{Not used}","int(1/(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^3+3\,a^2\,b+6\,a\,b^2\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(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)\,\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({\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)-{\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)+3\,a\,b^2+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{atanh}\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,"((tan(c/2 + (d*x)/2)^5*(6*a*b^2 + 3*a^2*b + 2*a^3))/((a + b)^3*(a - b)) - (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)*(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*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 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*atanh((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"
517,1,380,206,4.379024,"\text{Not used}","int(1/(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(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)}^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{\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({\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)-{\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)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)\right)}+\frac{a\,\mathrm{atanh}\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}}","Not used",1,"((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)^5*(2*a*b^2 + 6*a^2*b + a^3 + 2*b^3))/((a + b)^3*(a - b)) + (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*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 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*atanh((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))","B"
518,1,382,192,4.343403,"\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)}^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({\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)-{\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)+3\,a\,b^2+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{atanh}\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*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 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*atanh((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"
519,1,378,184,4.320102,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^4),x)","\frac{a\,\mathrm{atanh}\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{{\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{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)\,\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({\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)-{\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)+3\,a\,b^2+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*atanh((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)) - ((tan(c/2 + (d*x)/2)^5*(3*a*b^2 + 6*a^2*b + 2*b^3))/((a + b)^3*(a - b)) - (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)*(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*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 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"
520,1,7234,242,12.789805,"\text{Not used}","int(1/(a + b/cos(c + d*x))^4,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\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{\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{\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)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}}{a^4}-\frac{-\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{\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{\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)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}}{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}}+\frac{\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{\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{\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)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}+\frac{\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{\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{\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)\,8{}\mathrm{i}}{a^4\,\left(a^{17}+a^{16}\,b-5\,a^{15}\,b^2-5\,a^{14}\,b^3+10\,a^{13}\,b^4+10\,a^{12}\,b^5-10\,a^{11}\,b^6-10\,a^{10}\,b^7+5\,a^9\,b^8+5\,a^8\,b^9-a^7\,b^{10}-a^6\,b^{11}\right)}\right)\,1{}\mathrm{i}}{a^4}\right)\,1{}\mathrm{i}}{a^4}}\right)}{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({\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)-{\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)+3\,a\,b^2+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,"(2*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) - (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)*8i)/(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)))*1i)/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) + (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)*8i)/(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)))*1i)/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) - (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)*8i)/(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)))*1i)/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) + (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)*8i)/(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)))*1i)/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 + (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))))/(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*(tan(c/2 + (d*x)/2)^2*(3*a*b^2 - 3*a^2*b - 3*a^3 + 3*b^3) - tan(c/2 + (d*x)/2)^4*(3*a*b^2 + 3*a^2*b - 3*a^3 - 3*b^3) + 3*a*b^2 + 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"
521,1,7534,299,10.384096,"\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)}^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)}{\left(a^4\,b-a^5\right)\,{\left(a+b\right)}^3}+\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\,{\left(a+b\right)}^2\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}-\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)}{\left(a+b\right)\,\left(-a^7+3\,a^6\,b-3\,a^5\,b^2+a^4\,b^3\right)}+\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\,\left(a^4\,b-a^5\right)\,{\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{8\,b\,\mathrm{atan}\left(\frac{\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{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{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)\,32{}\mathrm{i}}{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)\,4{}\mathrm{i}}{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{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{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)\,32{}\mathrm{i}}{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)\,4{}\mathrm{i}}{a^5}\right)}{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{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{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{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)\,32{}\mathrm{i}}{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)\,4{}\mathrm{i}}{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{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{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)\,32{}\mathrm{i}}{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)\,4{}\mathrm{i}}{a^5}\right)\,4{}\mathrm{i}}{a^5}}\right)}{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,"- ((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*b - a^5)*(a + b)^3) + (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 + b)^2*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*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 + b)*(3*a^6*b - a^7 + a^4*b^3 - 3*a^5*b^2)) + (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*b - a^5)*(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))) - (8*b*atan(((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) + (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) - (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)*32i)/(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)))*4i)/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) - (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) + (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)*32i)/(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)))*4i)/a^5))/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) - (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) + (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) - (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)*32i)/(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)))*4i)/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) - (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) + (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)*32i)/(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)))*4i)/a^5)*4i)/a^5)))/(a^5*d) - (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"
522,1,8133,387,10.803136,"\text{Not used}","int(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)}^9\,\left(a^8+7\,a^7\,b-11\,a^6\,b^2-21\,a^5\,b^3+57\,a^4\,b^4+27\,a^3\,b^5-59\,a^2\,b^6-10\,a\,b^7+20\,b^8\right)}{a^5\,{\left(a+b\right)}^3\,\left(a-b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-6\,a^9+21\,a^8\,b-3\,a^7\,b^2-111\,a^6\,b^3+45\,a^5\,b^4+369\,a^4\,b^5-71\,a^3\,b^6-364\,a^2\,b^7+30\,a\,b^8+120\,b^9\right)}{3\,a^5\,{\left(a+b\right)}^2\,{\left(a-b\right)}^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(6\,a^9+21\,a^8\,b+3\,a^7\,b^2-111\,a^6\,b^3-45\,a^5\,b^4+369\,a^4\,b^5+71\,a^3\,b^6-364\,a^2\,b^7-30\,a\,b^8+120\,b^9\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(9\,a^{10}+36\,a^8\,b^2-324\,a^6\,b^4+740\,a^4\,b^6-611\,a^2\,b^8+180\,b^{10}\right)}{3\,a^5\,{\left(a+b\right)}^3\,{\left(a-b\right)}^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^8-7\,a^7\,b-11\,a^6\,b^2+21\,a^5\,b^3+57\,a^4\,b^4-27\,a^3\,b^5-59\,a^2\,b^6+10\,a\,b^7+20\,b^8\right)}{a^5\,\left(a+b\right)\,{\left(a-b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^3+3\,a^2\,b+9\,a\,b^2+5\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-2\,a^3-6\,a^2\,b+6\,a\,b^2+10\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-2\,a^3+6\,a^2\,b+6\,a\,b^2-10\,b^3\right)+3\,a\,b^2+3\,a^2\,b+a^3+b^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(a^3-3\,a^2\,b+3\,a\,b^2-b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^3+3\,a^2\,b-9\,a\,b^2+5\,b^3\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)}{2\,a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,a^6}-\frac{\left(\frac{\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)}{2\,a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)\,1{}\mathrm{i}}{2\,a^6}}{-\frac{8\,\left(40\,a^{16}\,b^3-40\,a^{15}\,b^4+1396\,a^{14}\,b^5+204\,a^{13}\,b^6+8281\,a^{12}\,b^7+16999\,a^{11}\,b^8-64479\,a^{10}\,b^9-57345\,a^9\,b^{10}+155991\,a^8\,b^{11}+82337\,a^7\,b^{12}-193689\,a^6\,b^{13}-62030\,a^5\,b^{14}+135260\,a^4\,b^{15}+24400\,a^3\,b^{16}-50800\,a^2\,b^{17}-4000\,a\,b^{18}+8000\,b^{19}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{\left(\frac{\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)}{2\,a^6}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)}{2\,a^6}+\frac{\left(\frac{\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{a^6\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)}{2\,a^6}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)}{2\,a^6}}\right)\,\left(a^2\,1{}\mathrm{i}+b^2\,20{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^6\,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^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{b^3\,\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)\,1{}\mathrm{i}}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}+\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b^3\,\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)\,1{}\mathrm{i}}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}}{\frac{8\,\left(40\,a^{16}\,b^3-40\,a^{15}\,b^4+1396\,a^{14}\,b^5+204\,a^{13}\,b^6+8281\,a^{12}\,b^7+16999\,a^{11}\,b^8-64479\,a^{10}\,b^9-57345\,a^9\,b^{10}+155991\,a^8\,b^{11}+82337\,a^7\,b^{12}-193689\,a^6\,b^{13}-62030\,a^5\,b^{14}+135260\,a^4\,b^{15}+24400\,a^3\,b^{16}-50800\,a^2\,b^{17}-4000\,a\,b^{18}+8000\,b^{19}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}-\frac{b^3\,\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}-\frac{4\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}-\frac{b^3\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^{18}+2\,a^{17}\,b-35\,a^{16}\,b^2+68\,a^{15}\,b^3-209\,a^{14}\,b^4+350\,a^{13}\,b^5+45\,a^{12}\,b^6-3640\,a^{11}\,b^7+3325\,a^{10}\,b^8+10430\,a^9\,b^9-10385\,a^8\,b^{10}-14812\,a^7\,b^{11}+14837\,a^6\,b^{12}+11522\,a^5\,b^{13}-11522\,a^4\,b^{14}-4720\,a^3\,b^{15}+4720\,a^2\,b^{16}+800\,a\,b^{17}-800\,b^{18}\right)}{a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}}+\frac{b^3\,\left(\frac{4\,\left(4\,a^{27}+52\,a^{25}\,b^2-160\,a^{24}\,b^3-316\,a^{23}\,b^4+816\,a^{22}\,b^5+724\,a^{21}\,b^6-1764\,a^{20}\,b^7-896\,a^{19}\,b^8+2076\,a^{18}\,b^9+640\,a^{17}\,b^{10}-1404\,a^{16}\,b^{11}-248\,a^{15}\,b^{12}+516\,a^{14}\,b^{13}+40\,a^{13}\,b^{14}-80\,a^{12}\,b^{15}\right)}{a^{26}+a^{25}\,b-5\,a^{24}\,b^2-5\,a^{23}\,b^3+10\,a^{22}\,b^4+10\,a^{21}\,b^5-10\,a^{20}\,b^6-10\,a^{19}\,b^7+5\,a^{18}\,b^8+5\,a^{17}\,b^9-a^{16}\,b^{10}-a^{15}\,b^{11}}+\frac{4\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)\,\left(8\,a^{25}\,b-8\,a^{24}\,b^2-48\,a^{23}\,b^3+48\,a^{22}\,b^4+120\,a^{21}\,b^5-120\,a^{20}\,b^6-160\,a^{19}\,b^7+160\,a^{18}\,b^8+120\,a^{17}\,b^9-120\,a^{16}\,b^{10}-48\,a^{15}\,b^{11}+48\,a^{14}\,b^{12}+8\,a^{13}\,b^{13}-8\,a^{12}\,b^{14}\right)}{\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)\,\left(a^{21}+a^{20}\,b-5\,a^{19}\,b^2-5\,a^{18}\,b^3+10\,a^{17}\,b^4+10\,a^{16}\,b^5-10\,a^{15}\,b^6-10\,a^{14}\,b^7+5\,a^{13}\,b^8+5\,a^{12}\,b^9-a^{11}\,b^{10}-a^{10}\,b^{11}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)}{2\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}}\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(40\,a^6-84\,a^4\,b^2+69\,a^2\,b^4-20\,b^6\right)\,1{}\mathrm{i}}{d\,\left(a^{20}-7\,a^{18}\,b^2+21\,a^{16}\,b^4-35\,a^{14}\,b^6+35\,a^{12}\,b^8-21\,a^{10}\,b^{10}+7\,a^8\,b^{12}-a^6\,b^{14}\right)}","Not used",1,"((tan(c/2 + (d*x)/2)^9*(7*a^7*b - 10*a*b^7 + a^8 + 20*b^8 - 59*a^2*b^6 + 27*a^3*b^5 + 57*a^4*b^4 - 21*a^5*b^3 - 11*a^6*b^2))/(a^5*(a + b)^3*(a - b)) + (2*tan(c/2 + (d*x)/2)^3*(30*a*b^8 + 21*a^8*b - 6*a^9 + 120*b^9 - 364*a^2*b^7 - 71*a^3*b^6 + 369*a^4*b^5 + 45*a^5*b^4 - 111*a^6*b^3 - 3*a^7*b^2))/(3*a^5*(a + b)^2*(a - b)^3) - (2*tan(c/2 + (d*x)/2)^7*(21*a^8*b - 30*a*b^8 + 6*a^9 + 120*b^9 - 364*a^2*b^7 + 71*a^3*b^6 + 369*a^4*b^5 - 45*a^5*b^4 - 111*a^6*b^3 + 3*a^7*b^2))/(3*a^5*(a + b)^3*(a - b)^2) + (2*tan(c/2 + (d*x)/2)^5*(9*a^10 + 180*b^10 - 611*a^2*b^8 + 740*a^4*b^6 - 324*a^6*b^4 + 36*a^8*b^2))/(3*a^5*(a + b)^3*(a - b)^3) + (tan(c/2 + (d*x)/2)*(10*a*b^7 - 7*a^7*b + a^8 + 20*b^8 - 59*a^2*b^6 - 27*a^3*b^5 + 57*a^4*b^4 + 21*a^5*b^3 - 11*a^6*b^2))/(a^5*(a + b)*(a - b)^3))/(d*(tan(c/2 + (d*x)/2)^2*(9*a*b^2 + 3*a^2*b - a^3 + 5*b^3) + tan(c/2 + (d*x)/2)^4*(6*a*b^2 - 6*a^2*b - 2*a^3 + 10*b^3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 + 6*a^2*b - 2*a^3 - 10*b^3) + 3*a*b^2 + 3*a^2*b + a^3 + b^3 - tan(c/2 + (d*x)/2)^10*(3*a*b^2 - 3*a^2*b + a^3 - b^3) + tan(c/2 + (d*x)/2)^8*(3*a^2*b - 9*a*b^2 + a^3 + 5*b^3))) - (atan(((((((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2*1i + b^2*20i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(a^2*1i + b^2*20i))/(2*a^6) - (8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*(a^2*1i + b^2*20i)*1i)/(2*a^6) - (((((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2*1i + b^2*20i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(a^2*1i + b^2*20i))/(2*a^6) + (8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*(a^2*1i + b^2*20i)*1i)/(2*a^6))/((((((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2*1i + b^2*20i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(a^2*1i + b^2*20i))/(2*a^6) - (8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*(a^2*1i + b^2*20i))/(2*a^6) - (8*(8000*b^19 - 4000*a*b^18 - 50800*a^2*b^17 + 24400*a^3*b^16 + 135260*a^4*b^15 - 62030*a^5*b^14 - 193689*a^6*b^13 + 82337*a^7*b^12 + 155991*a^8*b^11 - 57345*a^9*b^10 - 64479*a^10*b^9 + 16999*a^11*b^8 + 8281*a^12*b^7 + 204*a^13*b^6 + 1396*a^14*b^5 - 40*a^15*b^4 + 40*a^16*b^3))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (((((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2*1i + b^2*20i)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/(a^6*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*(a^2*1i + b^2*20i))/(2*a^6) + (8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2))*(a^2*1i + b^2*20i))/(2*a^6)))*(a^2*1i + b^2*20i)*1i)/(a^6*d) - (b^3*atan(((b^3*((8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b^3*((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b^3*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) + (b^3*((8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b^3*((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b^3*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2)*1i)/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))/((8*(8000*b^19 - 4000*a*b^18 - 50800*a^2*b^17 + 24400*a^3*b^16 + 135260*a^4*b^15 - 62030*a^5*b^14 - 193689*a^6*b^13 + 82337*a^7*b^12 + 155991*a^8*b^11 - 57345*a^9*b^10 - 64479*a^10*b^9 + 16999*a^11*b^8 + 8281*a^12*b^7 + 204*a^13*b^6 + 1396*a^14*b^5 - 40*a^15*b^4 + 40*a^16*b^3))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (b^3*((8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) - (b^3*((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) - (4*b^3*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)) - (b^3*((8*tan(c/2 + (d*x)/2)*(800*a*b^17 + 2*a^17*b - a^18 - 800*b^18 + 4720*a^2*b^16 - 4720*a^3*b^15 - 11522*a^4*b^14 + 11522*a^5*b^13 + 14837*a^6*b^12 - 14812*a^7*b^11 - 10385*a^8*b^10 + 10430*a^9*b^9 + 3325*a^10*b^8 - 3640*a^11*b^7 + 45*a^12*b^6 + 350*a^13*b^5 - 209*a^14*b^4 + 68*a^15*b^3 - 35*a^16*b^2))/(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2) + (b^3*((4*(4*a^27 - 80*a^12*b^15 + 40*a^13*b^14 + 516*a^14*b^13 - 248*a^15*b^12 - 1404*a^16*b^11 + 640*a^17*b^10 + 2076*a^18*b^9 - 896*a^19*b^8 - 1764*a^20*b^7 + 724*a^21*b^6 + 816*a^22*b^5 - 316*a^23*b^4 - 160*a^24*b^3 + 52*a^25*b^2))/(a^25*b + a^26 - a^15*b^11 - a^16*b^10 + 5*a^17*b^9 + 5*a^18*b^8 - 10*a^19*b^7 - 10*a^20*b^6 + 10*a^21*b^5 + 10*a^22*b^4 - 5*a^23*b^3 - 5*a^24*b^2) + (4*b^3*tan(c/2 + (d*x)/2)*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2)*(8*a^25*b - 8*a^12*b^14 + 8*a^13*b^13 + 48*a^14*b^12 - 48*a^15*b^11 - 120*a^16*b^10 + 120*a^17*b^9 + 160*a^18*b^8 - 160*a^19*b^7 - 120*a^20*b^6 + 120*a^21*b^5 + 48*a^22*b^4 - 48*a^23*b^3 - 8*a^24*b^2))/((a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)*(a^20*b + a^21 - a^10*b^11 - a^11*b^10 + 5*a^12*b^9 + 5*a^13*b^8 - 10*a^14*b^7 - 10*a^15*b^6 + 10*a^16*b^5 + 10*a^17*b^4 - 5*a^18*b^3 - 5*a^19*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2)))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2))/(2*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))))*((a + b)^7*(a - b)^7)^(1/2)*(40*a^6 - 20*b^6 + 69*a^2*b^4 - 84*a^4*b^2)*1i)/(d*(a^20 - a^6*b^14 + 7*a^8*b^12 - 21*a^10*b^10 + 35*a^12*b^8 - 35*a^14*b^6 + 21*a^16*b^4 - 7*a^18*b^2))","B"
523,1,21,31,0.823929,"\text{Not used}","int(1/(5/cos(c + d*x) + 3),x)","\frac{x}{3}-\frac{5\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{6\,d}","Not used",1,"x/3 - (5*atan(tan(c/2 + (d*x)/2)/2))/(6*d)","B"
524,1,52,56,0.858898,"\text{Not used}","int(1/(5/cos(c + d*x) + 3)^2,x)","\frac{x}{9}-\frac{\frac{35\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{288}+\frac{25\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{48\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\right)}}{d}","Not used",1,"x/9 - ((35*atan(tan(c/2 + (d*x)/2)/2))/288 + (25*tan(c/2 + (d*x)/2))/(48*(tan(c/2 + (d*x)/2)^2 + 4)))/d","B"
525,1,79,81,0.906665,"\text{Not used}","int(1/(5/cos(c + d*x) + 3)^3,x)","\frac{x}{27}-\frac{3055\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{27648\,d}-\frac{\frac{275\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{1152}-\frac{475\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4608}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+16\right)}","Not used",1,"x/27 - (3055*atan(tan(c/2 + (d*x)/2)/2))/(27648*d) - ((275*tan(c/2 + (d*x)/2))/1152 - (475*tan(c/2 + (d*x)/2)^3)/4608)/(d*(8*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 16))","B"
526,1,105,106,1.094251,"\text{Not used}","int(1/(5/cos(c + d*x) + 3)^4,x)","\frac{x}{81}-\frac{11215\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{1327104\,d}-\frac{\frac{25925\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{221184}+\frac{3575\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6912}+\frac{17675\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{13824}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+64\right)}","Not used",1,"x/81 - (11215*atan(tan(c/2 + (d*x)/2)/2))/(1327104*d) - ((17675*tan(c/2 + (d*x)/2))/13824 + (3575*tan(c/2 + (d*x)/2)^3)/6912 + (25925*tan(c/2 + (d*x)/2)^5)/221184)/(d*(48*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 64))","B"
527,1,21,70,0.875232,"\text{Not used}","int(1/(3/cos(c + d*x) + 5),x)","\frac{x}{5}-\frac{3\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{10\,d}","Not used",1,"x/5 - (3*atanh(tan(c/2 + (d*x)/2)/2))/(10*d)","B"
528,1,52,95,0.880962,"\text{Not used}","int(1/(3/cos(c + d*x) + 5)^2,x)","\frac{x}{25}-\frac{\frac{123\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{800}+\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{80\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\right)}}{d}","Not used",1,"x/25 - ((123*atanh(tan(c/2 + (d*x)/2)/2))/800 + (9*tan(c/2 + (d*x)/2))/(80*(tan(c/2 + (d*x)/2)^2 - 4)))/d","B"
529,1,78,120,0.952577,"\text{Not used}","int(1/(3/cos(c + d*x) + 5)^3,x)","\frac{x}{125}-\frac{8361\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{128000\,d}+\frac{\frac{1053\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3200}-\frac{1323\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12800}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+16\right)}","Not used",1,"x/125 - (8361*atanh(tan(c/2 + (d*x)/2)/2))/(128000*d) + ((1053*tan(c/2 + (d*x)/2))/3200 - (1323*tan(c/2 + (d*x)/2)^3)/12800)/(d*(tan(c/2 + (d*x)/2)^4 - 8*tan(c/2 + (d*x)/2)^2 + 16))","B"
530,1,105,145,1.099459,"\text{Not used}","int(1/(3/cos(c + d*x) + 5)^4,x)","\frac{x}{625}-\frac{278151\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}\right)}{10240000\,d}-\frac{\frac{69093\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{1024000}-\frac{13527\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32000}+\frac{44523\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64000}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-64\right)}","Not used",1,"x/625 - (278151*atanh(tan(c/2 + (d*x)/2)/2))/(10240000*d) - ((44523*tan(c/2 + (d*x)/2))/64000 - (13527*tan(c/2 + (d*x)/2)^3)/32000 + (69093*tan(c/2 + (d*x)/2)^5)/1024000)/(d*(48*tan(c/2 + (d*x)/2)^2 - 12*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 64))","B"
531,0,-1,292,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/cos(c + d*x)^3,x)","\int \frac{\sqrt{a+\frac{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"
532,0,-1,241,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/cos(c + d*x)^2,x)","\int \frac{\sqrt{a+\frac{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"
533,0,-1,209,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/cos(c + d*x),x)","\int \frac{\sqrt{a+\frac{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"
534,0,-1,125,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(1/2), x)","F"
535,0,-1,330,0.000000,"\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+\frac{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"
536,0,-1,396,0.000000,"\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+\frac{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"
537,0,-1,405,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/cos(c + d*x)^4,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(3/2)/cos(c + d*x)^4, x)","F"
538,0,-1,342,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/cos(c + d*x)^3,x)","\int \frac{{\left(a+\frac{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"
539,0,-1,282,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{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"
540,0,-1,249,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{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"
541,0,-1,309,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
542,0,-1,334,0.000000,"\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+\frac{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"
543,0,-1,390,0.000000,"\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+\frac{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"
544,0,-1,463,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/cos(c + d*x)^4,x)","\int \frac{{\left(a+\frac{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"
545,0,-1,399,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/cos(c + d*x)^3,x)","\int \frac{{\left(a+\frac{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"
546,0,-1,333,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{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"
547,0,-1,296,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{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"
548,0,-1,352,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2),x)","\int {\left(a+\frac{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"
549,0,-1,353,0.000000,"\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+\frac{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"
550,0,-1,399,0.000000,"\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+\frac{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"
551,0,-1,460,0.000000,"\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+\frac{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"
552,0,-1,530,0.000000,"\text{Not used}","int(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{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"
553,0,-1,403,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(7/2),x)","\int {\left(a+\frac{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"
554,0,-1,359,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))^(1/2)), x)","F"
555,0,-1,301,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(1/2)), x)","F"
556,0,-1,244,0.000000,"\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+\frac{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"
557,0,-1,204,0.000000,"\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+\frac{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"
558,0,-1,99,0.000000,"\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+\frac{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"
559,0,-1,106,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/(a + b/cos(c + d*x))^(1/2), x)","F"
560,0,-1,338,0.000000,"\text{Not used}","int(cos(c + d*x)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\cos\left(c+d\,x\right)}{\sqrt{a+\frac{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"
561,0,-1,401,0.000000,"\text{Not used}","int(cos(c + d*x)^2/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{\sqrt{a+\frac{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"
562,0,-1,399,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))^(3/2)), x)","F"
563,0,-1,325,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(3/2)), x)","F"
564,0,-1,257,0.000000,"\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+\frac{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"
565,0,-1,237,0.000000,"\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+\frac{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"
566,0,-1,236,0.000000,"\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+\frac{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"
567,0,-1,347,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{1}{{\left(a+\frac{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"
568,0,-1,396,0.000000,"\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+\frac{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"
569,0,-1,470,0.000000,"\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+\frac{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"
570,0,-1,427,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^5\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^5*(a + b/cos(c + d*x))^(5/2)), x)","F"
571,0,-1,362,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/2)), x)","F"
572,0,-1,337,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/2)), x)","F"
573,0,-1,317,0.000000,"\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+\frac{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"
574,0,-1,304,0.000000,"\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+\frac{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"
575,0,-1,448,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{1}{{\left(a+\frac{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"
576,0,-1,510,0.000000,"\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+\frac{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"
577,0,-1,562,0.000000,"\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+\frac{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"
578,0,-1,535,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(7/2),x)","\int \frac{1}{{\left(a+\frac{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"
579,0,-1,151,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(5/2),x)","\int \left(a+\frac{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"
580,0,-1,123,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2),x)","\int \left(a+\frac{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"
581,0,-1,97,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2),x)","\int \left(a+\frac{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"
582,0,-1,75,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))/(1/cos(c + d*x))^(1/2),x)","\int \frac{a+\frac{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"
583,0,-1,101,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))/(1/cos(c + d*x))^(3/2),x)","\int \frac{a+\frac{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"
584,0,-1,127,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))/(1/cos(c + d*x))^(5/2),x)","\int \frac{a+\frac{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"
585,0,-1,151,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))/(1/cos(c + d*x))^(7/2),x)","\int \frac{a+\frac{b}{\cos\left(c+d\,x\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"
586,0,-1,200,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(5/2),x)","\int {\left(a+\frac{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"
587,0,-1,175,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
588,0,-1,135,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
589,0,-1,108,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
590,0,-1,112,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{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"
591,0,-1,141,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{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"
592,0,-1,175,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^2/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^2/(1/cos(c + d*x))^(7/2), x)","F"
593,0,-1,234,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
594,0,-1,189,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
595,0,-1,158,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
596,0,-1,166,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{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"
597,0,-1,156,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(5/2), x)","F"
598,0,-1,199,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(7/2), x)","F"
599,0,-1,234,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^3/(1/cos(c + d*x))^(9/2), x)","F"
600,0,-1,287,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4*(1/cos(c + d*x))^(3/2), x)","F"
601,0,-1,247,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4*(1/cos(c + d*x))^(1/2), x)","F"
602,0,-1,209,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4}{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(1/2), x)","F"
603,0,-1,208,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(3/2), x)","F"
604,0,-1,207,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(5/2), x)","F"
605,0,-1,211,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(7/2), x)","F"
606,0,-1,245,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(9/2), x)","F"
607,0,-1,289,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(11/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^4}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{11/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^4/(1/cos(c + d*x))^(11/2), x)","F"
608,0,-1,188,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + b/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{a+\frac{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)), x)","F"
609,0,-1,117,0.000000,"\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+\frac{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"
610,0,-1,49,0.000000,"\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+\frac{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"
611,0,-1,93,0.000000,"\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+\frac{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"
612,0,-1,135,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/2)), x)","F"
613,0,-1,172,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{\left(a+\frac{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(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(3/2)), x)","F"
614,0,-1,342,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)/(a + b/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{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"
615,0,-1,279,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + b/cos(c + d*x))^2,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{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"
616,0,-1,214,0.000000,"\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+\frac{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"
617,0,-1,208,0.000000,"\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+\frac{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"
618,0,-1,227,0.000000,"\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+\frac{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"
619,0,-1,244,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(1/2)), x)","F"
620,0,-1,304,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + b/cos(c + d*x))^2*(1/cos(c + d*x))^(3/2)), x)","F"
621,0,-1,388,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)/(a + b/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{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"
622,0,-1,315,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + b/cos(c + d*x))^3,x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{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"
623,0,-1,313,0.000000,"\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+\frac{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"
624,0,-1,306,0.000000,"\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+\frac{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"
625,0,-1,323,0.000000,"\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+\frac{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"
626,0,-1,342,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(1/2)), x)","F"
627,0,-1,406,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + b/cos(c + d*x))^3*(1/cos(c + d*x))^(3/2)), x)","F"
628,0,-1,237,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2),x)","\int \sqrt{a+\frac{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"
629,0,-1,138,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2),x)","\int \sqrt{a+\frac{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"
630,0,-1,67,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{a+\frac{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"
631,0,-1,192,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{\sqrt{a+\frac{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"
632,0,-1,244,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(5/2),x)","\int \frac{\sqrt{a+\frac{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))^(1/2)/(1/cos(c + d*x))^(5/2), x)","F"
633,0,-1,305,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(7/2),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\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))^(1/2)/(1/cos(c + d*x))^(7/2), x)","F"
634,0,-1,299,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
635,0,-1,249,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
636,0,-1,209,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
637,0,-1,187,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{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"
638,0,-1,240,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(5/2), x)","F"
639,0,-1,303,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(7/2), x)","F"
640,0,-1,369,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2),x)","\int {\left(a+\frac{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"
641,0,-1,314,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2),x)","\int {\left(a+\frac{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"
642,0,-1,263,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{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"
643,0,-1,262,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{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"
644,0,-1,239,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(5/2), x)","F"
645,0,-1,303,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(7/2), x)","F"
646,0,-1,363,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(9/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(9/2), x)","F"
647,0,-1,312,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{\sqrt{a+\frac{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"
648,0,-1,246,0.000000,"\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+\frac{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"
649,0,-1,68,0.000000,"\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+\frac{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"
650,0,-1,67,0.000000,"\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+\frac{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"
651,0,-1,142,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
652,0,-1,195,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{\sqrt{a+\frac{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(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(3/2)), x)","F"
653,0,-1,249,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{\sqrt{a+\frac{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(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/2)), x)","F"
654,0,-1,345,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{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"
655,0,-1,206,0.000000,"\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+\frac{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"
656,0,-1,126,0.000000,"\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+\frac{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"
657,0,-1,200,0.000000,"\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+\frac{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"
658,0,-1,214,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/2)), x)","F"
659,0,-1,289,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(3/2)), x)","F"
660,0,-1,360,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/2)), x)","F"
661,0,-1,458,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(9/2)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{9/2}}{{\left(a+\frac{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"
662,0,-1,370,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/2)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/2}}{{\left(a+\frac{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"
663,0,-1,277,0.000000,"\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+\frac{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"
664,0,-1,281,0.000000,"\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+\frac{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"
665,0,-1,302,0.000000,"\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+\frac{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"
666,0,-1,317,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/2)), x)","F"
667,0,-1,391,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)),x)","\int \frac{1}{{\left(a+\frac{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(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(3/2)), x)","F"
668,0,-1,474,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/2)), x)","F"
669,0,-1,122,0.000000,"\text{Not used}","int(1/((3/cos(c + d*x) + 2)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\frac{3}{\cos\left(c+d\,x\right)}+2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((3/cos(c + d*x) + 2)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
670,0,-1,109,0.000000,"\text{Not used}","int(1/((3/cos(c + d*x) - 2)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\frac{3}{\cos\left(c+d\,x\right)}-2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((3/cos(c + d*x) - 2)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
671,0,-1,108,0.000000,"\text{Not used}","int(1/((2 - 3/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{2-\frac{3}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((2 - 3/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
672,0,-1,123,0.000000,"\text{Not used}","int(1/((- 3/cos(c + d*x) - 2)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{-\frac{3}{\cos\left(c+d\,x\right)}-2}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((- 3/cos(c + d*x) - 2)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
673,0,-1,127,0.000000,"\text{Not used}","int(1/((2/cos(c + d*x) + 3)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\frac{2}{\cos\left(c+d\,x\right)}+3}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((2/cos(c + d*x) + 3)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
674,0,-1,113,0.000000,"\text{Not used}","int(1/((3 - 2/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{3-\frac{2}{\cos\left(c+d\,x\right)}}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((3 - 2/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
675,0,-1,129,0.000000,"\text{Not used}","int(1/((2/cos(c + d*x) - 3)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{\frac{2}{\cos\left(c+d\,x\right)}-3}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((2/cos(c + d*x) - 3)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
676,0,-1,115,0.000000,"\text{Not used}","int(1/((- 2/cos(c + d*x) - 3)^(1/2)*(1/cos(c + d*x))^(1/2)),x)","\int \frac{1}{\sqrt{-\frac{2}{\cos\left(c+d\,x\right)}-3}\,\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(1/((- 2/cos(c + d*x) - 3)^(1/2)*(1/cos(c + d*x))^(1/2)), x)","F"
677,0,-1,61,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(3/cos(c + d*x) + 2)^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{\frac{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"
678,0,-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{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{\frac{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"
679,0,-1,54,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(2 - 3/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{2-\frac{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"
680,0,-1,61,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(- 3/cos(c + d*x) - 2)^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{-\frac{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"
681,0,-1,61,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(2/cos(c + d*x) + 3)^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{\frac{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"
682,0,-1,54,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(3 - 2/cos(c + d*x))^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{3-\frac{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"
683,0,-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{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{\frac{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"
684,0,-1,55,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/2)/(- 2/cos(c + d*x) - 3)^(1/2),x)","\int \frac{\sqrt{\frac{1}{\cos\left(c+d\,x\right)}}}{\sqrt{-\frac{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"
685,0,-1,105,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/3)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(1/3)/cos(c + d*x), x)","F"
686,0,-1,17,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/3), x)","F"
687,0,-1,362,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x)^4,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x)^4, x)","F"
688,0,-1,305,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x)^3,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x)^3, x)","F"
689,0,-1,260,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x)^2, x)","F"
690,0,-1,105,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(2/3)/cos(c + d*x), x)","F"
691,0,-1,17,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(2/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(2/3), x)","F"
692,0,-1,108,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(4/3)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(4/3)/cos(c + d*x), x)","F"
693,0,-1,17,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(4/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(4/3), x)","F"
694,0,-1,412,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x)^4,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{{\cos\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x)^4, x)","F"
695,0,-1,356,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x)^3,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{{\cos\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x)^3, x)","F"
696,0,-1,299,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x)^2,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{{\cos\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x)^2, x)","F"
697,0,-1,108,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b/cos(c + d*x))^(5/3)/cos(c + d*x), x)","F"
698,0,-1,17,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/3), x)","F"
699,0,-1,313,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(1/3)), x)","F"
700,0,-1,265,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(1/3)), x)","F"
701,0,-1,219,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(1/3)), x)","F"
702,0,-1,105,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/3)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(1/3)), x)","F"
703,0,-1,17,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(1/3),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int(1/(a + b/cos(c + d*x))^(1/3), x)","F"
704,0,-1,105,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(2/3)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(2/3)), x)","F"
705,0,-1,17,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(2/3),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int(1/(a + b/cos(c + d*x))^(2/3), x)","F"
706,0,-1,110,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(4/3)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(4/3)), x)","F"
707,0,-1,17,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(4/3),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",0,"int(1/(a + b/cos(c + d*x))^(4/3), x)","F"
708,0,-1,378,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^4*(a + b/cos(c + d*x))^(5/3)), x)","F"
709,0,-1,307,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^3*(a + b/cos(c + d*x))^(5/3)), x)","F"
710,0,-1,289,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)^2*(a + b/cos(c + d*x))^(5/3)), x)","F"
711,0,-1,110,0.000000,"\text{Not used}","int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/3)),x)","\int \frac{1}{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",1,"int(1/(cos(c + d*x)*(a + b/cos(c + d*x))^(5/3)), x)","F"
712,0,-1,17,0.000000,"\text{Not used}","int(1/(a + b/cos(c + d*x))^(5/3),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",0,"int(1/(a + b/cos(c + d*x))^(5/3), x)","F"
713,0,-1,174,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(2/3)/(a + b/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((1/cos(c + d*x))^(2/3)/(a + b/cos(c + d*x)), x)","F"
714,0,-1,174,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/3)/(a + b/cos(c + d*x)),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((1/cos(c + d*x))^(1/3)/(a + b/cos(c + d*x)), x)","F"
715,0,-1,174,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/3)),x)","\int \frac{1}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(1/3)), x)","F"
716,0,-1,174,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(2/3)),x)","\int \frac{1}{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",1,"int(1/((a + b/cos(c + d*x))*(1/cos(c + d*x))^(2/3)), x)","F"
717,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/3),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/3), x)","F"
718,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/3),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/3), x)","F"
719,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(4/3),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(4/3), x)","F"
720,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(2/3),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(2/3), x)","F"
721,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/3),x)","\int \sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/3), x)","F"
722,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(1/3),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(1/3), x)","F"
723,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(2/3),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(2/3), x)","F"
724,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(4/3),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(4/3), x)","F"
725,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(5/3),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(5/3), x)","F"
726,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(7/3),x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(1/2)/(1/cos(c + d*x))^(7/3), x)","F"
727,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(7/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(7/3), x)","F"
728,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/3), x)","F"
729,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(4/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(4/3), x)","F"
730,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(2/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(2/3), x)","F"
731,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/3), x)","F"
732,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(1/3), x)","F"
733,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(2/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(2/3), x)","F"
734,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(4/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(4/3), x)","F"
735,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(5/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(5/3), x)","F"
736,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(7/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(3/2)/(1/cos(c + d*x))^(7/3), x)","F"
737,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(7/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(7/3), x)","F"
738,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/3), x)","F"
739,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(4/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(4/3), x)","F"
740,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(2/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(2/3), x)","F"
741,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/3),x)","\int {\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/3), x)","F"
742,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(1/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(1/3), x)","F"
743,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(2/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(2/3), x)","F"
744,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(4/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(4/3), x)","F"
745,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(5/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(5/3), x)","F"
746,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(7/3),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^(5/2)/(1/cos(c + d*x))^(7/3), x)","F"
747,0,-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{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}}{\sqrt{a+\frac{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"
748,0,-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{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{\sqrt{a+\frac{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"
749,0,-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{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}}{\sqrt{a+\frac{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"
750,0,-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{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{\sqrt{a+\frac{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"
751,0,-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{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{\sqrt{a+\frac{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"
752,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/3)),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(1/3)), x)","F"
753,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(2/3)),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(2/3)), x)","F"
754,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(4/3)),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(4/3)), x)","F"
755,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/3)),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(5/3)), x)","F"
756,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/3)),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(1/2)*(1/cos(c + d*x))^(7/3)), x)","F"
757,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/3)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(7/3)/(a + b/cos(c + d*x))^(3/2), x)","F"
758,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/3)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(5/3)/(a + b/cos(c + d*x))^(3/2), x)","F"
759,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(4/3)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(4/3)/(a + b/cos(c + d*x))^(3/2), x)","F"
760,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(2/3)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(2/3)/(a + b/cos(c + d*x))^(3/2), x)","F"
761,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/3)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(1/3)/(a + b/cos(c + d*x))^(3/2), x)","F"
762,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(1/3)), x)","F"
763,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(2/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(2/3)), x)","F"
764,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(4/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(4/3)), x)","F"
765,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(5/3)), x)","F"
766,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(7/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(3/2)*(1/cos(c + d*x))^(7/3)), x)","F"
767,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(7/3)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(7/3)/(a + b/cos(c + d*x))^(5/2), x)","F"
768,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(5/3)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(5/3)/(a + b/cos(c + d*x))^(5/2), x)","F"
769,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(4/3)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(4/3)/(a + b/cos(c + d*x))^(5/2), x)","F"
770,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(2/3)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(2/3)/(a + b/cos(c + d*x))^(5/2), x)","F"
771,0,-1,28,0.000000,"\text{Not used}","int((1/cos(c + d*x))^(1/3)/(a + b/cos(c + d*x))^(5/2),x)","\int \frac{{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",0,"int((1/cos(c + d*x))^(1/3)/(a + b/cos(c + d*x))^(5/2), x)","F"
772,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{1/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(1/3)), x)","F"
773,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(2/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{2/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(2/3)), x)","F"
774,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(4/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{4/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(4/3)), x)","F"
775,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{5/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(5/3)), x)","F"
776,0,-1,28,0.000000,"\text{Not used}","int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(7/3)),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2}\,{\left(\frac{1}{\cos\left(c+d\,x\right)}\right)}^{7/3}} \,d x","Not used",0,"int(1/((a + b/cos(c + d*x))^(5/2)*(1/cos(c + d*x))^(7/3)), x)","F"
777,0,-1,251,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^3*(d/cos(e + f*x))^n,x)","\int {\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^3\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + b/cos(e + f*x))^3*(d/cos(e + f*x))^n, x)","F"
778,0,-1,181,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^2*(d/cos(e + f*x))^n,x)","\int {\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^2\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + b/cos(e + f*x))^2*(d/cos(e + f*x))^n, x)","F"
779,0,-1,137,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))*(d/cos(e + f*x))^n,x)","\int \left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",1,"int((a + b/cos(e + f*x))*(d/cos(e + f*x))^n, x)","F"
780,0,-1,192,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(a + b/cos(e + f*x)),x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{a+\frac{b}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((d/cos(e + f*x))^n/(a + b/cos(e + f*x)), x)","F"
781,0,-1,299,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(a + b/cos(e + f*x))^2,x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^2} \,d x","Not used",1,"int((d/cos(e + f*x))^n/(a + b/cos(e + f*x))^2, x)","F"
782,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^(3/2)*(d/cos(e + f*x))^n,x)","\int {\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^{3/2}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",0,"int((a + b/cos(e + f*x))^(3/2)*(d/cos(e + f*x))^n, x)","F"
783,0,-1,28,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^(1/2)*(d/cos(e + f*x))^n,x)","\int \sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}}\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",0,"int((a + b/cos(e + f*x))^(1/2)*(d/cos(e + f*x))^n, x)","F"
784,0,-1,28,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(a + b/cos(e + f*x))^(1/2),x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{\sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}}} \,d x","Not used",0,"int((d/cos(e + f*x))^n/(a + b/cos(e + f*x))^(1/2), x)","F"
785,0,-1,28,0.000000,"\text{Not used}","int((d/cos(e + f*x))^n/(a + b/cos(e + f*x))^(3/2),x)","\int \frac{{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n}{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",0,"int((d/cos(e + f*x))^n/(a + b/cos(e + f*x))^(3/2), x)","F"
786,0,-1,24,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^m*(1/cos(e + f*x))^n,x)","\int {\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{1}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",0,"int((a + b/cos(e + f*x))^m*(1/cos(e + f*x))^n, x)","F"
787,0,-1,26,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^m*(d/cos(e + f*x))^n,x)","\int {\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m\,{\left(\frac{d}{\cos\left(e+f\,x\right)}\right)}^n \,d x","Not used",0,"int((a + b/cos(e + f*x))^m*(d/cos(e + f*x))^n, x)","F"
788,0,-1,273,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^m/cos(e + f*x)^3,x)","\int \frac{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m}{{\cos\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b/cos(e + f*x))^m/cos(e + f*x)^3, x)","F"
789,0,-1,220,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^m/cos(e + f*x)^2,x)","\int \frac{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m}{{\cos\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b/cos(e + f*x))^m/cos(e + f*x)^2, x)","F"
790,0,-1,103,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^m/cos(e + f*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m}{\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((a + b/cos(e + f*x))^m/cos(e + f*x), x)","F"
791,0,-1,15,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^m,x)","\int {\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m \,d x","Not used",0,"int((a + b/cos(e + f*x))^m, x)","F"
792,0,-1,22,0.000000,"\text{Not used}","int(cos(e + f*x)*(a + b/cos(e + f*x))^m,x)","\int \cos\left(e+f\,x\right)\,{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m \,d x","Not used",0,"int(cos(e + f*x)*(a + b/cos(e + f*x))^m, x)","F"
793,0,-1,24,0.000000,"\text{Not used}","int(cos(e + f*x)^2*(a + b/cos(e + f*x))^m,x)","\int {\cos\left(e+f\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^m \,d x","Not used",0,"int(cos(e + f*x)^2*(a + b/cos(e + f*x))^m, x)","F"
794,1,87,135,1.310398,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x)),x)","-\frac{2\,a\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,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)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*b*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"
795,1,87,111,1.141968,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x)),x)","-\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}}-\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*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(9*d*(sin(c + d*x)^2)^(1/2)) - (2*b*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"
796,1,80,87,1.038978,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x)),x)","\frac{2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,b\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,a\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*b*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*b*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"
797,1,53,61,0.173195,"\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\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(2*a*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (2*a*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d)","B"
798,1,33,35,0.229089,"\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)}{d}","Not used",1,"(2*a*ellipticE(c/2 + (d*x)/2, 2))/d + (2*b*ellipticF(c/2 + (d*x)/2, 2))/d","B"
799,1,60,57,1.249012,"\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\,\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*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"
800,1,87,83,1.544017,"\text{Not used}","int((a + b/cos(c + d*x))/cos(c + d*x)^(3/2),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\,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([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2)) + (2*b*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"
801,1,87,111,1.695836,"\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{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*b*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(5*d*cos(c + d*x)^(5/2)*(sin(c + d*x)^2)^(1/2))","B"
802,1,135,160,1.313378,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^2,x)","-\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}}-\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}}-\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)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (2*b^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*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"
803,1,128,135,1.191426,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^2,x)","\frac{2\,\left(b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{3\,d}-\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}}-\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*(b^2*ellipticF(c/2 + (d*x)/2, 2) + b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/(3*d) - (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)) - (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"
804,1,102,101,1.110388,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^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)}{3\,d}+\frac{4\,a\,b\,\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*b^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*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"
805,1,76,72,1.045805,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a^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))/(3*d) + (2*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*a^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"
806,1,81,68,1.397793,"\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)}{d}+\frac{2\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^2*ellipticE(c/2 + (d*x)/2, 2))/d + (4*a*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
807,1,108,95,1.519806,"\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\,\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*a^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*b^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"
808,1,113,135,1.666157,"\text{Not used}","int((a + b/cos(c + d*x))^2/cos(c + d*x)^(3/2),x)","\frac{6\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+30\,a^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*b^2*sin(c + d*x)*hypergeom([-5/4, 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) + 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"
809,1,113,160,1.788584,"\text{Not used}","int((a + b/cos(c + d*x))^2/cos(c + d*x)^(5/2),x)","\frac{30\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)+70\,a^2\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)+84\,a\,b\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{105\,d\,{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{1-{\cos\left(c+d\,x\right)}^2}}","Not used",1,"(30*b^2*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2) + 70*a^2*cos(c + d*x)^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2) + 84*a*b*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/(105*d*cos(c + d*x)^(7/2)*(1 - cos(c + d*x)^2)^(1/2))","B"
810,1,178,194,1.343902,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^3,x)","\frac{2\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{3\,d}+\frac{2\,b^3\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)}{3\,d}-\frac{2\,a^3\,{\cos\left(c+d\,x\right)}^{11/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{11}{4};\ \frac{15}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{11\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{6\,a\,b^2\,{\cos\left(c+d\,x\right)}^{7/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{7}{4};\ \frac{11}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}-\frac{2\,a^2\,b\,{\cos\left(c+d\,x\right)}^{9/2}\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{9}{4};\ \frac{13}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{3\,d\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*b^3*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (2*b^3*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) - (2*a^3*cos(c + d*x)^(11/2)*sin(c + d*x)*hypergeom([1/2, 11/4], 15/4, cos(c + d*x)^2))/(11*d*(sin(c + d*x)^2)^(1/2)) - (6*a*b^2*cos(c + d*x)^(7/2)*sin(c + d*x)*hypergeom([1/2, 7/4], 11/4, cos(c + d*x)^2))/(7*d*(sin(c + d*x)^2)^(1/2)) - (2*a^2*b*cos(c + d*x)^(9/2)*sin(c + d*x)*hypergeom([1/2, 9/4], 13/4, cos(c + d*x)^2))/(3*d*(sin(c + d*x)^2)^(1/2))","B"
811,1,146,159,1.218581,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^3,x)","\frac{2\,\left(b^3\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a\,b^2\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)+a\,b^2\,\sqrt{\cos\left(c+d\,x\right)}\,\sin\left(c+d\,x\right)\right)}{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)}{9\,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}}","Not used",1,"(2*(b^3*ellipticE(c/2 + (d*x)/2, 2) + a*b^2*ellipticF(c/2 + (d*x)/2, 2) + a*b^2*cos(c + d*x)^(1/2)*sin(c + d*x)))/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))/(9*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))","B"
812,1,125,116,1.180226,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^3,x)","\frac{2\,b^3\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,a\,b^2\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a^2\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{2\,a^2\,b\,\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,"(2*b^3*ellipticF(c/2 + (d*x)/2, 2))/d + (6*a*b^2*ellipticE(c/2 + (d*x)/2, 2))/d + (2*a^2*b*ellipticF(c/2 + (d*x)/2, 2))/d + (2*a^2*b*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"
813,1,124,126,1.240767,"\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{6\,a^2\,b\,\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)}{d}+\frac{6\,a\,b^2\,\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)}{3\,d}+\frac{2\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^3*ellipticF(c/2 + (d*x)/2, 2))/(3*d) + (6*a^2*b*ellipticE(c/2 + (d*x)/2, 2))/d + (6*a*b^2*ellipticF(c/2 + (d*x)/2, 2))/d + (2*a^3*cos(c + d*x)^(1/2)*sin(c + d*x))/(3*d) + (2*b^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
814,1,128,118,2.097021,"\text{Not used}","int(cos(c + d*x)^(1/2)*(a + b/cos(c + d*x))^3,x)","\frac{2\,\left(\mathrm{E}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^3+3\,b\,\mathrm{F}\left(\frac{c}{2}+\frac{d\,x}{2}\middle|2\right)\,a^2\right)}{d}+\frac{2\,b^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\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,\sqrt{\cos\left(c+d\,x\right)}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*(a^3*ellipticE(c/2 + (d*x)/2, 2) + 3*a^2*b*ellipticF(c/2 + (d*x)/2, 2)))/d + (2*b^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*b^2*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(1/2)*(sin(c + d*x)^2)^(1/2))","B"
815,1,156,149,2.167059,"\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{2\,b^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^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}}+\frac{2\,a\,b^2\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{4},\frac{1}{2};\ \frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{d\,{\cos\left(c+d\,x\right)}^{3/2}\,\sqrt{{\sin\left(c+d\,x\right)}^2}}","Not used",1,"(2*a^3*ellipticF(c/2 + (d*x)/2, 2))/d + (2*b^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^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)) + (2*a*b^2*sin(c + d*x)*hypergeom([-3/4, 1/2], 1/4, cos(c + d*x)^2))/(d*cos(c + d*x)^(3/2)*(sin(c + d*x)^2)^(1/2))","B"
816,1,147,194,2.240405,"\text{Not used}","int((a + b/cos(c + d*x))^3/cos(c + d*x)^(3/2),x)","\frac{\frac{2\,b^3\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{7}{4},\frac{1}{2};\ -\frac{3}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{7}+2\,a^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\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{4},\frac{1}{2};\ -\frac{1}{4};\ {\cos\left(c+d\,x\right)}^2\right)}{5}+2\,a^2\,b\,{\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*b^3*sin(c + d*x)*hypergeom([-7/4, 1/2], -3/4, cos(c + d*x)^2))/7 + 2*a^3*cos(c + d*x)^3*sin(c + d*x)*hypergeom([-1/4, 1/2], 3/4, cos(c + d*x)^2) + (6*a*b^2*cos(c + d*x)*sin(c + d*x)*hypergeom([-5/4, 1/2], -1/4, cos(c + d*x)^2))/5 + 2*a^2*b*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"
817,0,-1,152,0.000000,"\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+\frac{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"
818,0,-1,112,0.000000,"\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+\frac{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"
819,0,-1,75,0.000000,"\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+\frac{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"
820,0,-1,53,0.000000,"\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+\frac{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"
821,0,-1,29,0.000000,"\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+\frac{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"
822,0,-1,77,0.000000,"\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+\frac{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"
823,0,-1,128,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)} \,d x","Not used",1,"int(1/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))), x)","F"
824,0,-1,244,0.000000,"\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+\frac{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"
825,0,-1,184,0.000000,"\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+\frac{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"
826,0,-1,167,0.000000,"\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+\frac{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"
827,0,-1,148,0.000000,"\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+\frac{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"
828,0,-1,154,0.000000,"\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+\frac{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"
829,0,-1,219,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{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"
830,0,-1,346,0.000000,"\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+\frac{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"
831,0,-1,282,0.000000,"\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+\frac{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"
832,0,-1,263,0.000000,"\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+\frac{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"
833,0,-1,246,0.000000,"\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+\frac{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"
834,0,-1,253,0.000000,"\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+\frac{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"
835,0,-1,255,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^3),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{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"
836,0,-1,328,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^3),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{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"
837,0,-1,244,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(1/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,\sqrt{a+\frac{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))^(1/2), x)","F"
838,0,-1,192,0.000000,"\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+\frac{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"
839,0,-1,67,0.000000,"\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+\frac{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"
840,0,-1,138,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/cos(c + d*x)^(1/2),x)","\int \frac{\sqrt{a+\frac{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"
841,0,-1,237,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(1/2)/cos(c + d*x)^(3/2),x)","\int \frac{\sqrt{a+\frac{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"
842,0,-1,303,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(3/2), x)","F"
843,0,-1,240,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(3/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{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"
844,0,-1,187,0.000000,"\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+\frac{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"
845,0,-1,209,0.000000,"\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+\frac{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"
846,0,-1,249,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{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"
847,0,-1,299,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(3/2)/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{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"
848,0,-1,363,0.000000,"\text{Not used}","int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{9/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(9/2)*(a + b/cos(c + d*x))^(5/2), x)","F"
849,0,-1,303,0.000000,"\text{Not used}","int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(5/2), x)","F"
850,0,-1,239,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{5/2}\,{\left(a+\frac{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"
851,0,-1,262,0.000000,"\text{Not used}","int(cos(c + d*x)^(3/2)*(a + b/cos(c + d*x))^(5/2),x)","\int {\cos\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{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"
852,0,-1,263,0.000000,"\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+\frac{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"
853,0,-1,314,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/cos(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{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"
854,0,-1,369,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^(5/2)/cos(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{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"
855,0,-1,249,0.000000,"\text{Not used}","int(cos(c + d*x)^(5/2)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\cos\left(c+d\,x\right)}^{5/2}}{\sqrt{a+\frac{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))^(1/2), x)","F"
856,0,-1,195,0.000000,"\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+\frac{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"
857,0,-1,142,0.000000,"\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+\frac{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"
858,0,-1,67,0.000000,"\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+\frac{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"
859,0,-1,68,0.000000,"\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+\frac{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"
860,0,-1,246,0.000000,"\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+\frac{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"
861,0,-1,312,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(1/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,\sqrt{a+\frac{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"
862,0,-1,360,0.000000,"\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+\frac{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"
863,0,-1,289,0.000000,"\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+\frac{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"
864,0,-1,214,0.000000,"\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+\frac{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"
865,0,-1,200,0.000000,"\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+\frac{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"
866,0,-1,126,0.000000,"\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+\frac{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"
867,0,-1,206,0.000000,"\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+\frac{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"
868,0,-1,345,0.000000,"\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+\frac{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"
869,0,-1,391,0.000000,"\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+\frac{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"
870,0,-1,317,0.000000,"\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+\frac{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"
871,0,-1,302,0.000000,"\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+\frac{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"
872,0,-1,281,0.000000,"\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+\frac{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"
873,0,-1,277,0.000000,"\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+\frac{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"
874,0,-1,370,0.000000,"\text{Not used}","int(1/(cos(c + d*x)^(7/2)*(a + b/cos(c + d*x))^(5/2)),x)","\int \frac{1}{{\cos\left(c+d\,x\right)}^{7/2}\,{\left(a+\frac{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"
875,0,-1,266,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n*(a + b/cos(e + f*x))^3,x)","\int {\left(d\,\cos\left(e+f\,x\right)\right)}^n\,{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^3 \,d x","Not used",1,"int((d*cos(e + f*x))^n*(a + b/cos(e + f*x))^3, x)","F"
876,0,-1,186,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n*(a + b/cos(e + f*x))^2,x)","\int {\left(d\,\cos\left(e+f\,x\right)\right)}^n\,{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^2 \,d x","Not used",1,"int((d*cos(e + f*x))^n*(a + b/cos(e + f*x))^2, x)","F"
877,0,-1,132,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n*(a + b/cos(e + f*x)),x)","\int {\left(d\,\cos\left(e+f\,x\right)\right)}^n\,\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right) \,d x","Not used",1,"int((d*cos(e + f*x))^n*(a + b/cos(e + f*x)), x)","F"
878,0,-1,196,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n/(a + b/cos(e + f*x)),x)","\int \frac{{\left(d\,\cos\left(e+f\,x\right)\right)}^n}{a+\frac{b}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((d*cos(e + f*x))^n/(a + b/cos(e + f*x)), x)","F"
879,0,-1,309,0.000000,"\text{Not used}","int((d*cos(e + f*x))^n/(a + b/cos(e + f*x))^2,x)","\int \frac{{\left(d\,\cos\left(e+f\,x\right)\right)}^n}{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^2} \,d x","Not used",1,"int((d*cos(e + f*x))^n/(a + b/cos(e + f*x))^2, x)","F"