1,1,259,151,5.132603,"\text{Not used}","int(tan(c + d*x)^9*(a + a/cos(c + d*x)),x)","\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-18\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{218\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-174\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{1382\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{5}-\frac{2114\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{1654\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}-\frac{326\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{256\,a}{315}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+9\,{\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)^2))/d - ((256*a)/315 - (326*a*tan(c/2 + (d*x)/2)^2)/35 + (1654*a*tan(c/2 + (d*x)/2)^4)/35 - (2114*a*tan(c/2 + (d*x)/2)^6)/15 + (1382*a*tan(c/2 + (d*x)/2)^8)/5 - 174*a*tan(c/2 + (d*x)/2)^10 + (218*a*tan(c/2 + (d*x)/2)^12)/3 - 18*a*tan(c/2 + (d*x)/2)^14 + 2*a*tan(c/2 + (d*x)/2)^16)/(d*(9*tan(c/2 + (d*x)/2)^2 - 36*tan(c/2 + (d*x)/2)^4 + 84*tan(c/2 + (d*x)/2)^6 - 126*tan(c/2 + (d*x)/2)^8 + 126*tan(c/2 + (d*x)/2)^10 - 84*tan(c/2 + (d*x)/2)^12 + 36*tan(c/2 + (d*x)/2)^14 - 9*tan(c/2 + (d*x)/2)^16 + tan(c/2 + (d*x)/2)^18 - 1))","B"
2,1,204,118,5.692555,"\text{Not used}","int(tan(c + d*x)^7*(a + a/cos(c + d*x)),x)","\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{128\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-\frac{224\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{166\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{42\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{32\,a}{35}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((32*a)/35 - (42*a*tan(c/2 + (d*x)/2)^2)/5 + (166*a*tan(c/2 + (d*x)/2)^4)/5 - (224*a*tan(c/2 + (d*x)/2)^6)/3 + (128*a*tan(c/2 + (d*x)/2)^8)/3 - 14*a*tan(c/2 + (d*x)/2)^10 + 2*a*tan(c/2 + (d*x)/2)^12)/(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)) - (2*a*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
3,1,151,87,5.734022,"\text{Not used}","int(tan(c + d*x)^5*(a + a/cos(c + d*x)),x)","\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{62\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{22\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{16\,a}{15}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)^2))/d - ((16*a)/15 - (22*a*tan(c/2 + (d*x)/2)^2)/3 + (62*a*tan(c/2 + (d*x)/2)^4)/3 - 10*a*tan(c/2 + (d*x)/2)^6 + 2*a*tan(c/2 + (d*x)/2)^8)/(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"
4,1,96,57,1.993335,"\text{Not used}","int(tan(c + d*x)^3*(a + a/cos(c + d*x)),x)","\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{4\,a}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((4*a)/3 - 6*a*tan(c/2 + (d*x)/2)^2 + 2*a*tan(c/2 + (d*x)/2)^4)/(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)) - (2*a*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
5,1,40,25,1.171916,"\text{Not used}","int(tan(c + d*x)*(a + a/cos(c + d*x)),x)","\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a}{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)^2))/d - (2*a)/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
6,1,34,16,1.238666,"\text{Not used}","int(cot(c + d*x)*(a + a/cos(c + d*x)),x)","\frac{a\,\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"(a*(2*log(tan(c/2 + (d*x)/2)) - log(tan(c/2 + (d*x)/2)^2 + 1)))/d","B"
7,1,46,57,1.275318,"\text{Not used}","int(cot(c + d*x)^3*(a + a/cos(c + d*x)),x)","-\frac{a\,\left({\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{4\,d}","Not used",1,"-(a*(6*log(tan(c/2 + (d*x)/2)) - 4*log(tan(c/2 + (d*x)/2)^2 + 1) + cot(c/2 + (d*x)/2)^2))/(4*d)","B"
8,1,88,95,1.177725,"\text{Not used}","int(cot(c + d*x)^5*(a + a/cos(c + d*x)),x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a}{4}-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}\right)}{8\,d}+\frac{11\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^2)/(16*d) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (cot(c/2 + (d*x)/2)^4*(a/4 - (5*a*tan(c/2 + (d*x)/2)^2)/2))/(8*d) + (11*a*log(tan(c/2 + (d*x)/2)))/(8*d)","B"
9,1,118,133,1.227179,"\text{Not used}","int(cot(c + d*x)^7*(a + a/cos(c + d*x)),x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{a}{6}\right)}{32\,d}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,d}-\frac{21\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{16\,d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (cot(c/2 + (d*x)/2)^6*(a/6 - (7*a*tan(c/2 + (d*x)/2)^2)/4 + 11*a*tan(c/2 + (d*x)/2)^4))/(32*d) - (7*a*tan(c/2 + (d*x)/2)^2)/(64*d) + (a*tan(c/2 + (d*x)/2)^4)/(128*d) - (21*a*log(tan(c/2 + (d*x)/2)))/(16*d)","B"
10,1,242,129,2.469097,"\text{Not used}","int(tan(c + d*x)^8*(a + a/cos(c + d*x)),x)","a\,x-\frac{-\frac{93\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{2395\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}-\frac{45859\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{960}+\frac{724649\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{6720}-\frac{359453\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2240}+\frac{24223\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320}-\frac{1335\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}+\frac{163\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{35\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,d}","Not used",1,"a*x - ((163*a*tan(c/2 + (d*x)/2))/64 - (1335*a*tan(c/2 + (d*x)/2)^3)/64 + (24223*a*tan(c/2 + (d*x)/2)^5)/320 - (359453*a*tan(c/2 + (d*x)/2)^7)/2240 + (724649*a*tan(c/2 + (d*x)/2)^9)/6720 - (45859*a*tan(c/2 + (d*x)/2)^11)/960 + (2395*a*tan(c/2 + (d*x)/2)^13)/192 - (93*a*tan(c/2 + (d*x)/2)^15)/64)/(d*(28*tan(c/2 + (d*x)/2)^4 - 8*tan(c/2 + (d*x)/2)^2 - 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 - 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 - 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) + (35*a*atanh(tan(c/2 + (d*x)/2)))/(64*d)","B"
11,1,188,102,2.382947,"\text{Not used}","int(tan(c + d*x)^6*(a + a/cos(c + d*x)),x)","\frac{-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{73\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}-\frac{523\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{853\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-\frac{389\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{21\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{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)}-a\,x-\frac{5\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}","Not used",1,"((21*a*tan(c/2 + (d*x)/2))/8 - (389*a*tan(c/2 + (d*x)/2)^3)/24 + (853*a*tan(c/2 + (d*x)/2)^5)/20 - (523*a*tan(c/2 + (d*x)/2)^7)/20 + (73*a*tan(c/2 + (d*x)/2)^9)/8 - (11*a*tan(c/2 + (d*x)/2)^11)/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)) - a*x - (5*a*atanh(tan(c/2 + (d*x)/2)))/(8*d)","B"
12,1,134,73,1.852115,"\text{Not used}","int(tan(c + d*x)^4*(a + a/cos(c + d*x)),x)","a\,x-\frac{-\frac{5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{71\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}-\frac{137\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{11\,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,"a*x - ((11*a*tan(c/2 + (d*x)/2))/4 - (137*a*tan(c/2 + (d*x)/2)^3)/12 + (71*a*tan(c/2 + (d*x)/2)^5)/12 - (5*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"
13,1,80,45,1.138908,"\text{Not used}","int(tan(c + d*x)^2*(a + a/cos(c + d*x)),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)}-a\,x-\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*x - (a*atanh(tan(c/2 + (d*x)/2)))/d","B"
14,1,19,26,1.073358,"\text{Not used}","int(cot(c + d*x)^2*(a + a/cos(c + d*x)),x)","-\frac{a\,\left(\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+d\,x\right)}{d}","Not used",1,"-(a*(cot(c/2 + (d*x)/2) + d*x))/d","B"
15,1,53,55,1.199538,"\text{Not used}","int(cot(c + d*x)^4*(a + a/cos(c + d*x)),x)","a\,x-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}-\frac{\frac{a}{12}-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"a*x - (a*tan(c/2 + (d*x)/2))/(4*d) - (a/12 - a*tan(c/2 + (d*x)/2)^2)/(d*tan(c/2 + (d*x)/2)^3)","B"
16,1,156,84,1.449308,"\text{Not used}","int(cot(c + d*x)^6*(a + a/cos(c + d*x)),x)","-\frac{a\,\left(3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-90\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-30\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(c+d\,x\right)\right)}{240\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(a*(3*cos(c/2 + (d*x)/2)^8 + 5*sin(c/2 + (d*x)/2)^8 - 90*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 + 240*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 - 30*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2 + 240*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^5*(c + d*x)))/(240*d*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^5)","B"
17,1,204,111,1.983247,"\text{Not used}","int(cot(c + d*x)^8*(a + a/cos(c + d*x)),x)","-\frac{a\,\left(15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-280\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+3045\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+1015\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-168\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(c+d\,x\right)\right)}{6720\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(a*(15*cos(c/2 + (d*x)/2)^12 + 21*sin(c/2 + (d*x)/2)^12 - 280*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 3045*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 6720*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6 + 1015*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 168*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 - 6720*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7*(c + d*x)))/(6720*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7)","B"
18,1,252,140,3.175379,"\text{Not used}","int(cot(c + d*x)^10*(a + a/cos(c + d*x)),x)","-\frac{a\,\left(35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+45\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+4830\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-40950\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+80640\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-13650\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2898\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-450\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+80640\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(c+d\,x\right)\right)}{80640\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(a*(35*cos(c/2 + (d*x)/2)^16 + 45*sin(c/2 + (d*x)/2)^16 - 630*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 + 4830*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 - 40950*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 + 80640*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8 - 13650*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 + 2898*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 - 450*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2 + 80640*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^9*(c + d*x)))/(80640*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^9)","B"
19,1,308,192,5.141601,"\text{Not used}","int(tan(c + d*x)^9*(a + a/cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+\frac{272\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3}-\frac{740\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}+\frac{2252\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{5}-588\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{2000\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{7}-\frac{652\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}+\frac{1150\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{63}-\frac{512\,a^2}{315}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-252\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+45\,{\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+1\right)}","Not used",1,"(2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d - ((1150*a^2*tan(c/2 + (d*x)/2)^2)/63 - (652*a^2*tan(c/2 + (d*x)/2)^4)/7 + (2000*a^2*tan(c/2 + (d*x)/2)^6)/7 - 588*a^2*tan(c/2 + (d*x)/2)^8 + (2252*a^2*tan(c/2 + (d*x)/2)^10)/5 - (740*a^2*tan(c/2 + (d*x)/2)^12)/3 + (272*a^2*tan(c/2 + (d*x)/2)^14)/3 - 20*a^2*tan(c/2 + (d*x)/2)^16 + 2*a^2*tan(c/2 + (d*x)/2)^18 - (512*a^2)/315)/(d*(45*tan(c/2 + (d*x)/2)^4 - 10*tan(c/2 + (d*x)/2)^2 - 120*tan(c/2 + (d*x)/2)^6 + 210*tan(c/2 + (d*x)/2)^8 - 252*tan(c/2 + (d*x)/2)^10 + 210*tan(c/2 + (d*x)/2)^12 - 120*tan(c/2 + (d*x)/2)^14 + 45*tan(c/2 + (d*x)/2)^16 - 10*tan(c/2 + (d*x)/2)^18 + tan(c/2 + (d*x)/2)^20 + 1))","B"
20,1,249,132,4.819168,"\text{Not used}","int(tan(c + d*x)^7*(a + a/cos(c + d*x))^2,x)","\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\frac{170\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}-\frac{352\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{2386\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}-\frac{336\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{582\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}-\frac{64\,a^2}{35}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((582*a^2*tan(c/2 + (d*x)/2)^2)/35 - (336*a^2*tan(c/2 + (d*x)/2)^4)/5 + (2386*a^2*tan(c/2 + (d*x)/2)^6)/15 - (352*a^2*tan(c/2 + (d*x)/2)^8)/3 + (170*a^2*tan(c/2 + (d*x)/2)^10)/3 - 16*a^2*tan(c/2 + (d*x)/2)^12 + 2*a^2*tan(c/2 + (d*x)/2)^14 - (64*a^2)/35)/(d*(28*tan(c/2 + (d*x)/2)^4 - 8*tan(c/2 + (d*x)/2)^2 - 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 - 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 - 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) - (2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
21,1,192,120,5.052443,"\text{Not used}","int(tan(c + d*x)^5*(a + a/cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{92\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}-44\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{74\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{32\,a^2}{15}}{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,"(2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d - ((74*a^2*tan(c/2 + (d*x)/2)^2)/5 - 44*a^2*tan(c/2 + (d*x)/2)^4 + (92*a^2*tan(c/2 + (d*x)/2)^6)/3 - 12*a^2*tan(c/2 + (d*x)/2)^8 + 2*a^2*tan(c/2 + (d*x)/2)^10 - (32*a^2)/15)/(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"
22,1,133,65,3.869665,"\text{Not used}","int(tan(c + d*x)^3*(a + a/cos(c + d*x))^2,x)","\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{38\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{8\,a^2}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((38*a^2*tan(c/2 + (d*x)/2)^2)/3 - 8*a^2*tan(c/2 + (d*x)/2)^4 + 2*a^2*tan(c/2 + (d*x)/2)^6 - (8*a^2)/3)/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
23,1,76,48,1.213533,"\text{Not used}","int(tan(c + d*x)*(a + a/cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,a^2}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d - (2*a^2*tan(c/2 + (d*x)/2)^2 - 4*a^2)/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1))","B"
24,1,36,35,1.254575,"\text{Not used}","int(cot(c + d*x)*(a + a/cos(c + d*x))^2,x)","\frac{a^2\,\left(4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)\right)}{d}","Not used",1,"(a^2*(4*log(tan(c/2 + (d*x)/2)) - log(tan(c/2 + (d*x)/2)^4 - 1)))/d","B"
25,1,50,40,1.228869,"\text{Not used}","int(cot(c + d*x)^3*(a + a/cos(c + d*x))^2,x)","-\frac{a^2\,\left(\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"-(a^2*(2*log(tan(c/2 + (d*x)/2)) - log(tan(c/2 + (d*x)/2)^2 + 1) + cot(c/2 + (d*x)/2)^2/2))/d","B"
26,1,62,85,1.260055,"\text{Not used}","int(cot(c + d*x)^5*(a + a/cos(c + d*x))^2,x)","\frac{a^2\,\left(-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{7\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"(a^2*((7*log(tan(c/2 + (d*x)/2)))/4 - log(tan(c/2 + (d*x)/2)^2 + 1) + cot(c/2 + (d*x)/2)^2/2 - cot(c/2 + (d*x)/2)^4/16))/d","B"
27,1,113,127,1.268685,"\text{Not used}","int(cot(c + d*x)^7*(a + a/cos(c + d*x))^2,x)","\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{13\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{a^2}{6}\right)}{16\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32\,d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (13*a^2*log(tan(c/2 + (d*x)/2)))/(8*d) - (cot(c/2 + (d*x)/2)^6*(8*a^2*tan(c/2 + (d*x)/2)^4 - (3*a^2*tan(c/2 + (d*x)/2)^2)/2 + a^2/6))/(16*d) - (a^2*tan(c/2 + (d*x)/2)^2)/(32*d)","B"
28,1,149,169,1.588671,"\text{Not used}","int(cot(c + d*x)^9*(a + a/cos(c + d*x))^2,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,d}+\frac{99\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{29\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4}+\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{a^2}{8}\right)}{64\,d}-\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(16*d) - (a^2*tan(c/2 + (d*x)/2)^4)/(256*d) + (99*a^2*log(tan(c/2 + (d*x)/2)))/(64*d) + (cot(c/2 + (d*x)/2)^8*((4*a^2*tan(c/2 + (d*x)/2)^2)/3 - (29*a^2*tan(c/2 + (d*x)/2)^4)/4 + 32*a^2*tan(c/2 + (d*x)/2)^6 - a^2/8))/(64*d) - (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
29,1,234,161,2.647592,"\text{Not used}","int(tan(c + d*x)^6*(a + a/cos(c + d*x))^2,x)","-a^2\,x-\frac{5\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}-\frac{\frac{3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{4}-\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{3}+\frac{1409\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{60}-\frac{1768\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{35}+\frac{1413\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-23\,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)}{4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"- a^2*x - (5*a^2*atanh(tan(c/2 + (d*x)/2)))/(4*d) - ((1413*a^2*tan(c/2 + (d*x)/2)^5)/20 - 23*a^2*tan(c/2 + (d*x)/2)^3 - (1768*a^2*tan(c/2 + (d*x)/2)^7)/35 + (1409*a^2*tan(c/2 + (d*x)/2)^9)/60 - (19*a^2*tan(c/2 + (d*x)/2)^11)/3 + (3*a^2*tan(c/2 + (d*x)/2)^13)/4 + (13*a^2*tan(c/2 + (d*x)/2))/4)/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1))","B"
30,1,174,119,1.952502,"\text{Not used}","int(tan(c + d*x)^4*(a + a/cos(c + d*x))^2,x)","a^2\,x+\frac{3\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}+\frac{\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}-\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{164\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}-\frac{53\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{7\,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,"a^2*x + (3*a^2*atanh(tan(c/2 + (d*x)/2)))/(2*d) + ((164*a^2*tan(c/2 + (d*x)/2)^5)/15 - (53*a^2*tan(c/2 + (d*x)/2)^3)/3 - (11*a^2*tan(c/2 + (d*x)/2)^7)/3 + (a^2*tan(c/2 + (d*x)/2)^9)/2 + (7*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"
31,1,101,72,1.207556,"\text{Not used}","int(tan(c + d*x)^2*(a + a/cos(c + d*x))^2,x)","\frac{\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-4\,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)}-\frac{2\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-a^2\,x","Not used",1,"((4*a^2*tan(c/2 + (d*x)/2)^3)/3 - 4*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)) - (2*a^2*atanh(tan(c/2 + (d*x)/2)))/d - a^2*x","B"
32,1,24,35,1.077647,"\text{Not used}","int(cot(c + d*x)^2*(a + a/cos(c + d*x))^2,x)","-a^2\,x-\frac{2\,a^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"- a^2*x - (2*a^2*cot(c/2 + (d*x)/2))/d","B"
33,1,39,69,1.096154,"\text{Not used}","int(cot(c + d*x)^4*(a + a/cos(c + d*x))^2,x)","a^2\,x+\frac{a^2\,\left(9\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}{6\,d}","Not used",1,"a^2*x + (a^2*(9*cot(c/2 + (d*x)/2) - cot(c/2 + (d*x)/2)^3))/(6*d)","B"
34,1,78,107,1.258609,"\text{Not used}","int(cot(c + d*x)^6*(a + a/cos(c + d*x))^2,x)","\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{8}-\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{24}+\frac{a^2}{40}}{d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}-a^2\,x","Not used",1,"(a^2*tan(c/2 + (d*x)/2))/(8*d) - ((11*a^2*tan(c/2 + (d*x)/2)^4)/8 - (5*a^2*tan(c/2 + (d*x)/2)^2)/24 + a^2/40)/(d*tan(c/2 + (d*x)/2)^5) - a^2*x","B"
35,1,182,139,1.754891,"\text{Not used}","int(cot(c + d*x)^8*(a + a/cos(c + d*x))^2,x)","\frac{a^2\,\left(35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-735\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4410\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-770\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+147\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(c+d\,x\right)\right)}{3360\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(a^2*(35*sin(c/2 + (d*x)/2)^10 - 15*cos(c/2 + (d*x)/2)^10 - 735*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 4410*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 770*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 147*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 3360*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7*(c + d*x)))/(3360*d*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7)","B"
36,1,230,179,2.778066,"\text{Not used}","int(cot(c + d*x)^10*(a + a/cos(c + d*x))^2,x)","-\frac{a^2\,\left(35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-63\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+945\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-11655\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+51345\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-9765\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2331\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-405\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+40320\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(c+d\,x\right)\right)}{40320\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(a^2*(35*cos(c/2 + (d*x)/2)^14 - 63*sin(c/2 + (d*x)/2)^14 + 945*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 11655*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 + 51345*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 9765*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 2331*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 - 405*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 40320*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9*(c + d*x)))/(40320*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9)","B"
37,1,337,210,5.262742,"\text{Not used}","int(tan(c + d*x)^9*(a + a/cos(c + d*x))^3,x)","\frac{2\,a^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-22\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+\frac{332\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{3}-\frac{1012\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3}+\frac{10456\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{15}-\frac{5192\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{5}+\frac{8164\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{7}-\frac{3676\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{7}+\frac{10090\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{63}-\frac{9334\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{315}+\frac{8704\,a^3}{3465}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{22}-11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+55\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-165\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+330\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-462\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+462\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-330\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+165\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-55\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a^3*atanh(tan(c/2 + (d*x)/2)^2))/d - ((10090*a^3*tan(c/2 + (d*x)/2)^4)/63 - (9334*a^3*tan(c/2 + (d*x)/2)^2)/315 - (3676*a^3*tan(c/2 + (d*x)/2)^6)/7 + (8164*a^3*tan(c/2 + (d*x)/2)^8)/7 - (5192*a^3*tan(c/2 + (d*x)/2)^10)/5 + (10456*a^3*tan(c/2 + (d*x)/2)^12)/15 - (1012*a^3*tan(c/2 + (d*x)/2)^14)/3 + (332*a^3*tan(c/2 + (d*x)/2)^16)/3 - 22*a^3*tan(c/2 + (d*x)/2)^18 + 2*a^3*tan(c/2 + (d*x)/2)^20 + (8704*a^3)/3465)/(d*(11*tan(c/2 + (d*x)/2)^2 - 55*tan(c/2 + (d*x)/2)^4 + 165*tan(c/2 + (d*x)/2)^6 - 330*tan(c/2 + (d*x)/2)^8 + 462*tan(c/2 + (d*x)/2)^10 - 462*tan(c/2 + (d*x)/2)^12 + 330*tan(c/2 + (d*x)/2)^14 - 165*tan(c/2 + (d*x)/2)^16 + 55*tan(c/2 + (d*x)/2)^18 - 11*tan(c/2 + (d*x)/2)^20 + tan(c/2 + (d*x)/2)^22 - 1))","B"
38,1,278,137,5.168567,"\text{Not used}","int(tan(c + d*x)^7*(a + a/cos(c + d*x))^3,x)","\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-18\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\frac{218\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-174\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{1382\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{5}-\frac{1558\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{602\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{138\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{128\,a^3}{45}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-36\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,a^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((602*a^3*tan(c/2 + (d*x)/2)^4)/5 - (138*a^3*tan(c/2 + (d*x)/2)^2)/5 - (1558*a^3*tan(c/2 + (d*x)/2)^6)/5 + (1382*a^3*tan(c/2 + (d*x)/2)^8)/5 - 174*a^3*tan(c/2 + (d*x)/2)^10 + (218*a^3*tan(c/2 + (d*x)/2)^12)/3 - 18*a^3*tan(c/2 + (d*x)/2)^14 + 2*a^3*tan(c/2 + (d*x)/2)^16 + (128*a^3)/45)/(d*(9*tan(c/2 + (d*x)/2)^2 - 36*tan(c/2 + (d*x)/2)^4 + 84*tan(c/2 + (d*x)/2)^6 - 126*tan(c/2 + (d*x)/2)^8 + 126*tan(c/2 + (d*x)/2)^10 - 84*tan(c/2 + (d*x)/2)^12 + 36*tan(c/2 + (d*x)/2)^14 - 9*tan(c/2 + (d*x)/2)^16 + tan(c/2 + (d*x)/2)^18 - 1)) - (2*a^3*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
39,1,221,138,5.482608,"\text{Not used}","int(tan(c + d*x)^5*(a + a/cos(c + d*x))^3,x)","\frac{2\,a^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-14\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{128\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-\frac{224\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{422\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{382\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{352\,a^3}{105}}{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,"(2*a^3*atanh(tan(c/2 + (d*x)/2)^2))/d - ((422*a^3*tan(c/2 + (d*x)/2)^4)/5 - (382*a^3*tan(c/2 + (d*x)/2)^2)/15 - (224*a^3*tan(c/2 + (d*x)/2)^6)/3 + (128*a^3*tan(c/2 + (d*x)/2)^8)/3 - 14*a^3*tan(c/2 + (d*x)/2)^10 + 2*a^3*tan(c/2 + (d*x)/2)^12 + (352*a^3)/105)/(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"
40,1,162,99,5.546417,"\text{Not used}","int(tan(c + d*x)^3*(a + a/cos(c + d*x))^3,x)","\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{62\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{70\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{64\,a^3}{15}}{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{2\,a^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((62*a^3*tan(c/2 + (d*x)/2)^4)/3 - (70*a^3*tan(c/2 + (d*x)/2)^2)/3 - 10*a^3*tan(c/2 + (d*x)/2)^6 + 2*a^3*tan(c/2 + (d*x)/2)^8 + (64*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)) - (2*a^3*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
41,1,105,66,1.940203,"\text{Not used}","int(tan(c + d*x)*(a + a/cos(c + d*x))^3,x)","\frac{2\,a^3\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{20\,a^3}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a^3*atanh(tan(c/2 + (d*x)/2)^2))/d - (2*a^3*tan(c/2 + (d*x)/2)^4 - 6*a^3*tan(c/2 + (d*x)/2)^2 + (20*a^3)/3)/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1))","B"
42,1,86,48,1.201076,"\text{Not used}","int(cot(c + d*x)*(a + a/cos(c + d*x))^3,x)","\frac{8\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{2\,a^3}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{3\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{d}-\frac{a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(8*a^3*log(tan(c/2 + (d*x)/2)))/d - (2*a^3)/(d*(tan(c/2 + (d*x)/2)^2 - 1)) - (3*a^3*log(tan(c/2 + (d*x)/2)^2 - 1))/d - (a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
43,1,48,40,1.234422,"\text{Not used}","int(cot(c + d*x)^3*(a + a/cos(c + d*x))^3,x)","-\frac{a^3\,\left({\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"-(a^3*(2*log(tan(c/2 + (d*x)/2)) - log(tan(c/2 + (d*x)/2)^2 + 1) + cot(c/2 + (d*x)/2)^2))/d","B"
44,1,78,61,1.220409,"\text{Not used}","int(cot(c + d*x)^5*(a + a/cos(c + d*x))^3,x)","\frac{2\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{a^3}{8}}{d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}-\frac{a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(2*a^3*log(tan(c/2 + (d*x)/2)))/d + ((3*a^3*tan(c/2 + (d*x)/2)^2)/4 - a^3/8)/(d*tan(c/2 + (d*x)/2)^4) - (a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
45,1,94,107,1.290639,"\text{Not used}","int(cot(c + d*x)^7*(a + a/cos(c + d*x))^3,x)","\frac{a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{a^3}{6}}{8\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}-\frac{15\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}","Not used",1,"(a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d - ((11*a^3*tan(c/2 + (d*x)/2)^4)/2 - (5*a^3*tan(c/2 + (d*x)/2)^2)/4 + a^3/6)/(8*d*tan(c/2 + (d*x)/2)^6) - (15*a^3*log(tan(c/2 + (d*x)/2)))/(8*d)","B"
46,1,130,149,1.203753,"\text{Not used}","int(cot(c + d*x)^9*(a + a/cos(c + d*x))^3,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64\,d}+\frac{57\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{32\,d}+\frac{21\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}-\frac{a^3}{8}}{32\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}-\frac{a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^2)/(64*d) + (57*a^3*log(tan(c/2 + (d*x)/2)))/(32*d) + ((7*a^3*tan(c/2 + (d*x)/2)^2)/6 - (11*a^3*tan(c/2 + (d*x)/2)^4)/2 + 21*a^3*tan(c/2 + (d*x)/2)^6 - a^3/8)/(32*d*tan(c/2 + (d*x)/2)^8) - (a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
47,1,263,237,2.429374,"\text{Not used}","int(tan(c + d*x)^6*(a + a/cos(c + d*x))^3,x)","-a^3\,x-\frac{125\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,d}-\frac{\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}-\frac{325\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}+\frac{11389\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{960}-\frac{269879\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{6720}+\frac{183363\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2240}-\frac{35713\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320}+\frac{2025\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}-\frac{253\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"- a^3*x - (125*a^3*atanh(tan(c/2 + (d*x)/2)))/(64*d) - ((2025*a^3*tan(c/2 + (d*x)/2)^3)/64 - (35713*a^3*tan(c/2 + (d*x)/2)^5)/320 + (183363*a^3*tan(c/2 + (d*x)/2)^7)/2240 - (269879*a^3*tan(c/2 + (d*x)/2)^9)/6720 + (11389*a^3*tan(c/2 + (d*x)/2)^11)/960 - (325*a^3*tan(c/2 + (d*x)/2)^13)/192 + (3*a^3*tan(c/2 + (d*x)/2)^15)/64 - (253*a^3*tan(c/2 + (d*x)/2))/64)/(d*(28*tan(c/2 + (d*x)/2)^4 - 8*tan(c/2 + (d*x)/2)^2 - 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 - 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 - 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1))","B"
48,1,203,169,2.438563,"\text{Not used}","int(tan(c + d*x)^4*(a + a/cos(c + d*x))^3,x)","a^3\,x+\frac{19\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}+\frac{-\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{19\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{61\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}-\frac{291\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{209\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}-\frac{35\,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)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"a^3*x + (19*a^3*atanh(tan(c/2 + (d*x)/2)))/(8*d) + ((209*a^3*tan(c/2 + (d*x)/2)^3)/8 - (291*a^3*tan(c/2 + (d*x)/2)^5)/20 + (61*a^3*tan(c/2 + (d*x)/2)^7)/20 + (19*a^3*tan(c/2 + (d*x)/2)^9)/24 - (3*a^3*tan(c/2 + (d*x)/2)^11)/8 - (35*a^3*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"
49,1,146,98,1.909036,"\text{Not used}","int(tan(c + d*x)^2*(a + a/cos(c + d*x))^3,x)","\frac{\frac{5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}-\frac{13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{21\,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)}-a^3\,x-\frac{13\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,d}","Not used",1,"((3*a^3*tan(c/2 + (d*x)/2)^3)/4 - (13*a^3*tan(c/2 + (d*x)/2)^5)/4 + (5*a^3*tan(c/2 + (d*x)/2)^7)/4 + (21*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)) - a^3*x - (13*a^3*atanh(tan(c/2 + (d*x)/2)))/(4*d)","B"
50,1,35,49,1.199693,"\text{Not used}","int(cot(c + d*x)^2*(a + a/cos(c + d*x))^3,x)","-\frac{a^3\,\left(4\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+d\,x\right)}{d}","Not used",1,"-(a^3*(4*cot(c/2 + (d*x)/2) - 2*atanh(tan(c/2 + (d*x)/2)) + d*x))/d","B"
51,1,39,69,1.197656,"\text{Not used}","int(cot(c + d*x)^4*(a + a/cos(c + d*x))^3,x)","a^3\,x+\frac{a^3\,\left(6\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}{3\,d}","Not used",1,"a^3*x + (a^3*(6*cot(c/2 + (d*x)/2) - cot(c/2 + (d*x)/2)^3))/(3*d)","B"
52,1,62,107,1.446031,"\text{Not used}","int(cot(c + d*x)^6*(a + a/cos(c + d*x))^3,x)","\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d}-a^3\,x-\frac{a^3\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20\,d}-\frac{7\,a^3\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(a^3*cot(c/2 + (d*x)/2)^3)/(3*d) - a^3*x - (a^3*cot(c/2 + (d*x)/2)^5)/(20*d) - (7*a^3*cot(c/2 + (d*x)/2))/(4*d)","B"
53,1,91,141,1.699894,"\text{Not used}","int(cot(c + d*x)^8*(a + a/cos(c + d*x))^3,x)","\frac{a^3\,\left(126\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-560\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2730\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-105\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+1680\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(c+d\,x\right)-15\right)}{1680\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(a^3*(126*tan(c/2 + (d*x)/2)^2 - 560*tan(c/2 + (d*x)/2)^4 + 2730*tan(c/2 + (d*x)/2)^6 - 105*tan(c/2 + (d*x)/2)^8 + 1680*tan(c/2 + (d*x)/2)^7*(c + d*x) - 15))/(1680*d*tan(c/2 + (d*x)/2)^7)","B"
54,1,206,179,1.943553,"\text{Not used}","int(cot(c + d*x)^10*(a + a/cos(c + d*x))^3,x)","-\frac{a^3\,\left(35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+105\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-2520\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+31185\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+1827\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+20160\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(c+d\,x\right)\right)}{20160\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(a^3*(35*cos(c/2 + (d*x)/2)^12 + 105*sin(c/2 + (d*x)/2)^12 - 2520*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 31185*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 6720*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6 + 1827*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 360*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 20160*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9*(c + d*x)))/(20160*d*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^9)","B"
55,1,254,213,3.032228,"\text{Not used}","int(cot(c + d*x)^12*(a + a/cos(c + d*x))^3,x)","-\frac{a^3\,\left(315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+693\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-11550\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+159390\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-1323630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+295680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-90090\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+22770\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3850\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-887040\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(c+d\,x\right)\right)}{887040\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}","Not used",1,"-(a^3*(315*cos(c/2 + (d*x)/2)^16 + 693*sin(c/2 + (d*x)/2)^16 - 11550*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 + 159390*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 - 1323630*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 + 295680*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8 - 90090*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 + 22770*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 - 3850*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2 - 887040*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^11*(c + d*x)))/(887040*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^11)","B"
56,1,208,135,5.141587,"\text{Not used}","int(tan(c + d*x)^9/(a + a/cos(c + d*x)),x)","\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a\,d}-\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-\frac{128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{26\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{32}{35}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-21\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+35\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-35\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)^2))/(a*d) - ((26*tan(c/2 + (d*x)/2)^4)/5 - (22*tan(c/2 + (d*x)/2)^2)/5 + (32*tan(c/2 + (d*x)/2)^6)/3 - (128*tan(c/2 + (d*x)/2)^8)/3 + 14*tan(c/2 + (d*x)/2)^10 - 2*tan(c/2 + (d*x)/2)^12 + 32/35)/(d*(a - 7*a*tan(c/2 + (d*x)/2)^2 + 21*a*tan(c/2 + (d*x)/2)^4 - 35*a*tan(c/2 + (d*x)/2)^6 + 35*a*tan(c/2 + (d*x)/2)^8 - 21*a*tan(c/2 + (d*x)/2)^10 + 7*a*tan(c/2 + (d*x)/2)^12 - a*tan(c/2 + (d*x)/2)^14))","B"
57,1,153,97,6.020916,"\text{Not used}","int(tan(c + d*x)^7/(a + a/cos(c + d*x)),x)","\frac{-2\,{\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+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{16}{15}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}-\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a\,d}","Not used",1,"((2*tan(c/2 + (d*x)/2)^4)/3 - (10*tan(c/2 + (d*x)/2)^2)/3 + 10*tan(c/2 + (d*x)/2)^6 - 2*tan(c/2 + (d*x)/2)^8 + 16/15)/(d*(a - 5*a*tan(c/2 + (d*x)/2)^2 + 10*a*tan(c/2 + (d*x)/2)^4 - 10*a*tan(c/2 + (d*x)/2)^6 + 5*a*tan(c/2 + (d*x)/2)^8 - a*tan(c/2 + (d*x)/2)^10)) - (2*atanh(tan(c/2 + (d*x)/2)^2))/(a*d)","B"
58,1,99,66,2.193179,"\text{Not used}","int(tan(c + d*x)^5/(a + a/cos(c + d*x)),x)","\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a\,d}+\frac{2\,{\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-\frac{4}{3}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)^2))/(a*d) + (2*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 4/3)/(d*(a - 3*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^4 - a*tan(c/2 + (d*x)/2)^6))","B"
59,1,44,28,1.224169,"\text{Not used}","int(tan(c + d*x)^3/(a + a/cos(c + d*x)),x)","\frac{2}{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)}^2\right)}{a\,d}","Not used",1,"2/(d*(a - a*tan(c/2 + (d*x)/2)^2)) - (2*atanh(tan(c/2 + (d*x)/2)^2))/(a*d)","B"
60,1,21,17,1.211044,"\text{Not used}","int(tan(c + d*x)/(a + a/cos(c + d*x)),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}","Not used",1,"log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d)","B"
61,1,49,61,1.251983,"\text{Not used}","int(cot(c + d*x)/(a + a/cos(c + d*x)),x)","\frac{\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}}{a\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2))/2 - log(tan(c/2 + (d*x)/2)^2 + 1) + tan(c/2 + (d*x)/2)^2/4)/(a*d)","B"
62,1,76,103,1.342589,"\text{Not used}","int(cot(c + d*x)^3/(a + a/cos(c + d*x)),x)","-\frac{\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32}}{a\,d}","Not used",1,"-((5*log(tan(c/2 + (d*x)/2)))/8 - log(tan(c/2 + (d*x)/2)^2 + 1) + cot(c/2 + (d*x)/2)^2/16 + (5*tan(c/2 + (d*x)/2)^2)/16 - tan(c/2 + (d*x)/2)^4/32)/(a*d)","B"
63,1,132,145,1.312538,"\text{Not used}","int(cot(c + d*x)^5/(a + a/cos(c + d*x)),x)","\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32\,a\,d}-\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192\,a\,d}+\frac{11\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{16\,a\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{1}{4}\right)}{32\,a\,d}","Not used",1,"(11*tan(c/2 + (d*x)/2)^2)/(32*a*d) - (7*tan(c/2 + (d*x)/2)^4)/(128*a*d) + tan(c/2 + (d*x)/2)^6/(192*a*d) + (11*log(tan(c/2 + (d*x)/2)))/(16*a*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) + (cot(c/2 + (d*x)/2)^4*((7*tan(c/2 + (d*x)/2)^2)/2 - 1/4))/(32*a*d)","B"
64,1,193,105,2.524013,"\text{Not used}","int(tan(c + d*x)^8/(a + a/cos(c + d*x)),x)","\frac{x}{a}-\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}-\frac{-\frac{21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{389\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}-\frac{853\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{523\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-\frac{73\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"x/a - (5*atanh(tan(c/2 + (d*x)/2)))/(8*a*d) - ((11*tan(c/2 + (d*x)/2))/8 - (73*tan(c/2 + (d*x)/2)^3)/8 + (523*tan(c/2 + (d*x)/2)^5)/20 - (853*tan(c/2 + (d*x)/2)^7)/20 + (389*tan(c/2 + (d*x)/2)^9)/24 - (21*tan(c/2 + (d*x)/2)^11)/8)/(d*(a - 6*a*tan(c/2 + (d*x)/2)^2 + 15*a*tan(c/2 + (d*x)/2)^4 - 20*a*tan(c/2 + (d*x)/2)^6 + 15*a*tan(c/2 + (d*x)/2)^8 - 6*a*tan(c/2 + (d*x)/2)^10 + a*tan(c/2 + (d*x)/2)^12))","B"
65,1,139,78,1.997391,"\text{Not used}","int(tan(c + d*x)^6/(a + a/cos(c + d*x)),x)","\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a\,d}-\frac{x}{a}+\frac{-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{137\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}-\frac{71\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a\right)}","Not used",1,"(3*atanh(tan(c/2 + (d*x)/2)))/(4*a*d) - x/a + ((5*tan(c/2 + (d*x)/2))/4 - (71*tan(c/2 + (d*x)/2)^3)/12 + (137*tan(c/2 + (d*x)/2)^5)/12 - (11*tan(c/2 + (d*x)/2)^7)/4)/(d*(a - 4*a*tan(c/2 + (d*x)/2)^2 + 6*a*tan(c/2 + (d*x)/2)^4 - 4*a*tan(c/2 + (d*x)/2)^6 + a*tan(c/2 + (d*x)/2)^8))","B"
66,1,83,49,1.287051,"\text{Not used}","int(tan(c + d*x)^4/(a + a/cos(c + d*x)),x)","\frac{x}{a}-\frac{\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)-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,"x/a - atanh(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"
67,1,25,21,1.107680,"\text{Not used}","int(tan(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)}{a\,d}-\frac{x}{a}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)))/(a*d) - x/a","B"
68,1,65,61,1.293181,"\text{Not used}","int(cot(c + d*x)^2/(a + a/cos(c + d*x)),x)","-\frac{x}{a}-\frac{\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{6}+\frac{1}{12}}{a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"- x/a - ((4*cos(c/2 + (d*x)/2)^4)/3 - (7*cos(c/2 + (d*x)/2)^2)/6 + 1/12)/(a*d*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2))","B"
69,1,158,88,1.434457,"\text{Not used}","int(cot(c + d*x)^4/(a + a/cos(c + d*x)),x)","-\frac{5\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-30\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-90\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-240\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(c+d\,x\right)}{240\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"-(5*cos(c/2 + (d*x)/2)^8 + 3*sin(c/2 + (d*x)/2)^8 - 30*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^6 + 240*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^4 - 90*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^2 - 240*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3*(c + d*x))/(240*a*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^3)","B"
70,1,206,117,2.035888,"\text{Not used}","int(cot(c + d*x)^6/(a + a/cos(c + d*x)),x)","-\frac{21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-168\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+1015\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+3045\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-280\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6720\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(c+d\,x\right)}{6720\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(21*cos(c/2 + (d*x)/2)^12 + 15*sin(c/2 + (d*x)/2)^12 - 168*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 1015*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 - 6720*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6 + 3045*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 - 280*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2 + 6720*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5*(c + d*x))/(6720*a*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)","B"
71,1,193,120,5.181023,"\text{Not used}","int(tan(c + d*x)^9/(a + a/cos(c + d*x))^2,x)","\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a^2\,d}+\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{54\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}-\frac{32}{15}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)^2))/(a^2*d) + ((54*tan(c/2 + (d*x)/2)^2)/5 - 20*tan(c/2 + (d*x)/2)^4 + 12*tan(c/2 + (d*x)/2)^6 + 12*tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^10 - 32/15)/(d*(15*a^2*tan(c/2 + (d*x)/2)^4 - 6*a^2*tan(c/2 + (d*x)/2)^2 - 20*a^2*tan(c/2 + (d*x)/2)^6 + 15*a^2*tan(c/2 + (d*x)/2)^8 - 6*a^2*tan(c/2 + (d*x)/2)^10 + a^2*tan(c/2 + (d*x)/2)^12 + a^2))","B"
72,1,135,65,3.868770,"\text{Not used}","int(tan(c + d*x)^7/(a + a/cos(c + d*x))^2,x)","\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{26\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{8}{3}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^2\right)}-\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a^2\,d}","Not used",1,"(8*tan(c/2 + (d*x)/2)^4 - (26*tan(c/2 + (d*x)/2)^2)/3 + 2*tan(c/2 + (d*x)/2)^6 + 8/3)/(d*(6*a^2*tan(c/2 + (d*x)/2)^4 - 4*a^2*tan(c/2 + (d*x)/2)^2 - 4*a^2*tan(c/2 + (d*x)/2)^6 + a^2*tan(c/2 + (d*x)/2)^8 + a^2)) - (2*atanh(tan(c/2 + (d*x)/2)^2))/(a^2*d)","B"
73,1,77,48,1.350286,"\text{Not used}","int(tan(c + d*x)^5/(a + a/cos(c + d*x))^2,x)","\frac{6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4}{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{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a^2\,d}","Not used",1,"(6*tan(c/2 + (d*x)/2)^2 - 4)/(d*(a^2*tan(c/2 + (d*x)/2)^4 - 2*a^2*tan(c/2 + (d*x)/2)^2 + a^2)) + (2*atanh(tan(c/2 + (d*x)/2)^2))/(a^2*d)","B"
74,1,22,33,1.388035,"\text{Not used}","int(tan(c + d*x)^3/(a + a/cos(c + d*x))^2,x)","-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}{a^2\,d}","Not used",1,"-log(tan(c/2 + (d*x)/2)^4 - 1)/(a^2*d)","B"
75,1,35,36,1.130440,"\text{Not used}","int(tan(c + d*x)/(a + a/cos(c + d*x))^2,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}}{a^2\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1) - tan(c/2 + (d*x)/2)^2/2)/(a^2*d)","B"
76,1,62,81,1.262613,"\text{Not used}","int(cot(c + d*x)/(a + a/cos(c + d*x))^2,x)","\frac{\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16}}{a^2\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2))/4 - log(tan(c/2 + (d*x)/2)^2 + 1) + tan(c/2 + (d*x)/2)^2/2 - tan(c/2 + (d*x)/2)^4/16)/(a^2*d)","B"
77,1,89,123,1.365623,"\text{Not used}","int(cot(c + d*x)^3/(a + a/cos(c + d*x))^2,x)","-\frac{\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{96}}{a^2\,d}","Not used",1,"-((3*log(tan(c/2 + (d*x)/2)))/8 - log(tan(c/2 + (d*x)/2)^2 + 1) + cot(c/2 + (d*x)/2)^2/32 + tan(c/2 + (d*x)/2)^2/2 - (3*tan(c/2 + (d*x)/2)^4)/32 + tan(c/2 + (d*x)/2)^6/96)/(a^2*d)","B"
78,1,151,165,1.244744,"\text{Not used}","int(cot(c + d*x)^5/(a + a/cos(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,a^2\,d}-\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{256\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{48\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{512\,a^2\,d}+\frac{29\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a^2\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{1}{4}\right)}{64\,a^2\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(2*a^2*d) - (29*tan(c/2 + (d*x)/2)^4)/(256*a^2*d) + tan(c/2 + (d*x)/2)^6/(48*a^2*d) - tan(c/2 + (d*x)/2)^8/(512*a^2*d) + (29*log(tan(c/2 + (d*x)/2)))/(64*a^2*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) + (cot(c/2 + (d*x)/2)^4*(4*tan(c/2 + (d*x)/2)^2 - 1/4))/(64*a^2*d)","B"
79,1,179,119,2.257619,"\text{Not used}","int(tan(c + d*x)^8/(a + a/cos(c + d*x))^2,x)","\frac{x}{a^2}-\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}+\frac{\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2}-\frac{53\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{164\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}","Not used",1,"x/a^2 - (3*atanh(tan(c/2 + (d*x)/2)))/(2*a^2*d) + (tan(c/2 + (d*x)/2)/2 - (11*tan(c/2 + (d*x)/2)^3)/3 + (164*tan(c/2 + (d*x)/2)^5)/15 - (53*tan(c/2 + (d*x)/2)^7)/3 + (7*tan(c/2 + (d*x)/2)^9)/2)/(d*(5*a^2*tan(c/2 + (d*x)/2)^2 - 10*a^2*tan(c/2 + (d*x)/2)^4 + 10*a^2*tan(c/2 + (d*x)/2)^6 - 5*a^2*tan(c/2 + (d*x)/2)^8 + a^2*tan(c/2 + (d*x)/2)^10 - a^2))","B"
80,1,111,72,1.389257,"\text{Not used}","int(tan(c + d*x)^6/(a + a/cos(c + d*x))^2,x)","\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{x}{a^2}+\frac{\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^2\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)))/(a^2*d) - x/a^2 + ((4*tan(c/2 + (d*x)/2)^3)/3 - 4*tan(c/2 + (d*x)/2)^5)/(d*(3*a^2*tan(c/2 + (d*x)/2)^2 - 3*a^2*tan(c/2 + (d*x)/2)^4 + a^2*tan(c/2 + (d*x)/2)^6 - a^2))","B"
81,1,61,34,1.192340,"\text{Not used}","int(tan(c + d*x)^4/(a + a/cos(c + d*x))^2,x)","\frac{x}{a^2}-\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)}","Not used",1,"x/a^2 - (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))","B"
82,1,22,33,1.096074,"\text{Not used}","int(tan(c + d*x)^2/(a + a/cos(c + d*x))^2,x)","\frac{2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{d\,x}{2}\right)}{a^2\,d}","Not used",1,"(2*(tan(c/2 + (d*x)/2) - (d*x)/2))/(a^2*d)","B"
83,1,78,107,1.395244,"\text{Not used}","int(cot(c + d*x)^2/(a + a/cos(c + d*x))^2,x)","-\frac{x}{a^2}-\frac{\frac{26\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}-\frac{28\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{17\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{60}-\frac{1}{40}}{a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"- x/a^2 - ((17*cos(c/2 + (d*x)/2)^2)/60 - (28*cos(c/2 + (d*x)/2)^4)/15 + (26*cos(c/2 + (d*x)/2)^6)/15 - 1/40)/(a^2*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2))","B"
84,1,182,139,1.645474,"\text{Not used}","int(cot(c + d*x)^4/(a + a/cos(c + d*x))^2,x)","\frac{15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-147\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+770\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-4410\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+735\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3360\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(c+d\,x\right)}{3360\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"(15*sin(c/2 + (d*x)/2)^10 - 35*cos(c/2 + (d*x)/2)^10 - 147*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^8 + 770*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6 - 4410*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4 + 735*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2 + 3360*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3*(c + d*x))/(3360*a^2*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3)","B"
85,1,230,179,2.507141,"\text{Not used}","int(cot(c + d*x)^6/(a + a/cos(c + d*x))^2,x)","-\frac{63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+405\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-2331\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+9765\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-51345\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+11655\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-945\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+40320\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(c+d\,x\right)}{40320\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(63*cos(c/2 + (d*x)/2)^14 - 35*sin(c/2 + (d*x)/2)^14 + 405*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 - 2331*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 + 9765*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 - 51345*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 11655*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 - 945*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 40320*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5*(c + d*x))/(40320*a^2*d*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5)","B"
86,1,225,137,5.287147,"\text{Not used}","int(tan(c + d*x)^11/(a + a/cos(c + d*x))^3,x)","-\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a^3\,d}-\frac{-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-\frac{224\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{282\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}-\frac{322\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{352}{105}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}","Not used",1,"- (2*atanh(tan(c/2 + (d*x)/2)^2))/(a^3*d) - ((282*tan(c/2 + (d*x)/2)^4)/5 - (322*tan(c/2 + (d*x)/2)^2)/15 - (224*tan(c/2 + (d*x)/2)^6)/3 + (128*tan(c/2 + (d*x)/2)^8)/3 + 14*tan(c/2 + (d*x)/2)^10 - 2*tan(c/2 + (d*x)/2)^12 + 352/105)/(d*(7*a^3*tan(c/2 + (d*x)/2)^2 - 21*a^3*tan(c/2 + (d*x)/2)^4 + 35*a^3*tan(c/2 + (d*x)/2)^6 - 35*a^3*tan(c/2 + (d*x)/2)^8 + 21*a^3*tan(c/2 + (d*x)/2)^10 - 7*a^3*tan(c/2 + (d*x)/2)^12 + a^3*tan(c/2 + (d*x)/2)^14 - a^3))","B"
87,1,167,99,5.915674,"\text{Not used}","int(tan(c + d*x)^9/(a + a/cos(c + d*x))^3,x)","\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a^3\,d}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+22\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{98\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{58\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}-\frac{64}{15}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}","Not used",1,"(2*atanh(tan(c/2 + (d*x)/2)^2))/(a^3*d) - ((58*tan(c/2 + (d*x)/2)^2)/3 - (98*tan(c/2 + (d*x)/2)^4)/3 + 22*tan(c/2 + (d*x)/2)^6 + 2*tan(c/2 + (d*x)/2)^8 - 64/15)/(d*(5*a^3*tan(c/2 + (d*x)/2)^2 - 10*a^3*tan(c/2 + (d*x)/2)^4 + 10*a^3*tan(c/2 + (d*x)/2)^6 - 5*a^3*tan(c/2 + (d*x)/2)^8 + a^3*tan(c/2 + (d*x)/2)^10 - a^3))","B"
88,1,109,65,2.032711,"\text{Not used}","int(tan(c + d*x)^7/(a + a/cos(c + d*x))^3,x)","-\frac{14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{20}{3}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}-\frac{2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a^3\,d}","Not used",1,"- (14*tan(c/2 + (d*x)/2)^4 - 18*tan(c/2 + (d*x)/2)^2 + 20/3)/(d*(3*a^3*tan(c/2 + (d*x)/2)^2 - 3*a^3*tan(c/2 + (d*x)/2)^4 + a^3*tan(c/2 + (d*x)/2)^6 - a^3)) - (2*atanh(tan(c/2 + (d*x)/2)^2))/(a^3*d)","B"
89,1,72,46,1.269052,"\text{Not used}","int(tan(c + d*x)^5/(a + a/cos(c + d*x))^3,x)","\frac{3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{a^3\,d}-\frac{2}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-a^3\right)}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^3\,d}","Not used",1,"(3*log(tan(c/2 + (d*x)/2)^2 - 1))/(a^3*d) - 2/(d*(a^3*tan(c/2 + (d*x)/2)^2 - a^3)) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a^3*d)","B"
90,1,36,35,1.171304,"\text{Not used}","int(tan(c + d*x)^3/(a + a/cos(c + d*x))^3,x)","-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^3\,d}","Not used",1,"-(log(tan(c/2 + (d*x)/2)^2 + 1) - tan(c/2 + (d*x)/2)^2)/(a^3*d)","B"
91,1,48,56,1.154238,"\text{Not used}","int(tan(c + d*x)/(a + a/cos(c + d*x))^3,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{8}}{a^3\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1) - (3*tan(c/2 + (d*x)/2)^2)/4 + tan(c/2 + (d*x)/2)^4/8)/(a^3*d)","B"
92,1,75,101,1.244861,"\text{Not used}","int(cot(c + d*x)/(a + a/cos(c + d*x))^3,x)","\frac{\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{48}}{a^3\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2))/8 - log(tan(c/2 + (d*x)/2)^2 + 1) + (11*tan(c/2 + (d*x)/2)^2)/16 - (5*tan(c/2 + (d*x)/2)^4)/32 + tan(c/2 + (d*x)/2)^6/48)/(a^3*d)","B"
93,1,102,143,1.399158,"\text{Not used}","int(cot(c + d*x)^3/(a + a/cos(c + d*x))^3,x)","-\frac{\frac{7\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{32}-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{64}+\frac{21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{192}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{256}}{a^3\,d}","Not used",1,"-((7*log(tan(c/2 + (d*x)/2)))/32 - log(tan(c/2 + (d*x)/2)^2 + 1) + cot(c/2 + (d*x)/2)^2/64 + (21*tan(c/2 + (d*x)/2)^2)/32 - (11*tan(c/2 + (d*x)/2)^4)/64 + (7*tan(c/2 + (d*x)/2)^6)/192 - tan(c/2 + (d*x)/2)^8/256)/(a^3*d)","B"
94,1,170,185,1.327794,"\text{Not used}","int(cot(c + d*x)^5/(a + a/cos(c + d*x))^3,x)","\frac{163\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{256\,a^3\,d}-\frac{93\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{512\,a^3\,d}+\frac{37\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{768\,a^3\,d}-\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{1024\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{1280\,a^3\,d}+\frac{37\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{128\,a^3\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^3\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{1}{4}\right)}{128\,a^3\,d}","Not used",1,"(163*tan(c/2 + (d*x)/2)^2)/(256*a^3*d) - (93*tan(c/2 + (d*x)/2)^4)/(512*a^3*d) + (37*tan(c/2 + (d*x)/2)^6)/(768*a^3*d) - (9*tan(c/2 + (d*x)/2)^8)/(1024*a^3*d) + tan(c/2 + (d*x)/2)^10/(1280*a^3*d) + (37*log(tan(c/2 + (d*x)/2)))/(128*a^3*d) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^3*d) + (cot(c/2 + (d*x)/2)^4*((9*tan(c/2 + (d*x)/2)^2)/2 - 1/4))/(128*a^3*d)","B"
95,1,265,237,2.563994,"\text{Not used}","int(tan(c + d*x)^12/(a + a/cos(c + d*x))^3,x)","\frac{x}{a^3}-\frac{125\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a^3\,d}-\frac{-\frac{253\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{2025\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}-\frac{35713\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{320}+\frac{183363\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2240}-\frac{269879\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6720}+\frac{11389\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{960}-\frac{325\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-56\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-56\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}","Not used",1,"x/a^3 - (125*atanh(tan(c/2 + (d*x)/2)))/(64*a^3*d) - ((3*tan(c/2 + (d*x)/2))/64 - (325*tan(c/2 + (d*x)/2)^3)/192 + (11389*tan(c/2 + (d*x)/2)^5)/960 - (269879*tan(c/2 + (d*x)/2)^7)/6720 + (183363*tan(c/2 + (d*x)/2)^9)/2240 - (35713*tan(c/2 + (d*x)/2)^11)/320 + (2025*tan(c/2 + (d*x)/2)^13)/64 - (253*tan(c/2 + (d*x)/2)^15)/64)/(d*(28*a^3*tan(c/2 + (d*x)/2)^4 - 8*a^3*tan(c/2 + (d*x)/2)^2 - 56*a^3*tan(c/2 + (d*x)/2)^6 + 70*a^3*tan(c/2 + (d*x)/2)^8 - 56*a^3*tan(c/2 + (d*x)/2)^10 + 28*a^3*tan(c/2 + (d*x)/2)^12 - 8*a^3*tan(c/2 + (d*x)/2)^14 + a^3*tan(c/2 + (d*x)/2)^16 + a^3))","B"
96,1,208,169,2.354796,"\text{Not used}","int(tan(c + d*x)^10/(a + a/cos(c + d*x))^3,x)","\frac{19\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a^3\,d}-\frac{x}{a^3}-\frac{\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}-\frac{209\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}+\frac{291\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}-\frac{61\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}-\frac{19\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}","Not used",1,"(19*atanh(tan(c/2 + (d*x)/2)))/(8*a^3*d) - x/a^3 - ((3*tan(c/2 + (d*x)/2))/8 - (19*tan(c/2 + (d*x)/2)^3)/24 - (61*tan(c/2 + (d*x)/2)^5)/20 + (291*tan(c/2 + (d*x)/2)^7)/20 - (209*tan(c/2 + (d*x)/2)^9)/8 + (35*tan(c/2 + (d*x)/2)^11)/8)/(d*(15*a^3*tan(c/2 + (d*x)/2)^4 - 6*a^3*tan(c/2 + (d*x)/2)^2 - 20*a^3*tan(c/2 + (d*x)/2)^6 + 15*a^3*tan(c/2 + (d*x)/2)^8 - 6*a^3*tan(c/2 + (d*x)/2)^10 + a^3*tan(c/2 + (d*x)/2)^12 + a^3))","B"
97,1,148,99,1.933584,"\text{Not used}","int(tan(c + d*x)^8/(a + a/cos(c + d*x))^3,x)","\frac{x}{a^3}-\frac{13\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a^3\,d}+\frac{\frac{21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3\right)}","Not used",1,"x/a^3 - (13*atanh(tan(c/2 + (d*x)/2)))/(4*a^3*d) + ((5*tan(c/2 + (d*x)/2))/4 - (13*tan(c/2 + (d*x)/2)^3)/4 + (3*tan(c/2 + (d*x)/2)^5)/4 + (21*tan(c/2 + (d*x)/2)^7)/4)/(d*(6*a^3*tan(c/2 + (d*x)/2)^4 - 4*a^3*tan(c/2 + (d*x)/2)^2 - 4*a^3*tan(c/2 + (d*x)/2)^6 + a^3*tan(c/2 + (d*x)/2)^8 + a^3))","B"
98,1,92,66,1.308776,"\text{Not used}","int(tan(c + d*x)^6/(a + a/cos(c + d*x))^3,x)","\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{x}{a^3}-\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)}","Not used",1,"(7*atanh(tan(c/2 + (d*x)/2)))/(a^3*d) - x/a^3 - (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))","B"
99,1,37,46,1.160994,"\text{Not used}","int(tan(c + d*x)^4/(a + a/cos(c + d*x))^3,x)","\frac{x}{a^3}+\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}","Not used",1,"x/a^3 + (2*atanh(tan(c/2 + (d*x)/2)) - 4*tan(c/2 + (d*x)/2))/(a^3*d)","B"
100,1,35,60,1.160846,"\text{Not used}","int(tan(c + d*x)^2/(a + a/cos(c + d*x))^3,x)","-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+3\,d\,x}{3\,a^3\,d}","Not used",1,"-(tan(c/2 + (d*x)/2)^3 - 6*tan(c/2 + (d*x)/2) + 3*d*x)/(3*a^3*d)","B"
101,1,91,143,1.703320,"\text{Not used}","int(cot(c + d*x)^2/(a + a/cos(c + d*x))^3,x)","-\frac{x}{a^3}-\frac{\frac{221\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{105}-\frac{268\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{105}+\frac{257\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{420}-\frac{31\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{280}+\frac{1}{112}}{a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"- x/a^3 - ((257*cos(c/2 + (d*x)/2)^4)/420 - (31*cos(c/2 + (d*x)/2)^2)/280 - (268*cos(c/2 + (d*x)/2)^6)/105 + (221*cos(c/2 + (d*x)/2)^8)/105 + 1/112)/(a^3*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2))","B"
102,1,205,177,2.075439,"\text{Not used}","int(cot(c + d*x)^4/(a + a/cos(c + d*x))^3,x)","\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(c+d\,x\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(c+d\,x\right)}{a^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\right)}-\frac{\frac{668\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{315}-\frac{983\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{210}+\frac{346\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{105}-\frac{2291\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2520}+\frac{173\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{840}-\frac{19\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{672}+\frac{1}{576}}{a^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(cos(c/2 + (d*x)/2)^9*(c + d*x) - cos(c/2 + (d*x)/2)^11*(c + d*x))/(a^3*d*(cos(c/2 + (d*x)/2)^9 - cos(c/2 + (d*x)/2)^11)) - ((173*cos(c/2 + (d*x)/2)^4)/840 - (19*cos(c/2 + (d*x)/2)^2)/672 - (2291*cos(c/2 + (d*x)/2)^6)/2520 + (346*cos(c/2 + (d*x)/2)^8)/105 - (983*cos(c/2 + (d*x)/2)^10)/210 + (668*cos(c/2 + (d*x)/2)^12)/315 + 1/576)/(a^3*d*(cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2) - cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)))","B"
103,1,254,215,3.236803,"\text{Not used}","int(cot(c + d*x)^6/(a + a/cos(c + d*x))^3,x)","-\frac{693\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+315\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-3850\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+22770\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-90090\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+295680\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-1323630\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+159390\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-11550\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+887040\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(c+d\,x\right)}{887040\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}","Not used",1,"-(693*cos(c/2 + (d*x)/2)^16 + 315*sin(c/2 + (d*x)/2)^16 - 3850*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 + 22770*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 - 90090*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 + 295680*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^8 - 1323630*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 + 159390*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 - 11550*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2 + 887040*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5*(c + d*x))/(887040*a^3*d*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5)","B"
104,0,-1,310,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(5/2)*(a + a/cos(c + d*x)),x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*tan(c + d*x))^(5/2)*(a + a/cos(c + d*x)), x)","F"
105,0,-1,282,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(3/2)*(a + a/cos(c + d*x)),x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*tan(c + d*x))^(3/2)*(a + a/cos(c + d*x)), x)","F"
106,0,-1,272,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(1/2)*(a + a/cos(c + d*x)),x)","\int \sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*tan(c + d*x))^(1/2)*(a + a/cos(c + d*x)), x)","F"
107,0,-1,244,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(1/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(1/2), x)","F"
108,0,-1,305,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(3/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(3/2), x)","F"
109,0,-1,282,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(5/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(5/2), x)","F"
110,0,-1,346,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(7/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*tan(c + d*x))^(7/2), x)","F"
111,0,-1,366,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(5/2)*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\mathrm{tan}\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((e*tan(c + d*x))^(5/2)*(a + a/cos(c + d*x))^2, x)","F"
112,0,-1,335,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(3/2)*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\mathrm{tan}\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((e*tan(c + d*x))^(3/2)*(a + a/cos(c + d*x))^2, x)","F"
113,0,-1,309,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2,x)","\int \sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2 \,d x","Not used",1,"int((e*tan(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2, x)","F"
114,0,-1,278,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(1/2), x)","F"
115,0,-1,310,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(3/2), x)","F"
116,0,-1,316,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(5/2), x)","F"
117,0,-1,370,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(7/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{7/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*tan(c + d*x))^(7/2), x)","F"
118,0,-1,330,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(11/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{11/2}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(11/2))/(a*(cos(c + d*x) + 1)), x)","F"
119,0,-1,326,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(9/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{9/2}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(9/2))/(a*(cos(c + d*x) + 1)), x)","F"
120,0,-1,295,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(7/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{7/2}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(7/2))/(a*(cos(c + d*x) + 1)), x)","F"
121,0,-1,285,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(5/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(5/2))/(a*(cos(c + d*x) + 1)), x)","F"
122,0,-1,257,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(3/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(3/2))/(a*(cos(c + d*x) + 1)), x)","F"
123,0,-1,315,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(1/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(1/2))/(a*(cos(c + d*x) + 1)), x)","F"
124,0,-1,290,0.000000,"\text{Not used}","int(1/((e*tan(c + d*x))^(1/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*tan(c + d*x))^(1/2)*(cos(c + d*x) + 1)), x)","F"
125,0,-1,359,0.000000,"\text{Not used}","int(1/((e*tan(c + d*x))^(3/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*tan(c + d*x))^(3/2)*(cos(c + d*x) + 1)), x)","F"
126,0,-1,328,0.000000,"\text{Not used}","int(1/((e*tan(c + d*x))^(5/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*tan(c + d*x))^(5/2)*(cos(c + d*x) + 1)), x)","F"
127,0,-1,372,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(13/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{13/2}}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^(13/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
128,0,-1,339,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(11/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{11/2}}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^(11/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
129,0,-1,312,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(9/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{9/2}}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^(9/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
130,0,-1,281,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(7/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{7/2}}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^(7/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
131,0,-1,310,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(5/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^(5/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
132,0,-1,316,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(3/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^(3/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
133,0,-1,363,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(1/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^(1/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
134,0,-1,365,0.000000,"\text{Not used}","int(1/((e*tan(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/(a^2*(e*tan(c + d*x))^(1/2)*(cos(c + d*x) + 1)^2), x)","F"
135,0,-1,147,0.000000,"\text{Not used}","int(tan(c + d*x)^5*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^5\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^5*(a + a/cos(c + d*x))^(1/2), x)","F"
136,0,-1,99,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^3\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^3*(a + a/cos(c + d*x))^(1/2), x)","F"
137,1,47,51,1.481492,"\text{Not used}","int(tan(c + d*x)*(a + a/cos(c + d*x))^(1/2),x)","\frac{2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{d}-\frac{2\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{d}","Not used",1,"(2*(a + a/cos(c + d*x))^(1/2))/d - (2*a^(1/2)*atanh((a + a/cos(c + d*x))^(1/2)/a^(1/2)))/d","B"
138,0,-1,73,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + a/cos(c + d*x))^(1/2),x)","\int \mathrm{cot}\left(c+d\,x\right)\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)*(a + a/cos(c + d*x))^(1/2), x)","F"
139,0,-1,131,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^3\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^3*(a + a/cos(c + d*x))^(1/2), x)","F"
140,0,-1,193,0.000000,"\text{Not used}","int(cot(c + d*x)^5*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^5\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^5*(a + a/cos(c + d*x))^(1/2), x)","F"
141,0,-1,222,0.000000,"\text{Not used}","int(tan(c + d*x)^6*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^6\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^6*(a + a/cos(c + d*x))^(1/2), x)","F"
142,0,-1,160,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^4\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^4*(a + a/cos(c + d*x))^(1/2), x)","F"
143,0,-1,96,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^2*(a + a/cos(c + d*x))^(1/2), x)","F"
144,0,-1,109,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^2*(a + a/cos(c + d*x))^(1/2), x)","F"
145,0,-1,196,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^4*(a + a/cos(c + d*x))^(1/2), x)","F"
146,0,-1,280,0.000000,"\text{Not used}","int(cot(c + d*x)^6*(a + a/cos(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^6\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^6*(a + a/cos(c + d*x))^(1/2), x)","F"
147,0,-1,169,0.000000,"\text{Not used}","int(tan(c + d*x)^5*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^5*(a + a/cos(c + d*x))^(3/2), x)","F"
148,0,-1,121,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^3*(a + a/cos(c + d*x))^(3/2), x)","F"
149,1,67,73,1.460307,"\text{Not used}","int(tan(c + d*x)*(a + a/cos(c + d*x))^(3/2),x)","\frac{2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{3\,d}-\frac{2\,a^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{d}+\frac{2\,a\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{d}","Not used",1,"(2*(a + a/cos(c + d*x))^(3/2))/(3*d) - (2*a^(3/2)*atanh((a + a/cos(c + d*x))^(1/2)/a^(1/2)))/d + (2*a*(a + a/cos(c + d*x))^(1/2))/d","B"
150,0,-1,73,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + a/cos(c + d*x))^(3/2),x)","\int \mathrm{cot}\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cot(c + d*x)*(a + a/cos(c + d*x))^(3/2), x)","F"
151,0,-1,109,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^3*(a + a/cos(c + d*x))^(3/2), x)","F"
152,0,-1,171,0.000000,"\text{Not used}","int(cot(c + d*x)^5*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^5*(a + a/cos(c + d*x))^(3/2), x)","F"
153,0,-1,258,0.000000,"\text{Not used}","int(tan(c + d*x)^6*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^6\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(tan(c + d*x)^6*(a + a/cos(c + d*x))^(3/2), x)","F"
154,0,-1,194,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^4*(a + a/cos(c + d*x))^(3/2), x)","F"
155,0,-1,128,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^2*(a + a/cos(c + d*x))^(3/2), x)","F"
156,0,-1,64,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^2*(a + a/cos(c + d*x))^(3/2), x)","F"
157,0,-1,144,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^4*(a + a/cos(c + d*x))^(3/2), x)","F"
158,0,-1,226,0.000000,"\text{Not used}","int(cot(c + d*x)^6*(a + a/cos(c + d*x))^(3/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^6\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int(cot(c + d*x)^6*(a + a/cos(c + d*x))^(3/2), x)","F"
159,0,-1,193,0.000000,"\text{Not used}","int(tan(c + d*x)^5*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^5*(a + a/cos(c + d*x))^(5/2), x)","F"
160,0,-1,145,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^3*(a + a/cos(c + d*x))^(5/2), x)","F"
161,1,92,97,1.823023,"\text{Not used}","int(tan(c + d*x)*(a + a/cos(c + d*x))^(5/2),x)","\frac{2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}}{5\,d}+\frac{2\,a\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}{3\,d}+\frac{2\,a^2\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{d}+\frac{a^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,2{}\mathrm{i}}{d}","Not used",1,"(2*(a + a/cos(c + d*x))^(5/2))/(5*d) + (a^(5/2)*atan(((a + a/cos(c + d*x))^(1/2)*1i)/a^(1/2))*2i)/d + (2*a*(a + a/cos(c + d*x))^(3/2))/(3*d) + (2*a^2*(a + a/cos(c + d*x))^(1/2))/d","B"
162,0,-1,95,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + a/cos(c + d*x))^(5/2),x)","\int \mathrm{cot}\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cot(c + d*x)*(a + a/cos(c + d*x))^(5/2), x)","F"
163,0,-1,106,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^3*(a + a/cos(c + d*x))^(5/2), x)","F"
164,0,-1,147,0.000000,"\text{Not used}","int(cot(c + d*x)^5*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^5*(a + a/cos(c + d*x))^(5/2), x)","F"
165,0,-1,290,0.000000,"\text{Not used}","int(tan(c + d*x)^6*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^6\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(tan(c + d*x)^6*(a + a/cos(c + d*x))^(5/2), x)","F"
166,0,-1,224,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^4*(a + a/cos(c + d*x))^(5/2), x)","F"
167,0,-1,160,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{tan}\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(tan(c + d*x)^2*(a + a/cos(c + d*x))^(5/2), x)","F"
168,0,-1,66,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^2*(a + a/cos(c + d*x))^(5/2), x)","F"
169,0,-1,96,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{cot}\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(cot(c + d*x)^4*(a + a/cos(c + d*x))^(5/2), x)","F"
170,0,-1,176,0.000000,"\text{Not used}","int(cot(c + d*x)^6*(a + a/cos(c + d*x))^(5/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^6\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int(cot(c + d*x)^6*(a + a/cos(c + d*x))^(5/2), x)","F"
171,0,-1,126,0.000000,"\text{Not used}","int(tan(c + d*x)^5/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^5}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^5/(a + a/cos(c + d*x))^(1/2), x)","F"
172,0,-1,78,0.000000,"\text{Not used}","int(tan(c + d*x)^3/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^3/(a + a/cos(c + d*x))^(1/2), x)","F"
173,1,27,31,1.414860,"\text{Not used}","int(tan(c + d*x)/(a + a/cos(c + d*x))^(1/2),x)","-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{\sqrt{a}\,d}","Not used",1,"-(2*atanh((a + a/cos(c + d*x))^(1/2)/a^(1/2)))/(a^(1/2)*d)","B"
174,0,-1,92,0.000000,"\text{Not used}","int(cot(c + d*x)/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{\mathrm{cot}\left(c+d\,x\right)}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)/(a + a/cos(c + d*x))^(1/2), x)","F"
175,0,-1,152,0.000000,"\text{Not used}","int(cot(c + d*x)^3/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^3}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)^3/(a + a/cos(c + d*x))^(1/2), x)","F"
176,0,-1,214,0.000000,"\text{Not used}","int(cot(c + d*x)^5/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^5}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)^5/(a + a/cos(c + d*x))^(1/2), x)","F"
177,0,-1,189,0.000000,"\text{Not used}","int(tan(c + d*x)^6/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^6}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^6/(a + a/cos(c + d*x))^(1/2), x)","F"
178,0,-1,125,0.000000,"\text{Not used}","int(tan(c + d*x)^4/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^4}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^4/(a + a/cos(c + d*x))^(1/2), x)","F"
179,0,-1,63,0.000000,"\text{Not used}","int(tan(c + d*x)^2/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^2}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^2/(a + a/cos(c + d*x))^(1/2), x)","F"
180,0,-1,165,0.000000,"\text{Not used}","int(cot(c + d*x)^2/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^2}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)^2/(a + a/cos(c + d*x))^(1/2), x)","F"
181,0,-1,251,0.000000,"\text{Not used}","int(cot(c + d*x)^4/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^4}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)^4/(a + a/cos(c + d*x))^(1/2), x)","F"
182,0,-1,335,0.000000,"\text{Not used}","int(cot(c + d*x)^6/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^6}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)^6/(a + a/cos(c + d*x))^(1/2), x)","F"
183,0,-1,100,0.000000,"\text{Not used}","int(tan(c + d*x)^5/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^5/(a + a/cos(c + d*x))^(3/2), x)","F"
184,0,-1,54,0.000000,"\text{Not used}","int(tan(c + d*x)^3/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^3/(a + a/cos(c + d*x))^(3/2), x)","F"
185,1,50,54,1.585897,"\text{Not used}","int(tan(c + d*x)/(a + a/cos(c + d*x))^(3/2),x)","\frac{2}{a\,d\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{a^{3/2}\,d}","Not used",1,"2/(a*d*(a + a/cos(c + d*x))^(1/2)) - (2*atanh((a + a/cos(c + d*x))^(1/2)/a^(1/2)))/(a^(3/2)*d)","B"
186,0,-1,120,0.000000,"\text{Not used}","int(cot(c + d*x)/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{\mathrm{cot}\left(c+d\,x\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(cot(c + d*x)/(a + a/cos(c + d*x))^(3/2), x)","F"
187,0,-1,176,0.000000,"\text{Not used}","int(cot(c + d*x)^3/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^3/(a + a/cos(c + d*x))^(3/2), x)","F"
188,0,-1,238,0.000000,"\text{Not used}","int(cot(c + d*x)^5/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^5/(a + a/cos(c + d*x))^(3/2), x)","F"
189,0,-1,157,0.000000,"\text{Not used}","int(tan(c + d*x)^6/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^6}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(tan(c + d*x)^6/(a + a/cos(c + d*x))^(3/2), x)","F"
190,0,-1,95,0.000000,"\text{Not used}","int(tan(c + d*x)^4/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^4/(a + a/cos(c + d*x))^(3/2), x)","F"
191,0,-1,85,0.000000,"\text{Not used}","int(tan(c + d*x)^2/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^2/(a + a/cos(c + d*x))^(3/2), x)","F"
192,0,-1,215,0.000000,"\text{Not used}","int(cot(c + d*x)^2/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^2/(a + a/cos(c + d*x))^(3/2), x)","F"
193,0,-1,303,0.000000,"\text{Not used}","int(cot(c + d*x)^4/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^4/(a + a/cos(c + d*x))^(3/2), x)","F"
194,0,-1,387,0.000000,"\text{Not used}","int(cot(c + d*x)^6/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^6}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(cot(c + d*x)^6/(a + a/cos(c + d*x))^(3/2), x)","F"
195,0,-1,78,0.000000,"\text{Not used}","int(tan(c + d*x)^5/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^5/(a + a/cos(c + d*x))^(5/2), x)","F"
196,0,-1,54,0.000000,"\text{Not used}","int(tan(c + d*x)^3/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^3/(a + a/cos(c + d*x))^(5/2), x)","F"
197,1,69,78,1.907292,"\text{Not used}","int(tan(c + d*x)/(a + a/cos(c + d*x))^(5/2),x)","\frac{\frac{2\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}{a^2}+\frac{2}{3\,a}}{d\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}}-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{a^{5/2}\,d}","Not used",1,"((2*(a + a/cos(c + d*x)))/a^2 + 2/(3*a))/(d*(a + a/cos(c + d*x))^(3/2)) - (2*atanh((a + a/cos(c + d*x))^(1/2)/a^(1/2)))/(a^(5/2)*d)","B"
198,0,-1,144,0.000000,"\text{Not used}","int(cot(c + d*x)/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{\mathrm{cot}\left(c+d\,x\right)}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(cot(c + d*x)/(a + a/cos(c + d*x))^(5/2), x)","F"
199,0,-1,200,0.000000,"\text{Not used}","int(cot(c + d*x)^3/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^3/(a + a/cos(c + d*x))^(5/2), x)","F"
200,0,-1,262,0.000000,"\text{Not used}","int(cot(c + d*x)^5/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^5/(a + a/cos(c + d*x))^(5/2), x)","F"
201,0,-1,127,0.000000,"\text{Not used}","int(tan(c + d*x)^6/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^6}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(tan(c + d*x)^6/(a + a/cos(c + d*x))^(5/2), x)","F"
202,0,-1,113,0.000000,"\text{Not used}","int(tan(c + d*x)^4/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^4/(a + a/cos(c + d*x))^(5/2), x)","F"
203,0,-1,127,0.000000,"\text{Not used}","int(tan(c + d*x)^2/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^2/(a + a/cos(c + d*x))^(5/2), x)","F"
204,0,-1,265,0.000000,"\text{Not used}","int(cot(c + d*x)^2/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^2/(a + a/cos(c + d*x))^(5/2), x)","F"
205,0,-1,355,0.000000,"\text{Not used}","int(cot(c + d*x)^4/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^4/(a + a/cos(c + d*x))^(5/2), x)","F"
206,0,-1,439,0.000000,"\text{Not used}","int(cot(c + d*x)^6/(a + a/cos(c + d*x))^(5/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^6}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int(cot(c + d*x)^6/(a + a/cos(c + d*x))^(5/2), x)","F"
207,0,-1,177,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + a/cos(e + f*x))^(9/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{{\left(a+\frac{a}{\cos\left(e+f\,x\right)}\right)}^{9/2}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + a/cos(e + f*x))^(9/2), x)","F"
208,0,-1,125,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^n,x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^n, x)","F"
209,0,-1,243,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^3,x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^3 \,d x","Not used",1,"int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^3, x)","F"
210,0,-1,161,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2 \,d x","Not used",1,"int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^2, x)","F"
211,0,-1,129,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + a/cos(c + d*x)),x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*tan(c + d*x))^m*(a + a/cos(c + d*x)), x)","F"
212,0,-1,130,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^m)/(a*(cos(c + d*x) + 1)), x)","F"
213,0,-1,169,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m}{a^2\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*tan(c + d*x))^m)/(a^2*(cos(c + d*x) + 1)^2), x)","F"
214,0,-1,252,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m/(a + a/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m}{a^3\,{\left(\cos\left(c+d\,x\right)+1\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^3*(e*tan(c + d*x))^m)/(a^3*(cos(c + d*x) + 1)^3), x)","F"
215,0,-1,131,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^(3/2),x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^(3/2), x)","F"
216,0,-1,131,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^(1/2),x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*tan(c + d*x))^m*(a + a/cos(c + d*x))^(1/2), x)","F"
217,0,-1,131,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((e*tan(c + d*x))^m/(a + a/cos(c + d*x))^(1/2), x)","F"
218,0,-1,131,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m}{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((e*tan(c + d*x))^m/(a + a/cos(c + d*x))^(3/2), x)","F"
219,0,-1,123,0.000000,"\text{Not used}","int(tan(c + d*x)^7*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^7\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^7*(a + a/cos(c + d*x))^n, x)","F"
220,0,-1,97,0.000000,"\text{Not used}","int(tan(c + d*x)^5*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^5\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^5*(a + a/cos(c + d*x))^n, x)","F"
221,0,-1,69,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^3*(a + a/cos(c + d*x))^n, x)","F"
222,0,-1,43,0.000000,"\text{Not used}","int(tan(c + d*x)*(a + a/cos(c + d*x))^n,x)","\int \mathrm{tan}\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)*(a + a/cos(c + d*x))^n, x)","F"
223,0,-1,74,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + a/cos(c + d*x))^n,x)","\int \mathrm{cot}\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cot(c + d*x)*(a + a/cos(c + d*x))^n, x)","F"
224,0,-1,127,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cot(c + d*x)^3*(a + a/cos(c + d*x))^n, x)","F"
225,0,-1,106,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^4*(a + a/cos(c + d*x))^n, x)","F"
226,0,-1,106,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^2*(a + a/cos(c + d*x))^n, x)","F"
227,0,-1,102,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cot(c + d*x)^2*(a + a/cos(c + d*x))^n, x)","F"
228,0,-1,106,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cot(c + d*x)^4*(a + a/cos(c + d*x))^n, x)","F"
229,0,-1,114,0.000000,"\text{Not used}","int(tan(c + d*x)^(3/2)*(a + a/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^(3/2)*(a + a/cos(c + d*x))^n, x)","F"
230,0,-1,114,0.000000,"\text{Not used}","int(tan(c + d*x)^(1/2)*(a + a/cos(c + d*x))^n,x)","\int \sqrt{\mathrm{tan}\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^(1/2)*(a + a/cos(c + d*x))^n, x)","F"
231,0,-1,111,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/tan(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{\sqrt{\mathrm{tan}\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/tan(c + d*x)^(1/2), x)","F"
232,0,-1,112,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/tan(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\mathrm{tan}\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/tan(c + d*x)^(3/2), x)","F"
233,0,-1,320,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(5/2)*(a + a/cos(c + d*x)),x)","\int {\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*cot(c + d*x))^(5/2)*(a + a/cos(c + d*x)), x)","F"
234,0,-1,346,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + a/cos(c + d*x)),x)","\int {\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*cot(c + d*x))^(3/2)*(a + a/cos(c + d*x)), x)","F"
235,0,-1,274,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + a/cos(c + d*x)),x)","\int \sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*cot(c + d*x))^(1/2)*(a + a/cos(c + d*x)), x)","F"
236,0,-1,299,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*cot(c + d*x))^(1/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*cot(c + d*x))^(1/2), x)","F"
237,0,-1,320,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*cot(c + d*x))^(3/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*cot(c + d*x))^(3/2), x)","F"
238,0,-1,357,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(5/2)*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\mathrm{cot}\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((e*cot(c + d*x))^(5/2)*(a + a/cos(c + d*x))^2, x)","F"
239,0,-1,343,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(3/2)*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\mathrm{cot}\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((e*cot(c + d*x))^(3/2)*(a + a/cos(c + d*x))^2, x)","F"
240,0,-1,311,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2,x)","\int \sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2 \,d x","Not used",1,"int((e*cot(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2, x)","F"
241,0,-1,339,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*cot(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*cot(c + d*x))^(1/2), x)","F"
242,0,-1,375,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*cot(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*cot(c + d*x))^(3/2), x)","F"
243,0,-1,405,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(3/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*cot(c + d*x))^(3/2))/(a*(cos(c + d*x) + 1)), x)","F"
244,0,-1,325,0.000000,"\text{Not used}","int((e*cot(c + d*x))^(1/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}}{a\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*cot(c + d*x))^(1/2))/(a*(cos(c + d*x) + 1)), x)","F"
245,0,-1,347,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*cot(c + d*x))^(1/2)*(cos(c + d*x) + 1)), x)","F"
246,0,-1,290,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*cot(c + d*x))^(3/2)*(cos(c + d*x) + 1)), x)","F"
247,0,-1,325,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(5/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*cot(c + d*x))^(5/2)*(cos(c + d*x) + 1)), x)","F"
248,0,-1,335,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(7/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*cot(c + d*x))^(7/2)*(cos(c + d*x) + 1)), x)","F"
249,0,-1,371,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(9/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{9/2}\,\left(\cos\left(c+d\,x\right)+1\right)} \,d x","Not used",1,"int(cos(c + d*x)/(a*(e*cot(c + d*x))^(9/2)*(cos(c + d*x) + 1)), x)","F"
250,0,-1,413,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,\sqrt{e\,\mathrm{cot}\left(c+d\,x\right)}\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/(a^2*(e*cot(c + d*x))^(1/2)*(cos(c + d*x) + 1)^2), x)","F"
251,0,-1,359,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(3/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{3/2}\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/(a^2*(e*cot(c + d*x))^(3/2)*(cos(c + d*x) + 1)^2), x)","F"
252,0,-1,355,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(5/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{5/2}\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/(a^2*(e*cot(c + d*x))^(5/2)*(cos(c + d*x) + 1)^2), x)","F"
253,0,-1,321,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(7/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{7/2}\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/(a^2*(e*cot(c + d*x))^(7/2)*(cos(c + d*x) + 1)^2), x)","F"
254,0,-1,357,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(9/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{9/2}\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/(a^2*(e*cot(c + d*x))^(9/2)*(cos(c + d*x) + 1)^2), x)","F"
255,0,-1,389,0.000000,"\text{Not used}","int(1/((e*cot(c + d*x))^(11/2)*(a + a/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(e\,\mathrm{cot}\left(c+d\,x\right)\right)}^{11/2}\,{\left(\cos\left(c+d\,x\right)+1\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/(a^2*(e*cot(c + d*x))^(11/2)*(cos(c + d*x) + 1)^2), x)","F"
256,1,221,111,5.240355,"\text{Not used}","int(tan(c + d*x)^7*(a + b/cos(c + d*x)),x)","\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{128\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\left(-\frac{128\,a}{3}-32\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(14\,a+\frac{96\,b}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-2\,a-\frac{32\,b}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{32\,b}{35}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((32*b)/35 - tan(c/2 + (d*x)/2)^2*(2*a + (32*b)/5) + tan(c/2 + (d*x)/2)^4*(14*a + (96*b)/5) - tan(c/2 + (d*x)/2)^6*((128*a)/3 + 32*b) + (128*a*tan(c/2 + (d*x)/2)^8)/3 - 14*a*tan(c/2 + (d*x)/2)^10 + 2*a*tan(c/2 + (d*x)/2)^12)/(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)) - (2*a*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
257,1,162,84,5.846477,"\text{Not used}","int(tan(c + d*x)^5*(a + b/cos(c + d*x)),x)","\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(10\,a+\frac{32\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-2\,a-\frac{16\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{16\,b}{15}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)^2))/d - ((16*b)/15 - tan(c/2 + (d*x)/2)^2*(2*a + (16*b)/3) + tan(c/2 + (d*x)/2)^4*(10*a + (32*b)/3) - 10*a*tan(c/2 + (d*x)/2)^6 + 2*a*tan(c/2 + (d*x)/2)^8)/(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"
258,1,102,55,2.227570,"\text{Not used}","int(tan(c + d*x)^3*(a + b/cos(c + d*x)),x)","\frac{2\,a\,{\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+\frac{4\,b}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((4*b)/3 - tan(c/2 + (d*x)/2)^2*(2*a + 4*b) + 2*a*tan(c/2 + (d*x)/2)^4)/(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)) - (2*a*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
259,1,40,25,1.301800,"\text{Not used}","int(tan(c + d*x)*(a + b/cos(c + d*x)),x)","\frac{2\,a\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}-\frac{2\,b}{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)^2))/d - (2*b)/(d*(tan(c/2 + (d*x)/2)^2 - 1))","B"
260,1,51,43,1.306133,"\text{Not used}","int(cot(c + d*x)*(a + b/cos(c + d*x)),x)","\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)))/d - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (b*log(tan(c/2 + (d*x)/2)))/d","B"
261,1,86,72,1.356356,"\text{Not used}","int(cot(c + d*x)^3*(a + b/cos(c + d*x)),x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a}{8}-\frac{b}{8}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a}{8}+\frac{b}{8}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a+\frac{b}{2}\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (tan(c/2 + (d*x)/2)^2*(a/8 - b/8))/d - (cot(c/2 + (d*x)/2)^2*(a/8 + b/8))/d - (log(tan(c/2 + (d*x)/2))*(a + b/2))/d","B"
262,1,128,102,1.343928,"\text{Not used}","int(cot(c + d*x)^5*(a + b/cos(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a}{16}-\frac{b}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a}{64}-\frac{b}{64}\right)}{d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\left(-3\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a}{4}+\frac{b}{4}\right)}{16\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a+\frac{3\,b}{8}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*((3*a)/16 - b/8))/d - (tan(c/2 + (d*x)/2)^4*(a/64 - b/64))/d - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (cot(c/2 + (d*x)/2)^4*(a/4 + b/4 - tan(c/2 + (d*x)/2)^2*(3*a + 2*b)))/(16*d) + (log(tan(c/2 + (d*x)/2))*(a + (3*b)/8))/d","B"
263,1,170,130,1.502688,"\text{Not used}","int(cot(c + d*x)^7*(a + b/cos(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a}{32}-\frac{3\,b}{128}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\left(\frac{29\,a}{2}+\frac{15\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-2\,a-\frac{3\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a}{6}+\frac{b}{6}\right)}{64\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{29\,a}{128}-\frac{15\,b}{128}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a}{384}-\frac{b}{384}\right)}{d}+\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a+\frac{5\,b}{16}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^4*(a/32 - (3*b)/128))/d - (cot(c/2 + (d*x)/2)^6*(a/6 + b/6 - tan(c/2 + (d*x)/2)^2*(2*a + (3*b)/2) + tan(c/2 + (d*x)/2)^4*((29*a)/2 + (15*b)/2)))/(64*d) - (tan(c/2 + (d*x)/2)^2*((29*a)/128 - (15*b)/128))/d - (tan(c/2 + (d*x)/2)^6*(a/384 - b/384))/d + (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (log(tan(c/2 + (d*x)/2))*(a + (5*b)/16))/d","B"
264,1,331,102,2.510291,"\text{Not used}","int(tan(c + d*x)^6*(a + b/cos(c + d*x)),x)","\frac{\left(\frac{5\,b}{8}-2\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{38\,a}{3}-\frac{85\,b}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{33\,b}{4}-\frac{172\,a}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{172\,a}{5}+\frac{33\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{38\,a}{3}-\frac{85\,b}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a+\frac{5\,b}{8}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{5\,b\,\mathrm{atanh}\left(\frac{125\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,\left(20\,a^2\,b+\frac{125\,b^3}{64}\right)}+\frac{20\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{20\,a^2\,b+\frac{125\,b^3}{64}}\right)}{8\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^3+\frac{25\,a\,b^2}{4}}+\frac{25\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(64\,a^3+\frac{25\,a\,b^2}{4}\right)}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(2*a + (5*b)/8) - tan(c/2 + (d*x)/2)^11*(2*a - (5*b)/8) - tan(c/2 + (d*x)/2)^3*((38*a)/3 + (85*b)/24) + tan(c/2 + (d*x)/2)^9*((38*a)/3 - (85*b)/24) + tan(c/2 + (d*x)/2)^5*((172*a)/5 + (33*b)/4) - tan(c/2 + (d*x)/2)^7*((172*a)/5 - (33*b)/4))/(d*(15*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^2 - 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 - 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) - (5*b*atanh((125*b^3*tan(c/2 + (d*x)/2))/(64*(20*a^2*b + (125*b^3)/64)) + (20*a^2*b*tan(c/2 + (d*x)/2))/(20*a^2*b + (125*b^3)/64)))/(8*d) - (2*a*atan((64*a^3*tan(c/2 + (d*x)/2))/((25*a*b^2)/4 + 64*a^3) + (25*a*b^2*tan(c/2 + (d*x)/2))/(4*((25*a*b^2)/4 + 64*a^3))))/d","B"
265,1,267,73,2.234170,"\text{Not used}","int(tan(c + d*x)^4*(a + b/cos(c + d*x)),x)","\frac{2\,a\,\mathrm{atan}\left(\frac{64\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^3+9\,a\,b^2}+\frac{9\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^3+9\,a\,b^2}\right)}{d}+\frac{3\,b\,\mathrm{atanh}\left(\frac{27\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(24\,a^2\,b+\frac{27\,b^3}{8}\right)}+\frac{24\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24\,a^2\,b+\frac{27\,b^3}{8}}\right)}{4\,d}-\frac{\left(\frac{3\,b}{4}-2\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{26\,a}{3}-\frac{11\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{26\,a}{3}-\frac{11\,b}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a+\frac{3\,b}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(2*a*atan((64*a^3*tan(c/2 + (d*x)/2))/(9*a*b^2 + 64*a^3) + (9*a*b^2*tan(c/2 + (d*x)/2))/(9*a*b^2 + 64*a^3)))/d + (3*b*atanh((27*b^3*tan(c/2 + (d*x)/2))/(8*(24*a^2*b + (27*b^3)/8)) + (24*a^2*b*tan(c/2 + (d*x)/2))/(24*a^2*b + (27*b^3)/8)))/(4*d) - (tan(c/2 + (d*x)/2)*(2*a + (3*b)/4) - tan(c/2 + (d*x)/2)^7*(2*a - (3*b)/4) - tan(c/2 + (d*x)/2)^3*((26*a)/3 + (11*b)/4) + tan(c/2 + (d*x)/2)^5*((26*a)/3 - (11*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))","B"
266,1,96,45,1.390642,"\text{Not used}","int(tan(c + d*x)^2*(a + b/cos(c + d*x)),x)","\frac{a\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(a*sin(c + d*x))/(d*cos(c + d*x)) - (b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b*sin(c + d*x))/(2*d*cos(c + d*x)^2)","B"
267,1,48,26,1.304583,"\text{Not used}","int(cot(c + d*x)^2*(a + b/cos(c + d*x)),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a}{2}-\frac{b}{2}\right)}{d}-\frac{\frac{a}{2}+\frac{b}{2}}{d\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-a\,x","Not used",1,"(tan(c/2 + (d*x)/2)*(a/2 - b/2))/d - (a/2 + b/2)/(d*tan(c/2 + (d*x)/2)) - a*x","B"
268,1,90,55,1.560892,"\text{Not used}","int(cot(c + d*x)^4*(a + b/cos(c + d*x)),x)","a\,x+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a}{24}-\frac{b}{24}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\left(-5\,a-3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a}{3}+\frac{b}{3}\right)}{8\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a}{8}-\frac{3\,b}{8}\right)}{d}","Not used",1,"a*x + (tan(c/2 + (d*x)/2)^3*(a/24 - b/24))/d - (cot(c/2 + (d*x)/2)^3*(a/3 + b/3 - tan(c/2 + (d*x)/2)^2*(5*a + 3*b)))/(8*d) - (tan(c/2 + (d*x)/2)*((5*a)/8 - (3*b)/8))/d","B"
269,1,132,84,1.386473,"\text{Not used}","int(cot(c + d*x)^6*(a + b/cos(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{a}{160}-\frac{b}{160}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\left(22\,a+10\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{7\,a}{3}-\frac{5\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a}{5}+\frac{b}{5}\right)}{32\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{7\,a}{96}-\frac{5\,b}{96}\right)}{d}-a\,x+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{11\,a}{16}-\frac{5\,b}{16}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(a/160 - b/160))/d - (cot(c/2 + (d*x)/2)^5*(a/5 + b/5 - tan(c/2 + (d*x)/2)^2*((7*a)/3 + (5*b)/3) + tan(c/2 + (d*x)/2)^4*(22*a + 10*b)))/(32*d) - (tan(c/2 + (d*x)/2)^3*((7*a)/96 - (5*b)/96))/d - a*x + (tan(c/2 + (d*x)/2)*((11*a)/16 - (5*b)/16))/d","B"
270,1,174,111,1.616837,"\text{Not used}","int(cot(c + d*x)^8*(a + b/cos(c + d*x)),x)","a\,x+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{37\,a}{384}-\frac{7\,b}{128}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{9\,a}{640}-\frac{7\,b}{640}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{a}{896}-\frac{b}{896}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\left(-93\,a-35\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(\frac{37\,a}{3}+7\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-\frac{9\,a}{5}-\frac{7\,b}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a}{7}+\frac{b}{7}\right)}{128\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{93\,a}{128}-\frac{35\,b}{128}\right)}{d}","Not used",1,"a*x + (tan(c/2 + (d*x)/2)^3*((37*a)/384 - (7*b)/128))/d - (tan(c/2 + (d*x)/2)^5*((9*a)/640 - (7*b)/640))/d + (tan(c/2 + (d*x)/2)^7*(a/896 - b/896))/d - (cot(c/2 + (d*x)/2)^7*(a/7 + b/7 - tan(c/2 + (d*x)/2)^2*((9*a)/5 + (7*b)/5) + tan(c/2 + (d*x)/2)^4*((37*a)/3 + 7*b) - tan(c/2 + (d*x)/2)^6*(93*a + 35*b)))/(128*d) - (tan(c/2 + (d*x)/2)*((93*a)/128 - (35*b)/128))/d","B"
271,1,344,185,5.071250,"\text{Not used}","int(tan(c + d*x)^9*(a + b/cos(c + d*x))^2,x)","\frac{\frac{512\,a\,b}{315}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(20\,a^2+\frac{512\,b\,a}{7}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+\frac{1024\,b\,a}{63}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{740\,a^2}{3}+\frac{1024\,b\,a}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{272\,a^2}{3}+\frac{4096\,b\,a}{21}\right)+\frac{740\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{3}-\frac{272\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{3}+20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(348\,a^2+\frac{1024\,a\,b}{5}-\frac{512\,b^2}{5}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+45\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-252\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+210\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-120\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+45\,{\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+1\right)}+\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"((512*a*b)/315 + tan(c/2 + (d*x)/2)^4*((512*a*b)/7 + 20*a^2) - tan(c/2 + (d*x)/2)^2*((1024*a*b)/63 + 2*a^2) + tan(c/2 + (d*x)/2)^8*((1024*a*b)/3 + (740*a^2)/3) - tan(c/2 + (d*x)/2)^6*((4096*a*b)/21 + (272*a^2)/3) + (740*a^2*tan(c/2 + (d*x)/2)^12)/3 - (272*a^2*tan(c/2 + (d*x)/2)^14)/3 + 20*a^2*tan(c/2 + (d*x)/2)^16 - 2*a^2*tan(c/2 + (d*x)/2)^18 - tan(c/2 + (d*x)/2)^10*((1024*a*b)/5 + 348*a^2 - (512*b^2)/5))/(d*(45*tan(c/2 + (d*x)/2)^4 - 10*tan(c/2 + (d*x)/2)^2 - 120*tan(c/2 + (d*x)/2)^6 + 210*tan(c/2 + (d*x)/2)^8 - 252*tan(c/2 + (d*x)/2)^10 + 210*tan(c/2 + (d*x)/2)^12 - 120*tan(c/2 + (d*x)/2)^14 + 45*tan(c/2 + (d*x)/2)^16 - 10*tan(c/2 + (d*x)/2)^18 + tan(c/2 + (d*x)/2)^20 + 1)) + (2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
272,1,280,149,5.172892,"\text{Not used}","int(tan(c + d*x)^7*(a + b/cos(c + d*x))^2,x)","-\frac{\frac{64\,a\,b}{35}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a^2+\frac{256\,b\,a}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+\frac{512\,b\,a}{35}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{170\,a^2}{3}+\frac{512\,b\,a}{5}\right)-\frac{170\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}+16\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{256\,a^2}{3}+64\,a\,b-32\,b^2\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+70\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-56\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"- ((64*a*b)/35 + tan(c/2 + (d*x)/2)^4*((256*a*b)/5 + 16*a^2) - tan(c/2 + (d*x)/2)^2*((512*a*b)/35 + 2*a^2) - tan(c/2 + (d*x)/2)^6*((512*a*b)/5 + (170*a^2)/3) - (170*a^2*tan(c/2 + (d*x)/2)^10)/3 + 16*a^2*tan(c/2 + (d*x)/2)^12 - 2*a^2*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^8*(64*a*b + (256*a^2)/3 - 32*b^2))/(d*(28*tan(c/2 + (d*x)/2)^4 - 8*tan(c/2 + (d*x)/2)^2 - 56*tan(c/2 + (d*x)/2)^6 + 70*tan(c/2 + (d*x)/2)^8 - 56*tan(c/2 + (d*x)/2)^10 + 28*tan(c/2 + (d*x)/2)^12 - 8*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1)) - (2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
273,1,215,115,4.968315,"\text{Not used}","int(tan(c + d*x)^5*(a + b/cos(c + d*x))^2,x)","\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}+\frac{\frac{32\,a\,b}{15}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(12\,a^2+32\,b\,a\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+\frac{64\,b\,a}{5}\right)+12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(20\,a^2+\frac{64\,a\,b}{3}-\frac{32\,b^2}{3}\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,"(2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d + ((32*a*b)/15 + tan(c/2 + (d*x)/2)^4*(32*a*b + 12*a^2) - tan(c/2 + (d*x)/2)^2*((64*a*b)/5 + 2*a^2) + 12*a^2*tan(c/2 + (d*x)/2)^8 - 2*a^2*tan(c/2 + (d*x)/2)^10 - tan(c/2 + (d*x)/2)^6*((64*a*b)/3 + 20*a^2 - (32*b^2)/3))/(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"
274,1,151,87,3.732847,"\text{Not used}","int(tan(c + d*x)^3*(a + b/cos(c + d*x))^2,x)","-\frac{\frac{8\,a\,b}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+\frac{32\,b\,a}{3}\right)-2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^2+8\,a\,b-4\,b^2\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"- ((8*a*b)/3 - tan(c/2 + (d*x)/2)^2*((32*a*b)/3 + 2*a^2) - 2*a^2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^4*(8*a*b + 4*a^2 - 4*b^2))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1)) - (2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
275,1,81,47,1.532848,"\text{Not used}","int(tan(c + d*x)*(a + b/cos(c + d*x))^2,x)","\frac{4\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a\,b-2\,b^2\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,a^2\,\mathrm{atanh}\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d}","Not used",1,"(4*a*b - tan(c/2 + (d*x)/2)^2*(4*a*b - 2*b^2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) + (2*a^2*atanh(tan(c/2 + (d*x)/2)^2))/d","B"
276,1,96,61,1.428664,"\text{Not used}","int(cot(c + d*x)*(a + b/cos(c + d*x))^2,x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{b^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{b^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{d}+\frac{2\,a\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (b^2*log(tan(c/2 + (d*x)/2)))/d - (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (b^2*log(tan(c/2 + (d*x)/2)^2 - 1))/d + (2*a*b*log(tan(c/2 + (d*x)/2)))/d","B"
277,1,98,92,1.363789,"\text{Not used}","int(cot(c + d*x)^3*(a + b/cos(c + d*x))^2,x)","\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\left(a-b\right)}^2}{8\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+b\,a\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{8}+\frac{a\,b}{4}+\frac{b^2}{8}\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (tan(c/2 + (d*x)/2)^2*(a - b)^2)/(8*d) - (log(tan(c/2 + (d*x)/2))*(a*b + a^2))/d - (cot(c/2 + (d*x)/2)^2*((a*b)/4 + a^2/8 + b^2/8))/d","B"
278,1,164,126,1.445296,"\text{Not used}","int(cot(c + d*x)^5*(a + b/cos(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^2}{32}-\frac{3\,a\,b}{16}+\frac{b^2}{32}+\frac{{\left(a-b\right)}^2}{32}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\left(a-b\right)}^2}{64\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2+\frac{3\,b\,a}{4}\right)}{d}-\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a\,b}{2}+\frac{a^2}{4}+\frac{b^2}{4}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2+4\,a\,b+b^2\right)\right)}{16\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*((5*a^2)/32 - (3*a*b)/16 + b^2/32 + (a - b)^2/32))/d - (tan(c/2 + (d*x)/2)^4*(a - b)^2)/(64*d) + (log(tan(c/2 + (d*x)/2))*((3*a*b)/4 + a^2))/d - (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (cot(c/2 + (d*x)/2)^4*((a*b)/2 + a^2/4 + b^2/4 - tan(c/2 + (d*x)/2)^2*(4*a*b + 3*a^2 + b^2)))/(16*d)","B"
279,1,403,157,2.644506,"\text{Not used}","int(tan(c + d*x)^6*(a + b/cos(c + d*x))^2,x)","\frac{\left(\frac{5\,a\,b}{4}-2\,a^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+\left(\frac{44\,a^2}{3}-\frac{25\,a\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{283\,a\,b}{12}-\frac{706\,a^2}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{344\,a^2}{5}-\frac{128\,b^2}{7}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(-\frac{706\,a^2}{15}-\frac{283\,b\,a}{12}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{44\,a^2}{3}+\frac{25\,b\,a}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^2-\frac{5\,b\,a}{4}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,a^2\,\mathrm{atan}\left(\frac{64\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^6+25\,a^4\,b^2}+\frac{25\,a^4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^6+25\,a^4\,b^2}\right)}{d}-\frac{5\,a\,b\,\mathrm{atanh}\left(\frac{40\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{40\,a^5\,b+\frac{125\,a^3\,b^3}{8}}+\frac{125\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(40\,a^5\,b+\frac{125\,a^3\,b^3}{8}\right)}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^7*((344*a^2)/5 - (128*b^2)/7) + tan(c/2 + (d*x)/2)^13*((5*a*b)/4 - 2*a^2) + tan(c/2 + (d*x)/2)^3*((25*a*b)/3 + (44*a^2)/3) - tan(c/2 + (d*x)/2)^11*((25*a*b)/3 - (44*a^2)/3) - tan(c/2 + (d*x)/2)^5*((283*a*b)/12 + (706*a^2)/15) + tan(c/2 + (d*x)/2)^9*((283*a*b)/12 - (706*a^2)/15) - tan(c/2 + (d*x)/2)*((5*a*b)/4 + 2*a^2))/(d*(7*tan(c/2 + (d*x)/2)^2 - 21*tan(c/2 + (d*x)/2)^4 + 35*tan(c/2 + (d*x)/2)^6 - 35*tan(c/2 + (d*x)/2)^8 + 21*tan(c/2 + (d*x)/2)^10 - 7*tan(c/2 + (d*x)/2)^12 + tan(c/2 + (d*x)/2)^14 - 1)) - (2*a^2*atan((64*a^6*tan(c/2 + (d*x)/2))/(64*a^6 + 25*a^4*b^2) + (25*a^4*b^2*tan(c/2 + (d*x)/2))/(64*a^6 + 25*a^4*b^2)))/d - (5*a*b*atanh((40*a^5*b*tan(c/2 + (d*x)/2))/(40*a^5*b + (125*a^3*b^3)/8) + (125*a^3*b^3*tan(c/2 + (d*x)/2))/(8*(40*a^5*b + (125*a^3*b^3)/8))))/(4*d)","B"
280,1,332,116,2.563033,"\text{Not used}","int(tan(c + d*x)^4*(a + b/cos(c + d*x))^2,x)","\frac{\left(2\,a^2-\frac{3\,a\,b}{2}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(7\,a\,b-\frac{32\,a^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{52\,a^2}{3}-\frac{32\,b^2}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-\frac{32\,a^2}{3}-7\,b\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^2+\frac{3\,b\,a}{2}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{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{2\,a^2\,\mathrm{atan}\left(\frac{64\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^6+36\,a^4\,b^2}+\frac{36\,a^4\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,a^6+36\,a^4\,b^2}\right)}{d}+\frac{3\,a\,b\,\mathrm{atanh}\left(\frac{48\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{48\,a^5\,b+27\,a^3\,b^3}+\frac{27\,a^3\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{48\,a^5\,b+27\,a^3\,b^3}\right)}{2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*((52*a^2)/3 - (32*b^2)/5) - tan(c/2 + (d*x)/2)^9*((3*a*b)/2 - 2*a^2) - tan(c/2 + (d*x)/2)^3*(7*a*b + (32*a^2)/3) + tan(c/2 + (d*x)/2)^7*(7*a*b - (32*a^2)/3) + tan(c/2 + (d*x)/2)*((3*a*b)/2 + 2*a^2))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) + (2*a^2*atan((64*a^6*tan(c/2 + (d*x)/2))/(64*a^6 + 36*a^4*b^2) + (36*a^4*b^2*tan(c/2 + (d*x)/2))/(64*a^6 + 36*a^4*b^2)))/d + (3*a*b*atanh((48*a^5*b*tan(c/2 + (d*x)/2))/(48*a^5*b + 27*a^3*b^3) + (27*a^3*b^3*tan(c/2 + (d*x)/2))/(48*a^5*b + 27*a^3*b^3)))/(2*d)","B"
281,1,227,70,1.669022,"\text{Not used}","int(tan(c + d*x)^2*(a + b/cos(c + d*x))^2,x)","-\frac{\frac{b^2\,\sin\left(3\,c+3\,d\,x\right)}{12}-\frac{b^2\,\sin\left(c+d\,x\right)}{4}-\frac{a^2\,\sin\left(3\,c+3\,d\,x\right)}{4}-\frac{a^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,a^2\,\cos\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}-\frac{a\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,a\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2}+\frac{a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(3\,c+3\,d\,x\right)}{2}}{d\,\left(\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{\cos\left(3\,c+3\,d\,x\right)}{4}\right)}","Not used",1,"-((b^2*sin(3*c + 3*d*x))/12 - (b^2*sin(c + d*x))/4 - (a^2*sin(3*c + 3*d*x))/4 - (a^2*sin(c + d*x))/4 + (3*a^2*cos(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2 - (a*b*sin(2*c + 2*d*x))/2 + (3*a*b*cos(c + d*x)*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/2 + (a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(3*c + 3*d*x))/2)/(d*((3*cos(c + d*x))/4 + cos(3*c + 3*d*x)/4))","B"
282,1,58,48,1.431241,"\text{Not used}","int(cot(c + d*x)^2*(a + b/cos(c + d*x))^2,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a-b\right)}^2}{2\,d}-\frac{\frac{a^2}{2}+a\,b+\frac{b^2}{2}}{d\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-a^2\,x","Not used",1,"(tan(c/2 + (d*x)/2)*(a - b)^2)/(2*d) - (a*b + a^2/2 + b^2/2)/(d*tan(c/2 + (d*x)/2)) - a^2*x","B"
283,1,118,85,1.459947,"\text{Not used}","int(cot(c + d*x)^4*(a + b/cos(c + d*x))^2,x)","a^2\,x+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\left(a-b\right)}^2}{24\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a\,\left(a-b\right)}{2}+\frac{{\left(a-b\right)}^2}{8}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,a\,b}{3}+\frac{a^2}{3}+\frac{b^2}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^2+6\,a\,b+b^2\right)\right)}{8\,d}","Not used",1,"a^2*x + (tan(c/2 + (d*x)/2)^3*(a - b)^2)/(24*d) - (tan(c/2 + (d*x)/2)*((a*(a - b))/2 + (a - b)^2/8))/d - (cot(c/2 + (d*x)/2)^3*((2*a*b)/3 + a^2/3 + b^2/3 - tan(c/2 + (d*x)/2)^2*(6*a*b + 5*a^2 + b^2)))/(8*d)","B"
284,1,191,122,1.497492,"\text{Not used}","int(cot(c + d*x)^6*(a + b/cos(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\left(a-b\right)}^2}{160\,d}-a^2\,x-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2}{16}-\frac{a\,b}{12}+\frac{b^2}{48}+\frac{{\left(a-b\right)}^2}{96}\right)}{d}-\frac{\frac{2\,a\,b}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(22\,a^2+20\,a\,b+2\,b^2\right)+\frac{a^2}{5}+\frac{b^2}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{7\,a^2}{3}+\frac{10\,a\,b}{3}+b^2\right)}{32\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{21\,a^2}{32}-\frac{9\,a\,b}{16}+\frac{b^2}{32}+\frac{{\left(a-b\right)}^2}{32}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(a - b)^2)/(160*d) - a^2*x - (tan(c/2 + (d*x)/2)^3*(a^2/16 - (a*b)/12 + b^2/48 + (a - b)^2/96))/d - ((2*a*b)/5 + tan(c/2 + (d*x)/2)^4*(20*a*b + 22*a^2 + 2*b^2) + a^2/5 + b^2/5 - tan(c/2 + (d*x)/2)^2*((10*a*b)/3 + (7*a^2)/3 + b^2))/(32*d*tan(c/2 + (d*x)/2)^5) + (tan(c/2 + (d*x)/2)*((21*a^2)/32 - (9*a*b)/16 + b^2/32 + (a - b)^2/32))/d","B"
285,1,258,153,1.497120,"\text{Not used}","int(cot(c + d*x)^8*(a + b/cos(c + d*x))^2,x)","a^2\,x+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\left(a-b\right)}^2}{896\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{3\,a^2}{32}-\frac{5\,a\,b}{48}+\frac{b^2}{48}+\frac{{\left(a-b\right)}^2}{384}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{a^2}{80}-\frac{3\,a\,b}{160}+\frac{b^2}{160}+\frac{{\left(a-b\right)}^2}{640}\right)}{d}-\frac{\frac{2\,a\,b}{7}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{37\,a^2}{3}+14\,a\,b+3\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(93\,a^2+70\,a\,b+5\,b^2\right)+\frac{a^2}{7}+\frac{b^2}{7}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{9\,a^2}{5}+\frac{14\,a\,b}{5}+b^2\right)}{128\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{23\,a^2}{32}-\frac{17\,a\,b}{32}+\frac{b^2}{32}+\frac{{\left(a-b\right)}^2}{128}\right)}{d}","Not used",1,"a^2*x + (tan(c/2 + (d*x)/2)^7*(a - b)^2)/(896*d) + (tan(c/2 + (d*x)/2)^3*((3*a^2)/32 - (5*a*b)/48 + b^2/48 + (a - b)^2/384))/d - (tan(c/2 + (d*x)/2)^5*(a^2/80 - (3*a*b)/160 + b^2/160 + (a - b)^2/640))/d - ((2*a*b)/7 + tan(c/2 + (d*x)/2)^4*(14*a*b + (37*a^2)/3 + 3*b^2) - tan(c/2 + (d*x)/2)^6*(70*a*b + 93*a^2 + 5*b^2) + a^2/7 + b^2/7 - tan(c/2 + (d*x)/2)^2*((14*a*b)/5 + (9*a^2)/5 + b^2))/(128*d*tan(c/2 + (d*x)/2)^7) - (tan(c/2 + (d*x)/2)*((23*a^2)/32 - (17*a*b)/32 + b^2/32 + (a - b)^2/128))/d","B"
286,1,631,250,2.968692,"\text{Not used}","int(tan(c + d*x)^9/(a + b/cos(c + d*x)),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{\frac{2\,\left(105\,a^6-385\,a^4\,b^2+511\,a^2\,b^4-279\,b^6\right)}{105\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(a^6+a^5\,b-3\,a^4\,b^2-3\,a^3\,b^3+3\,a^2\,b^4+3\,a\,b^5-b^6\right)}{b^7}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(6\,a^6+5\,a^5\,b-20\,a^4\,b^2-17\,a^3\,b^3+22\,a^2\,b^4+19\,a\,b^5-8\,b^6\right)}{b^7}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(30\,a^6+15\,a^5\,b-112\,a^4\,b^2-54\,a^3\,b^3+154\,a^2\,b^4+71\,a\,b^5-96\,b^6\right)}{3\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(45\,a^6+30\,a^5\,b-161\,a^4\,b^2-108\,a^3\,b^3+203\,a^2\,b^4+142\,a\,b^5-87\,b^6\right)}{3\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(75\,a^6+25\,a^5\,b-285\,a^4\,b^2-85\,a^3\,b^3+401\,a^2\,b^4+95\,a\,b^5-239\,b^6\right)}{5\,b^7}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(90\,a^6+15\,a^5\,b-340\,a^4\,b^2-45\,a^3\,b^3+466\,a^2\,b^4+45\,a\,b^5-264\,b^6\right)}{15\,b^7}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-21\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,\left(-a^7+4\,a^5\,b^2-6\,a^3\,b^4+4\,a\,b^6\right)}{b^8\,d}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,{\left(a^2-b^2\right)}^4}{a\,b^8\,d}","Not used",1,"log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - ((2*(105*a^6 - 279*b^6 + 511*a^2*b^4 - 385*a^4*b^2))/(105*b^7) + (2*tan(c/2 + (d*x)/2)^12*(3*a*b^5 + a^5*b + a^6 - b^6 + 3*a^2*b^4 - 3*a^3*b^3 - 3*a^4*b^2))/b^7 - (2*tan(c/2 + (d*x)/2)^10*(19*a*b^5 + 5*a^5*b + 6*a^6 - 8*b^6 + 22*a^2*b^4 - 17*a^3*b^3 - 20*a^4*b^2))/b^7 - (4*tan(c/2 + (d*x)/2)^6*(71*a*b^5 + 15*a^5*b + 30*a^6 - 96*b^6 + 154*a^2*b^4 - 54*a^3*b^3 - 112*a^4*b^2))/(3*b^7) + (2*tan(c/2 + (d*x)/2)^8*(142*a*b^5 + 30*a^5*b + 45*a^6 - 87*b^6 + 203*a^2*b^4 - 108*a^3*b^3 - 161*a^4*b^2))/(3*b^7) + (2*tan(c/2 + (d*x)/2)^4*(95*a*b^5 + 25*a^5*b + 75*a^6 - 239*b^6 + 401*a^2*b^4 - 85*a^3*b^3 - 285*a^4*b^2))/(5*b^7) - (2*tan(c/2 + (d*x)/2)^2*(45*a*b^5 + 15*a^5*b + 90*a^6 - 264*b^6 + 466*a^2*b^4 - 45*a^3*b^3 - 340*a^4*b^2))/(15*b^7))/(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)) - (log(tan(c/2 + (d*x)/2)^2 - 1)*(4*a*b^6 - a^7 - 6*a^3*b^4 + 4*a^5*b^2))/(b^8*d) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^4)/(a*b^8*d)","B"
287,1,395,170,2.402533,"\text{Not used}","int(tan(c + d*x)^7/(a + b/cos(c + d*x)),x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,\left(a^4-3\,a^2\,b^2+3\,b^4\right)}{b^6\,d}-\frac{\frac{2\,\left(15\,a^4-40\,a^2\,b^2+33\,b^4\right)}{15\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^4+a^3\,b-2\,a^2\,b^2-2\,a\,b^3+b^4\right)}{b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^4+3\,a^3\,b-10\,a^2\,b^2-8\,a\,b^3+6\,b^4\right)}{b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a^4+3\,a^3\,b-34\,a^2\,b^2-6\,a\,b^3+30\,b^4\right)}{3\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(18\,a^4+9\,a^3\,b-50\,a^2\,b^2-24\,a\,b^3+48\,b^4\right)}{3\,b^5}}{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{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,{\left(a^2-b^2\right)}^3}{a\,b^6\,d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 - 1)*(a^4 + 3*b^4 - 3*a^2*b^2))/(b^6*d) - ((2*(15*a^4 + 33*b^4 - 40*a^2*b^2))/(15*b^5) + (2*tan(c/2 + (d*x)/2)^8*(a^3*b - 2*a*b^3 + a^4 + b^4 - 2*a^2*b^2))/b^5 - (2*tan(c/2 + (d*x)/2)^6*(3*a^3*b - 8*a*b^3 + 4*a^4 + 6*b^4 - 10*a^2*b^2))/b^5 - (2*tan(c/2 + (d*x)/2)^2*(3*a^3*b - 6*a*b^3 + 12*a^4 + 30*b^4 - 34*a^2*b^2))/(3*b^5) + (2*tan(c/2 + (d*x)/2)^4*(9*a^3*b - 24*a*b^3 + 18*a^4 + 48*b^4 - 50*a^2*b^2))/(3*b^5))/(d*(5*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^4 + 10*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^3)/(a*b^6*d)","B"
288,1,227,108,1.880700,"\text{Not used}","int(tan(c + d*x)^5/(a + b/cos(c + d*x)),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{\frac{2\,\left(3\,a^2-5\,b^2\right)}{3\,b^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+a\,b-4\,b^2\right)}{b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+a\,b-b^2\right)}{b^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,\left(a^2-2\,b^2\right)}{b^4\,d}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,{\left(a^2-b^2\right)}^2}{a\,b^4\,d}","Not used",1,"log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - ((2*(3*a^2 - 5*b^2))/(3*b^3) - (2*tan(c/2 + (d*x)/2)^2*(a*b + 2*a^2 - 4*b^2))/b^3 + (2*tan(c/2 + (d*x)/2)^4*(a*b + 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)) + (a*log(tan(c/2 + (d*x)/2)^2 - 1)*(a^2 - 2*b^2))/(b^4*d) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^2)/(a*b^4*d)","B"
289,1,115,59,1.538408,"\text{Not used}","int(tan(c + d*x)^3/(a + b/cos(c + d*x)),x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{b^2\,d}-\frac{2}{b\,d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(\frac{a}{b^2}-\frac{1}{a}\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 - 1))/(b^2*d) - 2/(b*d*(tan(c/2 + (d*x)/2)^2 - 1)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(a/b^2 - 1/a))/d","B"
290,1,71,35,1.467999,"\text{Not used}","int(tan(c + d*x)/(a + b/cos(c + d*x)),x)","\frac{\mathrm{atan}\left(\frac{a\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}+b\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}+b\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,1{}\mathrm{i}}\right)\,2{}\mathrm{i}}{a\,d}","Not used",1,"(atan((a*sin(c/2 + (d*x)/2)^2)/(a*cos(c/2 + (d*x)/2)^2*1i + b*cos(c/2 + (d*x)/2)^2*1i + b*sin(c/2 + (d*x)/2)^2*1i))*2i)/(a*d)","B"
291,1,93,94,1.749322,"\text{Not used}","int(cot(c + d*x)/(a + b/cos(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a+b\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}+\frac{b^2\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{d\,\left(a\,b^2-a^3\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(a + b)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) + (b^2*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(d*(a*b^2 - a^3))","B"
292,1,174,157,1.845349,"\text{Not used}","int(cot(c + d*x)^3/(a + b/cos(c + d*x)),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d\,\left(4\,a-4\,b\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(2\,a+3\,b\right)}{d\,\left(2\,a^2+4\,a\,b+2\,b^2\right)}-\frac{a-b}{2\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a+b\right)\,\left(4\,a-4\,b\right)}-\frac{b^4\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a\,d\,{\left(a^2-b^2\right)}^2}","Not used",1,"log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - tan(c/2 + (d*x)/2)^2/(2*d*(4*a - 4*b)) - (log(tan(c/2 + (d*x)/2))*(2*a + 3*b))/(d*(4*a*b + 2*a^2 + 2*b^2)) - (a - b)/(2*d*tan(c/2 + (d*x)/2)^2*(a + b)*(4*a - 4*b)) - (b^4*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(a*d*(a^2 - b^2)^2)","B"
293,1,290,234,2.265654,"\text{Not used}","int(cot(c + d*x)^5/(a + b/cos(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(8\,a^2+21\,a\,b+15\,b^2\right)}{d\,\left(8\,a^3+24\,a^2\,b+24\,a\,b^2+8\,b^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{4\,d\,\left(16\,a-16\,b\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{16\,b}{{\left(16\,a-16\,b\right)}^2}-\frac{3}{16\,a-16\,b}\right)}{d}-\frac{\frac{a^2-2\,a\,b+b^2}{4\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-3\,a^3+2\,a^2\,b+5\,a\,b^2-4\,b^3\right)}{{\left(a+b\right)}^2}}{d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a^2-32\,a\,b+16\,b^2\right)}-\frac{b^6\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}{a\,d\,{\left(a^2-b^2\right)}^3}","Not used",1,"(log(tan(c/2 + (d*x)/2))*(21*a*b + 8*a^2 + 15*b^2))/(d*(24*a*b^2 + 24*a^2*b + 8*a^3 + 8*b^3)) - tan(c/2 + (d*x)/2)^4/(4*d*(16*a - 16*b)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a*d) - (tan(c/2 + (d*x)/2)^2*((16*b)/(16*a - 16*b)^2 - 3/(16*a - 16*b)))/d - ((a^2 - 2*a*b + b^2)/(4*(a + b)) + (tan(c/2 + (d*x)/2)^2*(5*a*b^2 + 2*a^2*b - 3*a^3 - 4*b^3))/(a + b)^2)/(d*tan(c/2 + (d*x)/2)^4*(16*a^2 - 32*a*b + 16*b^2)) - (b^6*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2))/(a*d*(a^2 - b^2)^3)","B"
294,1,9148,198,4.129325,"\text{Not used}","int(tan(c + d*x)^6/(a + b/cos(c + d*x)),x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-8\,a^3+4\,a^2\,b+16\,a\,b^2-7\,b^3\right)}{4\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(-8\,a^3-4\,a^2\,b+16\,a\,b^2+7\,b^3\right)}{4\,b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-72\,a^3+12\,a^2\,b+176\,a\,b^2-45\,b^3\right)}{12\,b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-72\,a^3-12\,a^2\,b+176\,a\,b^2+45\,b^3\right)}{12\,b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{2\,\mathrm{atan}\left(\frac{\frac{-\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{21}-64\,a^{20}\,b-704\,a^{19}\,b^2+704\,a^{18}\,b^3+3520\,a^{17}\,b^4-3520\,a^{16}\,b^5-10520\,a^{15}\,b^6+10520\,a^{14}\,b^7+20913\,a^{13}\,b^8-21169\,a^{12}\,b^9-28398\,a^{11}\,b^{10}+29678\,a^{10}\,b^{11}+25679\,a^9\,b^{12}-27983\,a^8\,b^{13}-14740\,a^7\,b^{14}+15860\,a^6\,b^{15}+6000\,a^5\,b^{16}-4340\,a^4\,b^{17}-3084\,a^3\,b^{18}+684\,a^2\,b^{19}+1414\,a\,b^{20}-514\,b^{21}\right)}{b^{16}}+\frac{\left(-\frac{128\,\left(-192\,a^{18}\,b^4+416\,a^{17}\,b^5+1248\,a^{16}\,b^6-3256\,a^{15}\,b^7-3080\,a^{14}\,b^8+11096\,a^{13}\,b^9+2736\,a^{12}\,b^{10}-21295\,a^{11}\,b^{11}+2308\,a^{10}\,b^{12}+24883\,a^9\,b^{13}-7672\,a^8\,b^{14}-18310\,a^7\,b^{15}+7376\,a^6\,b^{16}+8886\,a^5\,b^{17}-3575\,a^4\,b^{18}-2996\,a^3\,b^{19}+1043\,a^2\,b^{20}+576\,a\,b^{21}-192\,b^{22}\right)}{b^{16}}+\frac{\left(-\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{15}\,b^8-384\,a^{14}\,b^9-192\,a^{13}\,b^{10}+1472\,a^{12}\,b^{11}-512\,a^{11}\,b^{12}-1792\,a^{10}\,b^{13}+1000\,a^9\,b^{14}+120\,a^8\,b^{15}+905\,a^7\,b^{16}+755\,a^6\,b^{17}-3047\,a^5\,b^{18}+903\,a^4\,b^{19}+1222\,a^3\,b^{20}-322\,a^2\,b^{21}-384\,a\,b^{22}+128\,b^{23}\right)}{b^{16}}+\frac{\left(\frac{128\,\left(-192\,a^{10}\,b^{14}+416\,a^9\,b^{15}+288\,a^8\,b^{16}-1176\,a^7\,b^{17}+280\,a^6\,b^{18}+1016\,a^5\,b^{19}-568\,a^4\,b^{20}-256\,a^3\,b^{21}+192\,a^2\,b^{22}\right)}{b^{16}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{18}+384\,a^6\,b^{19}-512\,a^5\,b^{20}+512\,a^4\,b^{21}-384\,a^3\,b^{22}+128\,a^2\,b^{23}\right)\,128{}\mathrm{i}}{a\,b^{16}}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}}{a}-\frac{\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{21}-64\,a^{20}\,b-704\,a^{19}\,b^2+704\,a^{18}\,b^3+3520\,a^{17}\,b^4-3520\,a^{16}\,b^5-10520\,a^{15}\,b^6+10520\,a^{14}\,b^7+20913\,a^{13}\,b^8-21169\,a^{12}\,b^9-28398\,a^{11}\,b^{10}+29678\,a^{10}\,b^{11}+25679\,a^9\,b^{12}-27983\,a^8\,b^{13}-14740\,a^7\,b^{14}+15860\,a^6\,b^{15}+6000\,a^5\,b^{16}-4340\,a^4\,b^{17}-3084\,a^3\,b^{18}+684\,a^2\,b^{19}+1414\,a\,b^{20}-514\,b^{21}\right)}{b^{16}}+\frac{\left(-\frac{128\,\left(-192\,a^{18}\,b^4+416\,a^{17}\,b^5+1248\,a^{16}\,b^6-3256\,a^{15}\,b^7-3080\,a^{14}\,b^8+11096\,a^{13}\,b^9+2736\,a^{12}\,b^{10}-21295\,a^{11}\,b^{11}+2308\,a^{10}\,b^{12}+24883\,a^9\,b^{13}-7672\,a^8\,b^{14}-18310\,a^7\,b^{15}+7376\,a^6\,b^{16}+8886\,a^5\,b^{17}-3575\,a^4\,b^{18}-2996\,a^3\,b^{19}+1043\,a^2\,b^{20}+576\,a\,b^{21}-192\,b^{22}\right)}{b^{16}}+\frac{\left(\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{15}\,b^8-384\,a^{14}\,b^9-192\,a^{13}\,b^{10}+1472\,a^{12}\,b^{11}-512\,a^{11}\,b^{12}-1792\,a^{10}\,b^{13}+1000\,a^9\,b^{14}+120\,a^8\,b^{15}+905\,a^7\,b^{16}+755\,a^6\,b^{17}-3047\,a^5\,b^{18}+903\,a^4\,b^{19}+1222\,a^3\,b^{20}-322\,a^2\,b^{21}-384\,a\,b^{22}+128\,b^{23}\right)}{b^{16}}+\frac{\left(\frac{128\,\left(-192\,a^{10}\,b^{14}+416\,a^9\,b^{15}+288\,a^8\,b^{16}-1176\,a^7\,b^{17}+280\,a^6\,b^{18}+1016\,a^5\,b^{19}-568\,a^4\,b^{20}-256\,a^3\,b^{21}+192\,a^2\,b^{22}\right)}{b^{16}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-128\,a^7\,b^{18}+384\,a^6\,b^{19}-512\,a^5\,b^{20}+512\,a^4\,b^{21}-384\,a^3\,b^{22}+128\,a^2\,b^{23}\right)\,128{}\mathrm{i}}{a\,b^{16}}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}}{a}}{-\frac{256\,\left(-64\,a^{20}+64\,a^{19}\,b+704\,a^{18}\,b^2-704\,a^{17}\,b^3-3712\,a^{16}\,b^4+3936\,a^{15}\,b^5+11768\,a^{14}\,b^6-13776\,a^{13}\,b^7-23865\,a^{12}\,b^8+31881\,a^{11}\,b^9+30942\,a^{10}\,b^{10}-49501\,a^9\,b^{11}-23883\,a^8\,b^{12}+51074\,a^7\,b^{13}+7876\,a^6\,b^{14}-33634\,a^5\,b^{15}+2569\,a^4\,b^{16}+12805\,a^3\,b^{17}-3130\,a^2\,b^{18}-2145\,a\,b^{19}+795\,b^{20}\right)}{b^{16}}+\frac{\left(-\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{21}-64\,a^{20}\,b-704\,a^{19}\,b^2+704\,a^{18}\,b^3+3520\,a^{17}\,b^4-3520\,a^{16}\,b^5-10520\,a^{15}\,b^6+10520\,a^{14}\,b^7+20913\,a^{13}\,b^8-21169\,a^{12}\,b^9-28398\,a^{11}\,b^{10}+29678\,a^{10}\,b^{11}+25679\,a^9\,b^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,b^{18}+903\,a^4\,b^{19}+1222\,a^3\,b^{20}-322\,a^2\,b^{21}-384\,a\,b^{22}+128\,b^{23}\right)}{b^{16}}+\frac{\left(\frac{128\,\left(-192\,a^{10}\,b^{14}+416\,a^9\,b^{15}+288\,a^8\,b^{16}-1176\,a^7\,b^{17}+280\,a^6\,b^{18}+1016\,a^5\,b^{19}-568\,a^4\,b^{20}-256\,a^3\,b^{21}+192\,a^2\,b^{22}\right)}{b^{16}}+\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-128\,a^7\,b^{18}+384\,a^6\,b^{19}-512\,a^5\,b^{20}+512\,a^4\,b^{21}-384\,a^3\,b^{22}+128\,a^2\,b^{23}\right)}{a\,b^{21}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{a\,b^5}}{\frac{256\,\left(-64\,a^{20}+64\,a^{19}\,b+704\,a^{18}\,b^2-704\,a^{17}\,b^3-3712\,a^{16}\,b^4+3936\,a^{15}\,b^5+11768\,a^{14}\,b^6-13776\,a^{13}\,b^7-23865\,a^{12}\,b^8+31881\,a^{11}\,b^9+30942\,a^{10}\,b^{10}-49501\,a^9\,b^{11}-23883\,a^8\,b^{12}+51074\,a^7\,b^{13}+7876\,a^6\,b^{14}-33634\,a^5\,b^{15}+2569\,a^4\,b^{16}+12805\,a^3\,b^{17}-3130\,a^2\,b^{18}-2145\,a\,b^{19}+795\,b^{20}\right)}{b^{16}}+\frac{\left(\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{21}-64\,a^{20}\,b-704\,a^{19}\,b^2+704\,a^{18}\,b^3+3520\,a^{17}\,b^4-3520\,a^{16}\,b^5-10520\,a^{15}\,b^6+10520\,a^{14}\,b^7+20913\,a^{13}\,b^8-21169\,a^{12}\,b^9-28398\,a^{11}\,b^{10}+29678\,a^{10}\,b^{11}+25679\,a^9\,b^{12}-27983\,a^8\,b^{13}-14740\,a^7\,b^{14}+15860\,a^6\,b^{15}+6000\,a^5\,b^{16}-4340\,a^4\,b^{17}-3084\,a^3\,b^{18}+684\,a^2\,b^{19}+1414\,a\,b^{20}-514\,b^{21}\right)}{b^{16}}+\frac{\left(\frac{128\,\left(-192\,a^{18}\,b^4+416\,a^{17}\,b^5+1248\,a^{16}\,b^6-3256\,a^{15}\,b^7-3080\,a^{14}\,b^8+11096\,a^{13}\,b^9+2736\,a^{12}\,b^{10}-21295\,a^{11}\,b^{11}+2308\,a^{10}\,b^{12}+24883\,a^9\,b^{13}-7672\,a^8\,b^{14}-18310\,a^7\,b^{15}+7376\,a^6\,b^{16}+8886\,a^5\,b^{17}-3575\,a^4\,b^{18}-2996\,a^3\,b^{19}+1043\,a^2\,b^{20}+576\,a\,b^{21}-192\,b^{22}\right)}{b^{16}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{15}\,b^8-384\,a^{14}\,b^9-192\,a^{13}\,b^{10}+1472\,a^{12}\,b^{11}-512\,a^{11}\,b^{12}-1792\,a^{10}\,b^{13}+1000\,a^9\,b^{14}+120\,a^8\,b^{15}+905\,a^7\,b^{16}+755\,a^6\,b^{17}-3047\,a^5\,b^{18}+903\,a^4\,b^{19}+1222\,a^3\,b^{20}-322\,a^2\,b^{21}-384\,a\,b^{22}+128\,b^{23}\right)}{b^{16}}-\frac{\left(\frac{128\,\left(-192\,a^{10}\,b^{14}+416\,a^9\,b^{15}+288\,a^8\,b^{16}-1176\,a^7\,b^{17}+280\,a^6\,b^{18}+1016\,a^5\,b^{19}-568\,a^4\,b^{20}-256\,a^3\,b^{21}+192\,a^2\,b^{22}\right)}{b^{16}}-\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-128\,a^7\,b^{18}+384\,a^6\,b^{19}-512\,a^5\,b^{20}+512\,a^4\,b^{21}-384\,a^3\,b^{22}+128\,a^2\,b^{23}\right)}{a\,b^{21}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}-\frac{\left(\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{21}-64\,a^{20}\,b-704\,a^{19}\,b^2+704\,a^{18}\,b^3+3520\,a^{17}\,b^4-3520\,a^{16}\,b^5-10520\,a^{15}\,b^6+10520\,a^{14}\,b^7+20913\,a^{13}\,b^8-21169\,a^{12}\,b^9-28398\,a^{11}\,b^{10}+29678\,a^{10}\,b^{11}+25679\,a^9\,b^{12}-27983\,a^8\,b^{13}-14740\,a^7\,b^{14}+15860\,a^6\,b^{15}+6000\,a^5\,b^{16}-4340\,a^4\,b^{17}-3084\,a^3\,b^{18}+684\,a^2\,b^{19}+1414\,a\,b^{20}-514\,b^{21}\right)}{b^{16}}-\frac{\left(\frac{128\,\left(-192\,a^{18}\,b^4+416\,a^{17}\,b^5+1248\,a^{16}\,b^6-3256\,a^{15}\,b^7-3080\,a^{14}\,b^8+11096\,a^{13}\,b^9+2736\,a^{12}\,b^{10}-21295\,a^{11}\,b^{11}+2308\,a^{10}\,b^{12}+24883\,a^9\,b^{13}-7672\,a^8\,b^{14}-18310\,a^7\,b^{15}+7376\,a^6\,b^{16}+8886\,a^5\,b^{17}-3575\,a^4\,b^{18}-2996\,a^3\,b^{19}+1043\,a^2\,b^{20}+576\,a\,b^{21}-192\,b^{22}\right)}{b^{16}}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(128\,a^{15}\,b^8-384\,a^{14}\,b^9-192\,a^{13}\,b^{10}+1472\,a^{12}\,b^{11}-512\,a^{11}\,b^{12}-1792\,a^{10}\,b^{13}+1000\,a^9\,b^{14}+120\,a^8\,b^{15}+905\,a^7\,b^{16}+755\,a^6\,b^{17}-3047\,a^5\,b^{18}+903\,a^4\,b^{19}+1222\,a^3\,b^{20}-322\,a^2\,b^{21}-384\,a\,b^{22}+128\,b^{23}\right)}{b^{16}}+\frac{\left(\frac{128\,\left(-192\,a^{10}\,b^{14}+416\,a^9\,b^{15}+288\,a^8\,b^{16}-1176\,a^7\,b^{17}+280\,a^6\,b^{18}+1016\,a^5\,b^{19}-568\,a^4\,b^{20}-256\,a^3\,b^{21}+192\,a^2\,b^{22}\right)}{b^{16}}+\frac{128\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(-128\,a^7\,b^{18}+384\,a^6\,b^{19}-512\,a^5\,b^{20}+512\,a^4\,b^{21}-384\,a^3\,b^{22}+128\,a^2\,b^{23}\right)}{a\,b^{21}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a\,b^5\,d}","Not used",1,"((tan(c/2 + (d*x)/2)*(16*a*b^2 + 4*a^2*b - 8*a^3 - 7*b^3))/(4*b^4) - (tan(c/2 + (d*x)/2)^7*(16*a*b^2 - 4*a^2*b - 8*a^3 + 7*b^3))/(4*b^4) - (tan(c/2 + (d*x)/2)^3*(176*a*b^2 + 12*a^2*b - 72*a^3 - 45*b^3))/(12*b^4) + (tan(c/2 + (d*x)/2)^5*(176*a*b^2 - 12*a^2*b - 72*a^3 + 45*b^3))/(12*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)) + (2*atan((((((((((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 - (tan(c/2 + (d*x)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18)*128i)/(a*b^16))*1i)/a - (128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16)*1i)/a - (128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16)*1i)/a - (128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16)/a - ((((((((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 + (tan(c/2 + (d*x)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18)*128i)/(a*b^16))*1i)/a + (128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16)*1i)/a - (128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16)*1i)/a + (128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16)/a)/((((((((((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 - (tan(c/2 + (d*x)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18)*128i)/(a*b^16))*1i)/a - (128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16)*1i)/a - (128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16)*1i)/a - (128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16)*1i)/a + (((((((((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 + (tan(c/2 + (d*x)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18)*128i)/(a*b^16))*1i)/a + (128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16)*1i)/a - (128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16)*1i)/a + (128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16)*1i)/a - (256*(64*a^19*b - 2145*a*b^19 - 64*a^20 + 795*b^20 - 3130*a^2*b^18 + 12805*a^3*b^17 + 2569*a^4*b^16 - 33634*a^5*b^15 + 7876*a^6*b^14 + 51074*a^7*b^13 - 23883*a^8*b^12 - 49501*a^9*b^11 + 30942*a^10*b^10 + 31881*a^11*b^9 - 23865*a^12*b^8 - 13776*a^13*b^7 + 11768*a^14*b^6 + 3936*a^15*b^5 - 3712*a^16*b^4 - 704*a^17*b^3 + 704*a^18*b^2))/b^16)))/(a*d) + (atan(((((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 + (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 + (((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 - (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 - (128*tan(c/2 + (d*x)/2)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/b^21)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2)*1i)/b^5 + (((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 - (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 - (((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 + (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 + (128*tan(c/2 + (d*x)/2)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/b^21)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2)*1i)/b^5)/((256*(64*a^19*b - 2145*a*b^19 - 64*a^20 + 795*b^20 - 3130*a^2*b^18 + 12805*a^3*b^17 + 2569*a^4*b^16 - 33634*a^5*b^15 + 7876*a^6*b^14 + 51074*a^7*b^13 - 23883*a^8*b^12 - 49501*a^9*b^11 + 30942*a^10*b^10 + 31881*a^11*b^9 - 23865*a^12*b^8 - 13776*a^13*b^7 + 11768*a^14*b^6 + 3936*a^15*b^5 - 3712*a^16*b^4 - 704*a^17*b^3 + 704*a^18*b^2))/b^16 + (((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 + (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 + (((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 - (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 - (128*tan(c/2 + (d*x)/2)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/b^21)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5 - (((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 - (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 - (((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 + (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 + (128*tan(c/2 + (d*x)/2)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/b^21)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5)*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5))*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2)*2i)/(b^5*d) + (atan(((((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 + (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 + (((a + b)^5*(a - b)^5)^(1/2)*((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 - (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 - (128*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/(a*b^21))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2)*1i)/(a*b^5) + (((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 - (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 - (((a + b)^5*(a - b)^5)^(1/2)*((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 + (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 + (128*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/(a*b^21))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2)*1i)/(a*b^5))/((256*(64*a^19*b - 2145*a*b^19 - 64*a^20 + 795*b^20 - 3130*a^2*b^18 + 12805*a^3*b^17 + 2569*a^4*b^16 - 33634*a^5*b^15 + 7876*a^6*b^14 + 51074*a^7*b^13 - 23883*a^8*b^12 - 49501*a^9*b^11 + 30942*a^10*b^10 + 31881*a^11*b^9 - 23865*a^12*b^8 - 13776*a^13*b^7 + 11768*a^14*b^6 + 3936*a^15*b^5 - 3712*a^16*b^4 - 704*a^17*b^3 + 704*a^18*b^2))/b^16 + (((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 + (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 + (((a + b)^5*(a - b)^5)^(1/2)*((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 - (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 - (128*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/(a*b^21))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5) - (((128*tan(c/2 + (d*x)/2)*(1414*a*b^20 - 64*a^20*b + 64*a^21 - 514*b^21 + 684*a^2*b^19 - 3084*a^3*b^18 - 4340*a^4*b^17 + 6000*a^5*b^16 + 15860*a^6*b^15 - 14740*a^7*b^14 - 27983*a^8*b^13 + 25679*a^9*b^12 + 29678*a^10*b^11 - 28398*a^11*b^10 - 21169*a^12*b^9 + 20913*a^13*b^8 + 10520*a^14*b^7 - 10520*a^15*b^6 - 3520*a^16*b^5 + 3520*a^17*b^4 + 704*a^18*b^3 - 704*a^19*b^2))/b^16 - (((128*(576*a*b^21 - 192*b^22 + 1043*a^2*b^20 - 2996*a^3*b^19 - 3575*a^4*b^18 + 8886*a^5*b^17 + 7376*a^6*b^16 - 18310*a^7*b^15 - 7672*a^8*b^14 + 24883*a^9*b^13 + 2308*a^10*b^12 - 21295*a^11*b^11 + 2736*a^12*b^10 + 11096*a^13*b^9 - 3080*a^14*b^8 - 3256*a^15*b^7 + 1248*a^16*b^6 + 416*a^17*b^5 - 192*a^18*b^4))/b^16 - (((a + b)^5*(a - b)^5)^(1/2)*((128*tan(c/2 + (d*x)/2)*(128*b^23 - 384*a*b^22 - 322*a^2*b^21 + 1222*a^3*b^20 + 903*a^4*b^19 - 3047*a^5*b^18 + 755*a^6*b^17 + 905*a^7*b^16 + 120*a^8*b^15 + 1000*a^9*b^14 - 1792*a^10*b^13 - 512*a^11*b^12 + 1472*a^12*b^11 - 192*a^13*b^10 - 384*a^14*b^9 + 128*a^15*b^8))/b^16 + (((128*(192*a^2*b^22 - 256*a^3*b^21 - 568*a^4*b^20 + 1016*a^5*b^19 + 280*a^6*b^18 - 1176*a^7*b^17 + 288*a^8*b^16 + 416*a^9*b^15 - 192*a^10*b^14))/b^16 + (128*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(128*a^2*b^23 - 384*a^3*b^22 + 512*a^4*b^21 - 512*a^5*b^20 + 384*a^6*b^19 - 128*a^7*b^18))/(a*b^21))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5))*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))*((a + b)^5*(a - b)^5)^(1/2)*2i)/(a*b^5*d)","B"
295,1,6062,126,3.291819,"\text{Not used}","int(tan(c + d*x)^4/(a + b/cos(c + d*x)),x)","\frac{\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,3{}\mathrm{i}}{b\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{\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)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,3{}\mathrm{i}}{b\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{2\,\mathrm{atan}\left(\frac{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b-24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2-24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+57\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+57\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-59\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-59\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{12}+4\,a^{11}\,b-24\,a^{10}\,b^2-24\,a^9\,b^3+57\,a^8\,b^4+57\,a^7\,b^5-59\,a^6\,b^6-59\,a^5\,b^7+15\,a^4\,b^8+15\,a^3\,b^9+12\,a^2\,b^{10}+12\,a\,b^{11}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{2\,\mathrm{atan}\left(\frac{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b-24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2-24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+57\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+57\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-59\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-59\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{12}+4\,a^{11}\,b-24\,a^{10}\,b^2-24\,a^9\,b^3+57\,a^8\,b^4+57\,a^7\,b^5-59\,a^6\,b^6-59\,a^5\,b^7+15\,a^4\,b^8+15\,a^3\,b^9+12\,a^2\,b^{10}+12\,a\,b^{11}\right)}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,2{}\mathrm{i}}{b^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,2{}\mathrm{i}}{b^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,6{}\mathrm{i}}{b\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{2\,a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{b^2\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{2\,a\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{b^2\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{4\,\mathrm{atan}\left(\frac{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{13}+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{12}\,b-24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{11}\,b^2-24\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^{10}\,b^3+57\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^9\,b^4+57\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8\,b^5-59\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b^6-59\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^7+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^8+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^9+12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^{10}+12\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^{11}}{a\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^{12}+4\,a^{11}\,b-24\,a^{10}\,b^2-24\,a^9\,b^3+57\,a^8\,b^4+57\,a^7\,b^5-59\,a^6\,b^6-59\,a^5\,b^7+15\,a^4\,b^8+15\,a^3\,b^9+12\,a^2\,b^{10}+12\,a\,b^{11}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,1{}\mathrm{i}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,4{}\mathrm{i}}{b^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{\mathrm{atan}\left(\frac{\left(8\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-8\,a^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-26\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-6\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+21\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+9\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+12\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-20\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-22\,a^2\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+14\,a^3\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+36\,a^4\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+24\,a^5\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-47\,a^6\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-79\,a^7\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+49\,a^8\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+65\,a^9\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-24\,a^{10}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-24\,a^{11}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+4\,a^{12}\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+4\,a^{13}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-8\,a\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}-8\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-8\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}\right)\,1{}\mathrm{i}}{a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3\,a^{13}\,b^3+6\,a^{12}\,b^4+16\,a^{11}\,b^5-38\,a^{10}\,b^6-31\,a^9\,b^7+100\,a^8\,b^8+17\,a^7\,b^9-134\,a^6\,b^{10}+22\,a^5\,b^{11}+90\,a^4\,b^{12}-33\,a^3\,b^{13}-24\,a^2\,b^{14}+12\,a\,b^{15}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a\,b^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{\mathrm{atan}\left(\frac{\left(8\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-8\,a^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-26\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-6\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+21\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+9\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+12\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-20\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-22\,a^2\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+14\,a^3\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+36\,a^4\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+24\,a^5\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-47\,a^6\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-79\,a^7\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+49\,a^8\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+65\,a^9\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-24\,a^{10}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-24\,a^{11}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+4\,a^{12}\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+4\,a^{13}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-8\,a\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}-8\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-8\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}\right)\,1{}\mathrm{i}}{a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3\,a^{13}\,b^3+6\,a^{12}\,b^4+16\,a^{11}\,b^5-38\,a^{10}\,b^6-31\,a^9\,b^7+100\,a^8\,b^8+17\,a^7\,b^9-134\,a^6\,b^{10}+22\,a^5\,b^{11}+90\,a^4\,b^{12}-33\,a^3\,b^{13}-24\,a^2\,b^{14}+12\,a\,b^{15}\right)}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a\,b^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{\mathrm{atan}\left(\frac{\left(8\,a^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-8\,a^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-26\,a^2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-6\,a^3\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+21\,a^4\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+9\,a^5\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+12\,a^6\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-20\,a^7\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-22\,a^2\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+14\,a^3\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+36\,a^4\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+24\,a^5\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-47\,a^6\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-79\,a^7\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+49\,a^8\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+65\,a^9\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-24\,a^{10}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-24\,a^{11}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+4\,a^{12}\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+4\,a^{13}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-8\,a\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}+8\,a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{5/2}-8\,a\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-8\,a^8\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}\right)\,1{}\mathrm{i}}{a\,b\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3\,a^{13}\,b^3+6\,a^{12}\,b^4+16\,a^{11}\,b^5-38\,a^{10}\,b^6-31\,a^9\,b^7+100\,a^8\,b^8+17\,a^7\,b^9-134\,a^6\,b^{10}+22\,a^5\,b^{11}+90\,a^4\,b^{12}-33\,a^3\,b^{13}-24\,a^2\,b^{14}+12\,a\,b^{15}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,4{}\mathrm{i}}{a\,b^3\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}","Not used",1,"(atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^4*3i)/(b*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*sin(c/2 + (d*x)/2)^4*3i)/(b*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^3)/(b*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2))/(b*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (2*atan((4*a^13*sin(c/2 + (d*x)/2) + 4*a^12*b*sin(c/2 + (d*x)/2) + 12*a^2*b^11*sin(c/2 + (d*x)/2) + 12*a^3*b^10*sin(c/2 + (d*x)/2) + 15*a^4*b^9*sin(c/2 + (d*x)/2) + 15*a^5*b^8*sin(c/2 + (d*x)/2) - 59*a^6*b^7*sin(c/2 + (d*x)/2) - 59*a^7*b^6*sin(c/2 + (d*x)/2) + 57*a^8*b^5*sin(c/2 + (d*x)/2) + 57*a^9*b^4*sin(c/2 + (d*x)/2) - 24*a^10*b^3*sin(c/2 + (d*x)/2) - 24*a^11*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(12*a*b^11 + 4*a^11*b + 4*a^12 + 12*a^2*b^10 + 15*a^3*b^9 + 15*a^4*b^8 - 59*a^5*b^7 - 59*a^6*b^6 + 57*a^7*b^5 + 57*a^8*b^4 - 24*a^9*b^3 - 24*a^10*b^2)))*cos(c/2 + (d*x)/2)^4)/(a*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (2*atan((4*a^13*sin(c/2 + (d*x)/2) + 4*a^12*b*sin(c/2 + (d*x)/2) + 12*a^2*b^11*sin(c/2 + (d*x)/2) + 12*a^3*b^10*sin(c/2 + (d*x)/2) + 15*a^4*b^9*sin(c/2 + (d*x)/2) + 15*a^5*b^8*sin(c/2 + (d*x)/2) - 59*a^6*b^7*sin(c/2 + (d*x)/2) - 59*a^7*b^6*sin(c/2 + (d*x)/2) + 57*a^8*b^5*sin(c/2 + (d*x)/2) + 57*a^9*b^4*sin(c/2 + (d*x)/2) - 24*a^10*b^3*sin(c/2 + (d*x)/2) - 24*a^11*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(12*a*b^11 + 4*a^11*b + 4*a^12 + 12*a^2*b^10 + 15*a^3*b^9 + 15*a^4*b^8 - 59*a^5*b^7 - 59*a^6*b^6 + 57*a^7*b^5 + 57*a^8*b^4 - 24*a^9*b^3 - 24*a^10*b^2)))*sin(c/2 + (d*x)/2)^4)/(a*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) - (a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^4*2i)/(b^3*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) - (a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*sin(c/2 + (d*x)/2)^4*2i)/(b^3*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) - (atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2*6i)/(b*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (2*a*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^3)/(b^2*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) - (2*a*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2))/(b^2*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) - (4*atan((4*a^13*sin(c/2 + (d*x)/2) + 4*a^12*b*sin(c/2 + (d*x)/2) + 12*a^2*b^11*sin(c/2 + (d*x)/2) + 12*a^3*b^10*sin(c/2 + (d*x)/2) + 15*a^4*b^9*sin(c/2 + (d*x)/2) + 15*a^5*b^8*sin(c/2 + (d*x)/2) - 59*a^6*b^7*sin(c/2 + (d*x)/2) - 59*a^7*b^6*sin(c/2 + (d*x)/2) + 57*a^8*b^5*sin(c/2 + (d*x)/2) + 57*a^9*b^4*sin(c/2 + (d*x)/2) - 24*a^10*b^3*sin(c/2 + (d*x)/2) - 24*a^11*b^2*sin(c/2 + (d*x)/2))/(a*cos(c/2 + (d*x)/2)*(12*a*b^11 + 4*a^11*b + 4*a^12 + 12*a^2*b^10 + 15*a^3*b^9 + 15*a^4*b^8 - 59*a^5*b^7 - 59*a^6*b^6 + 57*a^7*b^5 + 57*a^8*b^4 - 24*a^9*b^3 - 24*a^10*b^2)))*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)/(a*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (a^2*atan((sin(c/2 + (d*x)/2)*1i)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2*4i)/(b^3*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (atan(((8*a^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 8*a^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*b^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 26*a^2*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 6*a^3*b^6*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 21*a^4*b^5*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 9*a^5*b^4*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 12*a^6*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 20*a^7*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 22*a^2*b^13*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 14*a^3*b^12*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 36*a^4*b^11*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 24*a^5*b^10*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 47*a^6*b^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 79*a^7*b^8*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 49*a^8*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 65*a^9*b^6*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 24*a^10*b^5*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 24*a^11*b^4*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 4*a^12*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 4*a^13*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 8*a*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*a^2*b*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) - 8*a*b^8*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 8*a^8*b*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2))*1i)/(a*b*cos(c/2 + (d*x)/2)*(12*a*b^15 - 24*a^2*b^14 - 33*a^3*b^13 + 90*a^4*b^12 + 22*a^5*b^11 - 134*a^6*b^10 + 17*a^7*b^9 + 100*a^8*b^8 - 31*a^9*b^7 - 38*a^10*b^6 + 16*a^11*b^5 + 6*a^12*b^4 - 3*a^13*b^3)))*cos(c/2 + (d*x)/2)^4*((a + b)^3*(a - b)^3)^(1/2)*2i)/(a*b^3*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) + (atan(((8*a^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 8*a^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*b^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 26*a^2*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 6*a^3*b^6*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 21*a^4*b^5*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 9*a^5*b^4*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 12*a^6*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 20*a^7*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 22*a^2*b^13*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 14*a^3*b^12*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 36*a^4*b^11*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 24*a^5*b^10*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 47*a^6*b^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 79*a^7*b^8*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 49*a^8*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 65*a^9*b^6*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 24*a^10*b^5*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 24*a^11*b^4*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 4*a^12*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 4*a^13*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 8*a*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*a^2*b*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) - 8*a*b^8*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 8*a^8*b*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2))*1i)/(a*b*cos(c/2 + (d*x)/2)*(12*a*b^15 - 24*a^2*b^14 - 33*a^3*b^13 + 90*a^4*b^12 + 22*a^5*b^11 - 134*a^6*b^10 + 17*a^7*b^9 + 100*a^8*b^8 - 31*a^9*b^7 - 38*a^10*b^6 + 16*a^11*b^5 + 6*a^12*b^4 - 3*a^13*b^3)))*sin(c/2 + (d*x)/2)^4*((a + b)^3*(a - b)^3)^(1/2)*2i)/(a*b^3*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2)) - (atan(((8*a^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 8*a^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*b^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 26*a^2*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 6*a^3*b^6*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 21*a^4*b^5*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 9*a^5*b^4*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 12*a^6*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 20*a^7*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 22*a^2*b^13*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 14*a^3*b^12*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 36*a^4*b^11*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 24*a^5*b^10*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 47*a^6*b^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 79*a^7*b^8*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 49*a^8*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 65*a^9*b^6*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 24*a^10*b^5*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 24*a^11*b^4*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 4*a^12*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 4*a^13*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 8*a*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) + 8*a^2*b*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(5/2) - 8*a*b^8*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 8*a^8*b*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2))*1i)/(a*b*cos(c/2 + (d*x)/2)*(12*a*b^15 - 24*a^2*b^14 - 33*a^3*b^13 + 90*a^4*b^12 + 22*a^5*b^11 - 134*a^6*b^10 + 17*a^7*b^9 + 100*a^8*b^8 - 31*a^9*b^7 - 38*a^10*b^6 + 16*a^11*b^5 + 6*a^12*b^4 - 3*a^13*b^3)))*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2*((a + b)^3*(a - b)^3)^(1/2)*4i)/(a*b^3*d*(cos(c/2 + (d*x)/2)^4 + sin(c/2 + (d*x)/2)^4 - 2*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^2))","B"
296,1,121,76,1.625345,"\text{Not used}","int(tan(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\,\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\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)}\right)\,\sqrt{a^2-b^2}}{a\,b\,d}","Not used",1,"(2*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(b*d) - (2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a*d) - (2*atanh((sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a + b)))*(a^2 - b^2)^(1/2))/(a*b*d)","B"
297,1,1002,106,3.939730,"\text{Not used}","int(cot(c + d*x)^2/(a + b/cos(c + d*x)),x)","-\frac{1{}\mathrm{i}\,\cos\left(c+d\,x\right)\,a^6-a^5\,b\,1{}\mathrm{i}-2{}\mathrm{i}\,\cos\left(c+d\,x\right)\,a^4\,b^2+a^3\,b^3\,2{}\mathrm{i}+1{}\mathrm{i}\,\cos\left(c+d\,x\right)\,a^2\,b^4-a\,b^5\,1{}\mathrm{i}}{1{}\mathrm{i}\,d\,\sin\left(c+d\,x\right)\,a^7-3{}\mathrm{i}\,d\,\sin\left(c+d\,x\right)\,a^5\,b^2+3{}\mathrm{i}\,d\,\sin\left(c+d\,x\right)\,a^3\,b^4-1{}\mathrm{i}\,d\,\sin\left(c+d\,x\right)\,a\,b^6}+\frac{-a^6\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}+b^6\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,2{}\mathrm{i}-a^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)\,6{}\mathrm{i}+a^4\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}+b^3\,\mathrm{atanh}\left(\frac{2\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-a^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+2\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-9\,a^2\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+3\,a^3\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+18\,a^4\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-12\,a^5\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-21\,a^6\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+19\,a^7\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+15\,a^8\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-15\,a^9\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-6\,a^{10}\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+6\,a^{11}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+a^{12}\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{16}-8\,a^{14}\,b^2+28\,a^{12}\,b^4-55\,a^{10}\,b^6+65\,a^8\,b^8-46\,a^6\,b^{10}+18\,a^4\,b^{12}-3\,a^2\,b^{14}\right)}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}\,2{}\mathrm{i}}{1{}\mathrm{i}\,d\,a^7-3{}\mathrm{i}\,d\,a^5\,b^2+3{}\mathrm{i}\,d\,a^3\,b^4-1{}\mathrm{i}\,d\,a\,b^6}","Not used",1,"(b^6*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*2i - a^6*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*2i - a^2*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*6i + a^4*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*6i + b^3*atanh((2*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - a^13*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 2*b^13*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 9*a^2*b^11*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 3*a^3*b^10*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 18*a^4*b^9*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 12*a^5*b^8*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 21*a^6*b^7*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 19*a^7*b^6*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 15*a^8*b^5*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 15*a^9*b^4*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 6*a^10*b^3*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 6*a^11*b^2*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + a^12*b*sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a^16 - 3*a^2*b^14 + 18*a^4*b^12 - 46*a^6*b^10 + 65*a^8*b^8 - 55*a^10*b^6 + 28*a^12*b^4 - 8*a^14*b^2)))*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2)*2i)/(a^7*d*1i + a^3*b^4*d*3i - a^5*b^2*d*3i - a*b^6*d*1i) - (a^6*cos(c + d*x)*1i - a*b^5*1i - a^5*b*1i + a^3*b^3*2i + a^2*b^4*cos(c + d*x)*1i - a^4*b^2*cos(c + d*x)*2i)/(a^7*d*sin(c + d*x)*1i - a*b^6*d*sin(c + d*x)*1i + a^3*b^4*d*sin(c + d*x)*3i - a^5*b^2*d*sin(c + d*x)*3i)","B"
298,1,3859,177,11.108975,"\text{Not used}","int(cot(c + d*x)^4/(a + b/cos(c + d*x)),x)","\frac{a^{10}\,\left(\frac{\cos\left(3\,c+3\,d\,x\right)\,4{}\mathrm{i}}{3}-\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}+\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)\,\sin\left(3\,c+3\,d\,x\right)\,2{}\mathrm{i}\right)+a\,\left(\frac{b^9\,8{}\mathrm{i}}{3}-b^9\,\cos\left(2\,c+2\,d\,x\right)\,4{}\mathrm{i}\right)-a^7\,\left(\frac{b^3\,14{}\mathrm{i}}{3}-b^3\,\cos\left(2\,c+2\,d\,x\right)\,10{}\mathrm{i}\right)+a^5\,\left(b^5\,10{}\mathrm{i}-b^5\,\cos\left(2\,c+2\,d\,x\right)\,18{}\mathrm{i}\right)-a^3\,\left(\frac{b^7\,26{}\mathrm{i}}{3}-b^7\,\cos\left(2\,c+2\,d\,x\right)\,14{}\mathrm{i}\right)+a^9\,\left(\frac{b\,2{}\mathrm{i}}{3}-b\,\cos\left(2\,c+2\,d\,x\right)\,2{}\mathrm{i}\right)+a^8\,\left(b^2\,\cos\left(c+d\,x\right)\,1{}\mathrm{i}-\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)\,19{}\mathrm{i}}{3}+b^2\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,30{}\mathrm{i}-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)\,\sin\left(3\,c+3\,d\,x\right)\,10{}\mathrm{i}\right)-a^2\,\left(b^8\,\cos\left(c+d\,x\right)\,1{}\mathrm{i}-\frac{b^8\,\cos\left(3\,c+3\,d\,x\right)\,7{}\mathrm{i}}{3}+b^8\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,30{}\mathrm{i}-b^8\,\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)\,\sin\left(3\,c+3\,d\,x\right)\,10{}\mathrm{i}\right)-a^6\,\left(b^4\,\cos\left(c+d\,x\right)\,3{}\mathrm{i}-b^4\,\cos\left(3\,c+3\,d\,x\right)\,11{}\mathrm{i}+b^4\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,60{}\mathrm{i}-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)\,\sin\left(3\,c+3\,d\,x\right)\,20{}\mathrm{i}\right)+a^4\,\left(b^6\,\cos\left(c+d\,x\right)\,3{}\mathrm{i}-\frac{b^6\,\cos\left(3\,c+3\,d\,x\right)\,25{}\mathrm{i}}{3}+b^6\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,60{}\mathrm{i}-b^6\,\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)\,\sin\left(3\,c+3\,d\,x\right)\,20{}\mathrm{i}\right)+b^{10}\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,6{}\mathrm{i}-b^{10}\,\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)\,\sin\left(3\,c+3\,d\,x\right)\,2{}\mathrm{i}+b^5\,\mathrm{atanh}\left(\frac{2\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}^{3/2}-a^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+2\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+a^{20}\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-15\,a^2\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+5\,a^3\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+55\,a^4\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-35\,a^5\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-130\,a^6\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+110\,a^7\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+215\,a^8\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-205\,a^9\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-253\,a^{10}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+251\,a^{11}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+210\,a^{12}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-210\,a^{13}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-120\,a^{14}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+120\,a^{15}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+45\,a^{16}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-45\,a^{17}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-10\,a^{18}\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+10\,a^{19}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{26}-13\,a^{24}\,b^2+78\,a^{22}\,b^4-286\,a^{20}\,b^6+715\,a^{18}\,b^8-1286\,a^{16}\,b^{10}+1708\,a^{14}\,b^{12}-1688\,a^{12}\,b^{14}+1231\,a^{10}\,b^{16}-645\,a^8\,b^{18}+230\,a^6\,b^{20}-50\,a^4\,b^{22}+5\,a^2\,b^{24}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}\,2{}\mathrm{i}-b^5\,\mathrm{atanh}\left(\frac{2\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}\right)}^{3/2}-a^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+2\,b^{21}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+a^{20}\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-15\,a^2\,b^{19}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+5\,a^3\,b^{18}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+55\,a^4\,b^{17}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-35\,a^5\,b^{16}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-130\,a^6\,b^{15}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+110\,a^7\,b^{14}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+215\,a^8\,b^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-205\,a^9\,b^{12}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-253\,a^{10}\,b^{11}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+251\,a^{11}\,b^{10}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+210\,a^{12}\,b^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-210\,a^{13}\,b^8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-120\,a^{14}\,b^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+120\,a^{15}\,b^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+45\,a^{16}\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-45\,a^{17}\,b^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}-10\,a^{18}\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}+10\,a^{19}\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{26}-13\,a^{24}\,b^2+78\,a^{22}\,b^4-286\,a^{20}\,b^6+715\,a^{18}\,b^8-1286\,a^{16}\,b^{10}+1708\,a^{14}\,b^{12}-1688\,a^{12}\,b^{14}+1231\,a^{10}\,b^{16}-645\,a^8\,b^{18}+230\,a^6\,b^{20}-50\,a^4\,b^{22}+5\,a^2\,b^{24}\right)}\right)\,\sin\left(c+d\,x\right)\,\sqrt{a^{10}-5\,a^8\,b^2+10\,a^6\,b^4-10\,a^4\,b^6+5\,a^2\,b^8-b^{10}}\,6{}\mathrm{i}}{a^{11}\,d\,\sin\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}-a^{11}\,d\,\sin\left(c+d\,x\right)\,3{}\mathrm{i}+a^3\,b^8\,d\,\sin\left(3\,c+3\,d\,x\right)\,5{}\mathrm{i}-a^5\,b^6\,d\,\sin\left(3\,c+3\,d\,x\right)\,10{}\mathrm{i}+a^7\,b^4\,d\,\sin\left(3\,c+3\,d\,x\right)\,10{}\mathrm{i}-a^9\,b^2\,d\,\sin\left(3\,c+3\,d\,x\right)\,5{}\mathrm{i}+a\,b^{10}\,d\,\sin\left(c+d\,x\right)\,3{}\mathrm{i}-a\,b^{10}\,d\,\sin\left(3\,c+3\,d\,x\right)\,1{}\mathrm{i}-a^3\,b^8\,d\,\sin\left(c+d\,x\right)\,15{}\mathrm{i}+a^5\,b^6\,d\,\sin\left(c+d\,x\right)\,30{}\mathrm{i}-a^7\,b^4\,d\,\sin\left(c+d\,x\right)\,30{}\mathrm{i}+a^9\,b^2\,d\,\sin\left(c+d\,x\right)\,15{}\mathrm{i}}","Not used",1,"(a^10*((cos(3*c + 3*d*x)*4i)/3 - sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*6i + atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x)*2i) + a*((b^9*8i)/3 - b^9*cos(2*c + 2*d*x)*4i) - a^7*((b^3*14i)/3 - b^3*cos(2*c + 2*d*x)*10i) + a^5*(b^5*10i - b^5*cos(2*c + 2*d*x)*18i) - a^3*((b^7*26i)/3 - b^7*cos(2*c + 2*d*x)*14i) + a^9*((b*2i)/3 - b*cos(2*c + 2*d*x)*2i) + a^8*(b^2*cos(c + d*x)*1i - (b^2*cos(3*c + 3*d*x)*19i)/3 + b^2*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*30i - b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x)*10i) - a^2*(b^8*cos(c + d*x)*1i - (b^8*cos(3*c + 3*d*x)*7i)/3 + b^8*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*30i - b^8*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x)*10i) - a^6*(b^4*cos(c + d*x)*3i - b^4*cos(3*c + 3*d*x)*11i + b^4*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*60i - b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x)*20i) + a^4*(b^6*cos(c + d*x)*3i - (b^6*cos(3*c + 3*d*x)*25i)/3 + b^6*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*60i - b^6*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x)*20i) + b^10*sin(c + d*x)*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*6i - b^10*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x)*2i + b^5*atanh((2*b^11*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(3/2) - a^21*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 2*b^21*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + a^20*b*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 15*a^2*b^19*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 5*a^3*b^18*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 55*a^4*b^17*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 35*a^5*b^16*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 130*a^6*b^15*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 110*a^7*b^14*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 215*a^8*b^13*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 205*a^9*b^12*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 253*a^10*b^11*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 251*a^11*b^10*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 210*a^12*b^9*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 210*a^13*b^8*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 120*a^14*b^7*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 120*a^15*b^6*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 45*a^16*b^5*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 45*a^17*b^4*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 10*a^18*b^3*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 10*a^19*b^2*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a^26 + 5*a^2*b^24 - 50*a^4*b^22 + 230*a^6*b^20 - 645*a^8*b^18 + 1231*a^10*b^16 - 1688*a^12*b^14 + 1708*a^14*b^12 - 1286*a^16*b^10 + 715*a^18*b^8 - 286*a^20*b^6 + 78*a^22*b^4 - 13*a^24*b^2)))*sin(3*c + 3*d*x)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2)*2i - b^5*atanh((2*b^11*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(3/2) - a^21*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 2*b^21*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + a^20*b*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 15*a^2*b^19*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 5*a^3*b^18*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 55*a^4*b^17*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 35*a^5*b^16*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 130*a^6*b^15*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 110*a^7*b^14*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 215*a^8*b^13*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 205*a^9*b^12*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 253*a^10*b^11*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 251*a^11*b^10*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 210*a^12*b^9*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 210*a^13*b^8*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 120*a^14*b^7*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 120*a^15*b^6*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 45*a^16*b^5*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 45*a^17*b^4*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) - 10*a^18*b^3*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2) + 10*a^19*b^2*sin(c/2 + (d*x)/2)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a^26 + 5*a^2*b^24 - 50*a^4*b^22 + 230*a^6*b^20 - 645*a^8*b^18 + 1231*a^10*b^16 - 1688*a^12*b^14 + 1708*a^14*b^12 - 1286*a^16*b^10 + 715*a^18*b^8 - 286*a^20*b^6 + 78*a^22*b^4 - 13*a^24*b^2)))*sin(c + d*x)*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2)^(1/2)*6i)/(a^11*d*sin(3*c + 3*d*x)*1i - a^11*d*sin(c + d*x)*3i + a^3*b^8*d*sin(3*c + 3*d*x)*5i - a^5*b^6*d*sin(3*c + 3*d*x)*10i + a^7*b^4*d*sin(3*c + 3*d*x)*10i - a^9*b^2*d*sin(3*c + 3*d*x)*5i + a*b^10*d*sin(c + d*x)*3i - a*b^10*d*sin(3*c + 3*d*x)*1i - a^3*b^8*d*sin(c + d*x)*15i + a^5*b^6*d*sin(c + d*x)*30i - a^7*b^4*d*sin(c + d*x)*30i + a^9*b^2*d*sin(c + d*x)*15i)","B"
299,1,760,255,4.769070,"\text{Not used}","int(tan(c + d*x)^9/(a + b/cos(c + d*x))^2,x)","\frac{\frac{2\,\left(-105\,a^7-105\,a^6\,b+265\,a^5\,b^2+265\,a^4\,b^3-191\,a^3\,b^4-191\,a^2\,b^5+15\,a\,b^6+15\,b^7\right)}{15\,a\,b^7}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(-42\,a^7-7\,a^6\,b+113\,a^5\,b^2+13\,a^4\,b^3-95\,a^3\,b^4-5\,a^2\,b^5+19\,a\,b^6+6\,b^7\right)}{a\,b^7}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-210\,a^7-105\,a^6\,b+523\,a^5\,b^2+244\,a^4\,b^3-362\,a^3\,b^4-145\,a^2\,b^5+7\,a\,b^6+30\,b^7\right)}{3\,a\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-315\,a^7-105\,a^6\,b+809\,a^5\,b^2+223\,a^4\,b^3-613\,a^3\,b^4-99\,a^2\,b^5+91\,a\,b^6+45\,b^7\right)}{3\,a\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-525\,a^7-350\,a^6\,b+1290\,a^5\,b^2+860\,a^4\,b^3-862\,a^3\,b^4-598\,a^2\,b^5+10\,a\,b^6+75\,b^7\right)}{5\,a\,b^7}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-630\,a^7-525\,a^6\,b+1555\,a^5\,b^2+1325\,a^4\,b^3-1067\,a^3\,b^4-955\,a^2\,b^5+45\,a\,b^6+90\,b^7\right)}{15\,a\,b^7}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(-7\,a^7+20\,a^5\,b^2-18\,a^3\,b^4+4\,a\,b^6+b^7\right)}{a\,b^7}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\left(7\,a-5\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\left(9\,b-21\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(35\,a-5\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(-35\,a-5\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(21\,a+9\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-7\,a-5\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,\left(7\,a^6-20\,a^4\,b^2+18\,a^2\,b^4-4\,b^6\right)}{b^8\,d}+\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,{\left(a^2-b^2\right)}^3\,\left(7\,a^2+b^2\right)}{a^2\,b^8\,d}","Not used",1,"((2*(15*a*b^6 - 105*a^6*b - 105*a^7 + 15*b^7 - 191*a^2*b^5 - 191*a^3*b^4 + 265*a^4*b^3 + 265*a^5*b^2))/(15*a*b^7) - (2*tan(c/2 + (d*x)/2)^10*(19*a*b^6 - 7*a^6*b - 42*a^7 + 6*b^7 - 5*a^2*b^5 - 95*a^3*b^4 + 13*a^4*b^3 + 113*a^5*b^2))/(a*b^7) - (4*tan(c/2 + (d*x)/2)^6*(7*a*b^6 - 105*a^6*b - 210*a^7 + 30*b^7 - 145*a^2*b^5 - 362*a^3*b^4 + 244*a^4*b^3 + 523*a^5*b^2))/(3*a*b^7) + (2*tan(c/2 + (d*x)/2)^8*(91*a*b^6 - 105*a^6*b - 315*a^7 + 45*b^7 - 99*a^2*b^5 - 613*a^3*b^4 + 223*a^4*b^3 + 809*a^5*b^2))/(3*a*b^7) + (2*tan(c/2 + (d*x)/2)^4*(10*a*b^6 - 350*a^6*b - 525*a^7 + 75*b^7 - 598*a^2*b^5 - 862*a^3*b^4 + 860*a^4*b^3 + 1290*a^5*b^2))/(5*a*b^7) - (2*tan(c/2 + (d*x)/2)^2*(45*a*b^6 - 525*a^6*b - 630*a^7 + 90*b^7 - 955*a^2*b^5 - 1067*a^3*b^4 + 1325*a^4*b^3 + 1555*a^5*b^2))/(15*a*b^7) + (2*tan(c/2 + (d*x)/2)^12*(4*a*b^6 - 7*a^7 + b^7 - 18*a^3*b^4 + 20*a^5*b^2))/(a*b^7))/(d*(a + b - tan(c/2 + (d*x)/2)^14*(a - b) - tan(c/2 + (d*x)/2)^2*(7*a + 5*b) + tan(c/2 + (d*x)/2)^12*(7*a - 5*b) + tan(c/2 + (d*x)/2)^4*(21*a + 9*b) - tan(c/2 + (d*x)/2)^10*(21*a - 9*b) - tan(c/2 + (d*x)/2)^6*(35*a + 5*b) + tan(c/2 + (d*x)/2)^8*(35*a - 5*b))) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - (log(tan(c/2 + (d*x)/2)^2 - 1)*(7*a^6 - 4*b^6 + 18*a^2*b^4 - 20*a^4*b^2))/(b^8*d) + (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^3*(7*a^2 + b^2))/(a^2*b^8*d)","B"
300,1,505,179,3.090291,"\text{Not used}","int(tan(c + d*x)^7/(a + b/cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(20\,a^5+5\,a^4\,b-31\,a^3\,b^2-4\,a^2\,b^3+8\,a\,b^4+4\,b^5\right)}{a\,b^5}-\frac{2\,\left(15\,a^5+15\,a^4\,b-22\,a^3\,b^2-22\,a^2\,b^3+3\,a\,b^4+3\,b^5\right)}{3\,a\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(60\,a^5+45\,a^4\,b-83\,a^3\,b^2-66\,a^2\,b^3+6\,a\,b^4+12\,b^5\right)}{3\,a\,b^5}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(90\,a^5+45\,a^4\,b-127\,a^3\,b^2-56\,a^2\,b^3+6\,a\,b^4+18\,b^5\right)}{3\,a\,b^5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a-b\right)\,\left(-5\,a^4-5\,a^3\,b+4\,a^2\,b^2+4\,a\,b^3+b^4\right)}{a\,b^5}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(5\,a-3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(2\,b-10\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(10\,a+2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-5\,a-3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,\left(5\,a^4-9\,a^2\,b^2+3\,b^4\right)}{b^6\,d}+\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,{\left(a^2-b^2\right)}^2\,\left(5\,a^2+b^2\right)}{a^2\,b^6\,d}","Not used",1,"((2*tan(c/2 + (d*x)/2)^6*(8*a*b^4 + 5*a^4*b + 20*a^5 + 4*b^5 - 4*a^2*b^3 - 31*a^3*b^2))/(a*b^5) - (2*(3*a*b^4 + 15*a^4*b + 15*a^5 + 3*b^5 - 22*a^2*b^3 - 22*a^3*b^2))/(3*a*b^5) + (2*tan(c/2 + (d*x)/2)^2*(6*a*b^4 + 45*a^4*b + 60*a^5 + 12*b^5 - 66*a^2*b^3 - 83*a^3*b^2))/(3*a*b^5) - (2*tan(c/2 + (d*x)/2)^4*(6*a*b^4 + 45*a^4*b + 90*a^5 + 18*b^5 - 56*a^2*b^3 - 127*a^3*b^2))/(3*a*b^5) + (2*tan(c/2 + (d*x)/2)^8*(a - b)*(4*a*b^3 - 5*a^3*b - 5*a^4 + b^4 + 4*a^2*b^2))/(a*b^5))/(d*(a + b - tan(c/2 + (d*x)/2)^10*(a - b) - tan(c/2 + (d*x)/2)^2*(5*a + 3*b) + tan(c/2 + (d*x)/2)^4*(10*a + 2*b) + tan(c/2 + (d*x)/2)^8*(5*a - 3*b) - tan(c/2 + (d*x)/2)^6*(10*a - 2*b))) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - (log(tan(c/2 + (d*x)/2)^2 - 1)*(5*a^4 + 3*b^4 - 9*a^2*b^2))/(b^6*d) + (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2)^2*(5*a^2 + b^2))/(a^2*b^6*d)","B"
301,1,286,121,2.127010,"\text{Not used}","int(tan(c + d*x)^5/(a + b/cos(c + d*x))^2,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-6\,a^3-3\,a^2\,b+a\,b^2+2\,b^3\right)}{a\,b^3}-\frac{2\,\left(-3\,a^3-3\,a^2\,b+a\,b^2+b^3\right)}{a\,b^3}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a-b\right)\,\left(3\,a^2+3\,a\,b+b^2\right)}{a\,b^3}}{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{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)\,\left(3\,a^2-2\,b^2\right)}{b^4\,d}-\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(-3\,a^4+2\,a^2\,b^2+b^4\right)}{a^2\,b^4\,d}","Not used",1,"log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - ((2*tan(c/2 + (d*x)/2)^2*(a*b^2 - 3*a^2*b - 6*a^3 + 2*b^3))/(a*b^3) - (2*(a*b^2 - 3*a^2*b - 3*a^3 + b^3))/(a*b^3) + (2*tan(c/2 + (d*x)/2)^4*(a - b)*(3*a*b + 3*a^2 + b^2))/(a*b^3))/(d*(a + b - tan(c/2 + (d*x)/2)^2*(3*a + b) - tan(c/2 + (d*x)/2)^6*(a - b) + tan(c/2 + (d*x)/2)^4*(3*a - b))) - (log(tan(c/2 + (d*x)/2)^2 - 1)*(3*a^2 - 2*b^2))/(b^4*d) - (log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(b^4 - 3*a^4 + 2*a^2*b^2))/(a^2*b^4*d)","B"
302,1,124,74,1.650662,"\text{Not used}","int(tan(c + d*x)^3/(a + b/cos(c + d*x))^2,x)","\frac{\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(\frac{1}{a^2}+\frac{1}{b^2}\right)}{d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}{b^2\,d}-\frac{2\,\left(a+b\right)}{a\,b\,d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"(log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(1/a^2 + 1/b^2))/d - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - log(tan(c/2 + (d*x)/2)^2 - 1)/(b^2*d) - (2*(a + b))/(a*b*d*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
303,1,257,54,1.484485,"\text{Not used}","int(tan(c + d*x)/(a + b/cos(c + d*x))^2,x)","\frac{2\,\mathrm{atanh}\left(\frac{a}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}-\frac{a\,\cos\left(c+d\,x\right)}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}\right)}{a^2\,d}-\frac{b\,\left(a+a\,\cos\left(c+d\,x\right)-2\,a\,\mathrm{atanh}\left(\frac{a}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}-\frac{a\,\cos\left(c+d\,x\right)}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}\right)+2\,a\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{a}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}-\frac{a\,\cos\left(c+d\,x\right)}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}\right)+\frac{2\,\mathrm{atanh}\left(\frac{a}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}-\frac{a\,\cos\left(c+d\,x\right)}{2\,\left(\frac{a}{2}+b+\frac{a\,\cos\left(c+d\,x\right)}{2}\right)}\right)\,\left(a^3\,d-a^3\,d\,\cos\left(c+d\,x\right)\right)}{a^2\,d}\right)}{a^2\,d\,\left(a-b\right)\,\left(b+a\,\cos\left(c+d\,x\right)\right)}","Not used",1,"(2*atanh(a/(2*(a/2 + b + (a*cos(c + d*x))/2)) - (a*cos(c + d*x))/(2*(a/2 + b + (a*cos(c + d*x))/2))))/(a^2*d) - (b*(a + a*cos(c + d*x) - 2*a*atanh(a/(2*(a/2 + b + (a*cos(c + d*x))/2)) - (a*cos(c + d*x))/(2*(a/2 + b + (a*cos(c + d*x))/2))) + 2*a*cos(c + d*x)*atanh(a/(2*(a/2 + b + (a*cos(c + d*x))/2)) - (a*cos(c + d*x))/(2*(a/2 + b + (a*cos(c + d*x))/2))) + (2*atanh(a/(2*(a/2 + b + (a*cos(c + d*x))/2)) - (a*cos(c + d*x))/(2*(a/2 + b + (a*cos(c + d*x))/2)))*(a^3*d - a^3*d*cos(c + d*x)))/(a^2*d)))/(a^2*d*(a - b)*(b + a*cos(c + d*x)))","B"
304,1,160,138,1.977910,"\text{Not used}","int(cot(c + d*x)/(a + b/cos(c + d*x))^2,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d\,\left(a^2+2\,a\,b+b^2\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{b^2\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(3\,a^2-b^2\right)}{a^2\,d\,{\left(a^2-b^2\right)}^2}-\frac{2\,b^3}{a\,d\,\left(a+b\right)\,{\left(a-b\right)}^2\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(d*(2*a*b + a^2 + b^2)) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - (b^2*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(3*a^2 - b^2))/(a^2*d*(a^2 - b^2)^2) - (2*b^3)/(a*d*(a + b)*(a - b)^2*(a + b - tan(c/2 + (d*x)/2)^2*(a - b)))","B"
305,1,313,197,2.484186,"\text{Not used}","int(cot(c + d*x)^3/(a + b/cos(c + d*x))^2,x)","\frac{\frac{a^2-2\,a\,b+b^2}{2\,\left(a+b\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^5-4\,a^4\,b+6\,a^3\,b^2-4\,a^2\,b^3+a\,b^4-16\,b^5\right)}{2\,a\,{\left(a+b\right)}^2\,\left(a-b\right)}}{d\,\left(\left(4\,a^3-12\,a^2\,b+12\,a\,b^2-4\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-4\,a^3+4\,a^2\,b+4\,a\,b^2-4\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d\,{\left(a-b\right)}^2}+\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a+2\,b\right)}{d\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}-\frac{b^4\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(5\,a^2-b^2\right)}{a^2\,d\,{\left(a^2-b^2\right)}^3}","Not used",1,"((a^2 - 2*a*b + b^2)/(2*(a + b)) - (tan(c/2 + (d*x)/2)^2*(a*b^4 - 4*a^4*b + a^5 - 16*b^5 - 4*a^2*b^3 + 6*a^3*b^2))/(2*a*(a + b)^2*(a - b)))/(d*(tan(c/2 + (d*x)/2)^2*(4*a*b^2 + 4*a^2*b - 4*a^3 - 4*b^3) + tan(c/2 + (d*x)/2)^4*(12*a*b^2 - 12*a^2*b + 4*a^3 - 4*b^3))) - tan(c/2 + (d*x)/2)^2/(8*d*(a - b)^2) + log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - (log(tan(c/2 + (d*x)/2))*(a + 2*b))/(d*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) - (b^4*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(5*a^2 - b^2))/(a^2*d*(a^2 - b^2)^3)","B"
306,1,471,278,2.966748,"\text{Not used}","int(cot(c + d*x)^5/(a + b/cos(c + d*x))^2,x)","\frac{\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{4\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-13\,a^4+20\,a^3\,b+18\,a^2\,b^2-44\,a\,b^3+19\,b^4\right)}{4\,{\left(a+b\right)}^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^7-10\,a^6\,b+5\,a^5\,b^2+20\,a^4\,b^3-35\,a^3\,b^4+22\,a^2\,b^5-5\,a\,b^6+32\,b^7\right)}{a\,{\left(a+b\right)}^3\,\left(a-b\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(16\,a^4-64\,a^3\,b+96\,a^2\,b^2-64\,a\,b^3+16\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(16\,a^4-32\,a^3\,b+32\,a\,b^3-16\,b^4\right)\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d\,{\left(a-b\right)}^2}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{16\,a^2+32\,a\,b-48\,b^2}{512\,{\left(a-b\right)}^4}-\frac{7}{32\,{\left(a-b\right)}^2}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(4\,a^2+13\,a\,b+12\,b^2\right)}{d\,\left(4\,a^4+16\,a^3\,b+24\,a^2\,b^2+16\,a\,b^3+4\,b^4\right)}-\frac{b^6\,\ln\left(a+b-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)\,\left(7\,a^2-b^2\right)}{a^2\,d\,{\left(a^2-b^2\right)}^4}","Not used",1,"((3*a*b^2 - 3*a^2*b + a^3 - b^3)/(4*(a + b)) + (tan(c/2 + (d*x)/2)^2*(20*a^3*b - 44*a*b^3 - 13*a^4 + 19*b^4 + 18*a^2*b^2))/(4*(a + b)^2) + (tan(c/2 + (d*x)/2)^4*(3*a^7 - 10*a^6*b - 5*a*b^6 + 32*b^7 + 22*a^2*b^5 - 35*a^3*b^4 + 20*a^4*b^3 + 5*a^5*b^2))/(a*(a + b)^3*(a - b)))/(d*(tan(c/2 + (d*x)/2)^6*(16*a^4 - 64*a^3*b - 64*a*b^3 + 16*b^4 + 96*a^2*b^2) - tan(c/2 + (d*x)/2)^4*(32*a*b^3 - 32*a^3*b + 16*a^4 - 16*b^4))) - tan(c/2 + (d*x)/2)^4/(64*d*(a - b)^2) - log(tan(c/2 + (d*x)/2)^2 + 1)/(a^2*d) - (tan(c/2 + (d*x)/2)^2*((32*a*b + 16*a^2 - 48*b^2)/(512*(a - b)^4) - 7/(32*(a - b)^2)))/d + (log(tan(c/2 + (d*x)/2))*(13*a*b + 4*a^2 + 12*b^2))/(d*(16*a*b^3 + 16*a^3*b + 4*a^4 + 4*b^4 + 24*a^2*b^2)) - (b^6*log(a + b - a*tan(c/2 + (d*x)/2)^2 + b*tan(c/2 + (d*x)/2)^2)*(7*a^2 - b^2))/(a^2*d*(a^2 - b^2)^4)","B"
307,1,9452,200,4.816346,"\text{Not used}","int(tan(c + d*x)^6/(a + b/cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(36\,a^4-6\,a^3\,b-37\,a^2\,b^2+10\,a\,b^3+9\,b^4\right)}{3\,a\,b^4}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^4+6\,a^3\,b-37\,a^2\,b^2-10\,a\,b^3+9\,b^4\right)}{3\,a\,b^4}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^4+2\,a^3\,b-5\,a^2\,b^2-2\,a\,b^3+b^4\right)}{a\,b^4}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a-b\right)\,\left(-4\,a^3-2\,a^2\,b+3\,a\,b^2+b^3\right)}{a\,b^4}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(2\,b-4\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(-4\,a-2\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}-\frac{2\,\mathrm{atan}\left(\frac{\frac{-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{21}-256\,a^{20}\,b-1536\,a^{19}\,b^2+1536\,a^{18}\,b^3+3680\,a^{17}\,b^4-3680\,a^{16}\,b^5-4320\,a^{15}\,b^6+4320\,a^{14}\,b^7+2297\,a^{13}\,b^8-2361\,a^{12}\,b^9+28\,a^{11}\,b^{10}+132\,a^{10}\,b^{11}-624\,a^9\,b^{12}+588\,a^8\,b^{13}+90\,a^7\,b^{14}-250\,a^6\,b^{15}+140\,a^5\,b^{16}-40\,a^4\,b^{17}+4\,a^3\,b^{18}-4\,a^2\,b^{19}+a\,b^{20}-b^{21}\right)}{a^4\,b^{16}}+\frac{\left(\frac{8192\,\left(192\,a^{18}\,b^4-416\,a^{17}\,b^5-528\,a^{16}\,b^6+1696\,a^{15}\,b^7+20\,a^{14}\,b^8-2366\,a^{13}\,b^9+1129\,a^{12}\,b^{10}+1040\,a^{11}\,b^{11}-1088\,a^{10}\,b^{12}+332\,a^9\,b^{13}+192\,a^8\,b^{14}-280\,a^7\,b^{15}+74\,a^6\,b^{16}-26\,a^5\,b^{17}+20\,a^4\,b^{18}+16\,a^3\,b^{19}-8\,a^2\,b^{20}+4\,a\,b^{21}-3\,b^{22}\right)}{a^3\,b^{16}}+\frac{\left(-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{17}\,b^8-96\,a^{16}\,b^9+32\,a^{15}\,b^{10}+128\,a^{14}\,b^{11}-118\,a^{13}\,b^{12}+82\,a^{12}\,b^{13}-100\,a^{11}\,b^{14}-60\,a^{10}\,b^{15}+160\,a^9\,b^{16}-60\,a^8\,b^{17}+12\,a^7\,b^{18}-8\,a^6\,b^{19}-12\,a^5\,b^{20}+12\,a^4\,b^{21}-6\,a^3\,b^{22}+2\,a^2\,b^{23}\right)}{a^4\,b^{16}}+\frac{\left(\frac{8192\,\left(-12\,a^{12}\,b^{14}+26\,a^{11}\,b^{15}+3\,a^{10}\,b^{16}-41\,a^9\,b^{17}+25\,a^8\,b^{18}+6\,a^7\,b^{19}-13\,a^6\,b^{20}+9\,a^5\,b^{21}-3\,a^4\,b^{22}\right)}{a^3\,b^{16}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{18}+6\,a^{10}\,b^{19}-8\,a^9\,b^{20}+8\,a^8\,b^{21}-6\,a^7\,b^{22}+2\,a^6\,b^{23}\right)\,8192{}\mathrm{i}}{a^6\,b^{16}}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}-\frac{\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{21}-256\,a^{20}\,b-1536\,a^{19}\,b^2+1536\,a^{18}\,b^3+3680\,a^{17}\,b^4-3680\,a^{16}\,b^5-4320\,a^{15}\,b^6+4320\,a^{14}\,b^7+2297\,a^{13}\,b^8-2361\,a^{12}\,b^9+28\,a^{11}\,b^{10}+132\,a^{10}\,b^{11}-624\,a^9\,b^{12}+588\,a^8\,b^{13}+90\,a^7\,b^{14}-250\,a^6\,b^{15}+140\,a^5\,b^{16}-40\,a^4\,b^{17}+4\,a^3\,b^{18}-4\,a^2\,b^{19}+a\,b^{20}-b^{21}\right)}{a^4\,b^{16}}+\frac{\left(\frac{8192\,\left(192\,a^{18}\,b^4-416\,a^{17}\,b^5-528\,a^{16}\,b^6+1696\,a^{15}\,b^7+20\,a^{14}\,b^8-2366\,a^{13}\,b^9+1129\,a^{12}\,b^{10}+1040\,a^{11}\,b^{11}-1088\,a^{10}\,b^{12}+332\,a^9\,b^{13}+192\,a^8\,b^{14}-280\,a^7\,b^{15}+74\,a^6\,b^{16}-26\,a^5\,b^{17}+20\,a^4\,b^{18}+16\,a^3\,b^{19}-8\,a^2\,b^{20}+4\,a\,b^{21}-3\,b^{22}\right)}{a^3\,b^{16}}+\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{17}\,b^8-96\,a^{16}\,b^9+32\,a^{15}\,b^{10}+128\,a^{14}\,b^{11}-118\,a^{13}\,b^{12}+82\,a^{12}\,b^{13}-100\,a^{11}\,b^{14}-60\,a^{10}\,b^{15}+160\,a^9\,b^{16}-60\,a^8\,b^{17}+12\,a^7\,b^{18}-8\,a^6\,b^{19}-12\,a^5\,b^{20}+12\,a^4\,b^{21}-6\,a^3\,b^{22}+2\,a^2\,b^{23}\right)}{a^4\,b^{16}}+\frac{\left(\frac{8192\,\left(-12\,a^{12}\,b^{14}+26\,a^{11}\,b^{15}+3\,a^{10}\,b^{16}-41\,a^9\,b^{17}+25\,a^8\,b^{18}+6\,a^7\,b^{19}-13\,a^6\,b^{20}+9\,a^5\,b^{21}-3\,a^4\,b^{22}\right)}{a^3\,b^{16}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{18}+6\,a^{10}\,b^{19}-8\,a^9\,b^{20}+8\,a^8\,b^{21}-6\,a^7\,b^{22}+2\,a^6\,b^{23}\right)\,8192{}\mathrm{i}}{a^6\,b^{16}}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}}{-\frac{16384\,\left(256\,a^{18}-256\,a^{17}\,b-1536\,a^{16}\,b^2+1536\,a^{15}\,b^3+3488\,a^{14}\,b^4-3264\,a^{13}\,b^5-3792\,a^{12}\,b^6+2624\,a^{11}\,b^7+2245\,a^{10}\,b^8+101\,a^9\,b^9-1133\,a^8\,b^{10}-1036\,a^7\,b^{11}+582\,a^6\,b^{12}+174\,a^5\,b^{13}-14\,a^4\,b^{14}+116\,a^3\,b^{15}-91\,a^2\,b^{16}+5\,a\,b^{17}-5\,b^{18}\right)}{a^3\,b^{16}}+\frac{\left(-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{21}-256\,a^{20}\,b-1536\,a^{19}\,b^2+1536\,a^{18}\,b^3+3680\,a^{17}\,b^4-3680\,a^{16}\,b^5-4320\,a^{15}\,b^6+4320\,a^{14}\,b^7+2297\,a^{13}\,b^8-2361\,a^{12}\,b^9+28\,a^{11}\,b^{10}+132\,a^{10}\,b^{11}-624\,a^9\,b^{12}+588\,a^8\,b^{13}+90\,a^7\,b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,b^{14}-60\,a^{10}\,b^{15}+160\,a^9\,b^{16}-60\,a^8\,b^{17}+12\,a^7\,b^{18}-8\,a^6\,b^{19}-12\,a^5\,b^{20}+12\,a^4\,b^{21}-6\,a^3\,b^{22}+2\,a^2\,b^{23}\right)}{a^4\,b^{16}}-\frac{a\,\left(\frac{8192\,\left(-12\,a^{12}\,b^{14}+26\,a^{11}\,b^{15}+3\,a^{10}\,b^{16}-41\,a^9\,b^{17}+25\,a^8\,b^{18}+6\,a^7\,b^{19}-13\,a^6\,b^{20}+9\,a^5\,b^{21}-3\,a^4\,b^{22}\right)}{a^3\,b^{16}}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2-5\,b^2\right)\,\left(-2\,a^{11}\,b^{18}+6\,a^{10}\,b^{19}-8\,a^9\,b^{20}+8\,a^8\,b^{21}-6\,a^7\,b^{22}+2\,a^6\,b^{23}\right)}{a^3\,b^{21}}\right)\,\left(4\,a^2-5\,b^2\right)}{b^5}\right)\,\left(4\,a^2-5\,b^2\right)}{b^5}\right)\,\left(4\,a^2-5\,b^2\right)}{b^5}\right)\,\left(4\,a^2-5\,b^2\right)}{b^5}}\right)\,\left(4\,a^2-5\,b^2\right)\,2{}\mathrm{i}}{b^5\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{21}-256\,a^{20}\,b-1536\,a^{19}\,b^2+1536\,a^{18}\,b^3+3680\,a^{17}\,b^4-3680\,a^{16}\,b^5-4320\,a^{15}\,b^6+4320\,a^{14}\,b^7+2297\,a^{13}\,b^8-2361\,a^{12}\,b^9+28\,a^{11}\,b^{10}+132\,a^{10}\,b^{11}-624\,a^9\,b^{12}+588\,a^8\,b^{13}+90\,a^7\,b^{14}-250\,a^6\,b^{15}+140\,a^5\,b^{16}-40\,a^4\,b^{17}+4\,a^3\,b^{18}-4\,a^2\,b^{19}+a\,b^{20}-b^{21}\right)}{a^4\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(192\,a^{18}\,b^4-416\,a^{17}\,b^5-528\,a^{16}\,b^6+1696\,a^{15}\,b^7+20\,a^{14}\,b^8-2366\,a^{13}\,b^9+1129\,a^{12}\,b^{10}+1040\,a^{11}\,b^{11}-1088\,a^{10}\,b^{12}+332\,a^9\,b^{13}+192\,a^8\,b^{14}-280\,a^7\,b^{15}+74\,a^6\,b^{16}-26\,a^5\,b^{17}+20\,a^4\,b^{18}+16\,a^3\,b^{19}-8\,a^2\,b^{20}+4\,a\,b^{21}-3\,b^{22}\right)}{a^3\,b^{16}}+\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{17}\,b^8-96\,a^{16}\,b^9+32\,a^{15}\,b^{10}+128\,a^{14}\,b^{11}-118\,a^{13}\,b^{12}+82\,a^{12}\,b^{13}-100\,a^{11}\,b^{14}-60\,a^{10}\,b^{15}+160\,a^9\,b^{16}-60\,a^8\,b^{17}+12\,a^7\,b^{18}-8\,a^6\,b^{19}-12\,a^5\,b^{20}+12\,a^4\,b^{21}-6\,a^3\,b^{22}+2\,a^2\,b^{23}\right)}{a^4\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(-12\,a^{12}\,b^{14}+26\,a^{11}\,b^{15}+3\,a^{10}\,b^{16}-41\,a^9\,b^{17}+25\,a^8\,b^{18}+6\,a^7\,b^{19}-13\,a^6\,b^{20}+9\,a^5\,b^{21}-3\,a^4\,b^{22}\right)}{a^3\,b^{16}}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^{11}\,b^{18}+6\,a^{10}\,b^{19}-8\,a^9\,b^{20}+8\,a^8\,b^{21}-6\,a^7\,b^{22}+2\,a^6\,b^{23}\right)}{a^6\,b^{21}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^2\,b^5}+\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{21}-256\,a^{20}\,b-1536\,a^{19}\,b^2+1536\,a^{18}\,b^3+3680\,a^{17}\,b^4-3680\,a^{16}\,b^5-4320\,a^{15}\,b^6+4320\,a^{14}\,b^7+2297\,a^{13}\,b^8-2361\,a^{12}\,b^9+28\,a^{11}\,b^{10}+132\,a^{10}\,b^{11}-624\,a^9\,b^{12}+588\,a^8\,b^{13}+90\,a^7\,b^{14}-250\,a^6\,b^{15}+140\,a^5\,b^{16}-40\,a^4\,b^{17}+4\,a^3\,b^{18}-4\,a^2\,b^{19}+a\,b^{20}-b^{21}\right)}{a^4\,b^{16}}-\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(192\,a^{18}\,b^4-416\,a^{17}\,b^5-528\,a^{16}\,b^6+1696\,a^{15}\,b^7+20\,a^{14}\,b^8-2366\,a^{13}\,b^9+1129\,a^{12}\,b^{10}+1040\,a^{11}\,b^{11}-1088\,a^{10}\,b^{12}+332\,a^9\,b^{13}+192\,a^8\,b^{14}-280\,a^7\,b^{15}+74\,a^6\,b^{16}-26\,a^5\,b^{17}+20\,a^4\,b^{18}+16\,a^3\,b^{19}-8\,a^2\,b^{20}+4\,a\,b^{21}-3\,b^{22}\right)}{a^3\,b^{16}}-\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{17}\,b^8-96\,a^{16}\,b^9+32\,a^{15}\,b^{10}+128\,a^{14}\,b^{11}-118\,a^{13}\,b^{12}+82\,a^{12}\,b^{13}-100\,a^{11}\,b^{14}-60\,a^{10}\,b^{15}+160\,a^9\,b^{16}-60\,a^8\,b^{17}+12\,a^7\,b^{18}-8\,a^6\,b^{19}-12\,a^5\,b^{20}+12\,a^4\,b^{21}-6\,a^3\,b^{22}+2\,a^2\,b^{23}\right)}{a^4\,b^{16}}-\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(-12\,a^{12}\,b^{14}+26\,a^{11}\,b^{15}+3\,a^{10}\,b^{16}-41\,a^9\,b^{17}+25\,a^8\,b^{18}+6\,a^7\,b^{19}-13\,a^6\,b^{20}+9\,a^5\,b^{21}-3\,a^4\,b^{22}\right)}{a^3\,b^{16}}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^{11}\,b^{18}+6\,a^{10}\,b^{19}-8\,a^9\,b^{20}+8\,a^8\,b^{21}-6\,a^7\,b^{22}+2\,a^6\,b^{23}\right)}{a^6\,b^{21}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^2\,b^5}}{\frac{16384\,\left(256\,a^{18}-256\,a^{17}\,b-1536\,a^{16}\,b^2+1536\,a^{15}\,b^3+3488\,a^{14}\,b^4-3264\,a^{13}\,b^5-3792\,a^{12}\,b^6+2624\,a^{11}\,b^7+2245\,a^{10}\,b^8+101\,a^9\,b^9-1133\,a^8\,b^{10}-1036\,a^7\,b^{11}+582\,a^6\,b^{12}+174\,a^5\,b^{13}-14\,a^4\,b^{14}+116\,a^3\,b^{15}-91\,a^2\,b^{16}+5\,a\,b^{17}-5\,b^{18}\right)}{a^3\,b^{16}}-\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{21}-256\,a^{20}\,b-1536\,a^{19}\,b^2+1536\,a^{18}\,b^3+3680\,a^{17}\,b^4-3680\,a^{16}\,b^5-4320\,a^{15}\,b^6+4320\,a^{14}\,b^7+2297\,a^{13}\,b^8-2361\,a^{12}\,b^9+28\,a^{11}\,b^{10}+132\,a^{10}\,b^{11}-624\,a^9\,b^{12}+588\,a^8\,b^{13}+90\,a^7\,b^{14}-250\,a^6\,b^{15}+140\,a^5\,b^{16}-40\,a^4\,b^{17}+4\,a^3\,b^{18}-4\,a^2\,b^{19}+a\,b^{20}-b^{21}\right)}{a^4\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(192\,a^{18}\,b^4-416\,a^{17}\,b^5-528\,a^{16}\,b^6+1696\,a^{15}\,b^7+20\,a^{14}\,b^8-2366\,a^{13}\,b^9+1129\,a^{12}\,b^{10}+1040\,a^{11}\,b^{11}-1088\,a^{10}\,b^{12}+332\,a^9\,b^{13}+192\,a^8\,b^{14}-280\,a^7\,b^{15}+74\,a^6\,b^{16}-26\,a^5\,b^{17}+20\,a^4\,b^{18}+16\,a^3\,b^{19}-8\,a^2\,b^{20}+4\,a\,b^{21}-3\,b^{22}\right)}{a^3\,b^{16}}+\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{17}\,b^8-96\,a^{16}\,b^9+32\,a^{15}\,b^{10}+128\,a^{14}\,b^{11}-118\,a^{13}\,b^{12}+82\,a^{12}\,b^{13}-100\,a^{11}\,b^{14}-60\,a^{10}\,b^{15}+160\,a^9\,b^{16}-60\,a^8\,b^{17}+12\,a^7\,b^{18}-8\,a^6\,b^{19}-12\,a^5\,b^{20}+12\,a^4\,b^{21}-6\,a^3\,b^{22}+2\,a^2\,b^{23}\right)}{a^4\,b^{16}}+\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(-12\,a^{12}\,b^{14}+26\,a^{11}\,b^{15}+3\,a^{10}\,b^{16}-41\,a^9\,b^{17}+25\,a^8\,b^{18}+6\,a^7\,b^{19}-13\,a^6\,b^{20}+9\,a^5\,b^{21}-3\,a^4\,b^{22}\right)}{a^3\,b^{16}}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^{11}\,b^{18}+6\,a^{10}\,b^{19}-8\,a^9\,b^{20}+8\,a^8\,b^{21}-6\,a^7\,b^{22}+2\,a^6\,b^{23}\right)}{a^6\,b^{21}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}+\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(256\,a^{21}-256\,a^{20}\,b-1536\,a^{19}\,b^2+1536\,a^{18}\,b^3+3680\,a^{17}\,b^4-3680\,a^{16}\,b^5-4320\,a^{15}\,b^6+4320\,a^{14}\,b^7+2297\,a^{13}\,b^8-2361\,a^{12}\,b^9+28\,a^{11}\,b^{10}+132\,a^{10}\,b^{11}-624\,a^9\,b^{12}+588\,a^8\,b^{13}+90\,a^7\,b^{14}-250\,a^6\,b^{15}+140\,a^5\,b^{16}-40\,a^4\,b^{17}+4\,a^3\,b^{18}-4\,a^2\,b^{19}+a\,b^{20}-b^{21}\right)}{a^4\,b^{16}}-\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(192\,a^{18}\,b^4-416\,a^{17}\,b^5-528\,a^{16}\,b^6+1696\,a^{15}\,b^7+20\,a^{14}\,b^8-2366\,a^{13}\,b^9+1129\,a^{12}\,b^{10}+1040\,a^{11}\,b^{11}-1088\,a^{10}\,b^{12}+332\,a^9\,b^{13}+192\,a^8\,b^{14}-280\,a^7\,b^{15}+74\,a^6\,b^{16}-26\,a^5\,b^{17}+20\,a^4\,b^{18}+16\,a^3\,b^{19}-8\,a^2\,b^{20}+4\,a\,b^{21}-3\,b^{22}\right)}{a^3\,b^{16}}-\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{17}\,b^8-96\,a^{16}\,b^9+32\,a^{15}\,b^{10}+128\,a^{14}\,b^{11}-118\,a^{13}\,b^{12}+82\,a^{12}\,b^{13}-100\,a^{11}\,b^{14}-60\,a^{10}\,b^{15}+160\,a^9\,b^{16}-60\,a^8\,b^{17}+12\,a^7\,b^{18}-8\,a^6\,b^{19}-12\,a^5\,b^{20}+12\,a^4\,b^{21}-6\,a^3\,b^{22}+2\,a^2\,b^{23}\right)}{a^4\,b^{16}}-\frac{\left(4\,a^2+b^2\right)\,\left(\frac{8192\,\left(-12\,a^{12}\,b^{14}+26\,a^{11}\,b^{15}+3\,a^{10}\,b^{16}-41\,a^9\,b^{17}+25\,a^8\,b^{18}+6\,a^7\,b^{19}-13\,a^6\,b^{20}+9\,a^5\,b^{21}-3\,a^4\,b^{22}\right)}{a^3\,b^{16}}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(-2\,a^{11}\,b^{18}+6\,a^{10}\,b^{19}-8\,a^9\,b^{20}+8\,a^8\,b^{21}-6\,a^7\,b^{22}+2\,a^6\,b^{23}\right)}{a^6\,b^{21}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^2\,b^5}}\right)\,\left(4\,a^2+b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^2\,b^5\,d}","Not used",1,"((2*tan(c/2 + (d*x)/2)^5*(10*a*b^3 - 6*a^3*b + 36*a^4 + 9*b^4 - 37*a^2*b^2))/(3*a*b^4) - (2*tan(c/2 + (d*x)/2)^3*(6*a^3*b - 10*a*b^3 + 36*a^4 + 9*b^4 - 37*a^2*b^2))/(3*a*b^4) + (2*tan(c/2 + (d*x)/2)*(2*a^3*b - 2*a*b^3 + 4*a^4 + b^4 - 5*a^2*b^2))/(a*b^4) + (2*tan(c/2 + (d*x)/2)^7*(a - b)*(3*a*b^2 - 2*a^2*b - 4*a^3 + b^3))/(a*b^4))/(d*(a + b + tan(c/2 + (d*x)/2)^8*(a - b) - tan(c/2 + (d*x)/2)^2*(4*a + 2*b) - tan(c/2 + (d*x)/2)^6*(4*a - 2*b) + 6*a*tan(c/2 + (d*x)/2)^4)) - (2*atan((((((((((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) - (tan(c/2 + (d*x)/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18)*8192i)/(a^6*b^16))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16))*1i)/a^2 + (8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16))/a^2 - ((((((((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) + (tan(c/2 + (d*x)/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18)*8192i)/(a^6*b^16))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16))*1i)/a^2 + (8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16))/a^2)/((((((((((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) - (tan(c/2 + (d*x)/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18)*8192i)/(a^6*b^16))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16))*1i)/a^2 + (8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16))*1i)/a^2 + (((((((((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) + (tan(c/2 + (d*x)/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18)*8192i)/(a^6*b^16))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16))*1i)/a^2 + (8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16))*1i)/a^2 - (16384*(5*a*b^17 - 256*a^17*b + 256*a^18 - 5*b^18 - 91*a^2*b^16 + 116*a^3*b^15 - 14*a^4*b^14 + 174*a^5*b^13 + 582*a^6*b^12 - 1036*a^7*b^11 - 1133*a^8*b^10 + 101*a^9*b^9 + 2245*a^10*b^8 + 2624*a^11*b^7 - 3792*a^12*b^6 - 3264*a^13*b^5 + 3488*a^14*b^4 + 1536*a^15*b^3 - 1536*a^16*b^2))/(a^3*b^16))))/(a^2*d) - (a*atan(((a*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) + (a*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) + (a*((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) + (a*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) + (8192*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^3*b^21))*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2)*1i)/b^5 + (a*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) - (a*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) - (a*((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) - (a*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) - (8192*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^3*b^21))*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2)*1i)/b^5)/((16384*(5*a*b^17 - 256*a^17*b + 256*a^18 - 5*b^18 - 91*a^2*b^16 + 116*a^3*b^15 - 14*a^4*b^14 + 174*a^5*b^13 + 582*a^6*b^12 - 1036*a^7*b^11 - 1133*a^8*b^10 + 101*a^9*b^9 + 2245*a^10*b^8 + 2624*a^11*b^7 - 3792*a^12*b^6 - 3264*a^13*b^5 + 3488*a^14*b^4 + 1536*a^15*b^3 - 1536*a^16*b^2))/(a^3*b^16) - (a*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) + (a*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) + (a*((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) + (a*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) + (8192*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^3*b^21))*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5 + (a*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) - (a*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) - (a*((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) - (a*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) - (8192*tan(c/2 + (d*x)/2)*(4*a^2 - 5*b^2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^3*b^21))*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5)*(4*a^2 - 5*b^2))/b^5))*(4*a^2 - 5*b^2)*2i)/(b^5*d) - (atan((((4*a^2 + b^2)*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) + ((4*a^2 + b^2)*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) + (((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) + ((4*a^2 + b^2)*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) + (8192*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^6*b^21))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2)*1i)/(a^2*b^5) + ((4*a^2 + b^2)*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) - ((4*a^2 + b^2)*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) - (((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) - ((4*a^2 + b^2)*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) - (8192*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^6*b^21))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2)*1i)/(a^2*b^5))/((16384*(5*a*b^17 - 256*a^17*b + 256*a^18 - 5*b^18 - 91*a^2*b^16 + 116*a^3*b^15 - 14*a^4*b^14 + 174*a^5*b^13 + 582*a^6*b^12 - 1036*a^7*b^11 - 1133*a^8*b^10 + 101*a^9*b^9 + 2245*a^10*b^8 + 2624*a^11*b^7 - 3792*a^12*b^6 - 3264*a^13*b^5 + 3488*a^14*b^4 + 1536*a^15*b^3 - 1536*a^16*b^2))/(a^3*b^16) - ((4*a^2 + b^2)*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) + ((4*a^2 + b^2)*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) + (((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) + ((4*a^2 + b^2)*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) + (8192*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^6*b^21))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5) + ((4*a^2 + b^2)*((8192*tan(c/2 + (d*x)/2)*(a*b^20 - 256*a^20*b + 256*a^21 - b^21 - 4*a^2*b^19 + 4*a^3*b^18 - 40*a^4*b^17 + 140*a^5*b^16 - 250*a^6*b^15 + 90*a^7*b^14 + 588*a^8*b^13 - 624*a^9*b^12 + 132*a^10*b^11 + 28*a^11*b^10 - 2361*a^12*b^9 + 2297*a^13*b^8 + 4320*a^14*b^7 - 4320*a^15*b^6 - 3680*a^16*b^5 + 3680*a^17*b^4 + 1536*a^18*b^3 - 1536*a^19*b^2))/(a^4*b^16) - ((4*a^2 + b^2)*((8192*(4*a*b^21 - 3*b^22 - 8*a^2*b^20 + 16*a^3*b^19 + 20*a^4*b^18 - 26*a^5*b^17 + 74*a^6*b^16 - 280*a^7*b^15 + 192*a^8*b^14 + 332*a^9*b^13 - 1088*a^10*b^12 + 1040*a^11*b^11 + 1129*a^12*b^10 - 2366*a^13*b^9 + 20*a^14*b^8 + 1696*a^15*b^7 - 528*a^16*b^6 - 416*a^17*b^5 + 192*a^18*b^4))/(a^3*b^16) - (((8192*tan(c/2 + (d*x)/2)*(2*a^2*b^23 - 6*a^3*b^22 + 12*a^4*b^21 - 12*a^5*b^20 - 8*a^6*b^19 + 12*a^7*b^18 - 60*a^8*b^17 + 160*a^9*b^16 - 60*a^10*b^15 - 100*a^11*b^14 + 82*a^12*b^13 - 118*a^13*b^12 + 128*a^14*b^11 + 32*a^15*b^10 - 96*a^16*b^9 + 32*a^17*b^8))/(a^4*b^16) - ((4*a^2 + b^2)*((8192*(9*a^5*b^21 - 3*a^4*b^22 - 13*a^6*b^20 + 6*a^7*b^19 + 25*a^8*b^18 - 41*a^9*b^17 + 3*a^10*b^16 + 26*a^11*b^15 - 12*a^12*b^14))/(a^3*b^16) - (8192*tan(c/2 + (d*x)/2)*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2)*(2*a^6*b^23 - 6*a^7*b^22 + 8*a^8*b^21 - 8*a^9*b^20 + 6*a^10*b^19 - 2*a^11*b^18))/(a^6*b^21))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5))*((a + b)^3*(a - b)^3)^(1/2))/(a^2*b^5)))*(4*a^2 + b^2)*((a + b)^3*(a - b)^3)^(1/2)*2i)/(a^2*b^5*d)","B"
308,1,7044,150,3.467851,"\text{Not used}","int(tan(c + d*x)^4/(a + b/cos(c + d*x))^2,x)","\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}+\frac{\left(-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}+\frac{\left(-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}+\frac{\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)\,8192{}\mathrm{i}}{a^6\,b^8}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}-\frac{-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}+\frac{\left(-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}+\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}+\frac{\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)\,8192{}\mathrm{i}}{a^6\,b^8}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}}{-\frac{16384\,\left(16\,a^{10}-16\,a^9\,b+8\,a^8\,b^2-36\,a^7\,b^3+12\,a^6\,b^4+26\,a^5\,b^5-18\,a^4\,b^6+24\,a^3\,b^7-16\,a^2\,b^8+2\,a\,b^9-2\,b^{10}\right)}{a^3\,b^8}+\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}+\frac{\left(-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}+\frac{\left(-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}+\frac{\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)\,8192{}\mathrm{i}}{a^6\,b^8}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{\left(-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}+\frac{\left(-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}+\frac{\left(\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}+\frac{\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)\,8192{}\mathrm{i}}{a^6\,b^8}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}+\frac{\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+a\,b-b^2\right)}{a\,b^2}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a-b\right)\,\left(2\,a+b\right)}{a\,b^2}}{d\,\left(\left(a-b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^4\,b^8}\right)-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)\,1{}\mathrm{i}-\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^4\,b^8}\right)+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)\,1{}\mathrm{i}}{\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^4\,b^8}\right)-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)+\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2\,\sqrt{a^2-b^2}}{b^3}+\frac{\sqrt{a^2-b^2}}{a^2\,b}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^4\,b^8}\right)+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)-\frac{16384\,\left(16\,a^{10}-16\,a^9\,b+8\,a^8\,b^2-36\,a^7\,b^3+12\,a^6\,b^4+26\,a^5\,b^5-18\,a^4\,b^6+24\,a^3\,b^7-16\,a^2\,b^8+2\,a\,b^9-2\,b^{10}\right)}{a^3\,b^8}}\right)\,\left(\frac{\sqrt{a^2-b^2}\,4{}\mathrm{i}}{b^3}+\frac{\sqrt{a^2-b^2}\,2{}\mathrm{i}}{a^2\,b}\right)}{d}+\frac{a\,\mathrm{atan}\left(\frac{\frac{a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}-\frac{16384\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^3\,b^{11}}\right)}{b^3}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)}{b^3}-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)}{b^3}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)\,2{}\mathrm{i}}{b^3}-\frac{a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}+\frac{16384\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^3\,b^{11}}\right)}{b^3}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)}{b^3}-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)}{b^3}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)\,2{}\mathrm{i}}{b^3}}{\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}-\frac{16384\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^3\,b^{11}}\right)}{b^3}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)}{b^3}-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)}{b^3}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)}{b^3}+\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{8192\,\left(6\,a^{10}\,b^8-13\,a^9\,b^9+6\,a^8\,b^{10}+5\,a^7\,b^{11}-9\,a^6\,b^{12}+8\,a^5\,b^{13}-3\,a^4\,b^{14}\right)}{a^3\,b^8}+\frac{16384\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^{11}\,b^{10}+6\,a^{10}\,b^{11}-8\,a^9\,b^{12}+8\,a^8\,b^{13}-6\,a^7\,b^{14}+2\,a^6\,b^{15}\right)}{a^3\,b^{11}}\right)}{b^3}+\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{13}\,b^4-24\,a^{12}\,b^5+28\,a^{11}\,b^6-28\,a^{10}\,b^7+25\,a^9\,b^8-9\,a^8\,b^9+3\,a^7\,b^{10}+a^6\,b^{11}-10\,a^5\,b^{12}+10\,a^4\,b^{13}-6\,a^3\,b^{14}+2\,a^2\,b^{15}\right)}{a^4\,b^8}\right)}{b^3}-\frac{8192\,\left(24\,a^{12}\,b^2-52\,a^{11}\,b^3+24\,a^{10}\,b^4+14\,a^9\,b^5-34\,a^8\,b^6+40\,a^7\,b^7-18\,a^6\,b^8+11\,a^5\,b^9-5\,a^4\,b^{10}-8\,a^3\,b^{11}+6\,a^2\,b^{12}-5\,a\,b^{13}+3\,b^{14}\right)}{a^3\,b^8}\right)}{b^3}-\frac{8192\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-16\,a^{13}+16\,a^{12}\,b+16\,a^{11}\,b^2-16\,a^{10}\,b^3+4\,a^9\,b^4+12\,a^8\,b^5-44\,a^7\,b^6+44\,a^6\,b^7-21\,a^5\,b^8+5\,a^4\,b^9-2\,a^3\,b^{10}+2\,a^2\,b^{11}-a\,b^{12}+b^{13}\right)}{a^4\,b^8}\right)}{b^3}-\frac{16384\,\left(16\,a^{10}-16\,a^9\,b+8\,a^8\,b^2-36\,a^7\,b^3+12\,a^6\,b^4+26\,a^5\,b^5-18\,a^4\,b^6+24\,a^3\,b^7-16\,a^2\,b^8+2\,a\,b^9-2\,b^{10}\right)}{a^3\,b^8}}\right)\,4{}\mathrm{i}}{b^3\,d}","Not used",1,"(2*atan((((((((((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) - (tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10)*8192i)/(a^6*b^8))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8))*1i)/a^2 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))/a^2 - ((((((((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) + (tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10)*8192i)/(a^6*b^8))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8))*1i)/a^2 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))/a^2)/((((((((((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) - (tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10)*8192i)/(a^6*b^8))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8))*1i)/a^2 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))*1i)/a^2 + (((((((((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) + (tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10)*8192i)/(a^6*b^8))*1i)/a^2 + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8))*1i)/a^2 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8))*1i)/a^2 - (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))*1i)/a^2 - (16384*(2*a*b^9 - 16*a^9*b + 16*a^10 - 2*b^10 - 16*a^2*b^8 + 24*a^3*b^7 - 18*a^4*b^6 + 26*a^5*b^5 + 12*a^6*b^4 - 36*a^7*b^3 + 8*a^8*b^2))/(a^3*b^8))))/(a^2*d) + ((2*tan(c/2 + (d*x)/2)*(a*b + 2*a^2 - b^2))/(a*b^2) - (2*tan(c/2 + (d*x)/2)^3*(a - b)*(2*a + b))/(a*b^2))/(d*(a + b + tan(c/2 + (d*x)/2)^4*(a - b) - 2*a*tan(c/2 + (d*x)/2)^2)) + (atan((((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) - (8192*tan(c/2 + (d*x)/2)*((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^4*b^8)) - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)) - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)) + (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))*1i - ((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) + (8192*tan(c/2 + (d*x)/2)*((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^4*b^8)) + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)) - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)) - (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))*1i)/(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) - (8192*tan(c/2 + (d*x)/2)*((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^4*b^8)) - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)) - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)) + (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8)) + ((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) + (8192*tan(c/2 + (d*x)/2)*((2*(a^2 - b^2)^(1/2))/b^3 + (a^2 - b^2)^(1/2)/(a^2*b))*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^4*b^8)) + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)) - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)) - (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8)) - (16384*(2*a*b^9 - 16*a^9*b + 16*a^10 - 2*b^10 - 16*a^2*b^8 + 24*a^3*b^7 - 18*a^4*b^6 + 26*a^5*b^5 + 12*a^6*b^4 - 36*a^7*b^3 + 8*a^8*b^2))/(a^3*b^8)))*(((a^2 - b^2)^(1/2)*4i)/b^3 + ((a^2 - b^2)^(1/2)*2i)/(a^2*b)))/d + (a*atan(((a*((2*a*((2*a*((2*a*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) - (16384*tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^3*b^11)))/b^3 - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)))/b^3 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)))/b^3 + (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))*2i)/b^3 - (a*((2*a*((2*a*((2*a*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) + (16384*tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^3*b^11)))/b^3 + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)))/b^3 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)))/b^3 - (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8))*2i)/b^3)/((2*a*((2*a*((2*a*((2*a*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) - (16384*tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^3*b^11)))/b^3 - (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)))/b^3 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)))/b^3 + (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8)))/b^3 + (2*a*((2*a*((2*a*((2*a*((8192*(8*a^5*b^13 - 3*a^4*b^14 - 9*a^6*b^12 + 5*a^7*b^11 + 6*a^8*b^10 - 13*a^9*b^9 + 6*a^10*b^8))/(a^3*b^8) + (16384*tan(c/2 + (d*x)/2)*(2*a^6*b^15 - 6*a^7*b^14 + 8*a^8*b^13 - 8*a^9*b^12 + 6*a^10*b^11 - 2*a^11*b^10))/(a^3*b^11)))/b^3 + (8192*tan(c/2 + (d*x)/2)*(2*a^2*b^15 - 6*a^3*b^14 + 10*a^4*b^13 - 10*a^5*b^12 + a^6*b^11 + 3*a^7*b^10 - 9*a^8*b^9 + 25*a^9*b^8 - 28*a^10*b^7 + 28*a^11*b^6 - 24*a^12*b^5 + 8*a^13*b^4))/(a^4*b^8)))/b^3 - (8192*(3*b^14 - 5*a*b^13 + 6*a^2*b^12 - 8*a^3*b^11 - 5*a^4*b^10 + 11*a^5*b^9 - 18*a^6*b^8 + 40*a^7*b^7 - 34*a^8*b^6 + 14*a^9*b^5 + 24*a^10*b^4 - 52*a^11*b^3 + 24*a^12*b^2))/(a^3*b^8)))/b^3 - (8192*tan(c/2 + (d*x)/2)*(16*a^12*b - a*b^12 - 16*a^13 + b^13 + 2*a^2*b^11 - 2*a^3*b^10 + 5*a^4*b^9 - 21*a^5*b^8 + 44*a^6*b^7 - 44*a^7*b^6 + 12*a^8*b^5 + 4*a^9*b^4 - 16*a^10*b^3 + 16*a^11*b^2))/(a^4*b^8)))/b^3 - (16384*(2*a*b^9 - 16*a^9*b + 16*a^10 - 2*b^10 - 16*a^2*b^8 + 24*a^3*b^7 - 18*a^4*b^6 + 26*a^5*b^5 + 12*a^6*b^4 - 36*a^7*b^3 + 8*a^8*b^2))/(a^3*b^8)))*4i)/(b^3*d)","B"
309,1,551,85,2.144621,"\text{Not used}","int(tan(c + d*x)^2/(a + b/cos(c + d*x))^2,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^2\,d}-\frac{b^2\,\left(a\,\sin\left(c+d\,x\right)+2\,\mathrm{atanh}\left(\frac{2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(b\,\left(a^2-b^2\right)+a\,b^2-a^2\,b-a^3+b^3\right)}\right)\,\sqrt{a^2-b^2}\right)-a^3\,\sin\left(c+d\,x\right)+2\,a\,b\,\cos\left(c+d\,x\right)\,\mathrm{atanh}\left(\frac{2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a^2-b^2\right)}^{3/2}-a^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+2\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}-3\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+a^3\,b^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}+a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a\,b^2-a^3\right)\,\left(b\,\left(a^2-b^2\right)+a\,b^2-a^2\,b-a^3+b^3\right)}\right)\,\sqrt{a^2-b^2}}{a^2\,d\,\left(a^2-b^2\right)\,\left(b+a\,\cos\left(c+d\,x\right)\right)}","Not used",1,"- (2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^2*d) - (b^2*(a*sin(c + d*x) + 2*atanh((2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - a^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(b*(a^2 - b^2) + a*b^2 - a^2*b - a^3 + b^3)))*(a^2 - b^2)^(1/2)) - a^3*sin(c + d*x) + 2*a*b*cos(c + d*x)*atanh((2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(3/2) - a^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + 2*b^5*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) - 3*a^2*b^3*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + a^3*b^2*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2) + a^4*b*sin(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2))/(cos(c/2 + (d*x)/2)*(a*b^2 - a^3)*(b*(a^2 - b^2) + a*b^2 - a^2*b - a^3 + b^3)))*(a^2 - b^2)^(1/2))/(a^2*d*(a^2 - b^2)*(b + a*cos(c + d*x)))","B"
310,1,6093,227,6.458343,"\text{Not used}","int(cot(c + d*x)^2/(a + b/cos(c + d*x))^2,x)","\frac{\frac{a^2-2\,a\,b+b^2}{a+b}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4-3\,a^3\,b+3\,a^2\,b^2-a\,b^3+4\,b^4\right)}{a\,{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^3-6\,a^2\,b+6\,a\,b^2-2\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(-2\,a^3+2\,a^2\,b+2\,a\,b^2-2\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{2\,\mathrm{atan}\left(-\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}}{64\,a^2\,b^{22}-192\,a^3\,b^{21}-640\,a^4\,b^{20}+1984\,a^5\,b^{19}+2624\,a^6\,b^{18}-8192\,a^7\,b^{17}-6400\,a^8\,b^{16}+18496\,a^9\,b^{15}+11072\,a^{10}\,b^{14}-25856\,a^{11}\,b^{13}-14464\,a^{12}\,b^{12}+23872\,a^{13}\,b^{11}+13760\,a^{14}\,b^{10}-15104\,a^{15}\,b^9-8704\,a^{16}\,b^8+6592\,a^{17}\,b^7+3200\,a^{18}\,b^6-1856\,a^{19}\,b^5-512\,a^{20}\,b^4+256\,a^{21}\,b^3-\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}+\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}+\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,1{}\mathrm{i}}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}{64\,a^2\,b^{22}-192\,a^3\,b^{21}-640\,a^4\,b^{20}+1984\,a^5\,b^{19}+2624\,a^6\,b^{18}-8192\,a^7\,b^{17}-6400\,a^8\,b^{16}+18496\,a^9\,b^{15}+11072\,a^{10}\,b^{14}-25856\,a^{11}\,b^{13}-14464\,a^{12}\,b^{12}+23872\,a^{13}\,b^{11}+13760\,a^{14}\,b^{10}-15104\,a^{15}\,b^9-8704\,a^{16}\,b^8+6592\,a^{17}\,b^7+3200\,a^{18}\,b^6-1856\,a^{19}\,b^5-512\,a^{20}\,b^4+256\,a^{21}\,b^3+\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)+\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2+\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}-\frac{b^3\,\left(2\,a+b\right)\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{26}-96\,a^{25}\,b-224\,a^{24}\,b^2+928\,a^{23}\,b^3+480\,a^{22}\,b^4-4000\,a^{21}\,b^5+992\,a^{20}\,b^6+9568\,a^{19}\,b^7-8128\,a^{18}\,b^8-12992\,a^{17}\,b^9+21344\,a^{16}\,b^{10}+8224\,a^{15}\,b^{11}-31744\,a^{14}\,b^{12}+2176\,a^{13}\,b^{13}+29600\,a^{12}\,b^{14}-8480\,a^{11}\,b^{15}-17632\,a^{10}\,b^{16}+7072\,a^9\,b^{17}+6528\,a^8\,b^{18}-3008\,a^7\,b^{19}-1376\,a^6\,b^{20}+672\,a^5\,b^{21}+128\,a^4\,b^{22}-64\,a^3\,b^{23}\right)-\frac{b^3\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(32\,a^{28}-32\,a^{27}\,b+32\,a^6\,b^{22}-416\,a^8\,b^{20}+224\,a^9\,b^{19}+2080\,a^{10}\,b^{18}-1824\,a^{11}\,b^{17}-5472\,a^{12}\,b^{16}+6528\,a^{13}\,b^{15}+8256\,a^{14}\,b^{14}-13440\,a^{15}\,b^{13}-6720\,a^{16}\,b^{12}+17472\,a^{17}\,b^{11}+1344\,a^{18}\,b^{10}-14784\,a^{19}\,b^9+2880\,a^{20}\,b^8+8064\,a^{21}\,b^7-3168\,a^{22}\,b^6-2688\,a^{23}\,b^5+1504\,a^{24}\,b^4+480\,a^{25}\,b^3-352\,a^{26}\,b^2-\frac{b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,\left(-64\,a^{29}\,b+128\,a^{28}\,b^2+576\,a^{27}\,b^3-1280\,a^{26}\,b^4-2240\,a^{25}\,b^5+5760\,a^{24}\,b^6+4800\,a^{23}\,b^7-15360\,a^{22}\,b^8-5760\,a^{21}\,b^9+26880\,a^{20}\,b^{10}+2688\,a^{19}\,b^{11}-32256\,a^{18}\,b^{12}+2688\,a^{17}\,b^{13}+26880\,a^{16}\,b^{14}-5760\,a^{15}\,b^{15}-15360\,a^{14}\,b^{16}+4800\,a^{13}\,b^{17}+5760\,a^{12}\,b^{18}-2240\,a^{11}\,b^{19}-1280\,a^{10}\,b^{20}+576\,a^9\,b^{21}+128\,a^8\,b^{22}-64\,a^7\,b^{23}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)}{a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}}}\right)\,\left(2\,a+b\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(2\,a-b\right)\,2{}\mathrm{i}}{d\,\left(a^{12}-5\,a^{10}\,b^2+10\,a^8\,b^4-10\,a^6\,b^6+5\,a^4\,b^8-a^2\,b^{10}\right)}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) - (tan(c/2 + (d*x)/2)^2*(a^4 - 3*a^3*b - a*b^3 + 4*b^4 + 3*a^2*b^2))/(a*(a + b)^2))/(d*(tan(c/2 + (d*x)/2)^3*(6*a*b^2 - 6*a^2*b + 2*a^3 - 2*b^3) + tan(c/2 + (d*x)/2)*(2*a*b^2 + 2*a^2*b - 2*a^3 - 2*b^3))) - (2*atan(-((tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)/a^2 + (tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)/a^2)/(64*a^2*b^22 - 192*a^3*b^21 - 640*a^4*b^20 + 1984*a^5*b^19 + 2624*a^6*b^18 - 8192*a^7*b^17 - 6400*a^8*b^16 + 18496*a^9*b^15 + 11072*a^10*b^14 - 25856*a^11*b^13 - 14464*a^12*b^12 + 23872*a^13*b^11 + 13760*a^14*b^10 - 15104*a^15*b^9 - 8704*a^16*b^8 + 6592*a^17*b^7 + 3200*a^18*b^6 - 1856*a^19*b^5 - 512*a^20*b^4 + 256*a^21*b^3 - ((tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)*1i)/a^2 + ((tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + ((32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (tan(c/2 + (d*x)/2)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2)*1i)/a^2)*1i)/a^2)*1i)/a^2)))/(a^2*d) + tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + (b^3*atan(((b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) + (b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*1i)/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))/(64*a^2*b^22 - 192*a^3*b^21 - 640*a^4*b^20 + 1984*a^5*b^19 + 2624*a^6*b^18 - 8192*a^7*b^17 - 6400*a^8*b^16 + 18496*a^9*b^15 + 11072*a^10*b^14 - 25856*a^11*b^13 - 14464*a^12*b^12 + 23872*a^13*b^11 + 13760*a^14*b^10 - 15104*a^15*b^9 - 8704*a^16*b^8 + 6592*a^17*b^7 + 3200*a^18*b^6 - 1856*a^19*b^5 - 512*a^20*b^4 + 256*a^21*b^3 + (b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) + (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 + (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2) - (b^3*(2*a + b)*(tan(c/2 + (d*x)/2)*(32*a^26 - 96*a^25*b - 64*a^3*b^23 + 128*a^4*b^22 + 672*a^5*b^21 - 1376*a^6*b^20 - 3008*a^7*b^19 + 6528*a^8*b^18 + 7072*a^9*b^17 - 17632*a^10*b^16 - 8480*a^11*b^15 + 29600*a^12*b^14 + 2176*a^13*b^13 - 31744*a^14*b^12 + 8224*a^15*b^11 + 21344*a^16*b^10 - 12992*a^17*b^9 - 8128*a^18*b^8 + 9568*a^19*b^7 + 992*a^20*b^6 - 4000*a^21*b^5 + 480*a^22*b^4 + 928*a^23*b^3 - 224*a^24*b^2) - (b^3*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(32*a^28 - 32*a^27*b + 32*a^6*b^22 - 416*a^8*b^20 + 224*a^9*b^19 + 2080*a^10*b^18 - 1824*a^11*b^17 - 5472*a^12*b^16 + 6528*a^13*b^15 + 8256*a^14*b^14 - 13440*a^15*b^13 - 6720*a^16*b^12 + 17472*a^17*b^11 + 1344*a^18*b^10 - 14784*a^19*b^9 + 2880*a^20*b^8 + 8064*a^21*b^7 - 3168*a^22*b^6 - 2688*a^23*b^5 + 1504*a^24*b^4 + 480*a^25*b^3 - 352*a^26*b^2 - (b^3*tan(c/2 + (d*x)/2)*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*(128*a^8*b^22 - 64*a^7*b^23 - 64*a^29*b + 576*a^9*b^21 - 1280*a^10*b^20 - 2240*a^11*b^19 + 5760*a^12*b^18 + 4800*a^13*b^17 - 15360*a^14*b^16 - 5760*a^15*b^15 + 26880*a^16*b^14 + 2688*a^17*b^13 - 32256*a^18*b^12 + 2688*a^19*b^11 + 26880*a^20*b^10 - 5760*a^21*b^9 - 15360*a^22*b^8 + 4800*a^23*b^7 + 5760*a^24*b^6 - 2240*a^25*b^5 - 1280*a^26*b^4 + 576*a^27*b^3 + 128*a^28*b^2))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b))/(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2)))*(2*a + b)*((a + b)^5*(a - b)^5)^(1/2)*(2*a - b)*2i)/(d*(a^12 - a^2*b^10 + 5*a^4*b^8 - 10*a^6*b^6 + 10*a^8*b^4 - 5*a^10*b^2))","B"
311,1,8348,360,6.972075,"\text{Not used}","int(cot(c + d*x)^4/(a + b/cos(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d\,{\left(a-b\right)}^2}+\frac{\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{3\,\left(a+b\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-8\,a^4+11\,a^3\,b+15\,a^2\,b^2-31\,a\,b^3+13\,b^4\right)}{3\,{\left(a+b\right)}^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-5\,a^6+11\,a^5\,b+6\,a^4\,b^2-34\,a^3\,b^3+31\,a^2\,b^4-9\,a\,b^5+16\,b^6\right)}{a\,{\left(a+b\right)}^3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(8\,a^4-32\,a^3\,b+48\,a^2\,b^2-32\,a\,b^3+8\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(8\,a^4-16\,a^3\,b+16\,a\,b^3-8\,b^4\right)\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{8\,a^2+16\,a\,b-24\,b^2}{64\,{\left(a-b\right)}^4}-\frac{3}{4\,{\left(a-b\right)}^2}\right)}{d}+\frac{2\,\mathrm{atan}\left(\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{\left(32\,a^{38}-32\,a^{37}\,b-32\,a^6\,b^{32}-32\,a^7\,b^{31}+640\,a^8\,b^{30}-4992\,a^{10}\,b^{28}+2624\,a^{11}\,b^{27}+21504\,a^{12}\,b^{26}-19872\,a^{13}\,b^{25}-57920\,a^{14}\,b^{24}+77472\,a^{15}\,b^{23}+100992\,a^{16}\,b^{22}-195008\,a^{17}\,b^{21}-107008\,a^{18}\,b^{20}+344960\,a^{19}\,b^{19}+39424\,a^{20}\,b^{18}-446688\,a^{21}\,b^{17}+76032\,a^{22}\,b^{16}+431904\,a^{23}\,b^{15}-161920\,a^{24}\,b^{14}-313984\,a^{25}\,b^{13}+167552\,a^{26}\,b^{12}+171072\,a^{27}\,b^{11}-113664\,a^{28}\,b^{10}-68960\,a^{29}\,b^9+53568\,a^{30}\,b^8+20064\,a^{31}\,b^7-17536\,a^{32}\,b^6-4032\,a^{33}\,b^5+3840\,a^{34}\,b^4+512\,a^{35}\,b^3-512\,a^{36}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{\left(32\,a^{37}\,b-32\,a^{38}+32\,a^6\,b^{32}+32\,a^7\,b^{31}-640\,a^8\,b^{30}+4992\,a^{10}\,b^{28}-2624\,a^{11}\,b^{27}-21504\,a^{12}\,b^{26}+19872\,a^{13}\,b^{25}+57920\,a^{14}\,b^{24}-77472\,a^{15}\,b^{23}-100992\,a^{16}\,b^{22}+195008\,a^{17}\,b^{21}+107008\,a^{18}\,b^{20}-344960\,a^{19}\,b^{19}-39424\,a^{20}\,b^{18}+446688\,a^{21}\,b^{17}-76032\,a^{22}\,b^{16}-431904\,a^{23}\,b^{15}+161920\,a^{24}\,b^{14}+313984\,a^{25}\,b^{13}-167552\,a^{26}\,b^{12}-171072\,a^{27}\,b^{11}+113664\,a^{28}\,b^{10}+68960\,a^{29}\,b^9-53568\,a^{30}\,b^8-20064\,a^{31}\,b^7+17536\,a^{32}\,b^6+4032\,a^{33}\,b^5-3840\,a^{34}\,b^4-512\,a^{35}\,b^3+512\,a^{36}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}{a^2}}{64\,a^2\,b^{32}-256\,a^3\,b^{31}-960\,a^4\,b^{30}+3840\,a^5\,b^{29}+6144\,a^6\,b^{28}-23168\,a^7\,b^{27}-25088\,a^8\,b^{26}+78784\,a^9\,b^{25}+76800\,a^{10}\,b^{24}-173760\,a^{11}\,b^{23}-183168\,a^{12}\,b^{22}+269952\,a^{13}\,b^{21}+334080\,a^{14}\,b^{20}-314880\,a^{15}\,b^{19}-453888\,a^{16}\,b^{18}+291456\,a^{17}\,b^{17}+449856\,a^{18}\,b^{16}-221568\,a^{19}\,b^{15}-318400\,a^{20}\,b^{14}+136960\,a^{21}\,b^{13}+155904\,a^{22}\,b^{12}-64896\,a^{23}\,b^{11}-49920\,a^{24}\,b^{10}+21440\,a^{25}\,b^9+9344\,a^{26}\,b^8-4288\,a^{27}\,b^7-768\,a^{28}\,b^6+384\,a^{29}\,b^5+\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{\left(32\,a^{38}-32\,a^{37}\,b-32\,a^6\,b^{32}-32\,a^7\,b^{31}+640\,a^8\,b^{30}-4992\,a^{10}\,b^{28}+2624\,a^{11}\,b^{27}+21504\,a^{12}\,b^{26}-19872\,a^{13}\,b^{25}-57920\,a^{14}\,b^{24}+77472\,a^{15}\,b^{23}+100992\,a^{16}\,b^{22}-195008\,a^{17}\,b^{21}-107008\,a^{18}\,b^{20}+344960\,a^{19}\,b^{19}+39424\,a^{20}\,b^{18}-446688\,a^{21}\,b^{17}+76032\,a^{22}\,b^{16}+431904\,a^{23}\,b^{15}-161920\,a^{24}\,b^{14}-313984\,a^{25}\,b^{13}+167552\,a^{26}\,b^{12}+171072\,a^{27}\,b^{11}-113664\,a^{28}\,b^{10}-68960\,a^{29}\,b^9+53568\,a^{30}\,b^8+20064\,a^{31}\,b^7-17536\,a^{32}\,b^6-4032\,a^{33}\,b^5+3840\,a^{34}\,b^4+512\,a^{35}\,b^3-512\,a^{36}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}-\frac{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{\left(32\,a^{37}\,b-32\,a^{38}+32\,a^6\,b^{32}+32\,a^7\,b^{31}-640\,a^8\,b^{30}+4992\,a^{10}\,b^{28}-2624\,a^{11}\,b^{27}-21504\,a^{12}\,b^{26}+19872\,a^{13}\,b^{25}+57920\,a^{14}\,b^{24}-77472\,a^{15}\,b^{23}-100992\,a^{16}\,b^{22}+195008\,a^{17}\,b^{21}+107008\,a^{18}\,b^{20}-344960\,a^{19}\,b^{19}-39424\,a^{20}\,b^{18}+446688\,a^{21}\,b^{17}-76032\,a^{22}\,b^{16}-431904\,a^{23}\,b^{15}+161920\,a^{24}\,b^{14}+313984\,a^{25}\,b^{13}-167552\,a^{26}\,b^{12}-171072\,a^{27}\,b^{11}+113664\,a^{28}\,b^{10}+68960\,a^{29}\,b^9-53568\,a^{30}\,b^8-20064\,a^{31}\,b^7+17536\,a^{32}\,b^6+4032\,a^{33}\,b^5-3840\,a^{34}\,b^4-512\,a^{35}\,b^3+512\,a^{36}\,b^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}\right)\,1{}\mathrm{i}}{a^2}}\right)}{a^2\,d}+\frac{b^5\,\mathrm{atan}\left(\frac{\frac{b^5\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{b^5\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(32\,a^{38}-32\,a^{37}\,b-32\,a^6\,b^{32}-32\,a^7\,b^{31}+640\,a^8\,b^{30}-4992\,a^{10}\,b^{28}+2624\,a^{11}\,b^{27}+21504\,a^{12}\,b^{26}-19872\,a^{13}\,b^{25}-57920\,a^{14}\,b^{24}+77472\,a^{15}\,b^{23}+100992\,a^{16}\,b^{22}-195008\,a^{17}\,b^{21}-107008\,a^{18}\,b^{20}+344960\,a^{19}\,b^{19}+39424\,a^{20}\,b^{18}-446688\,a^{21}\,b^{17}+76032\,a^{22}\,b^{16}+431904\,a^{23}\,b^{15}-161920\,a^{24}\,b^{14}-313984\,a^{25}\,b^{13}+167552\,a^{26}\,b^{12}+171072\,a^{27}\,b^{11}-113664\,a^{28}\,b^{10}-68960\,a^{29}\,b^9+53568\,a^{30}\,b^8+20064\,a^{31}\,b^7-17536\,a^{32}\,b^6-4032\,a^{33}\,b^5+3840\,a^{34}\,b^4+512\,a^{35}\,b^3-512\,a^{36}\,b^2+\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,1{}\mathrm{i}}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}+\frac{b^5\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{b^5\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(32\,a^{37}\,b-32\,a^{38}+32\,a^6\,b^{32}+32\,a^7\,b^{31}-640\,a^8\,b^{30}+4992\,a^{10}\,b^{28}-2624\,a^{11}\,b^{27}-21504\,a^{12}\,b^{26}+19872\,a^{13}\,b^{25}+57920\,a^{14}\,b^{24}-77472\,a^{15}\,b^{23}-100992\,a^{16}\,b^{22}+195008\,a^{17}\,b^{21}+107008\,a^{18}\,b^{20}-344960\,a^{19}\,b^{19}-39424\,a^{20}\,b^{18}+446688\,a^{21}\,b^{17}-76032\,a^{22}\,b^{16}-431904\,a^{23}\,b^{15}+161920\,a^{24}\,b^{14}+313984\,a^{25}\,b^{13}-167552\,a^{26}\,b^{12}-171072\,a^{27}\,b^{11}+113664\,a^{28}\,b^{10}+68960\,a^{29}\,b^9-53568\,a^{30}\,b^8-20064\,a^{31}\,b^7+17536\,a^{32}\,b^6+4032\,a^{33}\,b^5-3840\,a^{34}\,b^4-512\,a^{35}\,b^3+512\,a^{36}\,b^2+\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,1{}\mathrm{i}}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}}{64\,a^2\,b^{32}-256\,a^3\,b^{31}-960\,a^4\,b^{30}+3840\,a^5\,b^{29}+6144\,a^6\,b^{28}-23168\,a^7\,b^{27}-25088\,a^8\,b^{26}+78784\,a^9\,b^{25}+76800\,a^{10}\,b^{24}-173760\,a^{11}\,b^{23}-183168\,a^{12}\,b^{22}+269952\,a^{13}\,b^{21}+334080\,a^{14}\,b^{20}-314880\,a^{15}\,b^{19}-453888\,a^{16}\,b^{18}+291456\,a^{17}\,b^{17}+449856\,a^{18}\,b^{16}-221568\,a^{19}\,b^{15}-318400\,a^{20}\,b^{14}+136960\,a^{21}\,b^{13}+155904\,a^{22}\,b^{12}-64896\,a^{23}\,b^{11}-49920\,a^{24}\,b^{10}+21440\,a^{25}\,b^9+9344\,a^{26}\,b^8-4288\,a^{27}\,b^7-768\,a^{28}\,b^6+384\,a^{29}\,b^5+\frac{b^5\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{b^5\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(32\,a^{38}-32\,a^{37}\,b-32\,a^6\,b^{32}-32\,a^7\,b^{31}+640\,a^8\,b^{30}-4992\,a^{10}\,b^{28}+2624\,a^{11}\,b^{27}+21504\,a^{12}\,b^{26}-19872\,a^{13}\,b^{25}-57920\,a^{14}\,b^{24}+77472\,a^{15}\,b^{23}+100992\,a^{16}\,b^{22}-195008\,a^{17}\,b^{21}-107008\,a^{18}\,b^{20}+344960\,a^{19}\,b^{19}+39424\,a^{20}\,b^{18}-446688\,a^{21}\,b^{17}+76032\,a^{22}\,b^{16}+431904\,a^{23}\,b^{15}-161920\,a^{24}\,b^{14}-313984\,a^{25}\,b^{13}+167552\,a^{26}\,b^{12}+171072\,a^{27}\,b^{11}-113664\,a^{28}\,b^{10}-68960\,a^{29}\,b^9+53568\,a^{30}\,b^8+20064\,a^{31}\,b^7-17536\,a^{32}\,b^6-4032\,a^{33}\,b^5+3840\,a^{34}\,b^4+512\,a^{35}\,b^3-512\,a^{36}\,b^2+\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}-\frac{b^5\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(32\,a^{36}-96\,a^{35}\,b-384\,a^{34}\,b^2+1408\,a^{33}\,b^3+1920\,a^{32}\,b^4-9600\,a^{31}\,b^5-4480\,a^{30}\,b^6+40320\,a^{29}\,b^7-116480\,a^{27}\,b^9+36096\,a^{26}\,b^{10}+243456\,a^{25}\,b^{11}-138880\,a^{24}\,b^{12}-373632\,a^{23}\,b^{13}+319520\,a^{22}\,b^{14}+412640\,a^{21}\,b^{15}-522720\,a^{20}\,b^{16}-300960\,a^{19}\,b^{17}+636160\,a^{18}\,b^{18}+96000\,a^{17}\,b^{19}-580608\,a^{16}\,b^{20}+68096\,a^{15}\,b^{21}+393792\,a^{14}\,b^{22}-114240\,a^{13}\,b^{23}-194240\,a^{12}\,b^{24}+77760\,a^{11}\,b^{25}+67200\,a^{10}\,b^{26}-31360\,a^9\,b^{27}-15360\,a^8\,b^{28}+7680\,a^7\,b^{29}+2080\,a^6\,b^{30}-1056\,a^5\,b^{31}-128\,a^4\,b^{32}+64\,a^3\,b^{33}\right)-\frac{b^5\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(32\,a^{37}\,b-32\,a^{38}+32\,a^6\,b^{32}+32\,a^7\,b^{31}-640\,a^8\,b^{30}+4992\,a^{10}\,b^{28}-2624\,a^{11}\,b^{27}-21504\,a^{12}\,b^{26}+19872\,a^{13}\,b^{25}+57920\,a^{14}\,b^{24}-77472\,a^{15}\,b^{23}-100992\,a^{16}\,b^{22}+195008\,a^{17}\,b^{21}+107008\,a^{18}\,b^{20}-344960\,a^{19}\,b^{19}-39424\,a^{20}\,b^{18}+446688\,a^{21}\,b^{17}-76032\,a^{22}\,b^{16}-431904\,a^{23}\,b^{15}+161920\,a^{24}\,b^{14}+313984\,a^{25}\,b^{13}-167552\,a^{26}\,b^{12}-171072\,a^{27}\,b^{11}+113664\,a^{28}\,b^{10}+68960\,a^{29}\,b^9-53568\,a^{30}\,b^8-20064\,a^{31}\,b^7+17536\,a^{32}\,b^6+4032\,a^{33}\,b^5-3840\,a^{34}\,b^4-512\,a^{35}\,b^3+512\,a^{36}\,b^2+\frac{b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,\left(64\,a^{39}\,b-128\,a^{38}\,b^2-896\,a^{37}\,b^3+1920\,a^{36}\,b^4+5760\,a^{35}\,b^5-13440\,a^{34}\,b^6-22400\,a^{33}\,b^7+58240\,a^{32}\,b^8+58240\,a^{31}\,b^9-174720\,a^{30}\,b^{10}-104832\,a^{29}\,b^{11}+384384\,a^{28}\,b^{12}+128128\,a^{27}\,b^{13}-640640\,a^{26}\,b^{14}-91520\,a^{25}\,b^{15}+823680\,a^{24}\,b^{16}-823680\,a^{22}\,b^{18}+91520\,a^{21}\,b^{19}+640640\,a^{20}\,b^{20}-128128\,a^{19}\,b^{21}-384384\,a^{18}\,b^{22}+104832\,a^{17}\,b^{23}+174720\,a^{16}\,b^{24}-58240\,a^{15}\,b^{25}-58240\,a^{14}\,b^{26}+22400\,a^{13}\,b^{27}+13440\,a^{12}\,b^{28}-5760\,a^{11}\,b^{29}-1920\,a^{10}\,b^{30}+896\,a^9\,b^{31}+128\,a^8\,b^{32}-64\,a^7\,b^{33}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}}{a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}}}\right)\,\left(6\,a^2-b^2\right)\,\sqrt{{\left(a+b\right)}^7\,{\left(a-b\right)}^7}\,2{}\mathrm{i}}{d\,\left(a^{16}-7\,a^{14}\,b^2+21\,a^{12}\,b^4-35\,a^{10}\,b^6+35\,a^8\,b^8-21\,a^6\,b^{10}+7\,a^4\,b^{12}-a^2\,b^{14}\right)}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*d*(a - b)^2) + ((3*a*b^2 - 3*a^2*b + a^3 - b^3)/(3*(a + b)) + (2*tan(c/2 + (d*x)/2)^2*(11*a^3*b - 31*a*b^3 - 8*a^4 + 13*b^4 + 15*a^2*b^2))/(3*(a + b)^2) - (tan(c/2 + (d*x)/2)^4*(11*a^5*b - 9*a*b^5 - 5*a^6 + 16*b^6 + 31*a^2*b^4 - 34*a^3*b^3 + 6*a^4*b^2))/(a*(a + b)^3))/(d*(tan(c/2 + (d*x)/2)^5*(8*a^4 - 32*a^3*b - 32*a*b^3 + 8*b^4 + 48*a^2*b^2) - tan(c/2 + (d*x)/2)^3*(16*a*b^3 - 16*a^3*b + 8*a^4 - 8*b^4))) + (tan(c/2 + (d*x)/2)*((16*a*b + 8*a^2 - 24*b^2)/(64*(a - b)^4) - 3/(4*(a - b)^2)))/d + (2*atan(((tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - ((32*a^38 - 32*a^37*b - 32*a^6*b^32 - 32*a^7*b^31 + 640*a^8*b^30 - 4992*a^10*b^28 + 2624*a^11*b^27 + 21504*a^12*b^26 - 19872*a^13*b^25 - 57920*a^14*b^24 + 77472*a^15*b^23 + 100992*a^16*b^22 - 195008*a^17*b^21 - 107008*a^18*b^20 + 344960*a^19*b^19 + 39424*a^20*b^18 - 446688*a^21*b^17 + 76032*a^22*b^16 + 431904*a^23*b^15 - 161920*a^24*b^14 - 313984*a^25*b^13 + 167552*a^26*b^12 + 171072*a^27*b^11 - 113664*a^28*b^10 - 68960*a^29*b^9 + 53568*a^30*b^8 + 20064*a^31*b^7 - 17536*a^32*b^6 - 4032*a^33*b^5 + 3840*a^34*b^4 + 512*a^35*b^3 - 512*a^36*b^2 + (tan(c/2 + (d*x)/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2)*1i)/a^2)*1i)/a^2)/a^2 + (tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - ((32*a^37*b - 32*a^38 + 32*a^6*b^32 + 32*a^7*b^31 - 640*a^8*b^30 + 4992*a^10*b^28 - 2624*a^11*b^27 - 21504*a^12*b^26 + 19872*a^13*b^25 + 57920*a^14*b^24 - 77472*a^15*b^23 - 100992*a^16*b^22 + 195008*a^17*b^21 + 107008*a^18*b^20 - 344960*a^19*b^19 - 39424*a^20*b^18 + 446688*a^21*b^17 - 76032*a^22*b^16 - 431904*a^23*b^15 + 161920*a^24*b^14 + 313984*a^25*b^13 - 167552*a^26*b^12 - 171072*a^27*b^11 + 113664*a^28*b^10 + 68960*a^29*b^9 - 53568*a^30*b^8 - 20064*a^31*b^7 + 17536*a^32*b^6 + 4032*a^33*b^5 - 3840*a^34*b^4 - 512*a^35*b^3 + 512*a^36*b^2 + (tan(c/2 + (d*x)/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2)*1i)/a^2)*1i)/a^2)/a^2)/(((tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - ((32*a^38 - 32*a^37*b - 32*a^6*b^32 - 32*a^7*b^31 + 640*a^8*b^30 - 4992*a^10*b^28 + 2624*a^11*b^27 + 21504*a^12*b^26 - 19872*a^13*b^25 - 57920*a^14*b^24 + 77472*a^15*b^23 + 100992*a^16*b^22 - 195008*a^17*b^21 - 107008*a^18*b^20 + 344960*a^19*b^19 + 39424*a^20*b^18 - 446688*a^21*b^17 + 76032*a^22*b^16 + 431904*a^23*b^15 - 161920*a^24*b^14 - 313984*a^25*b^13 + 167552*a^26*b^12 + 171072*a^27*b^11 - 113664*a^28*b^10 - 68960*a^29*b^9 + 53568*a^30*b^8 + 20064*a^31*b^7 - 17536*a^32*b^6 - 4032*a^33*b^5 + 3840*a^34*b^4 + 512*a^35*b^3 - 512*a^36*b^2 + (tan(c/2 + (d*x)/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2)*1i)/a^2)*1i)/a^2)*1i)/a^2 - ((tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - ((32*a^37*b - 32*a^38 + 32*a^6*b^32 + 32*a^7*b^31 - 640*a^8*b^30 + 4992*a^10*b^28 - 2624*a^11*b^27 - 21504*a^12*b^26 + 19872*a^13*b^25 + 57920*a^14*b^24 - 77472*a^15*b^23 - 100992*a^16*b^22 + 195008*a^17*b^21 + 107008*a^18*b^20 - 344960*a^19*b^19 - 39424*a^20*b^18 + 446688*a^21*b^17 - 76032*a^22*b^16 - 431904*a^23*b^15 + 161920*a^24*b^14 + 313984*a^25*b^13 - 167552*a^26*b^12 - 171072*a^27*b^11 + 113664*a^28*b^10 + 68960*a^29*b^9 - 53568*a^30*b^8 - 20064*a^31*b^7 + 17536*a^32*b^6 + 4032*a^33*b^5 - 3840*a^34*b^4 - 512*a^35*b^3 + 512*a^36*b^2 + (tan(c/2 + (d*x)/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2)*1i)/a^2)*1i)/a^2)*1i)/a^2 + 64*a^2*b^32 - 256*a^3*b^31 - 960*a^4*b^30 + 3840*a^5*b^29 + 6144*a^6*b^28 - 23168*a^7*b^27 - 25088*a^8*b^26 + 78784*a^9*b^25 + 76800*a^10*b^24 - 173760*a^11*b^23 - 183168*a^12*b^22 + 269952*a^13*b^21 + 334080*a^14*b^20 - 314880*a^15*b^19 - 453888*a^16*b^18 + 291456*a^17*b^17 + 449856*a^18*b^16 - 221568*a^19*b^15 - 318400*a^20*b^14 + 136960*a^21*b^13 + 155904*a^22*b^12 - 64896*a^23*b^11 - 49920*a^24*b^10 + 21440*a^25*b^9 + 9344*a^26*b^8 - 4288*a^27*b^7 - 768*a^28*b^6 + 384*a^29*b^5)))/(a^2*d) + (b^5*atan(((b^5*(tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - (b^5*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(32*a^38 - 32*a^37*b - 32*a^6*b^32 - 32*a^7*b^31 + 640*a^8*b^30 - 4992*a^10*b^28 + 2624*a^11*b^27 + 21504*a^12*b^26 - 19872*a^13*b^25 - 57920*a^14*b^24 + 77472*a^15*b^23 + 100992*a^16*b^22 - 195008*a^17*b^21 - 107008*a^18*b^20 + 344960*a^19*b^19 + 39424*a^20*b^18 - 446688*a^21*b^17 + 76032*a^22*b^16 + 431904*a^23*b^15 - 161920*a^24*b^14 - 313984*a^25*b^13 + 167552*a^26*b^12 + 171072*a^27*b^11 - 113664*a^28*b^10 - 68960*a^29*b^9 + 53568*a^30*b^8 + 20064*a^31*b^7 - 17536*a^32*b^6 - 4032*a^33*b^5 + 3840*a^34*b^4 + 512*a^35*b^3 - 512*a^36*b^2 + (b^5*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2)))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2))*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*1i)/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2) + (b^5*(tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - (b^5*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(32*a^37*b - 32*a^38 + 32*a^6*b^32 + 32*a^7*b^31 - 640*a^8*b^30 + 4992*a^10*b^28 - 2624*a^11*b^27 - 21504*a^12*b^26 + 19872*a^13*b^25 + 57920*a^14*b^24 - 77472*a^15*b^23 - 100992*a^16*b^22 + 195008*a^17*b^21 + 107008*a^18*b^20 - 344960*a^19*b^19 - 39424*a^20*b^18 + 446688*a^21*b^17 - 76032*a^22*b^16 - 431904*a^23*b^15 + 161920*a^24*b^14 + 313984*a^25*b^13 - 167552*a^26*b^12 - 171072*a^27*b^11 + 113664*a^28*b^10 + 68960*a^29*b^9 - 53568*a^30*b^8 - 20064*a^31*b^7 + 17536*a^32*b^6 + 4032*a^33*b^5 - 3840*a^34*b^4 - 512*a^35*b^3 + 512*a^36*b^2 + (b^5*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2)))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2))*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*1i)/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2))/(64*a^2*b^32 - 256*a^3*b^31 - 960*a^4*b^30 + 3840*a^5*b^29 + 6144*a^6*b^28 - 23168*a^7*b^27 - 25088*a^8*b^26 + 78784*a^9*b^25 + 76800*a^10*b^24 - 173760*a^11*b^23 - 183168*a^12*b^22 + 269952*a^13*b^21 + 334080*a^14*b^20 - 314880*a^15*b^19 - 453888*a^16*b^18 + 291456*a^17*b^17 + 449856*a^18*b^16 - 221568*a^19*b^15 - 318400*a^20*b^14 + 136960*a^21*b^13 + 155904*a^22*b^12 - 64896*a^23*b^11 - 49920*a^24*b^10 + 21440*a^25*b^9 + 9344*a^26*b^8 - 4288*a^27*b^7 - 768*a^28*b^6 + 384*a^29*b^5 + (b^5*(tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - (b^5*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(32*a^38 - 32*a^37*b - 32*a^6*b^32 - 32*a^7*b^31 + 640*a^8*b^30 - 4992*a^10*b^28 + 2624*a^11*b^27 + 21504*a^12*b^26 - 19872*a^13*b^25 - 57920*a^14*b^24 + 77472*a^15*b^23 + 100992*a^16*b^22 - 195008*a^17*b^21 - 107008*a^18*b^20 + 344960*a^19*b^19 + 39424*a^20*b^18 - 446688*a^21*b^17 + 76032*a^22*b^16 + 431904*a^23*b^15 - 161920*a^24*b^14 - 313984*a^25*b^13 + 167552*a^26*b^12 + 171072*a^27*b^11 - 113664*a^28*b^10 - 68960*a^29*b^9 + 53568*a^30*b^8 + 20064*a^31*b^7 - 17536*a^32*b^6 - 4032*a^33*b^5 + 3840*a^34*b^4 + 512*a^35*b^3 - 512*a^36*b^2 + (b^5*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2)))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2))*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2) - (b^5*(tan(c/2 + (d*x)/2)*(32*a^36 - 96*a^35*b + 64*a^3*b^33 - 128*a^4*b^32 - 1056*a^5*b^31 + 2080*a^6*b^30 + 7680*a^7*b^29 - 15360*a^8*b^28 - 31360*a^9*b^27 + 67200*a^10*b^26 + 77760*a^11*b^25 - 194240*a^12*b^24 - 114240*a^13*b^23 + 393792*a^14*b^22 + 68096*a^15*b^21 - 580608*a^16*b^20 + 96000*a^17*b^19 + 636160*a^18*b^18 - 300960*a^19*b^17 - 522720*a^20*b^16 + 412640*a^21*b^15 + 319520*a^22*b^14 - 373632*a^23*b^13 - 138880*a^24*b^12 + 243456*a^25*b^11 + 36096*a^26*b^10 - 116480*a^27*b^9 + 40320*a^29*b^7 - 4480*a^30*b^6 - 9600*a^31*b^5 + 1920*a^32*b^4 + 1408*a^33*b^3 - 384*a^34*b^2) - (b^5*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(32*a^37*b - 32*a^38 + 32*a^6*b^32 + 32*a^7*b^31 - 640*a^8*b^30 + 4992*a^10*b^28 - 2624*a^11*b^27 - 21504*a^12*b^26 + 19872*a^13*b^25 + 57920*a^14*b^24 - 77472*a^15*b^23 - 100992*a^16*b^22 + 195008*a^17*b^21 + 107008*a^18*b^20 - 344960*a^19*b^19 - 39424*a^20*b^18 + 446688*a^21*b^17 - 76032*a^22*b^16 - 431904*a^23*b^15 + 161920*a^24*b^14 + 313984*a^25*b^13 - 167552*a^26*b^12 - 171072*a^27*b^11 + 113664*a^28*b^10 + 68960*a^29*b^9 - 53568*a^30*b^8 - 20064*a^31*b^7 + 17536*a^32*b^6 + 4032*a^33*b^5 - 3840*a^34*b^4 - 512*a^35*b^3 + 512*a^36*b^2 + (b^5*tan(c/2 + (d*x)/2)*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*(64*a^39*b - 64*a^7*b^33 + 128*a^8*b^32 + 896*a^9*b^31 - 1920*a^10*b^30 - 5760*a^11*b^29 + 13440*a^12*b^28 + 22400*a^13*b^27 - 58240*a^14*b^26 - 58240*a^15*b^25 + 174720*a^16*b^24 + 104832*a^17*b^23 - 384384*a^18*b^22 - 128128*a^19*b^21 + 640640*a^20*b^20 + 91520*a^21*b^19 - 823680*a^22*b^18 + 823680*a^24*b^16 - 91520*a^25*b^15 - 640640*a^26*b^14 + 128128*a^27*b^13 + 384384*a^28*b^12 - 104832*a^29*b^11 - 174720*a^30*b^10 + 58240*a^31*b^9 + 58240*a^32*b^8 - 22400*a^33*b^7 - 13440*a^34*b^6 + 5760*a^35*b^5 + 1920*a^36*b^4 - 896*a^37*b^3 - 128*a^38*b^2))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2)))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2))*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2))/(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2)))*(6*a^2 - b^2)*((a + b)^7*(a - b)^7)^(1/2)*2i)/(d*(a^16 - a^2*b^14 + 7*a^4*b^12 - 21*a^6*b^10 + 35*a^8*b^8 - 35*a^10*b^6 + 21*a^12*b^4 - 7*a^14*b^2))","B"
312,0,-1,761,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(5/2)/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}}{b+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(5/2))/(b + a*cos(c + d*x)), x)","F"
313,0,-1,740,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(3/2)/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}}{b+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(3/2))/(b + a*cos(c + d*x)), x)","F"
314,0,-1,415,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(1/2)/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}}{b+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*tan(c + d*x))^(1/2))/(b + a*cos(c + d*x)), x)","F"
315,0,-1,422,0.000000,"\text{Not used}","int(1/((e*tan(c + d*x))^(1/2)*(a + b/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}\,\left(b+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(cos(c + d*x)/((e*tan(c + d*x))^(1/2)*(b + a*cos(c + d*x))), x)","F"
316,0,-1,863,0.000000,"\text{Not used}","int(1/((e*tan(c + d*x))^(3/2)*(a + b/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{3/2}\,\left(b+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(cos(c + d*x)/((e*tan(c + d*x))^(3/2)*(b + a*cos(c + d*x))), x)","F"
317,0,-1,836,0.000000,"\text{Not used}","int(1/((e*tan(c + d*x))^(5/2)*(a + b/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^{5/2}\,\left(b+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(cos(c + d*x)/((e*tan(c + d*x))^(5/2)*(b + a*cos(c + d*x))), x)","F"
318,0,-1,169,0.000000,"\text{Not used}","int(tan(c + d*x)^5*(a + b/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^5\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^5*(a + b/cos(c + d*x))^(1/2), x)","F"
319,0,-1,100,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + b/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^3\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^3*(a + b/cos(c + d*x))^(1/2), x)","F"
320,1,47,51,1.861394,"\text{Not used}","int(tan(c + d*x)*(a + b/cos(c + d*x))^(1/2),x)","\frac{2\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{d}-\frac{2\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{d}","Not used",1,"(2*(a + b/cos(c + d*x))^(1/2))/d - (2*a^(1/2)*atanh((a + b/cos(c + d*x))^(1/2)/a^(1/2)))/d","B"
321,0,-1,106,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + b/cos(c + d*x))^(1/2),x)","\int \mathrm{cot}\left(c+d\,x\right)\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)*(a + b/cos(c + d*x))^(1/2), x)","F"
322,0,-1,215,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + b/cos(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^3\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^3*(a + b/cos(c + d*x))^(1/2), x)","F"
323,0,-1,344,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + b/cos(c + d*x))^(1/2),x)","\int {\mathrm{tan}\left(c+d\,x\right)}^2\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(tan(c + d*x)^2*(a + b/cos(c + d*x))^(1/2), x)","F"
324,0,-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"
325,0,-1,246,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + b/cos(c + d*x))^(1/2),x)","\int {\mathrm{cot}\left(c+d\,x\right)}^2\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int(cot(c + d*x)^2*(a + b/cos(c + d*x))^(1/2), x)","F"
326,0,-1,148,0.000000,"\text{Not used}","int(tan(c + d*x)^5/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^5}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^5/(a + b/cos(c + d*x))^(1/2), x)","F"
327,0,-1,79,0.000000,"\text{Not used}","int(tan(c + d*x)^3/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^3}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^3/(a + b/cos(c + d*x))^(1/2), x)","F"
328,1,27,31,1.634454,"\text{Not used}","int(tan(c + d*x)/(a + b/cos(c + d*x))^(1/2),x)","-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{\sqrt{a}\,d}","Not used",1,"-(2*atanh((a + b/cos(c + d*x))^(1/2)/a^(1/2)))/(a^(1/2)*d)","B"
329,0,-1,106,0.000000,"\text{Not used}","int(cot(c + d*x)/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{\mathrm{cot}\left(c+d\,x\right)}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)/(a + b/cos(c + d*x))^(1/2), x)","F"
330,0,-1,260,0.000000,"\text{Not used}","int(cot(c + d*x)^3/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^3}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)^3/(a + b/cos(c + d*x))^(1/2), x)","F"
331,0,-1,404,0.000000,"\text{Not used}","int(tan(c + d*x)^4/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^4}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^4/(a + b/cos(c + d*x))^(1/2), x)","F"
332,0,-1,310,0.000000,"\text{Not used}","int(tan(c + d*x)^2/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(c+d\,x\right)}^2}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(tan(c + d*x)^2/(a + b/cos(c + d*x))^(1/2), x)","F"
333,0,-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"
334,0,-1,361,0.000000,"\text{Not used}","int(cot(c + d*x)^2/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(c+d\,x\right)}^2}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int(cot(c + d*x)^2/(a + b/cos(c + d*x))^(1/2), x)","F"
335,0,-1,148,0.000000,"\text{Not used}","int(tan(c + d*x)^5/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^5/(a + b/cos(c + d*x))^(3/2), x)","F"
336,0,-1,88,0.000000,"\text{Not used}","int(tan(c + d*x)^3/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^3/(a + b/cos(c + d*x))^(3/2), x)","F"
337,1,50,54,1.954623,"\text{Not used}","int(tan(c + d*x)/(a + b/cos(c + d*x))^(3/2),x)","\frac{2}{a\,d\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}}{\sqrt{a}}\right)}{a^{3/2}\,d}","Not used",1,"2/(a*d*(a + b/cos(c + d*x))^(1/2)) - (2*atanh((a + b/cos(c + d*x))^(1/2)/a^(1/2)))/(a^(3/2)*d)","B"
338,0,-1,142,0.000000,"\text{Not used}","int(cot(c + d*x)/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{\mathrm{cot}\left(c+d\,x\right)}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(cot(c + d*x)/(a + b/cos(c + d*x))^(3/2), x)","F"
339,0,-1,236,0.000000,"\text{Not used}","int(cot(c + d*x)^3/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^3/(a + b/cos(c + d*x))^(3/2), x)","F"
340,0,-1,530,0.000000,"\text{Not used}","int(tan(c + d*x)^4/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^4/(a + b/cos(c + d*x))^(3/2), x)","F"
341,0,-1,344,0.000000,"\text{Not used}","int(tan(c + d*x)^2/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{tan}\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(tan(c + d*x)^2/(a + b/cos(c + d*x))^(3/2), x)","F"
342,0,-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"
343,0,-1,449,0.000000,"\text{Not used}","int(cot(c + d*x)^2/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\mathrm{cot}\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(cot(c + d*x)^2/(a + b/cos(c + d*x))^(3/2), x)","F"
344,0,-1,245,0.000000,"\text{Not used}","int((d*tan(e + f*x))^n*(a + b/cos(e + f*x))^3,x)","\int {\left(d\,\mathrm{tan}\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*tan(e + f*x))^n*(a + b/cos(e + f*x))^3, x)","F"
345,0,-1,160,0.000000,"\text{Not used}","int((d*tan(e + f*x))^n*(a + b/cos(e + f*x))^2,x)","\int {\left(d\,\mathrm{tan}\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*tan(e + f*x))^n*(a + b/cos(e + f*x))^2, x)","F"
346,0,-1,129,0.000000,"\text{Not used}","int((d*tan(e + f*x))^n*(a + b/cos(e + f*x)),x)","\int {\left(d\,\mathrm{tan}\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*tan(e + f*x))^n*(a + b/cos(e + f*x)), x)","F"
347,0,-1,266,0.000000,"\text{Not used}","int((d*tan(e + f*x))^n/(a + b/cos(e + f*x)),x)","\int \frac{\cos\left(e+f\,x\right)\,{\left(d\,\mathrm{tan}\left(e+f\,x\right)\right)}^n}{b+a\,\cos\left(e+f\,x\right)} \,d x","Not used",1,"int((cos(e + f*x)*(d*tan(e + f*x))^n)/(b + a*cos(e + f*x)), x)","F"
348,0,-1,28,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + b/cos(c + d*x))^(3/2),x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",0,"int((e*tan(c + d*x))^m*(a + b/cos(c + d*x))^(3/2), x)","F"
349,0,-1,28,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + b/cos(c + d*x))^(1/2),x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int((e*tan(c + d*x))^m*(a + b/cos(c + d*x))^(1/2), x)","F"
350,0,-1,28,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",0,"int((e*tan(c + d*x))^m/(a + b/cos(c + d*x))^(1/2), x)","F"
351,0,-1,28,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m}{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",0,"int((e*tan(c + d*x))^m/(a + b/cos(c + d*x))^(3/2), x)","F"
352,0,-1,26,0.000000,"\text{Not used}","int((e*tan(c + d*x))^m*(a + b/cos(c + d*x))^n,x)","\int {\left(e\,\mathrm{tan}\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int((e*tan(c + d*x))^m*(a + b/cos(c + d*x))^n, x)","F"
353,0,-1,177,0.000000,"\text{Not used}","int(tan(c + d*x)^5*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^5\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^5*(a + b/cos(c + d*x))^n, x)","F"
354,0,-1,102,0.000000,"\text{Not used}","int(tan(c + d*x)^3*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)^3*(a + b/cos(c + d*x))^n, x)","F"
355,0,-1,48,0.000000,"\text{Not used}","int(tan(c + d*x)*(a + b/cos(c + d*x))^n,x)","\int \mathrm{tan}\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(tan(c + d*x)*(a + b/cos(c + d*x))^n, x)","F"
356,0,-1,162,0.000000,"\text{Not used}","int(cot(c + d*x)*(a + b/cos(c + d*x))^n,x)","\int \mathrm{cot}\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cot(c + d*x)*(a + b/cos(c + d*x))^n, x)","F"
357,0,-1,279,0.000000,"\text{Not used}","int(cot(c + d*x)^3*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(cot(c + d*x)^3*(a + b/cos(c + d*x))^n, x)","F"
358,0,-1,24,0.000000,"\text{Not used}","int(tan(c + d*x)^4*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(tan(c + d*x)^4*(a + b/cos(c + d*x))^n, x)","F"
359,0,-1,237,0.000000,"\text{Not used}","int(tan(c + d*x)^2*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(tan(c + d*x)^2*(a + b/cos(c + d*x))^n, x)","F"
360,0,-1,24,0.000000,"\text{Not used}","int(cot(c + d*x)^2*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(cot(c + d*x)^2*(a + b/cos(c + d*x))^n, x)","F"
361,0,-1,24,0.000000,"\text{Not used}","int(cot(c + d*x)^4*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{cot}\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(cot(c + d*x)^4*(a + b/cos(c + d*x))^n, x)","F"
362,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^(3/2)*(a + b/cos(c + d*x))^n,x)","\int {\mathrm{tan}\left(c+d\,x\right)}^{3/2}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(tan(c + d*x)^(3/2)*(a + b/cos(c + d*x))^n, x)","F"
363,0,-1,26,0.000000,"\text{Not used}","int(tan(c + d*x)^(1/2)*(a + b/cos(c + d*x))^n,x)","\int \sqrt{\mathrm{tan}\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(tan(c + d*x)^(1/2)*(a + b/cos(c + d*x))^n, x)","F"
364,0,-1,26,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/tan(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{\sqrt{\mathrm{tan}\left(c+d\,x\right)}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^n/tan(c + d*x)^(1/2), x)","F"
365,0,-1,26,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/tan(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\mathrm{tan}\left(c+d\,x\right)}^{3/2}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^n/tan(c + d*x)^(3/2), x)","F"