1,1,111,152,0.131205,"\text{Not used}","int(sin(c + d*x)^9*(a + a/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)-2\,a\,{\cos\left(c+d\,x\right)}^2-\frac{4\,a\,{\cos\left(c+d\,x\right)}^3}{3}+\frac{3\,a\,{\cos\left(c+d\,x\right)}^4}{2}+\frac{6\,a\,{\cos\left(c+d\,x\right)}^5}{5}-\frac{2\,a\,{\cos\left(c+d\,x\right)}^6}{3}-\frac{4\,a\,{\cos\left(c+d\,x\right)}^7}{7}+\frac{a\,{\cos\left(c+d\,x\right)}^8}{8}+\frac{a\,{\cos\left(c+d\,x\right)}^9}{9}+a\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) - 2*a*cos(c + d*x)^2 - (4*a*cos(c + d*x)^3)/3 + (3*a*cos(c + d*x)^4)/2 + (6*a*cos(c + d*x)^5)/5 - (2*a*cos(c + d*x)^6)/3 - (4*a*cos(c + d*x)^7)/7 + (a*cos(c + d*x)^8)/8 + (a*cos(c + d*x)^9)/9 + a*log(cos(c + d*x)))/d","B"
2,1,89,119,0.079411,"\text{Not used}","int(sin(c + d*x)^7*(a + a/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)-\frac{3\,a\,{\cos\left(c+d\,x\right)}^2}{2}-a\,{\cos\left(c+d\,x\right)}^3+\frac{3\,a\,{\cos\left(c+d\,x\right)}^4}{4}+\frac{3\,a\,{\cos\left(c+d\,x\right)}^5}{5}-\frac{a\,{\cos\left(c+d\,x\right)}^6}{6}-\frac{a\,{\cos\left(c+d\,x\right)}^7}{7}+a\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) - (3*a*cos(c + d*x)^2)/2 - a*cos(c + d*x)^3 + (3*a*cos(c + d*x)^4)/4 + (3*a*cos(c + d*x)^5)/5 - (a*cos(c + d*x)^6)/6 - (a*cos(c + d*x)^7)/7 + a*log(cos(c + d*x)))/d","B"
3,1,67,87,0.056433,"\text{Not used}","int(sin(c + d*x)^5*(a + a/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)-a\,{\cos\left(c+d\,x\right)}^2-\frac{2\,a\,{\cos\left(c+d\,x\right)}^3}{3}+\frac{a\,{\cos\left(c+d\,x\right)}^4}{4}+\frac{a\,{\cos\left(c+d\,x\right)}^5}{5}+a\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) - a*cos(c + d*x)^2 - (2*a*cos(c + d*x)^3)/3 + (a*cos(c + d*x)^4)/4 + (a*cos(c + d*x)^5)/5 + a*log(cos(c + d*x)))/d","B"
4,1,45,58,0.063487,"\text{Not used}","int(sin(c + d*x)^3*(a + a/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)-\frac{a\,{\cos\left(c+d\,x\right)}^2}{2}-\frac{a\,{\cos\left(c+d\,x\right)}^3}{3}+a\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) - (a*cos(c + d*x)^2)/2 - (a*cos(c + d*x)^3)/3 + a*log(cos(c + d*x)))/d","B"
5,1,20,26,0.037949,"\text{Not used}","int(sin(c + d*x)*(a + a/cos(c + d*x)),x)","-\frac{a\,\left(\cos\left(c+d\,x\right)+\ln\left(\cos\left(c+d\,x\right)\right)\right)}{d}","Not used",1,"-(a*(cos(c + d*x) + log(cos(c + d*x))))/d","B"
6,1,17,30,0.123537,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x),x)","\frac{2\,a\,\mathrm{atanh}\left(1-2\,\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(2*a*atanh(1 - 2*cos(c + d*x)))/d","B"
7,1,53,73,0.963466,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^3,x)","\frac{\frac{a}{2\,\left(\cos\left(c+d\,x\right)-1\right)}-a\,\ln\left(\cos\left(c+d\,x\right)\right)+\frac{3\,a\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{4}+\frac{a\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{4}}{d}","Not used",1,"(a/(2*(cos(c + d*x) - 1)) - a*log(cos(c + d*x)) + (3*a*log(cos(c + d*x) - 1))/4 + (a*log(cos(c + d*x) + 1))/4)/d","B"
8,1,99,118,0.099403,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^5,x)","\frac{11\,a\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{16\,d}-\frac{a\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}+\frac{5\,a\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{16\,d}+\frac{\frac{3\,a\,{\cos\left(c+d\,x\right)}^2}{8}+\frac{a\,\cos\left(c+d\,x\right)}{8}-\frac{3\,a}{4}}{d\,\left({\cos\left(c+d\,x\right)}^3-\cos\left(c+d\,x\right)+{\sin\left(c+d\,x\right)}^2\right)}","Not used",1,"(11*a*log(cos(c + d*x) - 1))/(16*d) - (a*log(cos(c + d*x)))/d + (5*a*log(cos(c + d*x) + 1))/(16*d) + ((a*cos(c + d*x))/8 - (3*a)/4 + (3*a*cos(c + d*x)^2)/8)/(d*(cos(c + d*x)^3 - cos(c + d*x) + sin(c + d*x)^2))","B"
9,1,142,163,0.994452,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^7,x)","\frac{\frac{5\,a\,{\cos\left(c+d\,x\right)}^4}{16}+\frac{3\,a\,{\cos\left(c+d\,x\right)}^3}{16}-\frac{49\,a\,{\cos\left(c+d\,x\right)}^2}{48}-\frac{11\,a\,\cos\left(c+d\,x\right)}{48}+\frac{11\,a}{12}}{d\,\left({\cos\left(c+d\,x\right)}^5-{\cos\left(c+d\,x\right)}^4-2\,{\cos\left(c+d\,x\right)}^3+2\,{\cos\left(c+d\,x\right)}^2+\cos\left(c+d\,x\right)-1\right)}-\frac{a\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}+\frac{21\,a\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{32\,d}+\frac{11\,a\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{32\,d}","Not used",1,"((11*a)/12 - (11*a*cos(c + d*x))/48 - (49*a*cos(c + d*x)^2)/48 + (3*a*cos(c + d*x)^3)/16 + (5*a*cos(c + d*x)^4)/16)/(d*(cos(c + d*x) + 2*cos(c + d*x)^2 - 2*cos(c + d*x)^3 - cos(c + d*x)^4 + cos(c + d*x)^5 - 1)) - (a*log(cos(c + d*x)))/d + (21*a*log(cos(c + d*x) - 1))/(32*d) + (11*a*log(cos(c + d*x) + 1))/(32*d)","B"
10,1,150,165,1.143935,"\text{Not used}","int(sin(c + d*x)^8*(a + a/cos(c + d*x)),x)","\frac{35\,a\,x}{128}+\frac{2\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{7\,a\,\sin\left(2\,c+2\,d\,x\right)}{32\,d}+\frac{37\,a\,\sin\left(3\,c+3\,d\,x\right)}{192\,d}+\frac{7\,a\,\sin\left(4\,c+4\,d\,x\right)}{128\,d}-\frac{9\,a\,\sin\left(5\,c+5\,d\,x\right)}{320\,d}-\frac{a\,\sin\left(6\,c+6\,d\,x\right)}{96\,d}+\frac{a\,\sin\left(7\,c+7\,d\,x\right)}{448\,d}+\frac{a\,\sin\left(8\,c+8\,d\,x\right)}{1024\,d}-\frac{93\,a\,\sin\left(c+d\,x\right)}{64\,d}","Not used",1,"(35*a*x)/128 + (2*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (7*a*sin(2*c + 2*d*x))/(32*d) + (37*a*sin(3*c + 3*d*x))/(192*d) + (7*a*sin(4*c + 4*d*x))/(128*d) - (9*a*sin(5*c + 5*d*x))/(320*d) - (a*sin(6*c + 6*d*x))/(96*d) + (a*sin(7*c + 7*d*x))/(448*d) + (a*sin(8*c + 8*d*x))/(1024*d) - (93*a*sin(c + d*x))/(64*d)","B"
11,1,120,127,1.046588,"\text{Not used}","int(sin(c + d*x)^6*(a + a/cos(c + d*x)),x)","\frac{5\,a\,x}{16}+\frac{2\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{15\,a\,\sin\left(2\,c+2\,d\,x\right)}{64\,d}+\frac{7\,a\,\sin\left(3\,c+3\,d\,x\right)}{48\,d}+\frac{3\,a\,\sin\left(4\,c+4\,d\,x\right)}{64\,d}-\frac{a\,\sin\left(5\,c+5\,d\,x\right)}{80\,d}-\frac{a\,\sin\left(6\,c+6\,d\,x\right)}{192\,d}-\frac{11\,a\,\sin\left(c+d\,x\right)}{8\,d}","Not used",1,"(5*a*x)/16 + (2*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (15*a*sin(2*c + 2*d*x))/(64*d) + (7*a*sin(3*c + 3*d*x))/(48*d) + (3*a*sin(4*c + 4*d*x))/(64*d) - (a*sin(5*c + 5*d*x))/(80*d) - (a*sin(6*c + 6*d*x))/(192*d) - (11*a*sin(c + d*x))/(8*d)","B"
12,1,90,89,1.025372,"\text{Not used}","int(sin(c + d*x)^4*(a + a/cos(c + d*x)),x)","\frac{3\,a\,x}{8}+\frac{2\,a\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}+\frac{a\,\sin\left(3\,c+3\,d\,x\right)}{12\,d}+\frac{a\,\sin\left(4\,c+4\,d\,x\right)}{32\,d}-\frac{5\,a\,\sin\left(c+d\,x\right)}{4\,d}","Not used",1,"(3*a*x)/8 + (2*a*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*sin(2*c + 2*d*x))/(4*d) + (a*sin(3*c + 3*d*x))/(12*d) + (a*sin(4*c + 4*d*x))/(32*d) - (5*a*sin(c + d*x))/(4*d)","B"
13,1,80,51,1.068690,"\text{Not used}","int(sin(c + d*x)^2*(a + a/cos(c + d*x)),x)","\frac{a\,x}{2}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\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)\right)}{d}","Not used",1,"(a*x)/2 - (3*a*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^3)/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) + (2*a*atanh(tan(c/2 + (d*x)/2)))/d","B"
14,1,29,37,0.960520,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^2,x)","\frac{a\,\left(2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a*(2*atanh(tan(c/2 + (d*x)/2)) - cot(c/2 + (d*x)/2)))/d","B"
15,1,65,69,0.983445,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^4,x)","\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a}{12}}{d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)))/d - (a/12 + a*tan(c/2 + (d*x)/2)^2)/(d*tan(c/2 + (d*x)/2)^3) - (a*tan(c/2 + (d*x)/2))/(4*d)","B"
16,1,97,101,1.004930,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^6,x)","\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{48\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(16\,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+\frac{a}{5}\right)}{16\,d}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)))/d - (3*a*tan(c/2 + (d*x)/2))/(8*d) - (a*tan(c/2 + (d*x)/2)^3)/(48*d) - (cot(c/2 + (d*x)/2)^5*(a/5 + 2*a*tan(c/2 + (d*x)/2)^2 + 16*a*tan(c/2 + (d*x)/2)^4))/(16*d)","B"
17,1,128,131,1.165540,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^8,x)","\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{29\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(64\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{5}+\frac{a}{7}\right)}{64\,d}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)))/d - (29*a*tan(c/2 + (d*x)/2))/(64*d) - (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2)^5)/(320*d) - (cot(c/2 + (d*x)/2)^7*(a/7 + (8*a*tan(c/2 + (d*x)/2)^2)/5 + (29*a*tan(c/2 + (d*x)/2)^4)/3 + 64*a*tan(c/2 + (d*x)/2)^6))/(64*d)","B"
18,1,159,165,1.642839,"\text{Not used}","int((a + a/cos(c + d*x))/sin(c + d*x)^10,x)","\frac{2\,a\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{65\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}-\frac{23\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{128\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1792\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(256\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{130\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{46\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{5}+\frac{10\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{7}+\frac{a}{9}\right)}{256\,d}","Not used",1,"(2*a*atanh(tan(c/2 + (d*x)/2)))/d - (65*a*tan(c/2 + (d*x)/2))/(128*d) - (23*a*tan(c/2 + (d*x)/2)^3)/(384*d) - (a*tan(c/2 + (d*x)/2)^5)/(128*d) - (a*tan(c/2 + (d*x)/2)^7)/(1792*d) - (cot(c/2 + (d*x)/2)^9*(a/9 + (10*a*tan(c/2 + (d*x)/2)^2)/7 + (46*a*tan(c/2 + (d*x)/2)^4)/5 + (130*a*tan(c/2 + (d*x)/2)^6)/3 + 256*a*tan(c/2 + (d*x)/2)^8))/(256*d)","B"
19,1,146,183,0.992747,"\text{Not used}","int(sin(c + d*x)^9*(a + a/cos(c + d*x))^2,x)","-\frac{\frac{2\,a^2\,{\cos\left(c+d\,x\right)}^3}{3}-\frac{a^2}{\cos\left(c+d\,x\right)}-4\,a^2\,{\cos\left(c+d\,x\right)}^2-3\,a^2\,\cos\left(c+d\,x\right)+3\,a^2\,{\cos\left(c+d\,x\right)}^4+\frac{2\,a^2\,{\cos\left(c+d\,x\right)}^5}{5}-\frac{4\,a^2\,{\cos\left(c+d\,x\right)}^6}{3}-\frac{3\,a^2\,{\cos\left(c+d\,x\right)}^7}{7}+\frac{a^2\,{\cos\left(c+d\,x\right)}^8}{4}+\frac{a^2\,{\cos\left(c+d\,x\right)}^9}{9}+2\,a^2\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-((2*a^2*cos(c + d*x)^3)/3 - a^2/cos(c + d*x) - 4*a^2*cos(c + d*x)^2 - 3*a^2*cos(c + d*x) + 3*a^2*cos(c + d*x)^4 + (2*a^2*cos(c + d*x)^5)/5 - (4*a^2*cos(c + d*x)^6)/3 - (3*a^2*cos(c + d*x)^7)/7 + (a^2*cos(c + d*x)^8)/4 + (a^2*cos(c + d*x)^9)/9 + 2*a^2*log(cos(c + d*x)))/d","B"
20,1,105,131,0.949808,"\text{Not used}","int(sin(c + d*x)^7*(a + a/cos(c + d*x))^2,x)","\frac{2\,a^2\,\cos\left(c+d\,x\right)+\frac{a^2}{\cos\left(c+d\,x\right)}+3\,a^2\,{\cos\left(c+d\,x\right)}^2-\frac{3\,a^2\,{\cos\left(c+d\,x\right)}^4}{2}-\frac{2\,a^2\,{\cos\left(c+d\,x\right)}^5}{5}+\frac{a^2\,{\cos\left(c+d\,x\right)}^6}{3}+\frac{a^2\,{\cos\left(c+d\,x\right)}^7}{7}-2\,a^2\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(2*a^2*cos(c + d*x) + a^2/cos(c + d*x) + 3*a^2*cos(c + d*x)^2 - (3*a^2*cos(c + d*x)^4)/2 - (2*a^2*cos(c + d*x)^5)/5 + (a^2*cos(c + d*x)^6)/3 + (a^2*cos(c + d*x)^7)/7 - 2*a^2*log(cos(c + d*x)))/d","B"
21,1,91,112,0.885870,"\text{Not used}","int(sin(c + d*x)^5*(a + a/cos(c + d*x))^2,x)","\frac{a^2\,\cos\left(c+d\,x\right)+\frac{a^2}{\cos\left(c+d\,x\right)}+2\,a^2\,{\cos\left(c+d\,x\right)}^2+\frac{a^2\,{\cos\left(c+d\,x\right)}^3}{3}-\frac{a^2\,{\cos\left(c+d\,x\right)}^4}{2}-\frac{a^2\,{\cos\left(c+d\,x\right)}^5}{5}-2\,a^2\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(a^2*cos(c + d*x) + a^2/cos(c + d*x) + 2*a^2*cos(c + d*x)^2 + (a^2*cos(c + d*x)^3)/3 - (a^2*cos(c + d*x)^4)/2 - (a^2*cos(c + d*x)^5)/5 - 2*a^2*log(cos(c + d*x)))/d","B"
22,1,54,62,0.057772,"\text{Not used}","int(sin(c + d*x)^3*(a + a/cos(c + d*x))^2,x)","\frac{\frac{a^2}{\cos\left(c+d\,x\right)}+a^2\,{\cos\left(c+d\,x\right)}^2+\frac{a^2\,{\cos\left(c+d\,x\right)}^3}{3}-2\,a^2\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(a^2/cos(c + d*x) + a^2*cos(c + d*x)^2 + (a^2*cos(c + d*x)^3)/3 - 2*a^2*log(cos(c + d*x)))/d","B"
23,1,41,43,0.059433,"\text{Not used}","int(sin(c + d*x)*(a + a/cos(c + d*x))^2,x)","-\frac{a^2\,\left(2\,\cos\left(c+d\,x\right)\,\ln\left(\cos\left(c+d\,x\right)\right)+{\cos\left(c+d\,x\right)}^2-1\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"-(a^2*(2*cos(c + d*x)*log(cos(c + d*x)) + cos(c + d*x)^2 - 1))/(d*cos(c + d*x))","B"
24,1,35,48,0.081993,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x),x)","\frac{a^2}{d\,\cos\left(c+d\,x\right)}-\frac{4\,a^2\,\mathrm{atanh}\left(2\,\cos\left(c+d\,x\right)-1\right)}{d}","Not used",1,"a^2/(d*cos(c + d*x)) - (4*a^2*atanh(2*cos(c + d*x) - 1))/d","B"
25,1,61,69,0.901477,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^3,x)","-\frac{2\,a^2\,\cos\left(c+d\,x\right)-a^2}{d\,\left(\cos\left(c+d\,x\right)-{\cos\left(c+d\,x\right)}^2\right)}-\frac{4\,a^2\,\mathrm{atanh}\left(2\,\cos\left(c+d\,x\right)-1\right)}{d}","Not used",1,"- (2*a^2*cos(c + d*x) - a^2)/(d*(cos(c + d*x) - cos(c + d*x)^2)) - (4*a^2*atanh(2*cos(c + d*x) - 1))/d","B"
26,1,109,115,0.095190,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^5,x)","\frac{17\,a^2\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{8\,d}-\frac{a^2\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{8\,d}+\frac{\frac{9\,a^2\,{\cos\left(c+d\,x\right)}^2}{4}-\frac{7\,a^2\,\cos\left(c+d\,x\right)}{2}+a^2}{d\,\left({\cos\left(c+d\,x\right)}^3-2\,{\cos\left(c+d\,x\right)}^2+\cos\left(c+d\,x\right)\right)}-\frac{2\,a^2\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(17*a^2*log(cos(c + d*x) - 1))/(8*d) - (a^2*log(cos(c + d*x) + 1))/(8*d) + (a^2 - (7*a^2*cos(c + d*x))/2 + (9*a^2*cos(c + d*x)^2)/4)/(d*(cos(c + d*x) - 2*cos(c + d*x)^2 + cos(c + d*x)^3)) - (2*a^2*log(cos(c + d*x)))/d","B"
27,1,147,160,0.110275,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^7,x)","\frac{9\,a^2\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{4\,d}-\frac{a^2\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{4\,d}-\frac{2\,a^2\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}+\frac{-\frac{5\,a^2\,{\cos\left(c+d\,x\right)}^4}{2}+4\,a^2\,{\cos\left(c+d\,x\right)}^3+\frac{7\,a^2\,{\cos\left(c+d\,x\right)}^2}{6}-\frac{23\,a^2\,\cos\left(c+d\,x\right)}{6}+a^2}{d\,\left(-{\cos\left(c+d\,x\right)}^5+2\,{\cos\left(c+d\,x\right)}^4-2\,{\cos\left(c+d\,x\right)}^2+\cos\left(c+d\,x\right)\right)}","Not used",1,"(9*a^2*log(cos(c + d*x) - 1))/(4*d) - (a^2*log(cos(c + d*x) + 1))/(4*d) - (2*a^2*log(cos(c + d*x)))/d + (a^2 - (23*a^2*cos(c + d*x))/6 + (7*a^2*cos(c + d*x)^2)/6 + 4*a^2*cos(c + d*x)^3 - (5*a^2*cos(c + d*x)^4)/2)/(d*(cos(c + d*x) - 2*cos(c + d*x)^2 + 2*cos(c + d*x)^4 - cos(c + d*x)^5))","B"
28,1,203,205,0.171149,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^9,x)","\frac{-\frac{175\,a^2\,{\cos\left(c+d\,x\right)}^6}{64}+\frac{143\,a^2\,{\cos\left(c+d\,x\right)}^5}{32}+\frac{367\,a^2\,{\cos\left(c+d\,x\right)}^4}{96}-\frac{827\,a^2\,{\cos\left(c+d\,x\right)}^3}{96}+\frac{19\,a^2\,{\cos\left(c+d\,x\right)}^2}{192}+\frac{49\,a^2\,\cos\left(c+d\,x\right)}{12}-a^2}{d\,\left(-{\cos\left(c+d\,x\right)}^7+2\,{\cos\left(c+d\,x\right)}^6+{\cos\left(c+d\,x\right)}^5-4\,{\cos\left(c+d\,x\right)}^4+{\cos\left(c+d\,x\right)}^3+2\,{\cos\left(c+d\,x\right)}^2-\cos\left(c+d\,x\right)\right)}+\frac{303\,a^2\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{128\,d}-\frac{47\,a^2\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{128\,d}-\frac{2\,a^2\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"((49*a^2*cos(c + d*x))/12 - a^2 + (19*a^2*cos(c + d*x)^2)/192 - (827*a^2*cos(c + d*x)^3)/96 + (367*a^2*cos(c + d*x)^4)/96 + (143*a^2*cos(c + d*x)^5)/32 - (175*a^2*cos(c + d*x)^6)/64)/(d*(2*cos(c + d*x)^2 - cos(c + d*x) + cos(c + d*x)^3 - 4*cos(c + d*x)^4 + cos(c + d*x)^5 + 2*cos(c + d*x)^6 - cos(c + d*x)^7)) + (303*a^2*log(cos(c + d*x) - 1))/(128*d) - (47*a^2*log(cos(c + d*x) + 1))/(128*d) - (2*a^2*log(cos(c + d*x)))/d","B"
29,1,293,199,2.540279,"\text{Not used}","int(sin(c + d*x)^8*(a + a/cos(c + d*x))^2,x)","\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{245\,a^2\,x}{128}+\frac{\frac{501\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{64}+\frac{2633\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{48}+\frac{38047\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{240}+\frac{388613\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{1680}+\frac{13781\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{96}-\frac{32681\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{560}-\frac{1739\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{80}-\frac{61\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{16}-\frac{11\,a^2\,\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)}^{18}-7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-20\,{\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}-14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+28\,{\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+7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(4*a^2*atanh(tan(c/2 + (d*x)/2)))/d - (245*a^2*x)/128 + ((13781*a^2*tan(c/2 + (d*x)/2)^9)/96 - (1739*a^2*tan(c/2 + (d*x)/2)^5)/80 - (32681*a^2*tan(c/2 + (d*x)/2)^7)/560 - (61*a^2*tan(c/2 + (d*x)/2)^3)/16 + (388613*a^2*tan(c/2 + (d*x)/2)^11)/1680 + (38047*a^2*tan(c/2 + (d*x)/2)^13)/240 + (2633*a^2*tan(c/2 + (d*x)/2)^15)/48 + (501*a^2*tan(c/2 + (d*x)/2)^17)/64 - (11*a^2*tan(c/2 + (d*x)/2))/64)/(d*(7*tan(c/2 + (d*x)/2)^2 + 20*tan(c/2 + (d*x)/2)^4 + 28*tan(c/2 + (d*x)/2)^6 + 14*tan(c/2 + (d*x)/2)^8 - 14*tan(c/2 + (d*x)/2)^10 - 28*tan(c/2 + (d*x)/2)^12 - 20*tan(c/2 + (d*x)/2)^14 - 7*tan(c/2 + (d*x)/2)^16 - tan(c/2 + (d*x)/2)^18 + 1))","B"
30,1,235,157,2.156828,"\text{Not used}","int(sin(c + d*x)^6*(a + a/cos(c + d*x))^2,x)","\frac{\frac{57\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{8}+\frac{431\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{12}+\frac{8041\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{120}+\frac{91\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}-\frac{797\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}-\frac{27\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-\frac{7\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-9\,{\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+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+9\,{\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{25\,a^2\,x}{16}+\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"((91*a^2*tan(c/2 + (d*x)/2)^7)/2 - (797*a^2*tan(c/2 + (d*x)/2)^5)/40 - (27*a^2*tan(c/2 + (d*x)/2)^3)/4 + (8041*a^2*tan(c/2 + (d*x)/2)^9)/120 + (431*a^2*tan(c/2 + (d*x)/2)^11)/12 + (57*a^2*tan(c/2 + (d*x)/2)^13)/8 - (7*a^2*tan(c/2 + (d*x)/2))/8)/(d*(5*tan(c/2 + (d*x)/2)^2 + 9*tan(c/2 + (d*x)/2)^4 + 5*tan(c/2 + (d*x)/2)^6 - 5*tan(c/2 + (d*x)/2)^8 - 9*tan(c/2 + (d*x)/2)^10 - 5*tan(c/2 + (d*x)/2)^12 - tan(c/2 + (d*x)/2)^14 + 1)) - (25*a^2*x)/16 + (4*a^2*atanh(tan(c/2 + (d*x)/2)))/d","B"
31,1,177,115,1.825320,"\text{Not used}","int(sin(c + d*x)^4*(a + a/cos(c + d*x))^2,x)","\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{9\,a^2\,x}{8}+\frac{\frac{25\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{58\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+\frac{31\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}-\frac{22\,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)}{4}}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(4*a^2*atanh(tan(c/2 + (d*x)/2)))/d - (9*a^2*x)/8 + ((31*a^2*tan(c/2 + (d*x)/2)^5)/2 - (22*a^2*tan(c/2 + (d*x)/2)^3)/3 + (58*a^2*tan(c/2 + (d*x)/2)^7)/3 + (25*a^2*tan(c/2 + (d*x)/2)^9)/4 - (7*a^2*tan(c/2 + (d*x)/2))/4)/(d*(3*tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - 3*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^10 + 1))","B"
32,1,117,73,1.160146,"\text{Not used}","int(sin(c + d*x)^2*(a + a/cos(c + d*x))^2,x)","\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,x}{2}+\frac{5\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-3\,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-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(4*a^2*atanh(tan(c/2 + (d*x)/2)))/d - (a^2*x)/2 + (6*a^2*tan(c/2 + (d*x)/2)^3 + 5*a^2*tan(c/2 + (d*x)/2)^5 - 3*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 + 1))","B"
33,1,70,57,1.126421,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^2,x)","\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,a^2}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(4*a^2*tan(c/2 + (d*x)/2)^2 - 2*a^2)/(d*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^3)) + (4*a^2*atanh(tan(c/2 + (d*x)/2)))/d","B"
34,1,91,87,2.484948,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^4,x)","\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-9\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{14\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{a^2}{3}}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}","Not used",1,"(4*a^2*atanh(tan(c/2 + (d*x)/2)))/d - ((14*a^2*tan(c/2 + (d*x)/2)^2)/3 - 9*a^2*tan(c/2 + (d*x)/2)^4 + a^2/3)/(d*(2*tan(c/2 + (d*x)/2)^3 - 2*tan(c/2 + (d*x)/2)^5))","B"
35,1,124,129,1.283963,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^6,x)","\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-39\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{62\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{32\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{a^2}{5}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(4*a^2*atanh(tan(c/2 + (d*x)/2)))/d - ((32*a^2*tan(c/2 + (d*x)/2)^2)/15 + (62*a^2*tan(c/2 + (d*x)/2)^4)/3 - 39*a^2*tan(c/2 + (d*x)/2)^6 + a^2/5)/(d*(8*tan(c/2 + (d*x)/2)^5 - 8*tan(c/2 + (d*x)/2)^7)) + (a^2*tan(c/2 + (d*x)/2))/(8*d)","B"
36,1,159,163,0.988333,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^8,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{9\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32\,d}-\frac{-166\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{268\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{163\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{58\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{a^2}{7}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\right)}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^3)/(96*d) + (4*a^2*atanh(tan(c/2 + (d*x)/2)))/d + (9*a^2*tan(c/2 + (d*x)/2))/(32*d) - ((58*a^2*tan(c/2 + (d*x)/2)^2)/35 + (163*a^2*tan(c/2 + (d*x)/2)^4)/15 + (268*a^2*tan(c/2 + (d*x)/2)^6)/3 - 166*a^2*tan(c/2 + (d*x)/2)^8 + a^2/7)/(d*(32*tan(c/2 + (d*x)/2)^7 - 32*tan(c/2 + (d*x)/2)^9))","B"
37,1,194,201,0.972340,"\text{Not used}","int((a + a/cos(c + d*x))^2/sin(c + d*x)^10,x)","\frac{11\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{384\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{640\,d}+\frac{4\,a^2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{-699\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{1142\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{764\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{15}+\frac{344\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{35}+\frac{92\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{63}+\frac{a^2}{9}}{d\,\left(128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\right)}+\frac{57\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{128\,d}","Not used",1,"(11*a^2*tan(c/2 + (d*x)/2)^3)/(384*d) + (a^2*tan(c/2 + (d*x)/2)^5)/(640*d) + (4*a^2*atanh(tan(c/2 + (d*x)/2)))/d - ((92*a^2*tan(c/2 + (d*x)/2)^2)/63 + (344*a^2*tan(c/2 + (d*x)/2)^4)/35 + (764*a^2*tan(c/2 + (d*x)/2)^6)/15 + (1142*a^2*tan(c/2 + (d*x)/2)^8)/3 - 699*a^2*tan(c/2 + (d*x)/2)^10 + a^2/9)/(d*(128*tan(c/2 + (d*x)/2)^9 - 128*tan(c/2 + (d*x)/2)^11)) + (57*a^2*tan(c/2 + (d*x)/2))/(128*d)","B"
38,1,157,203,0.964745,"\text{Not used}","int(sin(c + d*x)^9*(a + a/cos(c + d*x))^3,x)","\frac{\frac{3\,a^3\,\cos\left(c+d\,x\right)+\frac{a^3}{2}}{{\cos\left(c+d\,x\right)}^2}+11\,a^3\,\cos\left(c+d\,x\right)+3\,a^3\,{\cos\left(c+d\,x\right)}^2-\frac{14\,a^3\,{\cos\left(c+d\,x\right)}^3}{3}-\frac{7\,a^3\,{\cos\left(c+d\,x\right)}^4}{2}+\frac{6\,a^3\,{\cos\left(c+d\,x\right)}^5}{5}+\frac{11\,a^3\,{\cos\left(c+d\,x\right)}^6}{6}+\frac{a^3\,{\cos\left(c+d\,x\right)}^7}{7}-\frac{3\,a^3\,{\cos\left(c+d\,x\right)}^8}{8}-\frac{a^3\,{\cos\left(c+d\,x\right)}^9}{9}+a^3\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"((3*a^3*cos(c + d*x) + a^3/2)/cos(c + d*x)^2 + 11*a^3*cos(c + d*x) + 3*a^3*cos(c + d*x)^2 - (14*a^3*cos(c + d*x)^3)/3 - (7*a^3*cos(c + d*x)^4)/2 + (6*a^3*cos(c + d*x)^5)/5 + (11*a^3*cos(c + d*x)^6)/6 + (a^3*cos(c + d*x)^7)/7 - (3*a^3*cos(c + d*x)^8)/8 - (a^3*cos(c + d*x)^9)/9 + a^3*log(cos(c + d*x)))/d","B"
39,1,107,131,0.896680,"\text{Not used}","int(sin(c + d*x)^7*(a + a/cos(c + d*x))^3,x)","\frac{\frac{3\,a^3\,\cos\left(c+d\,x\right)+\frac{a^3}{2}}{{\cos\left(c+d\,x\right)}^2}+8\,a^3\,\cos\left(c+d\,x\right)+3\,a^3\,{\cos\left(c+d\,x\right)}^2-2\,a^3\,{\cos\left(c+d\,x\right)}^3-2\,a^3\,{\cos\left(c+d\,x\right)}^4+\frac{a^3\,{\cos\left(c+d\,x\right)}^6}{2}+\frac{a^3\,{\cos\left(c+d\,x\right)}^7}{7}}{d}","Not used",1,"((3*a^3*cos(c + d*x) + a^3/2)/cos(c + d*x)^2 + 8*a^3*cos(c + d*x) + 3*a^3*cos(c + d*x)^2 - 2*a^3*cos(c + d*x)^3 - 2*a^3*cos(c + d*x)^4 + (a^3*cos(c + d*x)^6)/2 + (a^3*cos(c + d*x)^7)/7)/d","B"
40,1,107,134,0.887014,"\text{Not used}","int(sin(c + d*x)^5*(a + a/cos(c + d*x))^3,x)","-\frac{\frac{a^3\,{\cos\left(c+d\,x\right)}^3}{3}-5\,a^3\,\cos\left(c+d\,x\right)-\frac{5\,a^3\,{\cos\left(c+d\,x\right)}^2}{2}-\frac{3\,a^3\,\cos\left(c+d\,x\right)+\frac{a^3}{2}}{{\cos\left(c+d\,x\right)}^2}+\frac{3\,a^3\,{\cos\left(c+d\,x\right)}^4}{4}+\frac{a^3\,{\cos\left(c+d\,x\right)}^5}{5}+a^3\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-((a^3*cos(c + d*x)^3)/3 - 5*a^3*cos(c + d*x) - (5*a^3*cos(c + d*x)^2)/2 - (3*a^3*cos(c + d*x) + a^3/2)/cos(c + d*x)^2 + (3*a^3*cos(c + d*x)^4)/4 + (a^3*cos(c + d*x)^5)/5 + a^3*log(cos(c + d*x)))/d","B"
41,1,80,98,0.881674,"\text{Not used}","int(sin(c + d*x)^3*(a + a/cos(c + d*x))^3,x)","\frac{\frac{3\,a^3\,\cos\left(c+d\,x\right)+\frac{a^3}{2}}{{\cos\left(c+d\,x\right)}^2}+2\,a^3\,\cos\left(c+d\,x\right)+\frac{3\,a^3\,{\cos\left(c+d\,x\right)}^2}{2}+\frac{a^3\,{\cos\left(c+d\,x\right)}^3}{3}-2\,a^3\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"((3*a^3*cos(c + d*x) + a^3/2)/cos(c + d*x)^2 + 2*a^3*cos(c + d*x) + (3*a^3*cos(c + d*x)^2)/2 + (a^3*cos(c + d*x)^3)/3 - 2*a^3*log(cos(c + d*x)))/d","B"
42,1,52,62,0.055221,"\text{Not used}","int(sin(c + d*x)*(a + a/cos(c + d*x))^3,x)","\frac{a^3\,\left(3\,\cos\left(c+d\,x\right)-{\cos\left(c+d\,x\right)}^3-3\,{\cos\left(c+d\,x\right)}^2\,\ln\left(\cos\left(c+d\,x\right)\right)+\frac{1}{2}\right)}{d\,{\cos\left(c+d\,x\right)}^2}","Not used",1,"(a^3*(3*cos(c + d*x) - cos(c + d*x)^3 - 3*cos(c + d*x)^2*log(cos(c + d*x)) + 1/2))/(d*cos(c + d*x)^2)","B"
43,1,49,67,0.074277,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x),x)","\frac{3\,a^3\,\cos\left(c+d\,x\right)+\frac{a^3}{2}}{d\,{\cos\left(c+d\,x\right)}^2}-\frac{8\,a^3\,\mathrm{atanh}\left(2\,\cos\left(c+d\,x\right)-1\right)}{d}","Not used",1,"(3*a^3*cos(c + d*x) + a^3/2)/(d*cos(c + d*x)^2) - (8*a^3*atanh(2*cos(c + d*x) - 1))/d","B"
44,1,75,88,0.095418,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^3,x)","\frac{-5\,a^3\,{\cos\left(c+d\,x\right)}^2+\frac{5\,a^3\,\cos\left(c+d\,x\right)}{2}+\frac{a^3}{2}}{d\,\left({\cos\left(c+d\,x\right)}^2-{\cos\left(c+d\,x\right)}^3\right)}-\frac{10\,a^3\,\mathrm{atanh}\left(2\,\cos\left(c+d\,x\right)-1\right)}{d}","Not used",1,"((5*a^3*cos(c + d*x))/2 + a^3/2 - 5*a^3*cos(c + d*x)^2)/(d*(cos(c + d*x)^2 - cos(c + d*x)^3)) - (10*a^3*atanh(2*cos(c + d*x) - 1))/d","B"
45,1,96,111,0.930506,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^5,x)","\frac{6\,a^3\,{\cos\left(c+d\,x\right)}^3-9\,a^3\,{\cos\left(c+d\,x\right)}^2+2\,a^3\,\cos\left(c+d\,x\right)+\frac{a^3}{2}}{d\,\left({\cos\left(c+d\,x\right)}^4-2\,{\cos\left(c+d\,x\right)}^3+{\cos\left(c+d\,x\right)}^2\right)}-\frac{12\,a^3\,\mathrm{atanh}\left(2\,\cos\left(c+d\,x\right)-1\right)}{d}","Not used",1,"(2*a^3*cos(c + d*x) + a^3/2 - 9*a^3*cos(c + d*x)^2 + 6*a^3*cos(c + d*x)^3)/(d*(cos(c + d*x)^2 - 2*cos(c + d*x)^3 + cos(c + d*x)^4)) - (12*a^3*atanh(2*cos(c + d*x) - 1))/d","B"
46,1,151,157,0.964839,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^7,x)","\frac{111\,a^3\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{16\,d}+\frac{a^3\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{16\,d}+\frac{-\frac{55\,a^3\,{\cos\left(c+d\,x\right)}^4}{8}+\frac{137\,a^3\,{\cos\left(c+d\,x\right)}^3}{8}-\frac{149\,a^3\,{\cos\left(c+d\,x\right)}^2}{12}+\frac{3\,a^3\,\cos\left(c+d\,x\right)}{2}+\frac{a^3}{2}}{d\,\left(-{\cos\left(c+d\,x\right)}^5+3\,{\cos\left(c+d\,x\right)}^4-3\,{\cos\left(c+d\,x\right)}^3+{\cos\left(c+d\,x\right)}^2\right)}-\frac{7\,a^3\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(111*a^3*log(cos(c + d*x) - 1))/(16*d) + (a^3*log(cos(c + d*x) + 1))/(16*d) + ((3*a^3*cos(c + d*x))/2 + a^3/2 - (149*a^3*cos(c + d*x)^2)/12 + (137*a^3*cos(c + d*x)^3)/8 - (55*a^3*cos(c + d*x)^4)/8)/(d*(cos(c + d*x)^2 - 3*cos(c + d*x)^3 + 3*cos(c + d*x)^4 - cos(c + d*x)^5)) - (7*a^3*log(cos(c + d*x)))/d","B"
47,1,195,202,1.012651,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^9,x)","\frac{501\,a^3\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{64\,d}+\frac{11\,a^3\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{64\,d}+\frac{\frac{245\,a^3\,{\cos\left(c+d\,x\right)}^6}{32}-\frac{607\,a^3\,{\cos\left(c+d\,x\right)}^5}{32}+\frac{563\,a^3\,{\cos\left(c+d\,x\right)}^4}{96}+\frac{565\,a^3\,{\cos\left(c+d\,x\right)}^3}{32}-\frac{43\,a^3\,{\cos\left(c+d\,x\right)}^2}{3}+\frac{3\,a^3\,\cos\left(c+d\,x\right)}{2}+\frac{a^3}{2}}{d\,\left({\cos\left(c+d\,x\right)}^7-3\,{\cos\left(c+d\,x\right)}^6+2\,{\cos\left(c+d\,x\right)}^5+2\,{\cos\left(c+d\,x\right)}^4-3\,{\cos\left(c+d\,x\right)}^3+{\cos\left(c+d\,x\right)}^2\right)}-\frac{8\,a^3\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(501*a^3*log(cos(c + d*x) - 1))/(64*d) + (11*a^3*log(cos(c + d*x) + 1))/(64*d) + ((3*a^3*cos(c + d*x))/2 + a^3/2 - (43*a^3*cos(c + d*x)^2)/3 + (565*a^3*cos(c + d*x)^3)/32 + (563*a^3*cos(c + d*x)^4)/96 - (607*a^3*cos(c + d*x)^5)/32 + (245*a^3*cos(c + d*x)^6)/32)/(d*(cos(c + d*x)^2 - 3*cos(c + d*x)^3 + 2*cos(c + d*x)^4 + 2*cos(c + d*x)^5 - 3*cos(c + d*x)^6 + cos(c + d*x)^7)) - (8*a^3*log(cos(c + d*x)))/d","B"
48,1,320,210,2.453797,"\text{Not used}","int(sin(c + d*x)^8*(a + a/cos(c + d*x))^3,x)","\frac{-\frac{741\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{19}}{64}-\frac{12469\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{17}}{192}-\frac{5027\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{40}-\frac{19211\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{420}+\frac{199977\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{1120}+\frac{877061\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3360}+\frac{10233\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{140}+\frac{6243\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}+\frac{4967\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{64}+\frac{869\,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)}^{20}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+13\,{\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}-14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-28\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{805\,a^3\,x}{128}","Not used",1,"((4967*a^3*tan(c/2 + (d*x)/2)^3)/64 + (6243*a^3*tan(c/2 + (d*x)/2)^5)/40 + (10233*a^3*tan(c/2 + (d*x)/2)^7)/140 + (877061*a^3*tan(c/2 + (d*x)/2)^9)/3360 + (199977*a^3*tan(c/2 + (d*x)/2)^11)/1120 - (19211*a^3*tan(c/2 + (d*x)/2)^13)/420 - (5027*a^3*tan(c/2 + (d*x)/2)^15)/40 - (12469*a^3*tan(c/2 + (d*x)/2)^17)/192 - (741*a^3*tan(c/2 + (d*x)/2)^19)/64 + (869*a^3*tan(c/2 + (d*x)/2))/64)/(d*(6*tan(c/2 + (d*x)/2)^2 + 13*tan(c/2 + (d*x)/2)^4 + 8*tan(c/2 + (d*x)/2)^6 - 14*tan(c/2 + (d*x)/2)^8 - 28*tan(c/2 + (d*x)/2)^10 - 14*tan(c/2 + (d*x)/2)^12 + 8*tan(c/2 + (d*x)/2)^14 + 13*tan(c/2 + (d*x)/2)^16 + 6*tan(c/2 + (d*x)/2)^18 + tan(c/2 + (d*x)/2)^20 + 1)) - (a^3*atanh(tan(c/2 + (d*x)/2)))/d - (805*a^3*x)/128","B"
49,1,261,182,2.224521,"\text{Not used}","int(sin(c + d*x)^6*(a + a/cos(c + d*x))^3,x)","\frac{a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{85\,a^3\,x}{16}+\frac{-\frac{93\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{8}-\frac{1039\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{24}-\frac{4319\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{120}+\frac{6169\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{120}+\frac{3933\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{40}+\frac{997\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40}+\frac{277\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}+\frac{77\,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)}^{16}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-10\,{\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+4\,{\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,"(a^3*atanh(tan(c/2 + (d*x)/2)))/d - (85*a^3*x)/16 + ((277*a^3*tan(c/2 + (d*x)/2)^3)/8 + (997*a^3*tan(c/2 + (d*x)/2)^5)/40 + (3933*a^3*tan(c/2 + (d*x)/2)^7)/40 + (6169*a^3*tan(c/2 + (d*x)/2)^9)/120 - (4319*a^3*tan(c/2 + (d*x)/2)^11)/120 - (1039*a^3*tan(c/2 + (d*x)/2)^13)/24 - (93*a^3*tan(c/2 + (d*x)/2)^15)/8 + (77*a^3*tan(c/2 + (d*x)/2))/8)/(d*(4*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^6 - 10*tan(c/2 + (d*x)/2)^8 - 4*tan(c/2 + (d*x)/2)^10 + 4*tan(c/2 + (d*x)/2)^12 + 4*tan(c/2 + (d*x)/2)^14 + tan(c/2 + (d*x)/2)^16 + 1))","B"
50,1,204,138,1.966249,"\text{Not used}","int(sin(c + d*x)^4*(a + a/cos(c + d*x))^3,x)","\frac{3\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{33\,a^3\,x}{8}+\frac{-\frac{45\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{4}-\frac{83\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}+\frac{25\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}+\frac{79\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}+\frac{27\,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)}^{12}+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\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-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(3*a^3*atanh(tan(c/2 + (d*x)/2)))/d - (33*a^3*x)/8 + ((27*a^3*tan(c/2 + (d*x)/2)^3)/4 + (79*a^3*tan(c/2 + (d*x)/2)^5)/2 + (25*a^3*tan(c/2 + (d*x)/2)^7)/2 - (83*a^3*tan(c/2 + (d*x)/2)^9)/4 - (45*a^3*tan(c/2 + (d*x)/2)^11)/4 + (21*a^3*tan(c/2 + (d*x)/2))/4)/(d*(2*tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + 2*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
51,1,90,98,1.277753,"\text{Not used}","int(sin(c + d*x)^2*(a + a/cos(c + d*x))^3,x)","\frac{5\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{5\,a^3\,x}{2}+\frac{18\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-10\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+1\right)}","Not used",1,"(5*a^3*atanh(tan(c/2 + (d*x)/2)))/d - (5*a^3*x)/2 + (18*a^3*tan(c/2 + (d*x)/2)^3 - 10*a^3*tan(c/2 + (d*x)/2)^7)/(d*(tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^4 + 1))","B"
52,1,98,80,2.460391,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^2,x)","\frac{9\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{9\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^3}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"(9*a^3*atanh(tan(c/2 + (d*x)/2)))/d - (9*a^3*tan(c/2 + (d*x)/2)^4 - 15*a^3*tan(c/2 + (d*x)/2)^2 + 4*a^3)/(d*(tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^5))","B"
53,1,116,110,5.348340,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^4,x)","\frac{11\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-\frac{56\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{16\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{a^3}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(11*a^3*atanh(tan(c/2 + (d*x)/2)))/d - ((16*a^3*tan(c/2 + (d*x)/2)^2)/3 - (56*a^3*tan(c/2 + (d*x)/2)^4)/3 + 11*a^3*tan(c/2 + (d*x)/2)^6 + a^3/3)/(d*(tan(c/2 + (d*x)/2)^3 - 2*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^7))","B"
54,1,136,165,4.913267,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^6,x)","\frac{13\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{51\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-\frac{262\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{388\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{34\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{a^3}{5}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}","Not used",1,"(13*a^3*atanh(tan(c/2 + (d*x)/2)))/d - ((34*a^3*tan(c/2 + (d*x)/2)^2)/15 + (388*a^3*tan(c/2 + (d*x)/2)^4)/15 - (262*a^3*tan(c/2 + (d*x)/2)^6)/3 + 51*a^3*tan(c/2 + (d*x)/2)^8 + a^3/5)/(d*(4*tan(c/2 + (d*x)/2)^5 - 8*tan(c/2 + (d*x)/2)^7 + 4*tan(c/2 + (d*x)/2)^9))","B"
55,1,169,192,2.896173,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^8,x)","\frac{15\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{230\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-396\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+120\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{85\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{7}+\frac{12\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{7}+\frac{a^3}{7}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}-\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(15*a^3*atanh(tan(c/2 + (d*x)/2)))/d - ((12*a^3*tan(c/2 + (d*x)/2)^2)/7 + (85*a^3*tan(c/2 + (d*x)/2)^4)/7 + 120*a^3*tan(c/2 + (d*x)/2)^6 - 396*a^3*tan(c/2 + (d*x)/2)^8 + 230*a^3*tan(c/2 + (d*x)/2)^10 + a^3/7)/(d*(16*tan(c/2 + (d*x)/2)^7 - 32*tan(c/2 + (d*x)/2)^9 + 16*tan(c/2 + (d*x)/2)^11)) - (a^3*tan(c/2 + (d*x)/2))/(16*d)","B"
56,1,204,232,1.039006,"\text{Not used}","int((a + a/cos(c + d*x))^3/sin(c + d*x)^10,x)","\frac{17\,a^3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192\,d}-\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{1019\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-\frac{5282\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}+\frac{8132\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{15}+\frac{6242\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{105}+\frac{3302\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{315}+\frac{94\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{63}+\frac{a^3}{9}}{d\,\left(64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-128\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\right)}","Not used",1,"(17*a^3*atanh(tan(c/2 + (d*x)/2)))/d - (a^3*tan(c/2 + (d*x)/2)^3)/(192*d) - (3*a^3*tan(c/2 + (d*x)/2))/(16*d) - ((94*a^3*tan(c/2 + (d*x)/2)^2)/63 + (3302*a^3*tan(c/2 + (d*x)/2)^4)/315 + (6242*a^3*tan(c/2 + (d*x)/2)^6)/105 + (8132*a^3*tan(c/2 + (d*x)/2)^8)/15 - (5282*a^3*tan(c/2 + (d*x)/2)^10)/3 + 1019*a^3*tan(c/2 + (d*x)/2)^12 + a^3/9)/(d*(64*tan(c/2 + (d*x)/2)^9 - 128*tan(c/2 + (d*x)/2)^11 + 64*tan(c/2 + (d*x)/2)^13))","B"
57,1,110,91,0.087188,"\text{Not used}","int(sin(c + d*x)^9/(a + a/cos(c + d*x)),x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^2}{2\,a}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a}-\frac{3\,{\cos\left(c+d\,x\right)}^4}{4\,a}+\frac{3\,{\cos\left(c+d\,x\right)}^5}{5\,a}+\frac{{\cos\left(c+d\,x\right)}^6}{2\,a}-\frac{3\,{\cos\left(c+d\,x\right)}^7}{7\,a}-\frac{{\cos\left(c+d\,x\right)}^8}{8\,a}+\frac{{\cos\left(c+d\,x\right)}^9}{9\,a}}{d}","Not used",1,"-(cos(c + d*x)^2/(2*a) - cos(c + d*x)^3/(3*a) - (3*cos(c + d*x)^4)/(4*a) + (3*cos(c + d*x)^5)/(5*a) + cos(c + d*x)^6/(2*a) - (3*cos(c + d*x)^7)/(7*a) - cos(c + d*x)^8/(8*a) + cos(c + d*x)^9/(9*a))/d","B"
58,1,84,73,0.059799,"\text{Not used}","int(sin(c + d*x)^7/(a + a/cos(c + d*x)),x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^2}{2\,a}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a}-\frac{{\cos\left(c+d\,x\right)}^4}{2\,a}+\frac{2\,{\cos\left(c+d\,x\right)}^5}{5\,a}+\frac{{\cos\left(c+d\,x\right)}^6}{6\,a}-\frac{{\cos\left(c+d\,x\right)}^7}{7\,a}}{d}","Not used",1,"-(cos(c + d*x)^2/(2*a) - cos(c + d*x)^3/(3*a) - cos(c + d*x)^4/(2*a) + (2*cos(c + d*x)^5)/(5*a) + cos(c + d*x)^6/(6*a) - cos(c + d*x)^7/(7*a))/d","B"
59,1,58,55,0.073758,"\text{Not used}","int(sin(c + d*x)^5/(a + a/cos(c + d*x)),x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^2}{2\,a}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a}-\frac{{\cos\left(c+d\,x\right)}^4}{4\,a}+\frac{{\cos\left(c+d\,x\right)}^5}{5\,a}}{d}","Not used",1,"-(cos(c + d*x)^2/(2*a) - cos(c + d*x)^3/(3*a) - cos(c + d*x)^4/(4*a) + cos(c + d*x)^5/(5*a))/d","B"
60,1,26,37,0.881736,"\text{Not used}","int(sin(c + d*x)^3/(a + a/cos(c + d*x)),x)","\frac{{\cos\left(c+d\,x\right)}^2\,\left(2\,\cos\left(c+d\,x\right)-3\right)}{6\,a\,d}","Not used",1,"(cos(c + d*x)^2*(2*cos(c + d*x) - 3))/(6*a*d)","B"
61,1,25,31,0.054187,"\text{Not used}","int(sin(c + d*x)/(a + a/cos(c + d*x)),x)","\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)-\cos\left(c+d\,x\right)}{a\,d}","Not used",1,"(log(cos(c + d*x) + 1) - cos(c + d*x))/(a*d)","B"
62,1,33,58,0.919087,"\text{Not used}","int(1/(sin(c + d*x)*(a + a/cos(c + d*x))),x)","-\frac{1}{2\,d\,\left(a+a\,\cos\left(c+d\,x\right)\right)}-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{2\,a\,d}","Not used",1,"- 1/(2*d*(a + a*cos(c + d*x))) - atanh(cos(c + d*x))/(2*a*d)","B"
63,1,75,82,0.935388,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + a/cos(c + d*x))),x)","-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{8\,a\,d}-\frac{\frac{{\cos\left(c+d\,x\right)}^2}{8}+\frac{\cos\left(c+d\,x\right)}{8}+\frac{1}{4}}{d\,\left(-a\,{\cos\left(c+d\,x\right)}^3-a\,{\cos\left(c+d\,x\right)}^2+a\,\cos\left(c+d\,x\right)+a\right)}","Not used",1,"- atanh(cos(c + d*x))/(8*a*d) - (cos(c + d*x)/8 + cos(c + d*x)^2/8 + 1/4)/(d*(a + a*cos(c + d*x) - a*cos(c + d*x)^2 - a*cos(c + d*x)^3))","B"
64,1,115,106,1.007680,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + a/cos(c + d*x))),x)","-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{16\,a\,d}-\frac{-\frac{{\cos\left(c+d\,x\right)}^4}{16}-\frac{{\cos\left(c+d\,x\right)}^3}{16}+\frac{5\,{\cos\left(c+d\,x\right)}^2}{48}+\frac{5\,\cos\left(c+d\,x\right)}{48}+\frac{1}{6}}{d\,\left(a\,{\cos\left(c+d\,x\right)}^5+a\,{\cos\left(c+d\,x\right)}^4-2\,a\,{\cos\left(c+d\,x\right)}^3-2\,a\,{\cos\left(c+d\,x\right)}^2+a\,\cos\left(c+d\,x\right)+a\right)}","Not used",1,"- atanh(cos(c + d*x))/(16*a*d) - ((5*cos(c + d*x))/48 + (5*cos(c + d*x)^2)/48 - cos(c + d*x)^3/16 - cos(c + d*x)^4/16 + 1/6)/(d*(a + a*cos(c + d*x) - 2*a*cos(c + d*x)^2 - 2*a*cos(c + d*x)^3 + a*cos(c + d*x)^4 + a*cos(c + d*x)^5))","B"
65,1,132,125,3.895933,"\text{Not used}","int(sin(c + d*x)^8/(a + a/cos(c + d*x)),x)","\frac{-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}-\frac{115\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}-\frac{383\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{192}+\frac{44099\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{1344}+\frac{5053\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{1344}+\frac{383\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}+\frac{115\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}-\frac{5\,x}{128\,a}","Not used",1,"((5*tan(c/2 + (d*x)/2))/64 + (115*tan(c/2 + (d*x)/2)^3)/192 + (383*tan(c/2 + (d*x)/2)^5)/192 + (5053*tan(c/2 + (d*x)/2)^7)/1344 + (44099*tan(c/2 + (d*x)/2)^9)/1344 - (383*tan(c/2 + (d*x)/2)^11)/192 - (115*tan(c/2 + (d*x)/2)^13)/192 - (5*tan(c/2 + (d*x)/2)^15)/64)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^8) - (5*x)/(128*a)","B"
66,1,106,99,3.664427,"\text{Not used}","int(sin(c + d*x)^6/(a + a/cos(c + d*x)),x)","\frac{-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}-\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{223\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{33\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{a\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}-\frac{x}{16\,a}","Not used",1,"(tan(c/2 + (d*x)/2)/8 + (17*tan(c/2 + (d*x)/2)^3)/24 + (33*tan(c/2 + (d*x)/2)^5)/20 + (223*tan(c/2 + (d*x)/2)^7)/20 - (17*tan(c/2 + (d*x)/2)^9)/24 - tan(c/2 + (d*x)/2)^11/8)/(a*d*(tan(c/2 + (d*x)/2)^2 + 1)^6) - x/(16*a)","B"
67,1,55,73,0.983655,"\text{Not used}","int(sin(c + d*x)^4/(a + a/cos(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)}{4\,a\,d}-\frac{x}{8\,a}-\frac{\sin\left(3\,c+3\,d\,x\right)}{12\,a\,d}+\frac{\sin\left(4\,c+4\,d\,x\right)}{32\,a\,d}","Not used",1,"sin(c + d*x)/(4*a*d) - x/(8*a) - sin(3*c + 3*d*x)/(12*a*d) + sin(4*c + 4*d*x)/(32*a*d)","B"
68,1,30,44,0.962711,"\text{Not used}","int(sin(c + d*x)^2/(a + a/cos(c + d*x)),x)","-\frac{\sin\left(2\,c+2\,d\,x\right)-4\,\sin\left(c+d\,x\right)+2\,d\,x}{4\,a\,d}","Not used",1,"-(sin(2*c + 2*d*x) - 4*sin(c + d*x) + 2*d*x)/(4*a*d)","B"
69,1,32,37,0.926935,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a/cos(c + d*x))),x)","-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3}{12\,a\,d\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"-(tan(c/2 + (d*x)/2)^4 + 3)/(12*a*d*tan(c/2 + (d*x)/2))","B"
70,1,60,55,1.087420,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + a/cos(c + d*x))),x)","-\frac{3\,{\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+30\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+5}{240\,a\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"-(30*tan(c/2 + (d*x)/2)^2 + 10*tan(c/2 + (d*x)/2)^6 + 3*tan(c/2 + (d*x)/2)^8 + 5)/(240*a*d*tan(c/2 + (d*x)/2)^3)","B"
71,1,153,73,1.160849,"\text{Not used}","int(1/(sin(c + d*x)^6*(a + a/cos(c + d*x))),x)","-\frac{21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+140\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+525\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+175\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+84\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{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 + 84*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^10 + 175*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 525*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4 + 140*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^2)/(6720*a*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)","B"
72,1,201,91,1.454387,"\text{Not used}","int(1/(sin(c + d*x)^8*(a + a/cos(c + d*x))),x)","-\frac{45\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+378\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1470\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4410\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+1470\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+882\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+270\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+35\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{80640\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(45*cos(c/2 + (d*x)/2)^16 + 35*sin(c/2 + (d*x)/2)^16 + 270*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 + 882*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 + 1470*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 + 4410*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 + 1470*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 + 378*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2)/(80640*a*d*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^7)","B"
73,1,139,109,3.108222,"\text{Not used}","int(1/(sin(c + d*x)^10*(a + a/cos(c + d*x))),x)","-\frac{63\,\cos\left(c+d\,x\right)+\frac{21\,\cos\left(2\,c+2\,d\,x\right)}{2}-42\,\cos\left(3\,c+3\,d\,x\right)-12\,\cos\left(4\,c+4\,d\,x\right)+18\,\cos\left(5\,c+5\,d\,x\right)+\frac{27\,\cos\left(6\,c+6\,d\,x\right)}{4}-\frac{9\,\cos\left(7\,c+7\,d\,x\right)}{2}-2\,\cos\left(8\,c+8\,d\,x\right)+\frac{\cos\left(9\,c+9\,d\,x\right)}{2}+\frac{\cos\left(10\,c+10\,d\,x\right)}{4}+\frac{693}{2}}{3548160\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}","Not used",1,"-(63*cos(c + d*x) + (21*cos(2*c + 2*d*x))/2 - 42*cos(3*c + 3*d*x) - 12*cos(4*c + 4*d*x) + 18*cos(5*c + 5*d*x) + (27*cos(6*c + 6*d*x))/4 - (9*cos(7*c + 7*d*x))/2 - 2*cos(8*c + 8*d*x) + cos(9*c + 9*d*x)/2 + cos(10*c + 10*d*x)/4 + 693/2)/(3548160*a*d*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^9)","B"
74,1,109,137,0.087469,"\text{Not used}","int(sin(c + d*x)^11/(a + a/cos(c + d*x))^2,x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^2}-\frac{{\cos\left(c+d\,x\right)}^4}{2\,a^2}-\frac{2\,{\cos\left(c+d\,x\right)}^5}{5\,a^2}+\frac{{\cos\left(c+d\,x\right)}^6}{a^2}-\frac{3\,{\cos\left(c+d\,x\right)}^8}{4\,a^2}+\frac{2\,{\cos\left(c+d\,x\right)}^9}{9\,a^2}+\frac{{\cos\left(c+d\,x\right)}^{10}}{5\,a^2}-\frac{{\cos\left(c+d\,x\right)}^{11}}{11\,a^2}}{d}","Not used",1,"-(cos(c + d*x)^3/(3*a^2) - cos(c + d*x)^4/(2*a^2) - (2*cos(c + d*x)^5)/(5*a^2) + cos(c + d*x)^6/a^2 - (3*cos(c + d*x)^8)/(4*a^2) + (2*cos(c + d*x)^9)/(9*a^2) + cos(c + d*x)^10/(5*a^2) - cos(c + d*x)^11/(11*a^2))/d","B"
75,1,96,114,0.910149,"\text{Not used}","int(sin(c + d*x)^9/(a + a/cos(c + d*x))^2,x)","\frac{\frac{{\cos\left(c+d\,x\right)}^4}{2\,a^2}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^2}+\frac{{\cos\left(c+d\,x\right)}^5}{5\,a^2}-\frac{2\,{\cos\left(c+d\,x\right)}^6}{3\,a^2}+\frac{{\cos\left(c+d\,x\right)}^7}{7\,a^2}+\frac{{\cos\left(c+d\,x\right)}^8}{4\,a^2}-\frac{{\cos\left(c+d\,x\right)}^9}{9\,a^2}}{d}","Not used",1,"(cos(c + d*x)^4/(2*a^2) - cos(c + d*x)^3/(3*a^2) + cos(c + d*x)^5/(5*a^2) - (2*cos(c + d*x)^6)/(3*a^2) + cos(c + d*x)^7/(7*a^2) + cos(c + d*x)^8/(4*a^2) - cos(c + d*x)^9/(9*a^2))/d","B"
76,1,58,73,0.917538,"\text{Not used}","int(sin(c + d*x)^7/(a + a/cos(c + d*x))^2,x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^2}-\frac{{\cos\left(c+d\,x\right)}^4}{2\,a^2}+\frac{{\cos\left(c+d\,x\right)}^6}{3\,a^2}-\frac{{\cos\left(c+d\,x\right)}^7}{7\,a^2}}{d}","Not used",1,"-(cos(c + d*x)^3/(3*a^2) - cos(c + d*x)^4/(2*a^2) + cos(c + d*x)^6/(3*a^2) - cos(c + d*x)^7/(7*a^2))/d","B"
77,1,36,55,0.060516,"\text{Not used}","int(sin(c + d*x)^5/(a + a/cos(c + d*x))^2,x)","-\frac{{\cos\left(c+d\,x\right)}^3\,\left(6\,{\cos\left(c+d\,x\right)}^2-15\,\cos\left(c+d\,x\right)+10\right)}{30\,a^2\,d}","Not used",1,"-(cos(c + d*x)^3*(6*cos(c + d*x)^2 - 15*cos(c + d*x) + 10))/(30*a^2*d)","B"
78,1,56,66,0.063907,"\text{Not used}","int(sin(c + d*x)^3/(a + a/cos(c + d*x))^2,x)","-\frac{\frac{2\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{a^2}-\frac{2\,\cos\left(c+d\,x\right)}{a^2}+\frac{{\cos\left(c+d\,x\right)}^2}{a^2}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^2}}{d}","Not used",1,"-((2*log(cos(c + d*x) + 1))/a^2 - (2*cos(c + d*x))/a^2 + cos(c + d*x)^2/a^2 - cos(c + d*x)^3/(3*a^2))/d","B"
79,1,46,52,0.923321,"\text{Not used}","int(sin(c + d*x)/(a + a/cos(c + d*x))^2,x)","\frac{2\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{a^2\,d}-\frac{{\cos\left(c+d\,x\right)}^2-2}{a^2\,d\,\left(\cos\left(c+d\,x\right)+1\right)}","Not used",1,"(2*log(cos(c + d*x) + 1))/(a^2*d) - (cos(c + d*x)^2 - 2)/(a^2*d*(cos(c + d*x) + 1))","B"
80,1,60,60,0.096141,"\text{Not used}","int(1/(sin(c + d*x)*(a + a/cos(c + d*x))^2),x)","-\frac{\frac{3\,\cos\left(c+d\,x\right)}{4}+\frac{1}{2}}{d\,\left(a^2\,{\cos\left(c+d\,x\right)}^2+2\,a^2\,\cos\left(c+d\,x\right)+a^2\right)}-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{4\,a^2\,d}","Not used",1,"- ((3*cos(c + d*x))/4 + 1/2)/(d*(2*a^2*cos(c + d*x) + a^2 + a^2*cos(c + d*x)^2)) - atanh(cos(c + d*x))/(4*a^2*d)","B"
81,1,58,42,0.942123,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + a/cos(c + d*x))^2),x)","-\frac{\frac{\cos\left(c+d\,x\right)}{3}+\frac{1}{6}}{d\,\left(-a^2\,{\cos\left(c+d\,x\right)}^4-2\,a^2\,{\cos\left(c+d\,x\right)}^3+2\,a^2\,\cos\left(c+d\,x\right)+a^2\right)}","Not used",1,"-(cos(c + d*x)/3 + 1/6)/(d*(2*a^2*cos(c + d*x) + a^2 - 2*a^2*cos(c + d*x)^3 - a^2*cos(c + d*x)^4))","B"
82,1,152,146,1.052817,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + a/cos(c + d*x))^2),x)","\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{64\,a^2\,d}-\frac{\frac{{\cos\left(c+d\,x\right)}^5}{64}+\frac{{\cos\left(c+d\,x\right)}^4}{32}-\frac{{\cos\left(c+d\,x\right)}^3}{96}-\frac{5\,{\cos\left(c+d\,x\right)}^2}{96}+\frac{35\,\cos\left(c+d\,x\right)}{192}+\frac{1}{12}}{d\,\left(a^2\,{\cos\left(c+d\,x\right)}^6+2\,a^2\,{\cos\left(c+d\,x\right)}^5-a^2\,{\cos\left(c+d\,x\right)}^4-4\,a^2\,{\cos\left(c+d\,x\right)}^3-a^2\,{\cos\left(c+d\,x\right)}^2+2\,a^2\,\cos\left(c+d\,x\right)+a^2\right)}","Not used",1,"atanh(cos(c + d*x))/(64*a^2*d) - ((35*cos(c + d*x))/192 - (5*cos(c + d*x)^2)/96 - cos(c + d*x)^3/96 + cos(c + d*x)^4/32 + cos(c + d*x)^5/64 + 1/12)/(d*(2*a^2*cos(c + d*x) + a^2 - a^2*cos(c + d*x)^2 - 4*a^2*cos(c + d*x)^3 - a^2*cos(c + d*x)^4 + 2*a^2*cos(c + d*x)^5 + a^2*cos(c + d*x)^6))","B"
83,1,133,167,3.933726,"\text{Not used}","int(sin(c + d*x)^8/(a + a/cos(c + d*x))^2,x)","\frac{11\,x}{128\,a^2}-\frac{-\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}-\frac{253\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}+\frac{20363\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{960}-\frac{31007\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{6720}+\frac{55583\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6720}+\frac{4213\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{960}+\frac{253\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{11\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}","Not used",1,"(11*x)/(128*a^2) - ((11*tan(c/2 + (d*x)/2))/64 + (253*tan(c/2 + (d*x)/2)^3)/192 + (4213*tan(c/2 + (d*x)/2)^5)/960 + (55583*tan(c/2 + (d*x)/2)^7)/6720 - (31007*tan(c/2 + (d*x)/2)^9)/6720 + (20363*tan(c/2 + (d*x)/2)^11)/960 - (253*tan(c/2 + (d*x)/2)^13)/192 - (11*tan(c/2 + (d*x)/2)^15)/64)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^8)","B"
84,1,107,104,3.750411,"\text{Not used}","int(sin(c + d*x)^6/(a + a/cos(c + d*x))^2,x)","\frac{3\,x}{16\,a^2}-\frac{-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{205\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{24}+\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{99\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}","Not used",1,"(3*x)/(16*a^2) - ((3*tan(c/2 + (d*x)/2))/8 + (17*tan(c/2 + (d*x)/2)^3)/8 + (99*tan(c/2 + (d*x)/2)^5)/20 + (29*tan(c/2 + (d*x)/2)^7)/20 + (205*tan(c/2 + (d*x)/2)^9)/24 - (3*tan(c/2 + (d*x)/2)^11)/8)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^6)","B"
85,1,81,87,4.505452,"\text{Not used}","int(sin(c + d*x)^4/(a + a/cos(c + d*x))^2,x)","\frac{7\,x}{8\,a^2}-\frac{\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{83\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{77\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{a^2\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(7*x)/(8*a^2) - ((7*tan(c/2 + (d*x)/2))/4 + (77*tan(c/2 + (d*x)/2)^3)/12 + (83*tan(c/2 + (d*x)/2)^5)/12 + (25*tan(c/2 + (d*x)/2)^7)/4)/(a^2*d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
86,1,91,69,1.030318,"\text{Not used}","int(sin(c + d*x)^2/(a + a/cos(c + d*x))^2,x)","\frac{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(c+d\,x\right)+10\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}","Not used",1,"(4*sin(c/2 + (d*x)/2) - 5*cos(c/2 + (d*x)/2)*(c + d*x) + 10*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) - 4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2))/(2*a^2*d*cos(c/2 + (d*x)/2))","B"
87,1,71,73,0.981880,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a/cos(c + d*x))^2),x)","-\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+14\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-3}{120\,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,"-(14*cos(c/2 + (d*x)/2)^2 - 4*cos(c/2 + (d*x)/2)^4 + 8*cos(c/2 + (d*x)/2)^6 - 3)/(120*a^2*d*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2))","B"
88,1,121,91,1.068040,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + a/cos(c + d*x))^2),x)","-\frac{64\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-96\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+54\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-15}{3360\,a^2\,d\,\left({\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"-(54*cos(c/2 + (d*x)/2)^2 + 4*cos(c/2 + (d*x)/2)^4 + 24*cos(c/2 + (d*x)/2)^6 - 96*cos(c/2 + (d*x)/2)^8 + 64*cos(c/2 + (d*x)/2)^10 - 15)/(3360*a^2*d*(cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2) - cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)))","B"
89,1,106,109,2.184746,"\text{Not used}","int(1/(sin(c + d*x)^6*(a + a/cos(c + d*x))^2),x)","-\frac{\frac{375\,\cos\left(c+d\,x\right)}{8}-\frac{5\,\cos\left(2\,c+2\,d\,x\right)}{2}+\frac{19\,\cos\left(3\,c+3\,d\,x\right)}{8}+2\,\cos\left(4\,c+4\,d\,x\right)-\frac{\cos\left(5\,c+5\,d\,x\right)}{8}-\frac{\cos\left(6\,c+6\,d\,x\right)}{2}-\frac{\cos\left(7\,c+7\,d\,x\right)}{8}+15}{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,"-((375*cos(c + d*x))/8 - (5*cos(2*c + 2*d*x))/2 + (19*cos(3*c + 3*d*x))/8 + 2*cos(4*c + 4*d*x) - cos(5*c + 5*d*x)/8 - cos(6*c + 6*d*x)/2 - cos(7*c + 7*d*x)/8 + 15)/(40320*a^2*d*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5)","B"
90,1,201,125,1.686952,"\text{Not used}","int(1/(sin(c + d*x)^8*(a + a/cos(c + d*x))^2),x)","-\frac{99\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+693\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1848\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+9702\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+3234\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-792\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-385\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}-63\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}}{354816\,a^2\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(99*cos(c/2 + (d*x)/2)^18 - 63*sin(c/2 + (d*x)/2)^18 - 385*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^16 - 792*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^14 + 3234*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^10 + 9702*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^8 + 1848*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^4 + 693*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^2)/(354816*a^2*d*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^7)","B"
91,1,110,139,0.089006,"\text{Not used}","int(sin(c + d*x)^11/(a + a/cos(c + d*x))^3,x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^4}{4\,a^3}-\frac{3\,{\cos\left(c+d\,x\right)}^5}{5\,a^3}+\frac{{\cos\left(c+d\,x\right)}^6}{6\,a^3}+\frac{5\,{\cos\left(c+d\,x\right)}^7}{7\,a^3}-\frac{5\,{\cos\left(c+d\,x\right)}^8}{8\,a^3}-\frac{{\cos\left(c+d\,x\right)}^9}{9\,a^3}+\frac{3\,{\cos\left(c+d\,x\right)}^{10}}{10\,a^3}-\frac{{\cos\left(c+d\,x\right)}^{11}}{11\,a^3}}{d}","Not used",1,"-(cos(c + d*x)^4/(4*a^3) - (3*cos(c + d*x)^5)/(5*a^3) + cos(c + d*x)^6/(6*a^3) + (5*cos(c + d*x)^7)/(7*a^3) - (5*cos(c + d*x)^8)/(8*a^3) - cos(c + d*x)^9/(9*a^3) + (3*cos(c + d*x)^10)/(10*a^3) - cos(c + d*x)^11/(11*a^3))/d","B"
92,1,84,109,0.921423,"\text{Not used}","int(sin(c + d*x)^9/(a + a/cos(c + d*x))^3,x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^4}{4\,a^3}-\frac{3\,{\cos\left(c+d\,x\right)}^5}{5\,a^3}+\frac{{\cos\left(c+d\,x\right)}^6}{3\,a^3}+\frac{2\,{\cos\left(c+d\,x\right)}^7}{7\,a^3}-\frac{3\,{\cos\left(c+d\,x\right)}^8}{8\,a^3}+\frac{{\cos\left(c+d\,x\right)}^9}{9\,a^3}}{d}","Not used",1,"-(cos(c + d*x)^4/(4*a^3) - (3*cos(c + d*x)^5)/(5*a^3) + cos(c + d*x)^6/(3*a^3) + (2*cos(c + d*x)^7)/(7*a^3) - (3*cos(c + d*x)^8)/(8*a^3) + cos(c + d*x)^9/(9*a^3))/d","B"
93,1,58,73,0.070183,"\text{Not used}","int(sin(c + d*x)^7/(a + a/cos(c + d*x))^3,x)","-\frac{\frac{{\cos\left(c+d\,x\right)}^4}{4\,a^3}-\frac{3\,{\cos\left(c+d\,x\right)}^5}{5\,a^3}+\frac{{\cos\left(c+d\,x\right)}^6}{2\,a^3}-\frac{{\cos\left(c+d\,x\right)}^7}{7\,a^3}}{d}","Not used",1,"-(cos(c + d*x)^4/(4*a^3) - (3*cos(c + d*x)^5)/(5*a^3) + cos(c + d*x)^6/(2*a^3) - cos(c + d*x)^7/(7*a^3))/d","B"
94,1,82,102,0.895297,"\text{Not used}","int(sin(c + d*x)^5/(a + a/cos(c + d*x))^3,x)","\frac{\frac{4\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{a^3}-\frac{4\,\cos\left(c+d\,x\right)}{a^3}+\frac{2\,{\cos\left(c+d\,x\right)}^2}{a^3}-\frac{4\,{\cos\left(c+d\,x\right)}^3}{3\,a^3}+\frac{3\,{\cos\left(c+d\,x\right)}^4}{4\,a^3}-\frac{{\cos\left(c+d\,x\right)}^5}{5\,a^3}}{d}","Not used",1,"((4*log(cos(c + d*x) + 1))/a^3 - (4*cos(c + d*x))/a^3 + (2*cos(c + d*x)^2)/a^3 - (4*cos(c + d*x)^3)/(3*a^3) + (3*cos(c + d*x)^4)/(4*a^3) - cos(c + d*x)^5/(5*a^3))/d","B"
95,1,75,89,0.888199,"\text{Not used}","int(sin(c + d*x)^3/(a + a/cos(c + d*x))^3,x)","-\frac{\frac{2}{a^3\,\cos\left(c+d\,x\right)+a^3}+\frac{7\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{a^3}-\frac{5\,\cos\left(c+d\,x\right)}{a^3}+\frac{3\,{\cos\left(c+d\,x\right)}^2}{2\,a^3}-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^3}}{d}","Not used",1,"-(2/(a^3*cos(c + d*x) + a^3) + (7*log(cos(c + d*x) + 1))/a^3 - (5*cos(c + d*x))/a^3 + (3*cos(c + d*x)^2)/(2*a^3) - cos(c + d*x)^3/(3*a^3))/d","B"
96,1,59,75,0.079398,"\text{Not used}","int(sin(c + d*x)/(a + a/cos(c + d*x))^3,x)","\frac{3\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{a^3\,d}-\frac{\cos\left(c+d\,x\right)}{a^3\,d}+\frac{3\,\cos\left(c+d\,x\right)+\frac{5}{2}}{a^3\,d\,{\left(\cos\left(c+d\,x\right)+1\right)}^2}","Not used",1,"(3*log(cos(c + d*x) + 1))/(a^3*d) - cos(c + d*x)/(a^3*d) + (3*cos(c + d*x) + 5/2)/(a^3*d*(cos(c + d*x) + 1)^2)","B"
97,1,83,82,0.111331,"\text{Not used}","int(1/(sin(c + d*x)*(a + a/cos(c + d*x))^3),x)","-\frac{\frac{7\,{\cos\left(c+d\,x\right)}^2}{8}+\frac{9\,\cos\left(c+d\,x\right)}{8}+\frac{5}{12}}{d\,\left(a^3\,{\cos\left(c+d\,x\right)}^3+3\,a^3\,{\cos\left(c+d\,x\right)}^2+3\,a^3\,\cos\left(c+d\,x\right)+a^3\right)}-\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{8\,a^3\,d}","Not used",1,"- ((9*cos(c + d*x))/8 + (7*cos(c + d*x)^2)/8 + 5/12)/(d*(3*a^3*cos(c + d*x) + a^3 + 3*a^3*cos(c + d*x)^2 + a^3*cos(c + d*x)^3)) - atanh(cos(c + d*x))/(8*a^3*d)","B"
98,1,130,126,0.166528,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + a/cos(c + d*x))^3),x)","\frac{\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{32\,a^3\,d}-\frac{-\frac{{\cos\left(c+d\,x\right)}^4}{32}-\frac{3\,{\cos\left(c+d\,x\right)}^3}{32}+\frac{25\,{\cos\left(c+d\,x\right)}^2}{96}+\frac{9\,\cos\left(c+d\,x\right)}{32}+\frac{1}{12}}{d\,\left(-a^3\,{\cos\left(c+d\,x\right)}^5-3\,a^3\,{\cos\left(c+d\,x\right)}^4-2\,a^3\,{\cos\left(c+d\,x\right)}^3+2\,a^3\,{\cos\left(c+d\,x\right)}^2+3\,a^3\,\cos\left(c+d\,x\right)+a^3\right)}","Not used",1,"atanh(cos(c + d*x))/(32*a^3*d) - ((9*cos(c + d*x))/32 + (25*cos(c + d*x)^2)/96 - (3*cos(c + d*x)^3)/32 - cos(c + d*x)^4/32 + 1/12)/(d*(3*a^3*cos(c + d*x) + a^3 + 2*a^3*cos(c + d*x)^2 - 2*a^3*cos(c + d*x)^3 - 3*a^3*cos(c + d*x)^4 - a^3*cos(c + d*x)^5))","B"
99,1,173,128,1.089775,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + a/cos(c + d*x))^3),x)","\frac{3\,\mathrm{atanh}\left(\cos\left(c+d\,x\right)\right)}{128\,a^3\,d}-\frac{\frac{3\,{\cos\left(c+d\,x\right)}^6}{128}+\frac{9\,{\cos\left(c+d\,x\right)}^5}{128}+\frac{{\cos\left(c+d\,x\right)}^4}{32}-\frac{3\,{\cos\left(c+d\,x\right)}^3}{32}+\frac{61\,{\cos\left(c+d\,x\right)}^2}{640}+\frac{63\,\cos\left(c+d\,x\right)}{640}+\frac{1}{40}}{d\,\left(a^3\,{\cos\left(c+d\,x\right)}^7+3\,a^3\,{\cos\left(c+d\,x\right)}^6+a^3\,{\cos\left(c+d\,x\right)}^5-5\,a^3\,{\cos\left(c+d\,x\right)}^4-5\,a^3\,{\cos\left(c+d\,x\right)}^3+a^3\,{\cos\left(c+d\,x\right)}^2+3\,a^3\,\cos\left(c+d\,x\right)+a^3\right)}","Not used",1,"(3*atanh(cos(c + d*x)))/(128*a^3*d) - ((63*cos(c + d*x))/640 + (61*cos(c + d*x)^2)/640 - (3*cos(c + d*x)^3)/32 + cos(c + d*x)^4/32 + (9*cos(c + d*x)^5)/128 + (3*cos(c + d*x)^6)/128 + 1/40)/(d*(3*a^3*cos(c + d*x) + a^3 + a^3*cos(c + d*x)^2 - 5*a^3*cos(c + d*x)^3 - 5*a^3*cos(c + d*x)^4 + a^3*cos(c + d*x)^5 + 3*a^3*cos(c + d*x)^6 + a^3*cos(c + d*x)^7))","B"
100,1,132,157,3.865314,"\text{Not used}","int(sin(c + d*x)^8/(a + a/cos(c + d*x))^3,x)","\frac{-\frac{29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{1143\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{1759\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{320}+\frac{72669\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{2240}+\frac{146537\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6720}+\frac{11107\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{960}+\frac{667\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{29\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^8}-\frac{29\,x}{128\,a^3}","Not used",1,"((29*tan(c/2 + (d*x)/2))/64 + (667*tan(c/2 + (d*x)/2)^3)/192 + (11107*tan(c/2 + (d*x)/2)^5)/960 + (146537*tan(c/2 + (d*x)/2)^7)/6720 + (72669*tan(c/2 + (d*x)/2)^9)/2240 + (1759*tan(c/2 + (d*x)/2)^11)/320 + (1143*tan(c/2 + (d*x)/2)^13)/64 - (29*tan(c/2 + (d*x)/2)^15)/64)/(a^3*d*(tan(c/2 + (d*x)/2)^2 + 1)^8) - (29*x)/(128*a^3)","B"
101,1,106,129,3.669492,"\text{Not used}","int(sin(c + d*x)^6/(a + a/cos(c + d*x))^3,x)","\frac{\frac{105\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{8}+\frac{211\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}+\frac{969\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{20}+\frac{759\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{20}+\frac{391\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+\frac{23\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^6}-\frac{23\,x}{16\,a^3}","Not used",1,"((23*tan(c/2 + (d*x)/2))/8 + (391*tan(c/2 + (d*x)/2)^3)/24 + (759*tan(c/2 + (d*x)/2)^5)/20 + (969*tan(c/2 + (d*x)/2)^7)/20 + (211*tan(c/2 + (d*x)/2)^9)/8 + (105*tan(c/2 + (d*x)/2)^11)/8)/(a^3*d*(tan(c/2 + (d*x)/2)^2 + 1)^6) - (23*x)/(16*a^3)","B"
102,1,98,108,2.659271,"\text{Not used}","int(sin(c + d*x)^4/(a + a/cos(c + d*x))^3,x)","\frac{51\,x}{8\,a^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}-\frac{\frac{77\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{149\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{123\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{35\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{a^3\,d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(51*x)/(8*a^3) - (4*tan(c/2 + (d*x)/2))/(a^3*d) - ((35*tan(c/2 + (d*x)/2))/4 + (123*tan(c/2 + (d*x)/2)^3)/4 + (149*tan(c/2 + (d*x)/2)^5)/4 + (77*tan(c/2 + (d*x)/2)^7)/4)/(a^3*d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
103,1,115,97,1.057404,"\text{Not used}","int(sin(c + d*x)^2/(a + a/cos(c + d*x))^3,x)","-\frac{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-38\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-42\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+12\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)+33\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(c+d\,x\right)}{6\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"-(2*sin(c/2 + (d*x)/2) - 38*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2) - 42*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2) + 12*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2) + 33*cos(c/2 + (d*x)/2)^3*(c + d*x))/(6*a^3*d*cos(c/2 + (d*x)/2)^3)","B"
104,1,84,89,1.009007,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + a/cos(c + d*x))^3),x)","-\frac{-16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+72\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-34\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+5}{560\,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,"-(72*cos(c/2 + (d*x)/2)^4 - 34*cos(c/2 + (d*x)/2)^2 + 8*cos(c/2 + (d*x)/2)^6 - 16*cos(c/2 + (d*x)/2)^8 + 5)/(560*a^3*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2))","B"
105,1,105,103,1.112437,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + a/cos(c + d*x))^3),x)","-\frac{15\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+135\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-27\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{2880\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}","Not used",1,"-(15*cos(c/2 + (d*x)/2)^12 + 5*sin(c/2 + (d*x)/2)^12 - 27*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + 135*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/(2880*a^3*d*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^3)","B"
106,1,201,127,1.434952,"\text{Not used}","int(1/(sin(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}+2310\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6930\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+20790\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-4158\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-990\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+770\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+315\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}}{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 + 770*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^14 - 990*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^12 - 4158*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^10 + 20790*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^6 - 6930*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^4 + 2310*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^2)/(887040*a^3*d*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^5)","B"
107,1,249,145,2.127946,"\text{Not used}","int(1/(sin(c + d*x)^8*(a + a/cos(c + d*x))^3),x)","-\frac{2145\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}+12012\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+15015\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-120120\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+210210\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-42042\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-17160\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+5005\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+5460\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{18}+1155\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{20}}{15375360\,a^3\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"-(2145*cos(c/2 + (d*x)/2)^20 + 1155*sin(c/2 + (d*x)/2)^20 + 5460*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^18 + 5005*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^16 - 17160*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^14 - 42042*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^12 + 210210*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^8 - 120120*cos(c/2 + (d*x)/2)^14*sin(c/2 + (d*x)/2)^6 + 15015*cos(c/2 + (d*x)/2)^16*sin(c/2 + (d*x)/2)^4 + 12012*cos(c/2 + (d*x)/2)^18*sin(c/2 + (d*x)/2)^2)/(15375360*a^3*d*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2)^7)","B"
108,0,-1,157,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)*(a + a/cos(c + d*x)),x)","\int {\left(e\,\sin\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*sin(c + d*x))^(5/2)*(a + a/cos(c + d*x)), x)","F"
109,0,-1,154,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)*(a + a/cos(c + d*x)),x)","\int {\left(e\,\sin\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*sin(c + d*x))^(3/2)*(a + a/cos(c + d*x)), x)","F"
110,0,-1,104,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)*(a + a/cos(c + d*x)),x)","\int \sqrt{e\,\sin\left(c+d\,x\right)}\,\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*sin(c + d*x))^(1/2)*(a + a/cos(c + d*x)), x)","F"
111,0,-1,103,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*sin(c + d*x))^(1/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{\sqrt{e\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*sin(c + d*x))^(1/2), x)","F"
112,0,-1,155,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*sin(c + d*x))^(3/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*sin(c + d*x))^(3/2), x)","F"
113,0,-1,160,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e*sin(c + d*x))^(5/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e*sin(c + d*x))^(5/2), x)","F"
114,0,-1,194,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\sin\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*sin(c + d*x))^(5/2)*(a + a/cos(c + d*x))^2, x)","F"
115,0,-1,192,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\sin\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*sin(c + d*x))^(3/2)*(a + a/cos(c + d*x))^2, x)","F"
116,0,-1,138,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2,x)","\int \sqrt{e\,\sin\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2 \,d x","Not used",1,"int((e*sin(c + d*x))^(1/2)*(a + a/cos(c + d*x))^2, x)","F"
117,0,-1,139,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*sin(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{\sqrt{e\,\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*sin(c + d*x))^(1/2), x)","F"
118,0,-1,224,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*sin(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*sin(c + d*x))^(3/2), x)","F"
119,0,-1,234,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e*sin(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e*sin(c + d*x))^(5/2), x)","F"
120,0,-1,139,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\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*sin(c + d*x))^(7/2))/(a*(cos(c + d*x) + 1)), x)","F"
121,0,-1,104,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\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*sin(c + d*x))^(5/2))/(a*(cos(c + d*x) + 1)), x)","F"
122,0,-1,102,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\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*sin(c + d*x))^(3/2))/(a*(cos(c + d*x) + 1)), x)","F"
123,0,-1,95,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,\sqrt{e\,\sin\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*sin(c + d*x))^(1/2))/(a*(cos(c + d*x) + 1)), x)","F"
124,0,-1,101,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(1/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,\sqrt{e\,\sin\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*sin(c + d*x))^(1/2)*(cos(c + d*x) + 1)), x)","F"
125,0,-1,135,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(3/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\sin\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*sin(c + d*x))^(3/2)*(cos(c + d*x) + 1)), x)","F"
126,0,-1,135,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(5/2)*(a + a/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(e\,\sin\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*sin(c + d*x))^(5/2)*(cos(c + d*x) + 1)), x)","F"
127,0,-1,162,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\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*sin(c + d*x))^(7/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
128,0,-1,187,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\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*sin(c + d*x))^(5/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
129,0,-1,189,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\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*sin(c + d*x))^(3/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
130,0,-1,188,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{e\,\sin\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*sin(c + d*x))^(1/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
131,0,-1,190,0.000000,"\text{Not used}","int(1/((e*sin(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\,\sin\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*sin(c + d*x))^(1/2)*(cos(c + d*x) + 1)^2), x)","F"
132,0,-1,224,0.000000,"\text{Not used}","int(1/((e*sin(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\,\sin\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*sin(c + d*x))^(3/2)*(cos(c + d*x) + 1)^2), x)","F"
133,0,-1,224,0.000000,"\text{Not used}","int(1/((e*sin(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\,\sin\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*sin(c + d*x))^(5/2)*(cos(c + d*x) + 1)^2), x)","F"
134,0,-1,247,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + a/cos(c + d*x))^3,x)","\int {\left(e\,\sin\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*sin(c + d*x))^m*(a + a/cos(c + d*x))^3, x)","F"
135,0,-1,195,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + a/cos(c + d*x))^2,x)","\int {\left(e\,\sin\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*sin(c + d*x))^m*(a + a/cos(c + d*x))^2, x)","F"
136,0,-1,119,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + a/cos(c + d*x)),x)","\int {\left(e\,\sin\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*sin(c + d*x))^m*(a + a/cos(c + d*x)), x)","F"
137,0,-1,100,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\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*sin(c + d*x))^m)/(a*(cos(c + d*x) + 1)), x)","F"
138,0,-1,207,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\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*sin(c + d*x))^m)/(a^2*(cos(c + d*x) + 1)^2), x)","F"
139,0,-1,236,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + a/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,{\left(e\,\sin\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*sin(c + d*x))^m)/(a^3*(cos(c + d*x) + 1)^3), x)","F"
140,0,-1,106,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + a/cos(c + d*x))^(3/2),x)","\int {\left(e\,\sin\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*sin(c + d*x))^m*(a + a/cos(c + d*x))^(3/2), x)","F"
141,0,-1,107,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + a/cos(c + d*x))^(1/2),x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^m\,\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}} \,d x","Not used",1,"int((e*sin(c + d*x))^m*(a + a/cos(c + d*x))^(1/2), x)","F"
142,0,-1,115,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + a/cos(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^m}{\sqrt{a+\frac{a}{\cos\left(c+d\,x\right)}}} \,d x","Not used",1,"int((e*sin(c + d*x))^m/(a + a/cos(c + d*x))^(1/2), x)","F"
143,0,-1,120,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + a/cos(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\sin\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*sin(c + d*x))^m/(a + a/cos(c + d*x))^(3/2), x)","F"
144,0,-1,130,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + a/cos(c + d*x))^n,x)","\int {\left(e\,\sin\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*sin(c + d*x))^m*(a + a/cos(c + d*x))^n, x)","F"
145,0,-1,180,0.000000,"\text{Not used}","int(sin(c + d*x)^7*(a + a/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^7\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^7*(a + a/cos(c + d*x))^n, x)","F"
146,0,-1,123,0.000000,"\text{Not used}","int(sin(c + d*x)^5*(a + a/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^5\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^5*(a + a/cos(c + d*x))^n, x)","F"
147,0,-1,83,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + a/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^3*(a + a/cos(c + d*x))^n, x)","F"
148,1,64,42,1.182245,"\text{Not used}","int(sin(c + d*x)*(a + a/cos(c + d*x))^n,x)","\frac{\cos\left(c+d\,x\right)\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n\,{{}}_2{\mathrm{F}}_1\left(1-n,-n;\ 2-n;\ -\cos\left(c+d\,x\right)\right)}{d\,{\left(\cos\left(c+d\,x\right)+1\right)}^n\,\left(n-1\right)}","Not used",1,"(cos(c + d*x)*(a + a/cos(c + d*x))^n*hypergeom([1 - n, -n], 2 - n, -cos(c + d*x)))/(d*(cos(c + d*x) + 1)^n*(n - 1))","B"
149,0,-1,40,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/sin(c + d*x),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/sin(c + d*x), x)","F"
150,0,-1,112,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/sin(c + d*x)^3,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/sin(c + d*x)^3, x)","F"
151,0,-1,240,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/sin(c + d*x)^5,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^5} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/sin(c + d*x)^5, x)","F"
152,0,-1,230,0.000000,"\text{Not used}","int(sin(c + d*x)^4*(a + a/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^4\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^4*(a + a/cos(c + d*x))^n, x)","F"
153,0,-1,95,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + a/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^2*(a + a/cos(c + d*x))^n, x)","F"
154,0,-1,98,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/sin(c + d*x)^2,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/sin(c + d*x)^2, x)","F"
155,0,-1,349,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/sin(c + d*x)^4,x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/sin(c + d*x)^4, x)","F"
156,0,-1,105,0.000000,"\text{Not used}","int(sin(c + d*x)^(3/2)*(a + a/cos(c + d*x))^n,x)","\int {\sin\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(sin(c + d*x)^(3/2)*(a + a/cos(c + d*x))^n, x)","F"
157,0,-1,105,0.000000,"\text{Not used}","int(sin(c + d*x)^(1/2)*(a + a/cos(c + d*x))^n,x)","\int \sqrt{\sin\left(c+d\,x\right)}\,{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^(1/2)*(a + a/cos(c + d*x))^n, x)","F"
158,0,-1,105,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/sin(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{\sqrt{\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/sin(c + d*x)^(1/2), x)","F"
159,0,-1,105,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^n/sin(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^n/sin(c + d*x)^(3/2), x)","F"
160,1,89,119,0.933604,"\text{Not used}","int(sin(c + d*x)^7*(a + b/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)-a\,{\cos\left(c+d\,x\right)}^3+\frac{3\,a\,{\cos\left(c+d\,x\right)}^5}{5}-\frac{a\,{\cos\left(c+d\,x\right)}^7}{7}-\frac{3\,b\,{\cos\left(c+d\,x\right)}^2}{2}+\frac{3\,b\,{\cos\left(c+d\,x\right)}^4}{4}-\frac{b\,{\cos\left(c+d\,x\right)}^6}{6}+b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) - a*cos(c + d*x)^3 + (3*a*cos(c + d*x)^5)/5 - (a*cos(c + d*x)^7)/7 - (3*b*cos(c + d*x)^2)/2 + (3*b*cos(c + d*x)^4)/4 - (b*cos(c + d*x)^6)/6 + b*log(cos(c + d*x)))/d","B"
161,1,67,87,0.905654,"\text{Not used}","int(sin(c + d*x)^5*(a + b/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)-\frac{2\,a\,{\cos\left(c+d\,x\right)}^3}{3}+\frac{a\,{\cos\left(c+d\,x\right)}^5}{5}-b\,{\cos\left(c+d\,x\right)}^2+\frac{b\,{\cos\left(c+d\,x\right)}^4}{4}+b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) - (2*a*cos(c + d*x)^3)/3 + (a*cos(c + d*x)^5)/5 - b*cos(c + d*x)^2 + (b*cos(c + d*x)^4)/4 + b*log(cos(c + d*x)))/d","B"
162,1,45,58,0.056794,"\text{Not used}","int(sin(c + d*x)^3*(a + b/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)-\frac{a\,{\cos\left(c+d\,x\right)}^3}{3}-\frac{b\,{\cos\left(c+d\,x\right)}^2}{2}+b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) - (a*cos(c + d*x)^3)/3 - (b*cos(c + d*x)^2)/2 + b*log(cos(c + d*x)))/d","B"
163,1,23,26,0.041079,"\text{Not used}","int(sin(c + d*x)*(a + b/cos(c + d*x)),x)","-\frac{a\,\cos\left(c+d\,x\right)+b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a*cos(c + d*x) + b*log(cos(c + d*x)))/d","B"
164,1,63,26,0.107908,"\text{Not used}","int((a + b/cos(c + d*x))/sin(c + d*x),x)","\frac{\frac{a\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{2}-b\,\ln\left(\cos\left(c+d\,x\right)\right)-\frac{a\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{2}+\frac{b\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{2}+\frac{b\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{2}}{d}","Not used",1,"((a*log(cos(c + d*x) - 1))/2 - b*log(cos(c + d*x)) - (a*log(cos(c + d*x) + 1))/2 + (b*log(cos(c + d*x) - 1))/2 + (b*log(cos(c + d*x) + 1))/2)/d","B"
165,1,76,64,0.097174,"\text{Not used}","int((a + b/cos(c + d*x))/sin(c + d*x)^3,x)","\frac{\frac{\frac{b}{2}+\frac{a\,\cos\left(c+d\,x\right)}{2}}{{\cos\left(c+d\,x\right)}^2-1}+\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{a}{4}+\frac{b}{2}\right)-\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(\frac{a}{4}-\frac{b}{2}\right)-b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"((b/2 + (a*cos(c + d*x))/2)/(cos(c + d*x)^2 - 1) + log(cos(c + d*x) - 1)*(a/4 + b/2) - log(cos(c + d*x) + 1)*(a/4 - b/2) - b*log(cos(c + d*x)))/d","B"
166,1,117,100,0.984126,"\text{Not used}","int((a + b/cos(c + d*x))/sin(c + d*x)^5,x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{3\,a}{16}+\frac{b}{2}\right)}{d}-\frac{-\frac{3\,a\,{\cos\left(c+d\,x\right)}^3}{8}-\frac{b\,{\cos\left(c+d\,x\right)}^2}{2}+\frac{5\,a\,\cos\left(c+d\,x\right)}{8}+\frac{3\,b}{4}}{d\,\left({\cos\left(c+d\,x\right)}^4-2\,{\cos\left(c+d\,x\right)}^2+1\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(\frac{3\,a}{16}-\frac{b}{2}\right)}{d}-\frac{b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"(log(cos(c + d*x) - 1)*((3*a)/16 + b/2))/d - ((3*b)/4 + (5*a*cos(c + d*x))/8 - (3*a*cos(c + d*x)^3)/8 - (b*cos(c + d*x)^2)/2)/(d*(cos(c + d*x)^4 - 2*cos(c + d*x)^2 + 1)) - (log(cos(c + d*x) + 1)*((3*a)/16 - b/2))/d - (b*log(cos(c + d*x)))/d","B"
167,1,148,140,1.020885,"\text{Not used}","int((a + b/cos(c + d*x))/sin(c + d*x)^7,x)","\frac{\frac{5\,a\,{\cos\left(c+d\,x\right)}^5}{16}+\frac{b\,{\cos\left(c+d\,x\right)}^4}{2}-\frac{5\,a\,{\cos\left(c+d\,x\right)}^3}{6}-\frac{5\,b\,{\cos\left(c+d\,x\right)}^2}{4}+\frac{11\,a\,\cos\left(c+d\,x\right)}{16}+\frac{11\,b}{12}}{d\,\left({\cos\left(c+d\,x\right)}^6-3\,{\cos\left(c+d\,x\right)}^4+3\,{\cos\left(c+d\,x\right)}^2-1\right)}+\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{5\,a}{32}+\frac{b}{2}\right)}{d}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(\frac{5\,a}{32}-\frac{b}{2}\right)}{d}-\frac{b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"((11*b)/12 + (11*a*cos(c + d*x))/16 - (5*a*cos(c + d*x)^3)/6 + (5*a*cos(c + d*x)^5)/16 - (5*b*cos(c + d*x)^2)/4 + (b*cos(c + d*x)^4)/2)/(d*(3*cos(c + d*x)^2 - 3*cos(c + d*x)^4 + cos(c + d*x)^6 - 1)) + (log(cos(c + d*x) - 1)*((5*a)/32 + b/2))/d - (log(cos(c + d*x) + 1)*((5*a)/32 - b/2))/d - (b*log(cos(c + d*x)))/d","B"
168,1,332,127,2.169135,"\text{Not used}","int(sin(c + d*x)^6*(a + b/cos(c + d*x)),x)","\frac{5\,a\,\mathrm{atan}\left(\frac{125\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64\,\left(\frac{125\,a^3}{64}+20\,a\,b^2\right)}+\frac{20\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{125\,a^3}{64}+20\,a\,b^2}\right)}{8\,d}+\frac{2\,b\,\mathrm{atanh}\left(\frac{64\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{25\,a^2\,b}{4}+64\,b^3}+\frac{25\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{25\,a^2\,b}{4}+64\,b^3\right)}\right)}{d}-\frac{\left(2\,b-\frac{5\,a}{8}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+\left(\frac{38\,b}{3}-\frac{85\,a}{24}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{172\,b}{5}-\frac{33\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{33\,a}{4}+\frac{172\,b}{5}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{85\,a}{24}+\frac{38\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{5\,a}{8}+2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{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,"(5*a*atan((125*a^3*tan(c/2 + (d*x)/2))/(64*(20*a*b^2 + (125*a^3)/64)) + (20*a*b^2*tan(c/2 + (d*x)/2))/(20*a*b^2 + (125*a^3)/64)))/(8*d) + (2*b*atanh((64*b^3*tan(c/2 + (d*x)/2))/((25*a^2*b)/4 + 64*b^3) + (25*a^2*b*tan(c/2 + (d*x)/2))/(4*((25*a^2*b)/4 + 64*b^3))))/d - (tan(c/2 + (d*x)/2)*((5*a)/8 + 2*b) - tan(c/2 + (d*x)/2)^11*((5*a)/8 - 2*b) + tan(c/2 + (d*x)/2)^3*((85*a)/24 + (38*b)/3) - tan(c/2 + (d*x)/2)^9*((85*a)/24 - (38*b)/3) + tan(c/2 + (d*x)/2)^5*((33*a)/4 + (172*b)/5) - tan(c/2 + (d*x)/2)^7*((33*a)/4 - (172*b)/5))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1))","B"
169,1,267,89,1.884307,"\text{Not used}","int(sin(c + d*x)^4*(a + b/cos(c + d*x)),x)","\frac{3\,a\,\mathrm{atan}\left(\frac{27\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,\left(\frac{27\,a^3}{8}+24\,a\,b^2\right)}+\frac{24\,a\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{27\,a^3}{8}+24\,a\,b^2}\right)}{4\,d}+\frac{2\,b\,\mathrm{atanh}\left(\frac{64\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,a^2\,b+64\,b^3}+\frac{9\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{9\,a^2\,b+64\,b^3}\right)}{d}-\frac{\left(2\,b-\frac{3\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{26\,b}{3}-\frac{11\,a}{4}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{11\,a}{4}+\frac{26\,b}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(\frac{3\,a}{4}+2\,b\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(3*a*atan((27*a^3*tan(c/2 + (d*x)/2))/(8*(24*a*b^2 + (27*a^3)/8)) + (24*a*b^2*tan(c/2 + (d*x)/2))/(24*a*b^2 + (27*a^3)/8)))/(4*d) + (2*b*atanh((64*b^3*tan(c/2 + (d*x)/2))/(9*a^2*b + 64*b^3) + (9*a^2*b*tan(c/2 + (d*x)/2))/(9*a^2*b + 64*b^3)))/d - (tan(c/2 + (d*x)/2)*((3*a)/4 + 2*b) - tan(c/2 + (d*x)/2)^7*((3*a)/4 - 2*b) + tan(c/2 + (d*x)/2)^3*((11*a)/4 + (26*b)/3) - tan(c/2 + (d*x)/2)^5*((11*a)/4 - (26*b)/3))/(d*(4*tan(c/2 + (d*x)/2)^2 + 6*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
170,1,83,51,1.094135,"\text{Not used}","int(sin(c + d*x)^2*(a + b/cos(c + d*x)),x)","\frac{a\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{4\,d}-\frac{b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*sin(2*c + 2*d*x))/(4*d) - (b*sin(c + d*x))/d","B"
171,1,60,37,1.021556,"\text{Not used}","int((a + b/cos(c + d*x))/sin(c + d*x)^2,x)","\frac{2\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{\frac{a}{2}+\frac{b}{2}}{d\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a}{2}-\frac{b}{2}\right)}{d}","Not used",1,"(2*b*atanh(tan(c/2 + (d*x)/2)))/d - (a/2 + b/2)/(d*tan(c/2 + (d*x)/2)) + (tan(c/2 + (d*x)/2)*(a/2 - b/2))/d","B"
172,1,101,69,0.998987,"\text{Not used}","int((a + b/cos(c + d*x))/sin(c + d*x)^4,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(3\,a+5\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a}{3}+\frac{b}{3}\right)}{8\,d}+\frac{2\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a}{8}-\frac{5\,b}{8}\right)}{d}","Not used",1,"(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*(3*a + 5*b)))/(8*d) + (2*b*atanh(tan(c/2 + (d*x)/2)))/d + (tan(c/2 + (d*x)/2)*((3*a)/8 - (5*b)/8))/d","B"
173,1,142,101,1.093844,"\text{Not used}","int((a + b/cos(c + d*x))/sin(c + d*x)^6,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{5\,a}{96}-\frac{7\,b}{96}\right)}{d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\left(10\,a+22\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{5\,a}{3}+\frac{7\,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)}^5\,\left(\frac{a}{160}-\frac{b}{160}\right)}{d}+\frac{2\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a}{16}-\frac{11\,b}{16}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*((5*a)/96 - (7*b)/96))/d - (cot(c/2 + (d*x)/2)^5*(a/5 + b/5 + tan(c/2 + (d*x)/2)^2*((5*a)/3 + (7*b)/3) + tan(c/2 + (d*x)/2)^4*(10*a + 22*b)))/(32*d) + (tan(c/2 + (d*x)/2)^5*(a/160 - b/160))/d + (2*b*atanh(tan(c/2 + (d*x)/2)))/d + (tan(c/2 + (d*x)/2)*((5*a)/16 - (11*b)/16))/d","B"
174,1,104,124,0.950959,"\text{Not used}","int(sin(c + d*x)^5*(a + b/cos(c + d*x))^2,x)","-\frac{\cos\left(c+d\,x\right)\,\left(a^2-2\,b^2\right)-{\cos\left(c+d\,x\right)}^3\,\left(\frac{2\,a^2}{3}-\frac{b^2}{3}\right)+\frac{a^2\,{\cos\left(c+d\,x\right)}^5}{5}-\frac{b^2}{\cos\left(c+d\,x\right)}-2\,a\,b\,{\cos\left(c+d\,x\right)}^2+\frac{a\,b\,{\cos\left(c+d\,x\right)}^4}{2}+2\,a\,b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(cos(c + d*x)*(a^2 - 2*b^2) - cos(c + d*x)^3*((2*a^2)/3 - b^2/3) + (a^2*cos(c + d*x)^5)/5 - b^2/cos(c + d*x) - 2*a*b*cos(c + d*x)^2 + (a*b*cos(c + d*x)^4)/2 + 2*a*b*log(cos(c + d*x)))/d","B"
175,1,69,80,0.915265,"\text{Not used}","int(sin(c + d*x)^3*(a + b/cos(c + d*x))^2,x)","\frac{\frac{a^2\,{\cos\left(c+d\,x\right)}^3}{3}-\cos\left(c+d\,x\right)\,\left(a^2-b^2\right)+\frac{b^2}{\cos\left(c+d\,x\right)}+a\,b\,{\cos\left(c+d\,x\right)}^2-2\,a\,b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"((a^2*cos(c + d*x)^3)/3 - cos(c + d*x)*(a^2 - b^2) + b^2/cos(c + d*x) + a*b*cos(c + d*x)^2 - 2*a*b*log(cos(c + d*x)))/d","B"
176,1,40,42,0.052056,"\text{Not used}","int(sin(c + d*x)*(a + b/cos(c + d*x))^2,x)","-\frac{a^2\,\cos\left(c+d\,x\right)-\frac{b^2}{\cos\left(c+d\,x\right)}+2\,a\,b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a^2*cos(c + d*x) - b^2/cos(c + d*x) + 2*a*b*log(cos(c + d*x)))/d","B"
177,1,62,74,0.966161,"\text{Not used}","int((a + b/cos(c + d*x))^2/sin(c + d*x),x)","\frac{\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^2}{2}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^2}{2}+\frac{b^2}{\cos\left(c+d\,x\right)}-2\,a\,b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"((log(cos(c + d*x) - 1)*(a + b)^2)/2 - (log(cos(c + d*x) + 1)*(a - b)^2)/2 + b^2/cos(c + d*x) - 2*a*b*log(cos(c + d*x)))/d","B"
178,1,120,114,0.121279,"\text{Not used}","int((a + b/cos(c + d*x))^2/sin(c + d*x)^3,x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(a+b\right)\,\left(a+3\,b\right)}{4\,d}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(a-b\right)\,\left(a-3\,b\right)}{4\,d}-\frac{2\,a\,b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{a^2}{2}+\frac{3\,b^2}{2}\right)-b^2+a\,b\,\cos\left(c+d\,x\right)}{d\,\left(\cos\left(c+d\,x\right)-{\cos\left(c+d\,x\right)}^3\right)}","Not used",1,"(log(cos(c + d*x) - 1)*(a + b)*(a + 3*b))/(4*d) - (log(cos(c + d*x) + 1)*(a - b)*(a - 3*b))/(4*d) - (2*a*b*log(cos(c + d*x)))/d - (cos(c + d*x)^2*(a^2/2 + (3*b^2)/2) - b^2 + a*b*cos(c + d*x))/(d*(cos(c + d*x) - cos(c + d*x)^3))","B"
179,1,231,175,3.102034,"\text{Not used}","int(sin(c + d*x)^6*(a + b/cos(c + d*x))^2,x)","\frac{\frac{5\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,a^2}{8}+4\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,a\,b-\frac{15\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,b^2}{4}}{d}-\frac{\frac{15\,a^2\,\sin\left(c+d\,x\right)}{128}-\frac{5\,b^2\,\sin\left(c+d\,x\right)}{4}+\frac{3\,a^2\,\sin\left(3\,c+3\,d\,x\right)}{32}-\frac{a^2\,\sin\left(5\,c+5\,d\,x\right)}{48}+\frac{a^2\,\sin\left(7\,c+7\,d\,x\right)}{384}-\frac{15\,b^2\,\sin\left(3\,c+3\,d\,x\right)}{64}+\frac{b^2\,\sin\left(5\,c+5\,d\,x\right)}{64}+\frac{59\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{48}-\frac{2\,a\,b\,\sin\left(4\,c+4\,d\,x\right)}{15}+\frac{a\,b\,\sin\left(6\,c+6\,d\,x\right)}{80}}{d\,\cos\left(c+d\,x\right)}","Not used",1,"((5*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/8 - (15*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 + 4*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - ((15*a^2*sin(c + d*x))/128 - (5*b^2*sin(c + d*x))/4 + (3*a^2*sin(3*c + 3*d*x))/32 - (a^2*sin(5*c + 5*d*x))/48 + (a^2*sin(7*c + 7*d*x))/384 - (15*b^2*sin(3*c + 3*d*x))/64 + (b^2*sin(5*c + 5*d*x))/64 + (59*a*b*sin(2*c + 2*d*x))/48 - (2*a*b*sin(4*c + 4*d*x))/15 + (a*b*sin(6*c + 6*d*x))/80)/(d*cos(c + d*x))","B"
180,1,207,178,1.226748,"\text{Not used}","int(sin(c + d*x)^4*(a + b/cos(c + d*x))^2,x)","\frac{3\,a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}-\frac{3\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{8\,a\,b\,\sin\left(c+d\,x\right)}{3\,d}+\frac{4\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{5\,a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{2\,a\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(3*a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) - (3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^2*cos(c + d*x)^3*sin(c + d*x))/(4*d) + (b^2*sin(c + d*x))/(d*cos(c + d*x)) - (8*a*b*sin(c + d*x))/(3*d) + (4*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (5*a^2*cos(c + d*x)*sin(c + d*x))/(8*d) + (b^2*cos(c + d*x)*sin(c + d*x))/(2*d) + (2*a*b*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
181,1,143,77,1.167903,"\text{Not used}","int(sin(c + d*x)^2*(a + b/cos(c + d*x))^2,x)","\frac{a^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}-\frac{2\,a\,b\,\sin\left(c+d\,x\right)}{d}+\frac{4\,a\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{a^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}","Not used",1,"(a^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^2*sin(c + d*x))/(d*cos(c + d*x)) - (2*a*b*sin(c + d*x))/d + (4*a*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a^2*cos(c + d*x)*sin(c + d*x))/(2*d)","B"
182,1,108,59,1.070626,"\text{Not used}","int((a + b/cos(c + d*x))^2/sin(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{2\,a\,b+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+2\,a\,b+5\,b^2\right)}{d\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{4\,a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(a - b)^2)/(2*d) - (2*a*b + a^2 + b^2 - tan(c/2 + (d*x)/2)^2*(2*a*b + a^2 + 5*b^2))/(d*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^3)) + (4*a*b*atanh(tan(c/2 + (d*x)/2)))/d","B"
183,1,182,100,1.102031,"\text{Not used}","int((a + b/cos(c + d*x))^2/sin(c + d*x)^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\left(a-b\right)}^2}{24\,d}-\frac{\frac{2\,a\,b}{3}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^2+10\,a\,b+23\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{8\,a^2}{3}+\frac{28\,a\,b}{3}+\frac{20\,b^2}{3}\right)+\frac{a^2}{3}+\frac{b^2}{3}}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{a^2}{8}-\frac{3\,a\,b}{4}+\frac{5\,b^2}{8}+\frac{{\left(a-b\right)}^2}{4}\right)}{d}+\frac{4\,a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(a - b)^2)/(24*d) - ((2*a*b)/3 - tan(c/2 + (d*x)/2)^4*(10*a*b + 3*a^2 + 23*b^2) + tan(c/2 + (d*x)/2)^2*((28*a*b)/3 + (8*a^2)/3 + (20*b^2)/3) + a^2/3 + b^2/3)/(d*(8*tan(c/2 + (d*x)/2)^3 - 8*tan(c/2 + (d*x)/2)^5)) + (tan(c/2 + (d*x)/2)*(a^2/8 - (3*a*b)/4 + (5*b^2)/8 + (a - b)^2/4))/d + (4*a*b*atanh(tan(c/2 + (d*x)/2)))/d","B"
184,1,248,143,1.044888,"\text{Not used}","int((a + b/cos(c + d*x))^2/sin(c + d*x)^6,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\left(a-b\right)}^2}{160\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2}{32}-\frac{5\,a\,b}{48}+\frac{7\,b^2}{96}+\frac{{\left(a-b\right)}^2}{48}\right)}{d}-\frac{\frac{2\,a\,b}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{22\,a^2}{15}+\frac{64\,a\,b}{15}+\frac{14\,b^2}{5}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(10\,a^2+44\,a\,b+102\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{25\,a^2}{3}+\frac{118\,a\,b}{3}+35\,b^2\right)+\frac{a^2}{5}+\frac{b^2}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{7\,a^2}{32}-\frac{19\,a\,b}{16}+\frac{35\,b^2}{32}+\frac{3\,{\left(a-b\right)}^2}{32}\right)}{d}+\frac{4\,a\,b\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(a - b)^2)/(160*d) + (tan(c/2 + (d*x)/2)^3*(a^2/32 - (5*a*b)/48 + (7*b^2)/96 + (a - b)^2/48))/d - ((2*a*b)/5 + tan(c/2 + (d*x)/2)^2*((64*a*b)/15 + (22*a^2)/15 + (14*b^2)/5) - tan(c/2 + (d*x)/2)^6*(44*a*b + 10*a^2 + 102*b^2) + tan(c/2 + (d*x)/2)^4*((118*a*b)/3 + (25*a^2)/3 + 35*b^2) + a^2/5 + b^2/5)/(d*(32*tan(c/2 + (d*x)/2)^5 - 32*tan(c/2 + (d*x)/2)^7)) + (tan(c/2 + (d*x)/2)*((7*a^2)/32 - (19*a*b)/16 + (35*b^2)/32 + (3*(a - b)^2)/32))/d + (4*a*b*atanh(tan(c/2 + (d*x)/2)))/d","B"
185,1,143,170,0.964602,"\text{Not used}","int(sin(c + d*x)^5*(a + b/cos(c + d*x))^3,x)","-\frac{{\cos\left(c+d\,x\right)}^3\,\left(a\,b^2-\frac{2\,a^3}{3}\right)-{\cos\left(c+d\,x\right)}^2\,\left(3\,a^2\,b-\frac{b^3}{2}\right)+\ln\left(\cos\left(c+d\,x\right)\right)\,\left(3\,a^2\,b-2\,b^3\right)-\frac{\frac{b^3}{2}+3\,a\,\cos\left(c+d\,x\right)\,b^2}{{\cos\left(c+d\,x\right)}^2}-\cos\left(c+d\,x\right)\,\left(6\,a\,b^2-a^3\right)+\frac{a^3\,{\cos\left(c+d\,x\right)}^5}{5}+\frac{3\,a^2\,b\,{\cos\left(c+d\,x\right)}^4}{4}}{d}","Not used",1,"-(cos(c + d*x)^3*(a*b^2 - (2*a^3)/3) - cos(c + d*x)^2*(3*a^2*b - b^3/2) + log(cos(c + d*x))*(3*a^2*b - 2*b^3) - (b^3/2 + 3*a*b^2*cos(c + d*x))/cos(c + d*x)^2 - cos(c + d*x)*(6*a*b^2 - a^3) + (a^3*cos(c + d*x)^5)/5 + (3*a^2*b*cos(c + d*x)^4)/4)/d","B"
186,1,99,116,0.072255,"\text{Not used}","int(sin(c + d*x)^3*(a + b/cos(c + d*x))^3,x)","\frac{\frac{\frac{b^3}{2}+3\,a\,\cos\left(c+d\,x\right)\,b^2}{{\cos\left(c+d\,x\right)}^2}-\ln\left(\cos\left(c+d\,x\right)\right)\,\left(3\,a^2\,b-b^3\right)+\cos\left(c+d\,x\right)\,\left(3\,a\,b^2-a^3\right)+\frac{a^3\,{\cos\left(c+d\,x\right)}^3}{3}+\frac{3\,a^2\,b\,{\cos\left(c+d\,x\right)}^2}{2}}{d}","Not used",1,"((b^3/2 + 3*a*b^2*cos(c + d*x))/cos(c + d*x)^2 - log(cos(c + d*x))*(3*a^2*b - b^3) + cos(c + d*x)*(3*a*b^2 - a^3) + (a^3*cos(c + d*x)^3)/3 + (3*a^2*b*cos(c + d*x)^2)/2)/d","B"
187,1,57,64,0.925085,"\text{Not used}","int(sin(c + d*x)*(a + b/cos(c + d*x))^3,x)","-\frac{a^3\,\cos\left(c+d\,x\right)-\frac{\frac{b^3}{2}+3\,a\,\cos\left(c+d\,x\right)\,b^2}{{\cos\left(c+d\,x\right)}^2}+3\,a^2\,b\,\ln\left(\cos\left(c+d\,x\right)\right)}{d}","Not used",1,"-(a^3*cos(c + d*x) - (b^3/2 + 3*a*b^2*cos(c + d*x))/cos(c + d*x)^2 + 3*a^2*b*log(cos(c + d*x)))/d","B"
188,1,85,102,0.130135,"\text{Not used}","int((a + b/cos(c + d*x))^3/sin(c + d*x),x)","\frac{\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^3}{2}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^3}{2}+\frac{\frac{b^3}{2}+3\,a\,\cos\left(c+d\,x\right)\,b^2}{{\cos\left(c+d\,x\right)}^2}-\ln\left(\cos\left(c+d\,x\right)\right)\,\left(3\,a^2\,b+b^3\right)}{d}","Not used",1,"((log(cos(c + d*x) - 1)*(a + b)^3)/2 - (log(cos(c + d*x) + 1)*(a - b)^3)/2 + (b^3/2 + 3*a*b^2*cos(c + d*x))/cos(c + d*x)^2 - log(cos(c + d*x))*(3*a^2*b + b^3))/d","B"
189,1,159,162,1.007983,"\text{Not used}","int((a + b/cos(c + d*x))^3/sin(c + d*x)^3,x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,{\left(a+b\right)}^2\,\left(a+4\,b\right)}{4\,d}-\frac{\ln\left(\cos\left(c+d\,x\right)\right)\,\left(3\,a^2\,b+2\,b^3\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{a^3}{2}+\frac{9\,a\,b^2}{2}\right)-\frac{b^3}{2}+{\cos\left(c+d\,x\right)}^2\,\left(\frac{3\,a^2\,b}{2}+b^3\right)-3\,a\,b^2\,\cos\left(c+d\,x\right)}{d\,\left({\cos\left(c+d\,x\right)}^2-{\cos\left(c+d\,x\right)}^4\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,{\left(a-b\right)}^2\,\left(a-4\,b\right)}{4\,d}","Not used",1,"(log(cos(c + d*x) - 1)*(a + b)^2*(a + 4*b))/(4*d) - (log(cos(c + d*x))*(3*a^2*b + 2*b^3))/d - (cos(c + d*x)^3*((9*a*b^2)/2 + a^3/2) - b^3/2 + cos(c + d*x)^2*((3*a^2*b)/2 + b^3) - 3*a*b^2*cos(c + d*x))/(d*(cos(c + d*x)^2 - cos(c + d*x)^4)) - (log(cos(c + d*x) + 1)*(a - b)^2*(a - 4*b))/(4*d)","B"
190,1,373,299,1.685449,"\text{Not used}","int(sin(c + d*x)^6*(a + b/cos(c + d*x))^3,x)","\frac{7\,b^3\,\sin\left(c+d\,x\right)}{3\,d}+\frac{5\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{8\,d}-\frac{5\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{13\,a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{24\,d}-\frac{a^3\,{\cos\left(c+d\,x\right)}^5\,\sin\left(c+d\,x\right)}{6\,d}+\frac{b^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}-\frac{b^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}-\frac{11\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{16\,d}-\frac{23\,a^2\,b\,\sin\left(c+d\,x\right)}{5\,d}-\frac{45\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}+\frac{6\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{27\,a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{11\,a^2\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{5\,d}-\frac{3\,a\,b^2\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}-\frac{3\,a^2\,b\,{\cos\left(c+d\,x\right)}^4\,\sin\left(c+d\,x\right)}{5\,d}","Not used",1,"(7*b^3*sin(c + d*x))/(3*d) + (5*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(8*d) - (5*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (13*a^3*cos(c + d*x)^3*sin(c + d*x))/(24*d) - (a^3*cos(c + d*x)^5*sin(c + d*x))/(6*d) + (b^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) - (b^3*cos(c + d*x)^2*sin(c + d*x))/(3*d) - (11*a^3*cos(c + d*x)*sin(c + d*x))/(16*d) - (23*a^2*b*sin(c + d*x))/(5*d) - (45*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) + (6*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (27*a*b^2*cos(c + d*x)*sin(c + d*x))/(8*d) + (3*a*b^2*sin(c + d*x))/(d*cos(c + d*x)) + (11*a^2*b*cos(c + d*x)^2*sin(c + d*x))/(5*d) - (3*a*b^2*cos(c + d*x)^3*sin(c + d*x))/(4*d) - (3*a^2*b*cos(c + d*x)^4*sin(c + d*x))/(5*d)","B"
191,1,281,236,1.471863,"\text{Not used}","int(sin(c + d*x)^4*(a + b/cos(c + d*x))^3,x)","\frac{b^3\,\sin\left(c+d\,x\right)}{d}+\frac{3\,a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4\,d}-\frac{3\,b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^3\,{\cos\left(c+d\,x\right)}^3\,\sin\left(c+d\,x\right)}{4\,d}+\frac{b^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}-\frac{5\,a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{8\,d}-\frac{4\,a^2\,b\,\sin\left(c+d\,x\right)}{d}-\frac{9\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,a\,b^2\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}+\frac{a^2\,b\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(b^3*sin(c + d*x))/d + (3*a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(4*d) - (3*b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (a^3*cos(c + d*x)^3*sin(c + d*x))/(4*d) + (b^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) - (5*a^3*cos(c + d*x)*sin(c + d*x))/(8*d) - (4*a^2*b*sin(c + d*x))/d - (9*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*a*b^2*cos(c + d*x)*sin(c + d*x))/(2*d) + (3*a*b^2*sin(c + d*x))/(d*cos(c + d*x)) + (a^2*b*cos(c + d*x)^2*sin(c + d*x))/d","B"
192,1,202,138,1.268990,"\text{Not used}","int(sin(c + d*x)^2*(a + b/cos(c + d*x))^3,x)","\frac{a^3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}-\frac{b^3\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{b^3\,\sin\left(c+d\,x\right)}{2\,d\,{\cos\left(c+d\,x\right)}^2}-\frac{a^3\,\cos\left(c+d\,x\right)\,\sin\left(c+d\,x\right)}{2\,d}-\frac{3\,a^2\,b\,\sin\left(c+d\,x\right)}{d}-\frac{6\,a\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{6\,a^2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{3\,a\,b^2\,\sin\left(c+d\,x\right)}{d\,\cos\left(c+d\,x\right)}","Not used",1,"(a^3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (b^3*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (b^3*sin(c + d*x))/(2*d*cos(c + d*x)^2) - (a^3*cos(c + d*x)*sin(c + d*x))/(2*d) - (3*a^2*b*sin(c + d*x))/d - (6*a*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (6*a^2*b*atanh(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d + (3*a*b^2*sin(c + d*x))/(d*cos(c + d*x))","B"
193,1,181,133,1.465774,"\text{Not used}","int((a + b/cos(c + d*x))^3/sin(c + d*x)^2,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(6\,a^2\,b+3\,b^3\right)}{d}-\frac{3\,a\,b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^3+6\,a^2\,b+18\,a\,b^2+4\,b^3\right)+3\,a^2\,b+a^3+b^3+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^3+3\,a^2\,b+15\,a\,b^2-b^3\right)}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\left(a-b\right)}^3}{2\,d}","Not used",1,"(atanh(tan(c/2 + (d*x)/2))*(6*a^2*b + 3*b^3))/d - (3*a*b^2 - tan(c/2 + (d*x)/2)^2*(18*a*b^2 + 6*a^2*b + 2*a^3 + 4*b^3) + 3*a^2*b + a^3 + b^3 + tan(c/2 + (d*x)/2)^4*(15*a*b^2 + 3*a^2*b + a^3 - b^3))/(d*(2*tan(c/2 + (d*x)/2) - 4*tan(c/2 + (d*x)/2)^3 + 2*tan(c/2 + (d*x)/2)^5)) + (tan(c/2 + (d*x)/2)*(a - b)^3)/(2*d)","B"
194,1,260,205,1.165307,"\text{Not used}","int((a + b/cos(c + d*x))^3/sin(c + d*x)^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\left(a-b\right)}^3}{24\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,b\,{\left(a-b\right)}^2}{4}-\frac{3\,{\left(a-b\right)}^3}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{7\,a^3}{3}+13\,a^2\,b+19\,a\,b^2+\frac{25\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{17\,a^3}{3}+29\,a^2\,b+89\,a\,b^2+\frac{77\,b^3}{3}\right)+a\,b^2+a^2\,b+\frac{a^3}{3}+\frac{b^3}{3}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^3+15\,a^2\,b+69\,a\,b^2+b^3\right)}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2\,b\,6{}\mathrm{i}+b^3\,5{}\mathrm{i}\right)\,1{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(a - b)^3)/(24*d) - (tan(c/2 + (d*x)/2)*((3*b*(a - b)^2)/4 - (3*(a - b)^3)/8))/d - (atanh(tan(c/2 + (d*x)/2))*(a^2*b*6i + b^3*5i)*1i)/d - (tan(c/2 + (d*x)/2)^2*(19*a*b^2 + 13*a^2*b + (7*a^3)/3 + (25*b^3)/3) - tan(c/2 + (d*x)/2)^4*(89*a*b^2 + 29*a^2*b + (17*a^3)/3 + (77*b^3)/3) + a*b^2 + a^2*b + a^3/3 + b^3/3 + tan(c/2 + (d*x)/2)^6*(69*a*b^2 + 15*a^2*b + 3*a^3 + b^3))/(d*(8*tan(c/2 + (d*x)/2)^3 - 16*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7))","B"
195,1,363,279,1.221633,"\text{Not used}","int((a + b/cos(c + d*x))^3/sin(c + d*x)^6,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\left(a-b\right)}^3}{160\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{19\,a^3}{15}+\frac{29\,a^2\,b}{5}+\frac{39\,a\,b^2}{5}+\frac{49\,b^3}{15}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(10\,a^3+66\,a^2\,b+306\,a\,b^2+26\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{55\,a^3}{3}+125\,a^2\,b+411\,a\,b^2+\frac{433\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{103\,a^3}{15}+\frac{263\,a^2\,b}{5}+\frac{483\,a\,b^2}{5}+\frac{763\,b^3}{15}\right)+\frac{3\,a\,b^2}{5}+\frac{3\,a^2\,b}{5}+\frac{a^3}{5}+\frac{b^3}{5}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-64\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{21\,a\,b^2}{16}-\frac{3\,a^2\,b}{8}-\frac{a^3}{16}-\frac{7\,b^3}{8}+\frac{3\,{\left(a-b\right)}^2\,\left(a-4\,b\right)}{16}+\frac{3\,{\left(a-b\right)}^3}{16}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{{\left(a-b\right)}^2\,\left(a-4\,b\right)}{48}+\frac{{\left(a-b\right)}^3}{32}\right)}{d}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2\,b\,6{}\mathrm{i}+b^3\,7{}\mathrm{i}\right)\,1{}\mathrm{i}}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^5*(a - b)^3)/(160*d) - (tan(c/2 + (d*x)/2)^2*((39*a*b^2)/5 + (29*a^2*b)/5 + (19*a^3)/15 + (49*b^3)/15) + tan(c/2 + (d*x)/2)^8*(306*a*b^2 + 66*a^2*b + 10*a^3 + 26*b^3) - tan(c/2 + (d*x)/2)^6*(411*a*b^2 + 125*a^2*b + (55*a^3)/3 + (433*b^3)/3) + tan(c/2 + (d*x)/2)^4*((483*a*b^2)/5 + (263*a^2*b)/5 + (103*a^3)/15 + (763*b^3)/15) + (3*a*b^2)/5 + (3*a^2*b)/5 + a^3/5 + b^3/5)/(d*(32*tan(c/2 + (d*x)/2)^5 - 64*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9)) - (atanh(tan(c/2 + (d*x)/2))*(a^2*b*6i + b^3*7i)*1i)/d + (tan(c/2 + (d*x)/2)*((21*a*b^2)/16 - (3*a^2*b)/8 - a^3/16 - (7*b^3)/8 + (3*(a - b)^2*(a - 4*b))/16 + (3*(a - b)^3)/16))/d + (tan(c/2 + (d*x)/2)^3*(((a - b)^2*(a - 4*b))/48 + (a - b)^3/32))/d","B"
196,1,249,223,0.155198,"\text{Not used}","int(sin(c + d*x)^7/(a + b/cos(c + d*x)),x)","\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{1}{a}-\frac{b^2\,\left(\frac{1}{a}-\frac{b^2}{3\,a^3}\right)}{a^2}\right)-{\cos\left(c+d\,x\right)}^5\,\left(\frac{3}{5\,a}-\frac{b^2}{5\,a^3}\right)-\cos\left(c+d\,x\right)\,\left(\frac{1}{a}-\frac{b^2\,\left(\frac{3}{a}-\frac{b^2\,\left(\frac{3}{a}-\frac{b^2}{a^3}\right)}{a^2}\right)}{a^2}\right)+\frac{{\cos\left(c+d\,x\right)}^7}{7\,a}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(a^6\,b-3\,a^4\,b^3+3\,a^2\,b^5-b^7\right)}{a^8}-\frac{b\,{\cos\left(c+d\,x\right)}^6}{6\,a^2}-\frac{b\,{\cos\left(c+d\,x\right)}^2\,\left(\frac{3}{a}-\frac{b^2\,\left(\frac{3}{a}-\frac{b^2}{a^3}\right)}{a^2}\right)}{2\,a}+\frac{b\,{\cos\left(c+d\,x\right)}^4\,\left(\frac{3}{a}-\frac{b^2}{a^3}\right)}{4\,a}}{d}","Not used",1,"(cos(c + d*x)^3*(1/a - (b^2*(1/a - b^2/(3*a^3)))/a^2) - cos(c + d*x)^5*(3/(5*a) - b^2/(5*a^3)) - cos(c + d*x)*(1/a - (b^2*(3/a - (b^2*(3/a - b^2/a^3))/a^2))/a^2) + cos(c + d*x)^7/(7*a) + (log(b + a*cos(c + d*x))*(a^6*b - b^7 + 3*a^2*b^5 - 3*a^4*b^3))/a^8 - (b*cos(c + d*x)^6)/(6*a^2) - (b*cos(c + d*x)^2*(3/a - (b^2*(3/a - b^2/a^3))/a^2))/(2*a) + (b*cos(c + d*x)^4*(3/a - b^2/a^3))/(4*a))/d","B"
197,1,151,152,0.090623,"\text{Not used}","int(sin(c + d*x)^5/(a + b/cos(c + d*x)),x)","-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a}-\frac{b^2\,\left(\frac{2}{a}-\frac{b^2}{a^3}\right)}{a^2}\right)-{\cos\left(c+d\,x\right)}^3\,\left(\frac{2}{3\,a}-\frac{b^2}{3\,a^3}\right)+\frac{{\cos\left(c+d\,x\right)}^5}{5\,a}-\frac{b\,{\cos\left(c+d\,x\right)}^4}{4\,a^2}-\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(a^4\,b-2\,a^2\,b^3+b^5\right)}{a^6}+\frac{b\,{\cos\left(c+d\,x\right)}^2\,\left(\frac{2}{a}-\frac{b^2}{a^3}\right)}{2\,a}}{d}","Not used",1,"-(cos(c + d*x)*(1/a - (b^2*(2/a - b^2/a^3))/a^2) - cos(c + d*x)^3*(2/(3*a) - b^2/(3*a^3)) + cos(c + d*x)^5/(5*a) - (b*cos(c + d*x)^4)/(4*a^2) - (log(b + a*cos(c + d*x))*(a^4*b + b^5 - 2*a^2*b^3))/a^6 + (b*cos(c + d*x)^2*(2/a - b^2/a^3))/(2*a))/d","B"
198,1,79,89,1.023372,"\text{Not used}","int(sin(c + d*x)^3/(a + b/cos(c + d*x)),x)","-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a}-\frac{b^2}{a^3}\right)-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a}+\frac{b\,{\cos\left(c+d\,x\right)}^2}{2\,a^2}-\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(a^2\,b-b^3\right)}{a^4}}{d}","Not used",1,"-(cos(c + d*x)*(1/a - b^2/a^3) - cos(c + d*x)^3/(3*a) + (b*cos(c + d*x)^2)/(2*a^2) - (log(b + a*cos(c + d*x))*(a^2*b - b^3))/a^4)/d","B"
199,1,30,34,0.058301,"\text{Not used}","int(sin(c + d*x)/(a + b/cos(c + d*x)),x)","\frac{b\,\ln\left(b+a\,\cos\left(c+d\,x\right)\right)-a\,\cos\left(c+d\,x\right)}{a^2\,d}","Not used",1,"(b*log(b + a*cos(c + d*x)) - a*cos(c + d*x))/(a^2*d)","B"
200,1,68,74,1.146917,"\text{Not used}","int(1/(sin(c + d*x)*(a + b/cos(c + d*x))),x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)}{2\,d\,\left(a+b\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)}{2\,d\,\left(a-b\right)}+\frac{b\,\ln\left(b+a\,\cos\left(c+d\,x\right)\right)}{d\,\left(a^2-b^2\right)}","Not used",1,"log(cos(c + d*x) - 1)/(2*d*(a + b)) - log(cos(c + d*x) + 1)/(2*d*(a - b)) + (b*log(b + a*cos(c + d*x)))/(d*(a^2 - b^2))","B"
201,1,133,116,0.303453,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + b/cos(c + d*x))),x)","\frac{a\,\ln\left(\cos\left(c+d\,x\right)-1\right)}{4\,d\,{\left(a+b\right)}^2}-\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(\frac{a}{4\,{\left(a+b\right)}^2}-\frac{a}{4\,{\left(a-b\right)}^2}\right)}{d}-\frac{\frac{b}{2\,\left(a^2-b^2\right)}-\frac{a\,\cos\left(c+d\,x\right)}{2\,\left(a^2-b^2\right)}}{d\,\left({\cos\left(c+d\,x\right)}^2-1\right)}-\frac{a\,\ln\left(\cos\left(c+d\,x\right)+1\right)}{4\,d\,{\left(a-b\right)}^2}","Not used",1,"(a*log(cos(c + d*x) - 1))/(4*d*(a + b)^2) - (log(b + a*cos(c + d*x))*(a/(4*(a + b)^2) - a/(4*(a - b)^2)))/d - (b/(2*(a^2 - b^2)) - (a*cos(c + d*x))/(2*(a^2 - b^2)))/(d*(cos(c + d*x)^2 - 1)) - (a*log(cos(c + d*x) + 1))/(4*d*(a - b)^2)","B"
202,1,297,179,1.614284,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + b/cos(c + d*x))),x)","\frac{\frac{3\,a^2\,b-b^3}{4\,{\left(a^2-b^2\right)}^2}+\frac{{\cos\left(c+d\,x\right)}^3\,\left(3\,a^3+a\,b^2\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{a^2\,b\,{\cos\left(c+d\,x\right)}^2}{2\,{\left(a^2-b^2\right)}^2}-\frac{a\,\cos\left(c+d\,x\right)\,\left(5\,a^2-b^2\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\cos\left(c+d\,x\right)}^4-2\,{\cos\left(c+d\,x\right)}^2+1\right)}+\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{3}{16\,\left(a+b\right)}-\frac{5\,b}{16\,{\left(a+b\right)}^2}+\frac{b^2}{8\,{\left(a+b\right)}^3}\right)}{d}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(\frac{b^2}{8\,{\left(a-b\right)}^3}+\frac{5\,b}{16\,{\left(a-b\right)}^2}+\frac{3}{16\,\left(a-b\right)}\right)}{d}+\frac{a^4\,b\,\ln\left(b+a\,\cos\left(c+d\,x\right)\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"((3*a^2*b - b^3)/(4*(a^2 - b^2)^2) + (cos(c + d*x)^3*(a*b^2 + 3*a^3))/(8*(a^4 + b^4 - 2*a^2*b^2)) - (a^2*b*cos(c + d*x)^2)/(2*(a^2 - b^2)^2) - (a*cos(c + d*x)*(5*a^2 - b^2))/(8*(a^4 + b^4 - 2*a^2*b^2)))/(d*(cos(c + d*x)^4 - 2*cos(c + d*x)^2 + 1)) + (log(cos(c + d*x) - 1)*(3/(16*(a + b)) - (5*b)/(16*(a + b)^2) + b^2/(8*(a + b)^3)))/d - (log(cos(c + d*x) + 1)*(b^2/(8*(a - b)^3) + (5*b)/(16*(a - b)^2) + 3/(16*(a - b))))/d + (a^4*b*log(b + a*cos(c + d*x)))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
203,1,3341,230,3.878553,"\text{Not used}","int(sin(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(5\,a^5-16\,a^4\,b-14\,a^3\,b^2+32\,a^2\,b^3+8\,a\,b^4-16\,b^5\right)}{8\,a^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(5\,a^5+16\,a^4\,b-14\,a^3\,b^2-32\,a^2\,b^3+8\,a\,b^4+16\,b^5\right)}{8\,a^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(85\,a^5-304\,a^4\,b-174\,a^3\,b^2+544\,a^2\,b^3+72\,a\,b^4-240\,b^5\right)}{24\,a^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(85\,a^5+304\,a^4\,b-174\,a^3\,b^2-544\,a^2\,b^3+72\,a\,b^4+240\,b^5\right)}{24\,a^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(165\,a^5-688\,a^4\,b-110\,a^3\,b^2+960\,a^2\,b^3+40\,a\,b^4-400\,b^5\right)}{20\,a^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(165\,a^5+688\,a^4\,b-110\,a^3\,b^2-960\,a^2\,b^3+40\,a\,b^4+400\,b^5\right)}{20\,a^6}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+15\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{128\,a^{19}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{16\,a^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,a^7}-\frac{\left(\frac{\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{128\,a^{19}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{16\,a^7}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,a^7}}{\frac{\frac{25\,a^{19}\,b}{4}+\frac{15\,a^{18}\,b^2}{2}-\frac{215\,a^{17}\,b^3}{2}-\frac{105\,a^{16}\,b^4}{2}+715\,a^{15}\,b^5+\frac{85\,a^{14}\,b^6}{2}-\frac{4915\,a^{13}\,b^7}{2}+\frac{937\,a^{12}\,b^8}{2}+\frac{19951\,a^{11}\,b^9}{4}-1736\,a^{10}\,b^{10}-6359\,a^9\,b^{11}+2890\,a^8\,b^{12}+5179\,a^7\,b^{13}-2748\,a^6\,b^{14}-2628\,a^5\,b^{15}+1544\,a^4\,b^{16}+760\,a^3\,b^{17}-480\,a^2\,b^{18}-96\,a\,b^{19}+64\,b^{20}}{a^{18}}+\frac{\left(\frac{\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{128\,a^{19}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{16\,a^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{16\,a^7}+\frac{\left(\frac{\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{128\,a^{19}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{16\,a^7}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)}{16\,a^7}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,30{}\mathrm{i}+a^2\,b^4\,40{}\mathrm{i}-b^6\,16{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^7\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)}{8\,a^{19}}\right)}{a^7}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{a^7}+\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)}{8\,a^{19}}\right)}{a^7}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,1{}\mathrm{i}}{a^7}}{\frac{\frac{25\,a^{19}\,b}{4}+\frac{15\,a^{18}\,b^2}{2}-\frac{215\,a^{17}\,b^3}{2}-\frac{105\,a^{16}\,b^4}{2}+715\,a^{15}\,b^5+\frac{85\,a^{14}\,b^6}{2}-\frac{4915\,a^{13}\,b^7}{2}+\frac{937\,a^{12}\,b^8}{2}+\frac{19951\,a^{11}\,b^9}{4}-1736\,a^{10}\,b^{10}-6359\,a^9\,b^{11}+2890\,a^8\,b^{12}+5179\,a^7\,b^{13}-2748\,a^6\,b^{14}-2628\,a^5\,b^{15}+1544\,a^4\,b^{16}+760\,a^3\,b^{17}-480\,a^2\,b^{18}-96\,a\,b^{19}+64\,b^{20}}{a^{18}}+\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}+\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)}{8\,a^{19}}\right)}{a^7}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^7}-\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+31\,a^{13}\,b^2+619\,a^{12}\,b^3-1136\,a^{11}\,b^4-2064\,a^{10}\,b^5+5180\,a^9\,b^6+2540\,a^8\,b^7-10240\,a^7\,b^8+10240\,a^5\,b^{10}-2560\,a^4\,b^{11}-5120\,a^3\,b^{12}+2048\,a^2\,b^{13}+1024\,a\,b^{14}-512\,b^{15}\right)}{8\,a^{12}}-\frac{b\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{-10\,a^{22}+42\,a^{21}\,b+6\,a^{20}\,b^2-134\,a^{19}\,b^3+52\,a^{18}\,b^4+140\,a^{17}\,b^5-80\,a^{16}\,b^6-48\,a^{15}\,b^7+32\,a^{14}\,b^8}{a^{18}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(512\,a^{16}\,b-1024\,a^{15}\,b^2+512\,a^{14}\,b^3\right)}{8\,a^{19}}\right)}{a^7}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^7}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^7\,d}","Not used",1,"(atan(((((((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 - (tan(c/2 + (d*x)/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2)*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(128*a^19))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(16*a^7) + (tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i)*1i)/(16*a^7) - (((((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 + (tan(c/2 + (d*x)/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2)*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(128*a^19))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(16*a^7) - (tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i)*1i)/(16*a^7))/(((25*a^19*b)/4 - 96*a*b^19 + 64*b^20 - 480*a^2*b^18 + 760*a^3*b^17 + 1544*a^4*b^16 - 2628*a^5*b^15 - 2748*a^6*b^14 + 5179*a^7*b^13 + 2890*a^8*b^12 - 6359*a^9*b^11 - 1736*a^10*b^10 + (19951*a^11*b^9)/4 + (937*a^12*b^8)/2 - (4915*a^13*b^7)/2 + (85*a^14*b^6)/2 + 715*a^15*b^5 - (105*a^16*b^4)/2 - (215*a^17*b^3)/2 + (15*a^18*b^2)/2)/a^18 + (((((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 - (tan(c/2 + (d*x)/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2)*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(128*a^19))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(16*a^7) + (tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(16*a^7) + (((((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 + (tan(c/2 + (d*x)/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2)*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(128*a^19))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(16*a^7) - (tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i))/(16*a^7)))*(a^6*5i - b^6*16i + a^2*b^4*40i - a^4*b^2*30i)*1i)/(8*a^7*d) - ((tan(c/2 + (d*x)/2)*(8*a*b^4 - 16*a^4*b + 5*a^5 - 16*b^5 + 32*a^2*b^3 - 14*a^3*b^2))/(8*a^6) - (tan(c/2 + (d*x)/2)^11*(8*a*b^4 + 16*a^4*b + 5*a^5 + 16*b^5 - 32*a^2*b^3 - 14*a^3*b^2))/(8*a^6) + (tan(c/2 + (d*x)/2)^3*(72*a*b^4 - 304*a^4*b + 85*a^5 - 240*b^5 + 544*a^2*b^3 - 174*a^3*b^2))/(24*a^6) - (tan(c/2 + (d*x)/2)^9*(72*a*b^4 + 304*a^4*b + 85*a^5 + 240*b^5 - 544*a^2*b^3 - 174*a^3*b^2))/(24*a^6) + (tan(c/2 + (d*x)/2)^5*(40*a*b^4 - 688*a^4*b + 165*a^5 - 400*b^5 + 960*a^2*b^3 - 110*a^3*b^2))/(20*a^6) - (tan(c/2 + (d*x)/2)^7*(40*a*b^4 + 688*a^4*b + 165*a^5 + 400*b^5 - 960*a^2*b^3 - 110*a^3*b^2))/(20*a^6))/(d*(6*tan(c/2 + (d*x)/2)^2 + 15*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^6 + 15*tan(c/2 + (d*x)/2)^8 + 6*tan(c/2 + (d*x)/2)^10 + tan(c/2 + (d*x)/2)^12 + 1)) + (b*atan(((b*((tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12) + (b*((a + b)^5*(a - b)^5)^(1/2)*((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 - (b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2))/(8*a^19)))/a^7)*((a + b)^5*(a - b)^5)^(1/2)*1i)/a^7 + (b*((tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12) - (b*((a + b)^5*(a - b)^5)^(1/2)*((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 + (b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2))/(8*a^19)))/a^7)*((a + b)^5*(a - b)^5)^(1/2)*1i)/a^7)/(((25*a^19*b)/4 - 96*a*b^19 + 64*b^20 - 480*a^2*b^18 + 760*a^3*b^17 + 1544*a^4*b^16 - 2628*a^5*b^15 - 2748*a^6*b^14 + 5179*a^7*b^13 + 2890*a^8*b^12 - 6359*a^9*b^11 - 1736*a^10*b^10 + (19951*a^11*b^9)/4 + (937*a^12*b^8)/2 - (4915*a^13*b^7)/2 + (85*a^14*b^6)/2 + 715*a^15*b^5 - (105*a^16*b^4)/2 - (215*a^17*b^3)/2 + (15*a^18*b^2)/2)/a^18 + (b*((tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12) + (b*((a + b)^5*(a - b)^5)^(1/2)*((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 - (b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2))/(8*a^19)))/a^7)*((a + b)^5*(a - b)^5)^(1/2))/a^7 - (b*((tan(c/2 + (d*x)/2)*(1024*a*b^14 - 75*a^14*b + 25*a^15 - 512*b^15 + 2048*a^2*b^13 - 5120*a^3*b^12 - 2560*a^4*b^11 + 10240*a^5*b^10 - 10240*a^7*b^8 + 2540*a^8*b^7 + 5180*a^9*b^6 - 2064*a^10*b^5 - 1136*a^11*b^4 + 619*a^12*b^3 + 31*a^13*b^2))/(8*a^12) - (b*((a + b)^5*(a - b)^5)^(1/2)*((42*a^21*b - 10*a^22 + 32*a^14*b^8 - 48*a^15*b^7 - 80*a^16*b^6 + 140*a^17*b^5 + 52*a^18*b^4 - 134*a^19*b^3 + 6*a^20*b^2)/a^18 + (b*tan(c/2 + (d*x)/2)*((a + b)^5*(a - b)^5)^(1/2)*(512*a^16*b + 512*a^14*b^3 - 1024*a^15*b^2))/(8*a^19)))/a^7)*((a + b)^5*(a - b)^5)^(1/2))/a^7))*((a + b)^5*(a - b)^5)^(1/2)*2i)/(a^7*d)","B"
204,1,317,161,2.292905,"\text{Not used}","int(sin(c + d*x)^4/(a + b/cos(c + d*x)),x)","\frac{\frac{5\,b\,\sin\left(c+d\,x\right)}{4}-\frac{b\,\sin\left(3\,c+3\,d\,x\right)}{12}}{a^2\,d}-\frac{3\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{b^2\,\sin\left(2\,c+2\,d\,x\right)}{4}}{a^3\,d}+\frac{\frac{3\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{4}-\frac{\sin\left(2\,c+2\,d\,x\right)}{4}+\frac{\sin\left(4\,c+4\,d\,x\right)}{32}}{a\,d}-\frac{b^3\,\sin\left(c+d\,x\right)}{a^4\,d}+\frac{2\,b^4\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^5\,d}-\frac{2\,b\,\mathrm{atanh}\left(\frac{\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)\,a^3+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^2-\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^3}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{a^5\,d}","Not used",1,"((5*b*sin(c + d*x))/4 - (b*sin(3*c + 3*d*x))/12)/(a^2*d) - (3*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - (b^2*sin(2*c + 2*d*x))/4)/(a^3*d) + ((3*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - sin(2*c + 2*d*x)/4 + sin(4*c + 4*d*x)/32)/(a*d) - (b^3*sin(c + d*x))/(a^4*d) + (2*b^4*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^5*d) - (2*b*atanh((sin(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(a^3*cos(c/2 + (d*x)/2) - b^3*cos(c/2 + (d*x)/2) - a*b^2*cos(c/2 + (d*x)/2) + a^2*b*cos(c/2 + (d*x)/2)))*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(a^5*d)","B"
205,1,147,100,1.477760,"\text{Not used}","int(sin(c + d*x)^2/(a + b/cos(c + d*x)),x)","\frac{\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)-\frac{\sin\left(2\,c+2\,d\,x\right)}{4}}{a\,d}-\frac{2\,b^2\,\mathrm{atan}\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^3\,d}+\frac{b\,\sin\left(c+d\,x\right)}{a^2\,d}-\frac{2\,b\,\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^3\,d}","Not used",1,"(atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) - sin(2*c + 2*d*x)/4)/(a*d) - (2*b^2*atan(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^3*d) + (b*sin(c + d*x))/(a^2*d) - (2*b*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^3*d)","B"
206,1,109,84,1.303857,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + b/cos(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(2\,a-2\,b\right)}-\frac{a-b}{d\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)\,\left(2\,a-2\,b\right)}-\frac{2\,a\,b\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{{\left(a+b\right)}^{3/2}\,\sqrt{a-b}}\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"tan(c/2 + (d*x)/2)/(d*(2*a - 2*b)) - (a - b)/(d*tan(c/2 + (d*x)/2)*(a + b)*(2*a - 2*b)) - (2*a*b*atanh((tan(c/2 + (d*x)/2)*(a^2 - b^2))/((a + b)^(3/2)*(a - b)^(1/2))))/(d*(a + b)^(3/2)*(a - b)^(3/2))","B"
207,1,219,140,1.375286,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + b/cos(c + d*x))),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{2}{8\,a-8\,b}+\frac{8\,a+8\,b}{{\left(8\,a-8\,b\right)}^2}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3\,d\,\left(8\,a-8\,b\right)}-\frac{\frac{a^2-2\,a\,b+b^2}{3\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^3-5\,a^2\,b+a\,b^2+b^3\right)}{{\left(a+b\right)}^2}}{d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(8\,a^2-16\,a\,b+8\,b^2\right)}-\frac{2\,a^3\,b\,\mathrm{atanh}\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"(tan(c/2 + (d*x)/2)*(2/(8*a - 8*b) + (8*a + 8*b)/(8*a - 8*b)^2))/d + tan(c/2 + (d*x)/2)^3/(3*d*(8*a - 8*b)) - ((a^2 - 2*a*b + b^2)/(3*(a + b)) + (tan(c/2 + (d*x)/2)^2*(a*b^2 - 5*a^2*b + 3*a^3 + b^3))/(a + b)^2)/(d*tan(c/2 + (d*x)/2)^3*(8*a^2 - 16*a*b + 8*b^2)) - (2*a^3*b*atanh((tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(3/2))))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
208,1,387,201,1.687047,"\text{Not used}","int(1/(sin(c + d*x)^6*(a + b/cos(c + d*x))),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5\,d\,\left(32\,a-32\,b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{4}{3\,\left(32\,a-32\,b\right)}+\frac{32\,a+32\,b}{3\,{\left(32\,a-32\,b\right)}^2}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5}{32\,a-32\,b}+\frac{\left(\frac{4}{32\,a-32\,b}+\frac{32\,a+32\,b}{{\left(32\,a-32\,b\right)}^2}\right)\,\left(32\,a+32\,b\right)}{32\,a-32\,b}\right)}{d}-\frac{\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{5\,\left(a+b\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-5\,a^5+11\,a^4\,b-4\,a^3\,b^2-4\,a^2\,b^3+a\,b^4+b^5\right)}{{\left(a+b\right)}^3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^4-12\,a^3\,b+6\,a^2\,b^2+4\,a\,b^3-3\,b^4\right)}{3\,{\left(a+b\right)}^2}}{d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(32\,a^3-96\,a^2\,b+96\,a\,b^2-32\,b^3\right)}-\frac{2\,a^5\,b\,\mathrm{atanh}\left(\frac{\mathrm{tan}\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)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{5/2}}\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"tan(c/2 + (d*x)/2)^5/(5*d*(32*a - 32*b)) + (tan(c/2 + (d*x)/2)^3*(4/(3*(32*a - 32*b)) + (32*a + 32*b)/(3*(32*a - 32*b)^2)))/d + (tan(c/2 + (d*x)/2)*(5/(32*a - 32*b) + ((4/(32*a - 32*b) + (32*a + 32*b)/(32*a - 32*b)^2)*(32*a + 32*b))/(32*a - 32*b)))/d - ((3*a*b^2 - 3*a^2*b + a^3 - b^3)/(5*(a + b)) - (2*tan(c/2 + (d*x)/2)^4*(a*b^4 + 11*a^4*b - 5*a^5 + b^5 - 4*a^2*b^3 - 4*a^3*b^2))/(a + b)^3 + (tan(c/2 + (d*x)/2)^2*(4*a*b^3 - 12*a^3*b + 5*a^4 - 3*b^4 + 6*a^2*b^2))/(3*(a + b)^2))/(d*tan(c/2 + (d*x)/2)^5*(96*a*b^2 - 96*a^2*b + 32*a^3 - 32*b^3)) - (2*a^5*b*atanh((tan(c/2 + (d*x)/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/((a + b)^(7/2)*(a - b)^(5/2))))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
209,1,588,267,0.188115,"\text{Not used}","int(sin(c + d*x)^7/(a + b/cos(c + d*x))^2,x)","\frac{{\cos\left(c+d\,x\right)}^4\,\left(\frac{b^3}{2\,a^5}+\frac{b\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{2\,a}\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{b^2\,\left(\frac{2\,b^3}{a^5}+\frac{2\,b\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{2\,a^2}+\frac{b\,\left(\frac{3}{a^2}+\frac{b^2\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a^2}-\frac{2\,b\,\left(\frac{2\,b^3}{a^5}+\frac{2\,b\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{a}\right)}{a}\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^5\,\left(\frac{3}{5\,a^2}-\frac{3\,b^2}{5\,a^4}\right)}{d}+\frac{{\cos\left(c+d\,x\right)}^7}{7\,a^2\,d}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a^2}+\frac{b^2\,\left(\frac{3}{a^2}+\frac{b^2\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a^2}-\frac{2\,b\,\left(\frac{2\,b^3}{a^5}+\frac{2\,b\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{a}\right)}{a^2}-\frac{2\,b\,\left(\frac{b^2\,\left(\frac{2\,b^3}{a^5}+\frac{2\,b\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{a^2}+\frac{2\,b\,\left(\frac{3}{a^2}+\frac{b^2\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a^2}-\frac{2\,b\,\left(\frac{2\,b^3}{a^5}+\frac{2\,b\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{a}\right)}{a}\right)}{a}\right)}{d}+\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{1}{a^2}+\frac{b^2\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{3\,a^2}-\frac{2\,b\,\left(\frac{2\,b^3}{a^5}+\frac{2\,b\,\left(\frac{3}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{3\,a}\right)}{d}-\frac{b\,{\cos\left(c+d\,x\right)}^6}{3\,a^3\,d}-\frac{-a^6\,b^2+3\,a^4\,b^4-3\,a^2\,b^6+b^8}{a\,d\,\left(\cos\left(c+d\,x\right)\,a^9+b\,a^8\right)}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(2\,a^6\,b-12\,a^4\,b^3+18\,a^2\,b^5-8\,b^7\right)}{a^9\,d}","Not used",1,"(cos(c + d*x)^4*(b^3/(2*a^5) + (b*(3/a^2 - (3*b^2)/a^4))/(2*a)))/d - (cos(c + d*x)^2*((b^2*((2*b^3)/a^5 + (2*b*(3/a^2 - (3*b^2)/a^4))/a))/(2*a^2) + (b*(3/a^2 + (b^2*(3/a^2 - (3*b^2)/a^4))/a^2 - (2*b*((2*b^3)/a^5 + (2*b*(3/a^2 - (3*b^2)/a^4))/a))/a))/a))/d - (cos(c + d*x)^5*(3/(5*a^2) - (3*b^2)/(5*a^4)))/d + cos(c + d*x)^7/(7*a^2*d) - (cos(c + d*x)*(1/a^2 + (b^2*(3/a^2 + (b^2*(3/a^2 - (3*b^2)/a^4))/a^2 - (2*b*((2*b^3)/a^5 + (2*b*(3/a^2 - (3*b^2)/a^4))/a))/a))/a^2 - (2*b*((b^2*((2*b^3)/a^5 + (2*b*(3/a^2 - (3*b^2)/a^4))/a))/a^2 + (2*b*(3/a^2 + (b^2*(3/a^2 - (3*b^2)/a^4))/a^2 - (2*b*((2*b^3)/a^5 + (2*b*(3/a^2 - (3*b^2)/a^4))/a))/a))/a))/a))/d + (cos(c + d*x)^3*(1/a^2 + (b^2*(3/a^2 - (3*b^2)/a^4))/(3*a^2) - (2*b*((2*b^3)/a^5 + (2*b*(3/a^2 - (3*b^2)/a^4))/a))/(3*a)))/d - (b*cos(c + d*x)^6)/(3*a^3*d) - (b^8 - 3*a^2*b^6 + 3*a^4*b^4 - a^6*b^2)/(a*d*(a^9*cos(c + d*x) + a^8*b)) + (log(b + a*cos(c + d*x))*(2*a^6*b - 8*b^7 + 18*a^2*b^5 - 12*a^4*b^3))/(a^9*d)","B"
210,1,253,194,0.121619,"\text{Not used}","int(sin(c + d*x)^5/(a + b/cos(c + d*x))^2,x)","\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{2}{3\,a^2}-\frac{b^2}{a^4}\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{b^3}{a^5}+\frac{b\,\left(\frac{2}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{d}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a^2}+\frac{b^2\,\left(\frac{2}{a^2}-\frac{3\,b^2}{a^4}\right)}{a^2}-\frac{2\,b\,\left(\frac{2\,b^3}{a^5}+\frac{2\,b\,\left(\frac{2}{a^2}-\frac{3\,b^2}{a^4}\right)}{a}\right)}{a}\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^5}{5\,a^2\,d}+\frac{b\,{\cos\left(c+d\,x\right)}^4}{2\,a^3\,d}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(2\,a^4\,b-8\,a^2\,b^3+6\,b^5\right)}{a^7\,d}+\frac{a^4\,b^2-2\,a^2\,b^4+b^6}{a\,d\,\left(\cos\left(c+d\,x\right)\,a^7+b\,a^6\right)}","Not used",1,"(cos(c + d*x)^3*(2/(3*a^2) - b^2/a^4))/d - (cos(c + d*x)^2*(b^3/a^5 + (b*(2/a^2 - (3*b^2)/a^4))/a))/d - (cos(c + d*x)*(1/a^2 + (b^2*(2/a^2 - (3*b^2)/a^4))/a^2 - (2*b*((2*b^3)/a^5 + (2*b*(2/a^2 - (3*b^2)/a^4))/a))/a))/d - cos(c + d*x)^5/(5*a^2*d) + (b*cos(c + d*x)^4)/(2*a^3*d) + (log(b + a*cos(c + d*x))*(2*a^4*b + 6*b^5 - 8*a^2*b^3))/(a^7*d) + (b^6 - 2*a^2*b^4 + a^4*b^2)/(a*d*(a^7*cos(c + d*x) + a^6*b))","B"
211,1,113,119,0.090272,"\text{Not used}","int(sin(c + d*x)^3/(a + b/cos(c + d*x))^2,x)","-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a^2}-\frac{3\,b^2}{a^4}\right)-\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^2}+\frac{b\,{\cos\left(c+d\,x\right)}^2}{a^3}-\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(2\,a^2\,b-4\,b^3\right)}{a^5}+\frac{b^4-a^2\,b^2}{a\,\left(\cos\left(c+d\,x\right)\,a^5+b\,a^4\right)}}{d}","Not used",1,"-(cos(c + d*x)*(1/a^2 - (3*b^2)/a^4) - cos(c + d*x)^3/(3*a^2) + (b*cos(c + d*x)^2)/a^3 - (log(b + a*cos(c + d*x))*(2*a^2*b - 4*b^3))/a^5 + (b^4 - a^2*b^2)/(a*(a^5*cos(c + d*x) + a^4*b)))/d","B"
212,1,60,57,1.022977,"\text{Not used}","int(sin(c + d*x)/(a + b/cos(c + d*x))^2,x)","\frac{b^2}{d\,\left(\cos\left(c+d\,x\right)\,a^4+b\,a^3\right)}-\frac{\cos\left(c+d\,x\right)}{a^2\,d}+\frac{2\,b\,\ln\left(b+a\,\cos\left(c+d\,x\right)\right)}{a^3\,d}","Not used",1,"b^2/(d*(a^4*cos(c + d*x) + a^3*b)) - cos(c + d*x)/(a^2*d) + (2*b*log(b + a*cos(c + d*x)))/(a^3*d)","B"
213,1,103,109,0.226218,"\text{Not used}","int(1/(sin(c + d*x)*(a + b/cos(c + d*x))^2),x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)}{2\,d\,{\left(a+b\right)}^2}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{b^2}{a\,d\,\left(a^2-b^2\right)\,\left(b+a\,\cos\left(c+d\,x\right)\right)}+\frac{2\,a\,b\,\ln\left(b+a\,\cos\left(c+d\,x\right)\right)}{d\,{\left(a^2-b^2\right)}^2}","Not used",1,"log(cos(c + d*x) - 1)/(2*d*(a + b)^2) - log(cos(c + d*x) + 1)/(2*d*(a - b)^2) + b^2/(a*d*(a^2 - b^2)*(b + a*cos(c + d*x))) + (2*a*b*log(b + a*cos(c + d*x)))/(d*(a^2 - b^2)^2)","B"
214,1,228,168,1.468877,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + b/cos(c + d*x))^2),x)","\frac{\frac{2\,a\,b^2}{{\left(a^2-b^2\right)}^2}+\frac{b\,\cos\left(c+d\,x\right)}{2\,\left(a^2-b^2\right)}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(a^3+3\,a\,b^2\right)}{2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(-a\,{\cos\left(c+d\,x\right)}^3-b\,{\cos\left(c+d\,x\right)}^2+a\,\cos\left(c+d\,x\right)+b\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{b}{2\,{\left(a+b\right)}^3}-\frac{1}{4\,{\left(a+b\right)}^2}\right)}{d}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(2\,a^3\,b+2\,a\,b^3\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(a+b\right)}{4\,d\,{\left(a-b\right)}^3}","Not used",1,"((2*a*b^2)/(a^2 - b^2)^2 + (b*cos(c + d*x))/(2*(a^2 - b^2)) - (cos(c + d*x)^2*(3*a*b^2 + a^3))/(2*(a^4 + b^4 - 2*a^2*b^2)))/(d*(b + a*cos(c + d*x) - a*cos(c + d*x)^3 - b*cos(c + d*x)^2)) - (log(cos(c + d*x) - 1)*(b/(2*(a + b)^3) - 1/(4*(a + b)^2)))/d + (log(b + a*cos(c + d*x))*(2*a*b^3 + 2*a^3*b))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (log(cos(c + d*x) + 1)*(a + b))/(4*d*(a - b)^3)","B"
215,1,447,259,1.910799,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + b/cos(c + d*x))^2),x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{3}{16\,{\left(a+b\right)}^2}-\frac{5\,b}{8\,{\left(a+b\right)}^3}+\frac{3\,b^2}{8\,{\left(a+b\right)}^4}\right)}{d}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(\frac{3\,b^2}{8\,{\left(a-b\right)}^4}+\frac{5\,b}{8\,{\left(a-b\right)}^3}+\frac{3}{16\,{\left(a-b\right)}^2}\right)}{d}+\frac{\frac{{\cos\left(c+d\,x\right)}^4\,\left(3\,a^5+20\,a^3\,b^2+a\,b^4\right)}{8\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{\cos\left(c+d\,x\right)\,\left(7\,a^2\,b-b^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\cos\left(c+d\,x\right)}^3\,\left(5\,a^2\,b+b^3\right)}{8\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(5\,a^5+36\,a^3\,b^2+7\,a\,b^4\right)}{8\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,\left(5\,a^3\,b+a\,b^3\right)}{2\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(a\,{\cos\left(c+d\,x\right)}^5+b\,{\cos\left(c+d\,x\right)}^4-2\,a\,{\cos\left(c+d\,x\right)}^3-2\,b\,{\cos\left(c+d\,x\right)}^2+a\,\cos\left(c+d\,x\right)+b\right)}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(2\,a^5\,b+4\,a^3\,b^3\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}","Not used",1,"(log(cos(c + d*x) - 1)*(3/(16*(a + b)^2) - (5*b)/(8*(a + b)^3) + (3*b^2)/(8*(a + b)^4)))/d - (log(cos(c + d*x) + 1)*((3*b^2)/(8*(a - b)^4) + (5*b)/(8*(a - b)^3) + 3/(16*(a - b)^2)))/d + ((cos(c + d*x)^4*(a*b^4 + 3*a^5 + 20*a^3*b^2))/(8*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (cos(c + d*x)*(7*a^2*b - b^3))/(8*(a^4 + b^4 - 2*a^2*b^2)) - (cos(c + d*x)^3*(5*a^2*b + b^3))/(8*(a^4 + b^4 - 2*a^2*b^2)) - (cos(c + d*x)^2*(7*a*b^4 + 5*a^5 + 36*a^3*b^2))/(8*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b*(a*b^3 + 5*a^3*b))/(2*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)))/(d*(b + a*cos(c + d*x) - 2*a*cos(c + d*x)^3 + a*cos(c + d*x)^5 - 2*b*cos(c + d*x)^2 + b*cos(c + d*x)^4)) + (log(b + a*cos(c + d*x))*(2*a^5*b + 4*a^3*b^3))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
216,1,3692,473,4.865110,"\text{Not used}","int(sin(c + d*x)^6/(a + b/cos(c + d*x))^2,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(35\,a^6+206\,a^5\,b-694\,a^4\,b^2-572\,a^3\,b^3+1688\,a^2\,b^4+336\,a\,b^5-1008\,b^6\right)}{12\,a^7}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-35\,a^6+206\,a^5\,b+694\,a^4\,b^2-572\,a^3\,b^3-1688\,a^2\,b^4+336\,a\,b^5+1008\,b^6\right)}{12\,a^7}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-565\,a^6+3801\,a^5\,b+14266\,a^4\,b^2-7570\,a^3\,b^3-40520\,a^2\,b^4+4200\,a\,b^5+25200\,b^6\right)}{120\,a^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(565\,a^6+3801\,a^5\,b-14266\,a^4\,b^2-7570\,a^3\,b^3+40520\,a^2\,b^4+4200\,a\,b^5-25200\,b^6\right)}{120\,a^7}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(165\,a^6+1446\,a^4\,b^2-4440\,a^2\,b^4+2800\,b^6\right)}{10\,a^7}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(a-b\right)\,\left(5\,a^5+32\,a^4\,b-58\,a^3\,b^2-144\,a^2\,b^3+56\,a\,b^4+112\,b^5\right)}{8\,a^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)\,\left(5\,a^5-32\,a^4\,b-58\,a^3\,b^2+144\,a^2\,b^3+56\,a\,b^4-112\,b^5\right)}{8\,a^7}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+\left(7\,b-5\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+\left(21\,b-9\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(35\,b-5\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(5\,a+35\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(9\,a+21\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(5\,a+7\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{128\,a^{22}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{16\,a^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,a^8}-\frac{\left(\frac{\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{128\,a^{22}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{16\,a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,a^8}}{-\frac{-\frac{25\,a^{19}\,b}{2}-55\,a^{18}\,b^2+\frac{2345\,a^{17}\,b^3}{4}+\frac{2565\,a^{16}\,b^4}{2}-\frac{37705\,a^{15}\,b^5}{4}-7490\,a^{14}\,b^6+\frac{260375\,a^{13}\,b^7}{4}+\frac{22469\,a^{12}\,b^8}{2}-\frac{941393\,a^{11}\,b^9}{4}+35558\,a^{10}\,b^{10}+492572\,a^9\,b^{11}-169030\,a^8\,b^{12}-620037\,a^7\,b^{13}+290284\,a^6\,b^{14}+463764\,a^5\,b^{15}-257432\,a^4\,b^{16}-190120\,a^3\,b^{17}+117600\,a^2\,b^{18}+32928\,a\,b^{19}-21952\,b^{20}}{a^{21}}+\frac{\left(\frac{\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{128\,a^{22}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{16\,a^8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{16\,a^8}+\frac{\left(\frac{\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{128\,a^{22}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{16\,a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)}{16\,a^8}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,90{}\mathrm{i}+a^2\,b^4\,200{}\mathrm{i}-b^6\,112{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^8\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}+\frac{b\,\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)}{8\,a^{22}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^8}+\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}-\frac{b\,\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)}{8\,a^{22}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,1{}\mathrm{i}}{a^8}}{\frac{-\frac{25\,a^{19}\,b}{2}-55\,a^{18}\,b^2+\frac{2345\,a^{17}\,b^3}{4}+\frac{2565\,a^{16}\,b^4}{2}-\frac{37705\,a^{15}\,b^5}{4}-7490\,a^{14}\,b^6+\frac{260375\,a^{13}\,b^7}{4}+\frac{22469\,a^{12}\,b^8}{2}-\frac{941393\,a^{11}\,b^9}{4}+35558\,a^{10}\,b^{10}+492572\,a^9\,b^{11}-169030\,a^8\,b^{12}-620037\,a^7\,b^{13}+290284\,a^6\,b^{14}+463764\,a^5\,b^{15}-257432\,a^4\,b^{16}-190120\,a^3\,b^{17}+117600\,a^2\,b^{18}+32928\,a\,b^{19}-21952\,b^{20}}{a^{21}}-\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}+\frac{b\,\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)}{8\,a^{22}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}+\frac{b\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+199\,a^{13}\,b^2+1651\,a^{12}\,b^3-3864\,a^{11}\,b^4-18136\,a^{10}\,b^5+40540\,a^9\,b^6+53900\,a^8\,b^7-148480\,a^7\,b^8-46080\,a^6\,b^9+240640\,a^5\,b^{10}-30720\,a^4\,b^{11}-179200\,a^3\,b^{12}+64512\,a^2\,b^{13}+50176\,a\,b^{14}-25088\,b^{15}\right)}{8\,a^{14}}-\frac{b\,\left(\frac{-10\,a^{24}+74\,a^{23}\,b+62\,a^{22}\,b^2-478\,a^{21}\,b^3+124\,a^{20}\,b^4+740\,a^{19}\,b^5-400\,a^{18}\,b^6-336\,a^{17}\,b^7+224\,a^{16}\,b^8}{a^{21}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(512\,a^{18}\,b-1024\,a^{17}\,b^2+512\,a^{16}\,b^3\right)}{8\,a^{22}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^8}}\right)\,\left(2\,a^2-7\,b^2\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^8\,d}","Not used",1,"(atan(((((((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 - (tan(c/2 + (d*x)/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2)*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(128*a^22))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(16*a^8) + (tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i)*1i)/(16*a^8) - (((((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 + (tan(c/2 + (d*x)/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2)*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(128*a^22))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(16*a^8) - (tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i)*1i)/(16*a^8))/((((((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 - (tan(c/2 + (d*x)/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2)*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(128*a^22))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(16*a^8) + (tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(16*a^8) - (32928*a*b^19 - (25*a^19*b)/2 - 21952*b^20 + 117600*a^2*b^18 - 190120*a^3*b^17 - 257432*a^4*b^16 + 463764*a^5*b^15 + 290284*a^6*b^14 - 620037*a^7*b^13 - 169030*a^8*b^12 + 492572*a^9*b^11 + 35558*a^10*b^10 - (941393*a^11*b^9)/4 + (22469*a^12*b^8)/2 + (260375*a^13*b^7)/4 - 7490*a^14*b^6 - (37705*a^15*b^5)/4 + (2565*a^16*b^4)/2 + (2345*a^17*b^3)/4 - 55*a^18*b^2)/a^21 + (((((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 + (tan(c/2 + (d*x)/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2)*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(128*a^22))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(16*a^8) - (tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i))/(16*a^8)))*(a^6*5i - b^6*112i + a^2*b^4*200i - a^4*b^2*90i)*1i)/(8*a^8*d) - ((tan(c/2 + (d*x)/2)^11*(336*a*b^5 + 206*a^5*b + 35*a^6 - 1008*b^6 + 1688*a^2*b^4 - 572*a^3*b^3 - 694*a^4*b^2))/(12*a^7) - (tan(c/2 + (d*x)/2)^3*(336*a*b^5 + 206*a^5*b - 35*a^6 + 1008*b^6 - 1688*a^2*b^4 - 572*a^3*b^3 + 694*a^4*b^2))/(12*a^7) - (tan(c/2 + (d*x)/2)^5*(4200*a*b^5 + 3801*a^5*b - 565*a^6 + 25200*b^6 - 40520*a^2*b^4 - 7570*a^3*b^3 + 14266*a^4*b^2))/(120*a^7) + (tan(c/2 + (d*x)/2)^9*(4200*a*b^5 + 3801*a^5*b + 565*a^6 - 25200*b^6 + 40520*a^2*b^4 - 7570*a^3*b^3 - 14266*a^4*b^2))/(120*a^7) - (tan(c/2 + (d*x)/2)^7*(165*a^6 + 2800*b^6 - 4440*a^2*b^4 + 1446*a^4*b^2))/(10*a^7) + (tan(c/2 + (d*x)/2)^13*(a - b)*(56*a*b^4 + 32*a^4*b + 5*a^5 + 112*b^5 - 144*a^2*b^3 - 58*a^3*b^2))/(8*a^7) + (tan(c/2 + (d*x)/2)*(a + b)*(56*a*b^4 - 32*a^4*b + 5*a^5 - 112*b^5 + 144*a^2*b^3 - 58*a^3*b^2))/(8*a^7))/(d*(a + b - tan(c/2 + (d*x)/2)^14*(a - b) + tan(c/2 + (d*x)/2)^2*(5*a + 7*b) - tan(c/2 + (d*x)/2)^12*(5*a - 7*b) + tan(c/2 + (d*x)/2)^4*(9*a + 21*b) - tan(c/2 + (d*x)/2)^10*(9*a - 21*b) + tan(c/2 + (d*x)/2)^6*(5*a + 35*b) - tan(c/2 + (d*x)/2)^8*(5*a - 35*b))) - (b*atan(((b*((tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14) + (b*((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 - (b*tan(c/2 + (d*x)/2)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2))/(8*a^22))*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2))/a^8)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2)*1i)/a^8 + (b*((tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14) - (b*((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 + (b*tan(c/2 + (d*x)/2)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2))/(8*a^22))*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2))/a^8)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2)*1i)/a^8)/((32928*a*b^19 - (25*a^19*b)/2 - 21952*b^20 + 117600*a^2*b^18 - 190120*a^3*b^17 - 257432*a^4*b^16 + 463764*a^5*b^15 + 290284*a^6*b^14 - 620037*a^7*b^13 - 169030*a^8*b^12 + 492572*a^9*b^11 + 35558*a^10*b^10 - (941393*a^11*b^9)/4 + (22469*a^12*b^8)/2 + (260375*a^13*b^7)/4 - 7490*a^14*b^6 - (37705*a^15*b^5)/4 + (2565*a^16*b^4)/2 + (2345*a^17*b^3)/4 - 55*a^18*b^2)/a^21 - (b*((tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14) + (b*((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 - (b*tan(c/2 + (d*x)/2)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2))/(8*a^22))*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2))/a^8)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2))/a^8 + (b*((tan(c/2 + (d*x)/2)*(50176*a*b^14 - 75*a^14*b + 25*a^15 - 25088*b^15 + 64512*a^2*b^13 - 179200*a^3*b^12 - 30720*a^4*b^11 + 240640*a^5*b^10 - 46080*a^6*b^9 - 148480*a^7*b^8 + 53900*a^8*b^7 + 40540*a^9*b^6 - 18136*a^10*b^5 - 3864*a^11*b^4 + 1651*a^12*b^3 + 199*a^13*b^2))/(8*a^14) - (b*((74*a^23*b - 10*a^24 + 224*a^16*b^8 - 336*a^17*b^7 - 400*a^18*b^6 + 740*a^19*b^5 + 124*a^20*b^4 - 478*a^21*b^3 + 62*a^22*b^2)/a^21 + (b*tan(c/2 + (d*x)/2)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2)*(512*a^18*b + 512*a^16*b^3 - 1024*a^17*b^2))/(8*a^22))*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2))/a^8)*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2))/a^8))*(2*a^2 - 7*b^2)*((a + b)^3*(a - b)^3)^(1/2)*2i)/(a^8*d)","B"
217,1,2804,261,3.861127,"\text{Not used}","int(sin(c + d*x)^4/(a + b/cos(c + d*x))^2,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(33\,a^4+244\,a^2\,b^2-360\,b^4\right)}{6\,a^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^4-59\,a^3\,b-176\,a^2\,b^2+60\,a\,b^3+240\,b^4\right)}{6\,a^5}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(12\,a^4+59\,a^3\,b-176\,a^2\,b^2-60\,a\,b^3+240\,b^4\right)}{6\,a^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(a-b\right)\,\left(-3\,a^3-16\,a^2\,b+20\,a\,b^2+40\,b^3\right)}{4\,a^5}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)\,\left(-3\,a^3+16\,a^2\,b+20\,a\,b^2-40\,b^3\right)}{4\,a^5}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\left(5\,b-3\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(10\,b-2\,a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(2\,a+10\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(3\,a+5\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{16\,a^{16}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^6}-\frac{\left(\frac{\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{16\,a^{16}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^6}}{\frac{18\,a^{13}\,b+60\,a^{12}\,b^2-573\,a^{11}\,b^3-834\,a^{10}\,b^4+5958\,a^9\,b^5+1742\,a^8\,b^6-23963\,a^7\,b^7+4672\,a^6\,b^8+43960\,a^5\,b^9-19240\,a^4\,b^{10}-37400\,a^3\,b^{11}+21600\,a^2\,b^{12}+12000\,a\,b^{13}-8000\,b^{14}}{a^{15}}+\frac{\left(\frac{\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{16\,a^{16}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^6}+\frac{\left(\frac{\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{16\,a^{16}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^6}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^6}}\right)\,\left(a^4\,3{}\mathrm{i}-a^2\,b^2\,36{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,a^6\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}+\frac{b\,\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{2\,a^{16}}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)\,1{}\mathrm{i}}{a^6}+\frac{b\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}-\frac{b\,\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{2\,a^{16}}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)\,1{}\mathrm{i}}{a^6}}{\frac{18\,a^{13}\,b+60\,a^{12}\,b^2-573\,a^{11}\,b^3-834\,a^{10}\,b^4+5958\,a^9\,b^5+1742\,a^8\,b^6-23963\,a^7\,b^7+4672\,a^6\,b^8+43960\,a^5\,b^9-19240\,a^4\,b^{10}-37400\,a^3\,b^{11}+21600\,a^2\,b^{12}+12000\,a\,b^{13}-8000\,b^{14}}{a^{15}}+\frac{b\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}+\frac{b\,\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{2\,a^{16}}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)}{a^6}-\frac{b\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+67\,a^9\,b^2+383\,a^8\,b^3-904\,a^7\,b^4-2600\,a^6\,b^5+6144\,a^5\,b^6+2688\,a^4\,b^7-11520\,a^3\,b^8+2560\,a^2\,b^9+6400\,a\,b^{10}-3200\,b^{11}\right)}{2\,a^{10}}-\frac{b\,\left(\frac{-12\,a^{18}+76\,a^{17}\,b+28\,a^{16}\,b^2-316\,a^{15}\,b^3+144\,a^{14}\,b^4+240\,a^{13}\,b^5-160\,a^{12}\,b^6}{a^{15}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,\left(128\,a^{14}\,b-256\,a^{13}\,b^2+128\,a^{12}\,b^3\right)}{2\,a^{16}}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)}{a^6}\right)}{a^6}}\right)\,\sqrt{a^2-b^2}\,\left(2\,a^2-5\,b^2\right)\,2{}\mathrm{i}}{a^6\,d}","Not used",1,"((tan(c/2 + (d*x)/2)^5*(33*a^4 - 360*b^4 + 244*a^2*b^2))/(6*a^5) - (tan(c/2 + (d*x)/2)^3*(60*a*b^3 - 59*a^3*b + 12*a^4 + 240*b^4 - 176*a^2*b^2))/(6*a^5) - (tan(c/2 + (d*x)/2)^7*(59*a^3*b - 60*a*b^3 + 12*a^4 + 240*b^4 - 176*a^2*b^2))/(6*a^5) + (tan(c/2 + (d*x)/2)^9*(a - b)*(20*a*b^2 - 16*a^2*b - 3*a^3 + 40*b^3))/(4*a^5) + (tan(c/2 + (d*x)/2)*(a + b)*(20*a*b^2 + 16*a^2*b - 3*a^3 - 40*b^3))/(4*a^5))/(d*(a + b - tan(c/2 + (d*x)/2)^10*(a - b) + tan(c/2 + (d*x)/2)^2*(3*a + 5*b) + tan(c/2 + (d*x)/2)^4*(2*a + 10*b) - tan(c/2 + (d*x)/2)^8*(3*a - 5*b) - tan(c/2 + (d*x)/2)^6*(2*a - 10*b))) + (atan(((((((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 - (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*40i - a^2*b^2*36i)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(16*a^16))*(a^4*3i + b^4*40i - a^2*b^2*36i))/(8*a^6) + (tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10))*(a^4*3i + b^4*40i - a^2*b^2*36i)*1i)/(8*a^6) - (((((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 + (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*40i - a^2*b^2*36i)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(16*a^16))*(a^4*3i + b^4*40i - a^2*b^2*36i))/(8*a^6) - (tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10))*(a^4*3i + b^4*40i - a^2*b^2*36i)*1i)/(8*a^6))/((12000*a*b^13 + 18*a^13*b - 8000*b^14 + 21600*a^2*b^12 - 37400*a^3*b^11 - 19240*a^4*b^10 + 43960*a^5*b^9 + 4672*a^6*b^8 - 23963*a^7*b^7 + 1742*a^8*b^6 + 5958*a^9*b^5 - 834*a^10*b^4 - 573*a^11*b^3 + 60*a^12*b^2)/a^15 + (((((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 - (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*40i - a^2*b^2*36i)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(16*a^16))*(a^4*3i + b^4*40i - a^2*b^2*36i))/(8*a^6) + (tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10))*(a^4*3i + b^4*40i - a^2*b^2*36i))/(8*a^6) + (((((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 + (tan(c/2 + (d*x)/2)*(a^4*3i + b^4*40i - a^2*b^2*36i)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(16*a^16))*(a^4*3i + b^4*40i - a^2*b^2*36i))/(8*a^6) - (tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10))*(a^4*3i + b^4*40i - a^2*b^2*36i))/(8*a^6)))*(a^4*3i + b^4*40i - a^2*b^2*36i)*1i)/(4*a^6*d) + (b*atan(((b*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*((tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10) + (b*((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 - (b*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(2*a^16))*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2))/a^6)*1i)/a^6 + (b*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*((tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10) - (b*((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 + (b*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(2*a^16))*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2))/a^6)*1i)/a^6)/((12000*a*b^13 + 18*a^13*b - 8000*b^14 + 21600*a^2*b^12 - 37400*a^3*b^11 - 19240*a^4*b^10 + 43960*a^5*b^9 + 4672*a^6*b^8 - 23963*a^7*b^7 + 1742*a^8*b^6 + 5958*a^9*b^5 - 834*a^10*b^4 - 573*a^11*b^3 + 60*a^12*b^2)/a^15 + (b*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*((tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10) + (b*((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 - (b*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(2*a^16))*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2))/a^6))/a^6 - (b*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*((tan(c/2 + (d*x)/2)*(6400*a*b^10 - 27*a^10*b + 9*a^11 - 3200*b^11 + 2560*a^2*b^9 - 11520*a^3*b^8 + 2688*a^4*b^7 + 6144*a^5*b^6 - 2600*a^6*b^5 - 904*a^7*b^4 + 383*a^8*b^3 + 67*a^9*b^2))/(2*a^10) - (b*((76*a^17*b - 12*a^18 - 160*a^12*b^6 + 240*a^13*b^5 + 144*a^14*b^4 - 316*a^15*b^3 + 28*a^16*b^2)/a^15 + (b*tan(c/2 + (d*x)/2)*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*(128*a^14*b + 128*a^12*b^3 - 256*a^13*b^2))/(2*a^16))*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2))/a^6))/a^6))*(a^2 - b^2)^(1/2)*(2*a^2 - 5*b^2)*2i)/(a^6*d)","B"
218,1,1655,152,3.568681,"\text{Not used}","int(sin(c + d*x)^2/(a + b/cos(c + d*x))^2,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+6\,b^2\right)}{a^3}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-a^2+3\,a\,b+6\,b^2\right)}{a^3}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(a^2+3\,a\,b-6\,b^2\right)}{a^3}}{d\,\left(\left(b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(3\,b-a\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(a+3\,b\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a+b\right)}+\frac{\mathrm{atan}\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\frac{8\,b}{a}+\frac{24\,b^2}{a^2}-\frac{24\,b^3}{a^3}+\frac{144\,b^4}{a^4}-\frac{144\,b^5}{a^5}-8}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a-8\,b-\frac{24\,b^2}{a}+\frac{24\,b^3}{a^2}-\frac{144\,b^4}{a^3}+\frac{144\,b^5}{a^4}}-\frac{24\,b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,b-8\,a^2+24\,b^2-\frac{24\,b^3}{a}+\frac{144\,b^4}{a^2}-\frac{144\,b^5}{a^3}}+\frac{24\,b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24\,a\,b^2+8\,a^2\,b-8\,a^3-24\,b^3+\frac{144\,b^4}{a}-\frac{144\,b^5}{a^2}}+\frac{144\,b^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{24\,a\,b^3-8\,a^3\,b+8\,a^4-144\,b^4-24\,a^2\,b^2+\frac{144\,b^5}{a}}+\frac{144\,b^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{-8\,a^5+8\,a^4\,b+24\,a^3\,b^2-24\,a^2\,b^3+144\,a\,b^4-144\,b^5}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,6{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^4\,d}-\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)\,1{}\mathrm{i}}{a^6-a^4\,b^2}}{\frac{16\,\left(-2\,a^7\,b-4\,a^6\,b^2+33\,a^5\,b^3+18\,a^4\,b^4-153\,a^3\,b^5+54\,a^2\,b^6+162\,a\,b^7-108\,b^8\right)}{a^9}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}-\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^7-3\,a^6\,b+7\,a^5\,b^2+19\,a^4\,b^3-48\,a^3\,b^4-48\,a^2\,b^5+144\,a\,b^6-72\,b^7\right)}{a^6}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{8\,\left(2\,a^{12}-10\,a^{11}\,b+2\,a^{10}\,b^2+18\,a^9\,b^3-12\,a^8\,b^4\right)}{a^9}+\frac{8\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^6\,\left(a^6-a^4\,b^2\right)}\right)\,\left(2\,a^2-3\,b^2\right)}{a^6-a^4\,b^2}\right)}{a^6-a^4\,b^2}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2-3\,b^2\right)\,2{}\mathrm{i}}{d\,\left(a^6-a^4\,b^2\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^3*(a^2 + 6*b^2))/a^3 + (tan(c/2 + (d*x)/2)*(3*a*b - a^2 + 6*b^2))/a^3 - (tan(c/2 + (d*x)/2)^5*(3*a*b + a^2 - 6*b^2))/a^3)/(d*(a + b + tan(c/2 + (d*x)/2)^2*(a + 3*b) - tan(c/2 + (d*x)/2)^4*(a - 3*b) - tan(c/2 + (d*x)/2)^6*(a - b))) + (atan((8*tan(c/2 + (d*x)/2))/((8*b)/a + (24*b^2)/a^2 - (24*b^3)/a^3 + (144*b^4)/a^4 - (144*b^5)/a^5 - 8) + (8*b*tan(c/2 + (d*x)/2))/(8*a - 8*b - (24*b^2)/a + (24*b^3)/a^2 - (144*b^4)/a^3 + (144*b^5)/a^4) - (24*b^2*tan(c/2 + (d*x)/2))/(8*a*b - 8*a^2 + 24*b^2 - (24*b^3)/a + (144*b^4)/a^2 - (144*b^5)/a^3) + (24*b^3*tan(c/2 + (d*x)/2))/(24*a*b^2 + 8*a^2*b - 8*a^3 - 24*b^3 + (144*b^4)/a - (144*b^5)/a^2) + (144*b^4*tan(c/2 + (d*x)/2))/(24*a*b^3 - 8*a^3*b + 8*a^4 - 144*b^4 - 24*a^2*b^2 + (144*b^5)/a) + (144*b^5*tan(c/2 + (d*x)/2))/(144*a*b^4 + 8*a^4*b - 8*a^5 - 144*b^5 - 24*a^2*b^3 + 24*a^3*b^2))*(a^2*1i - b^2*6i)*1i)/(a^4*d) - (b*atan(((b*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 + (b*((a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 - (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2) + (b*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 - (b*((a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 + (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2))*1i)/(a^6 - a^4*b^2))/((16*(162*a*b^7 - 2*a^7*b - 108*b^8 + 54*a^2*b^6 - 153*a^3*b^5 + 18*a^4*b^4 + 33*a^5*b^3 - 4*a^6*b^2))/a^9 + (b*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 + (b*((a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 - (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2) - (b*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*((8*tan(c/2 + (d*x)/2)*(144*a*b^6 - 3*a^6*b + a^7 - 72*b^7 - 48*a^2*b^5 - 48*a^3*b^4 + 19*a^4*b^3 + 7*a^5*b^2))/a^6 - (b*((a + b)*(a - b))^(1/2)*((8*(2*a^12 - 10*a^11*b - 12*a^8*b^4 + 18*a^9*b^3 + 2*a^10*b^2))/a^9 + (8*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/(a^6*(a^6 - a^4*b^2)))*(2*a^2 - 3*b^2))/(a^6 - a^4*b^2)))/(a^6 - a^4*b^2)))*((a + b)*(a - b))^(1/2)*(2*a^2 - 3*b^2)*2i)/(d*(a^6 - a^4*b^2))","B"
219,1,245,203,1.788225,"\text{Not used}","int(1/(sin(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^3-3\,a^2\,b+7\,a\,b^2-b^3\right)}{{\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{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^2}+\frac{b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-2{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)\,\left(2\,a^2+b^2\right)\,2{}\mathrm{i}}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((a^2 - 2*a*b + b^2)/(a + b) - (tan(c/2 + (d*x)/2)^2*(7*a*b^2 - 3*a^2*b + a^3 - b^3))/(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))) + tan(c/2 + (d*x)/2)/(2*d*(a - b)^2) + (b*atan((a^4*tan(c/2 + (d*x)/2)*1i + b^4*tan(c/2 + (d*x)/2)*1i - a^2*b^2*tan(c/2 + (d*x)/2)*2i)/((a + b)^(5/2)*(a - b)^(3/2)))*(2*a^2 + b^2)*2i)/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
220,1,403,343,1.617588,"\text{Not used}","int(1/(sin(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(4\,a^4-13\,a^3\,b+15\,a^2\,b^2-7\,a\,b^3+b^4\right)}{3\,{\left(a+b\right)}^2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^5-13\,a^4\,b+38\,a^3\,b^2-18\,a^2\,b^3+7\,a\,b^4-b^5\right)}{{\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{16\,a^2-16\,b^2}{64\,{\left(a-b\right)}^4}+\frac{1}{8\,{\left(a-b\right)}^2}\right)}{d}+\frac{a^2\,b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6-3{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^2+3{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^4-1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,a^2+3\,b^2\right)\,2{}\mathrm{i}}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","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*(4*a^4 - 13*a^3*b - 7*a*b^3 + b^4 + 15*a^2*b^2))/(3*(a + b)^2) - (tan(c/2 + (d*x)/2)^4*(7*a*b^4 - 13*a^4*b + 3*a^5 - b^5 - 18*a^2*b^3 + 38*a^3*b^2))/(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^2 - 16*b^2)/(64*(a - b)^4) + 1/(8*(a - b)^2)))/d + (a^2*b*atan((a^6*tan(c/2 + (d*x)/2)*1i - b^6*tan(c/2 + (d*x)/2)*1i + a^2*b^4*tan(c/2 + (d*x)/2)*3i - a^4*b^2*tan(c/2 + (d*x)/2)*3i)/((a + b)^(7/2)*(a - b)^(5/2)))*(2*a^2 + 3*b^2)*2i)/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
221,1,762,329,0.235703,"\text{Not used}","int(sin(c + d*x)^7/(a + b/cos(c + d*x))^3,x)","\frac{{\cos\left(c+d\,x\right)}^4\,\left(\frac{2\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{4\,a}\right)}{d}-\frac{\frac{-5\,a^6\,b^3+27\,a^4\,b^5-39\,a^2\,b^7+17\,b^9}{2\,a}+\cos\left(c+d\,x\right)\,\left(-3\,a^6\,b^2+15\,a^4\,b^4-21\,a^2\,b^6+9\,b^8\right)}{d\,\left(a^{11}\,{\cos\left(c+d\,x\right)}^2+2\,a^{10}\,b\,\cos\left(c+d\,x\right)+a^9\,b^2\right)}-\frac{{\cos\left(c+d\,x\right)}^5\,\left(\frac{3}{5\,a^3}-\frac{6\,b^2}{5\,a^5}\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{3\,b^2\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{2\,a^2}-\frac{b^3\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{2\,a^3}+\frac{3\,b\,\left(\frac{3}{a^3}+\frac{3\,b^4}{a^7}+\frac{3\,b^2\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a^2}-\frac{3\,b\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{a}\right)}{2\,a}\right)}{d}+\frac{{\cos\left(c+d\,x\right)}^7}{7\,a^3\,d}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a^3}+\frac{b^3\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{a^3}+\frac{3\,b^2\,\left(\frac{3}{a^3}+\frac{3\,b^4}{a^7}+\frac{3\,b^2\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a^2}-\frac{3\,b\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{a}\right)}{a^2}-\frac{3\,b\,\left(\frac{3\,b^2\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{a^2}-\frac{b^3\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a^3}+\frac{3\,b\,\left(\frac{3}{a^3}+\frac{3\,b^4}{a^7}+\frac{3\,b^2\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a^2}-\frac{3\,b\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{a}\right)}{a}\right)}{a}\right)}{d}+\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{1}{a^3}+\frac{b^4}{a^7}+\frac{b^2\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a^2}-\frac{b\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{3}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{a}\right)}{d}-\frac{b\,{\cos\left(c+d\,x\right)}^6}{2\,a^4\,d}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(3\,a^6\,b-30\,a^4\,b^3+63\,a^2\,b^5-36\,b^7\right)}{a^{10}\,d}","Not used",1,"(cos(c + d*x)^4*((2*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/(4*a)))/d - ((17*b^9 - 39*a^2*b^7 + 27*a^4*b^5 - 5*a^6*b^3)/(2*a) + cos(c + d*x)*(9*b^8 - 21*a^2*b^6 + 15*a^4*b^4 - 3*a^6*b^2))/(d*(a^11*cos(c + d*x)^2 + a^9*b^2 + 2*a^10*b*cos(c + d*x))) - (cos(c + d*x)^5*(3/(5*a^3) - (6*b^2)/(5*a^5)))/d - (cos(c + d*x)^2*((3*b^2*((8*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/a))/(2*a^2) - (b^3*(3/a^3 - (6*b^2)/a^5))/(2*a^3) + (3*b*(3/a^3 + (3*b^4)/a^7 + (3*b^2*(3/a^3 - (6*b^2)/a^5))/a^2 - (3*b*((8*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/a))/a))/(2*a)))/d + cos(c + d*x)^7/(7*a^3*d) - (cos(c + d*x)*(1/a^3 + (b^3*((8*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/a))/a^3 + (3*b^2*(3/a^3 + (3*b^4)/a^7 + (3*b^2*(3/a^3 - (6*b^2)/a^5))/a^2 - (3*b*((8*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/a))/a))/a^2 - (3*b*((3*b^2*((8*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/a))/a^2 - (b^3*(3/a^3 - (6*b^2)/a^5))/a^3 + (3*b*(3/a^3 + (3*b^4)/a^7 + (3*b^2*(3/a^3 - (6*b^2)/a^5))/a^2 - (3*b*((8*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/a))/a))/a))/a))/d + (cos(c + d*x)^3*(1/a^3 + b^4/a^7 + (b^2*(3/a^3 - (6*b^2)/a^5))/a^2 - (b*((8*b^3)/a^6 + (3*b*(3/a^3 - (6*b^2)/a^5))/a))/a))/d - (b*cos(c + d*x)^6)/(2*a^4*d) + (log(b + a*cos(c + d*x))*(3*a^6*b - 36*b^7 + 63*a^2*b^5 - 30*a^4*b^3))/(a^10*d)","B"
222,1,315,239,1.110802,"\text{Not used}","int(sin(c + d*x)^5/(a + b/cos(c + d*x))^3,x)","\frac{{\cos\left(c+d\,x\right)}^3\,\left(\frac{2}{3\,a^3}-\frac{2\,b^2}{a^5}\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(\frac{4\,b^3}{a^6}+\frac{3\,b\,\left(\frac{2}{a^3}-\frac{6\,b^2}{a^5}\right)}{2\,a}\right)}{d}+\frac{\cos\left(c+d\,x\right)\,\left(3\,a^4\,b^2-10\,a^2\,b^4+7\,b^6\right)+\frac{5\,a^4\,b^3-18\,a^2\,b^5+13\,b^7}{2\,a}}{d\,\left(a^9\,{\cos\left(c+d\,x\right)}^2+2\,a^8\,b\,\cos\left(c+d\,x\right)+a^7\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a^3}+\frac{3\,b^4}{a^7}+\frac{3\,b^2\,\left(\frac{2}{a^3}-\frac{6\,b^2}{a^5}\right)}{a^2}-\frac{3\,b\,\left(\frac{8\,b^3}{a^6}+\frac{3\,b\,\left(\frac{2}{a^3}-\frac{6\,b^2}{a^5}\right)}{a}\right)}{a}\right)}{d}-\frac{{\cos\left(c+d\,x\right)}^5}{5\,a^3\,d}+\frac{3\,b\,{\cos\left(c+d\,x\right)}^4}{4\,a^4\,d}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(3\,a^4\,b-20\,a^2\,b^3+21\,b^5\right)}{a^8\,d}","Not used",1,"(cos(c + d*x)^3*(2/(3*a^3) - (2*b^2)/a^5))/d - (cos(c + d*x)^2*((4*b^3)/a^6 + (3*b*(2/a^3 - (6*b^2)/a^5))/(2*a)))/d + (cos(c + d*x)*(7*b^6 - 10*a^2*b^4 + 3*a^4*b^2) + (13*b^7 - 18*a^2*b^5 + 5*a^4*b^3)/(2*a))/(d*(a^9*cos(c + d*x)^2 + a^7*b^2 + 2*a^8*b*cos(c + d*x))) - (cos(c + d*x)*(1/a^3 + (3*b^4)/a^7 + (3*b^2*(2/a^3 - (6*b^2)/a^5))/a^2 - (3*b*((8*b^3)/a^6 + (3*b*(2/a^3 - (6*b^2)/a^5))/a))/a))/d - cos(c + d*x)^5/(5*a^3*d) + (3*b*cos(c + d*x)^4)/(4*a^4*d) + (log(b + a*cos(c + d*x))*(3*a^4*b + 21*b^5 - 20*a^2*b^3))/(a^8*d)","B"
223,1,167,158,0.104865,"\text{Not used}","int(sin(c + d*x)^3/(a + b/cos(c + d*x))^3,x)","\frac{{\cos\left(c+d\,x\right)}^3}{3\,a^3\,d}-\frac{\cos\left(c+d\,x\right)\,\left(5\,b^4-3\,a^2\,b^2\right)+\frac{9\,b^5-5\,a^2\,b^3}{2\,a}}{d\,\left(a^7\,{\cos\left(c+d\,x\right)}^2+2\,a^6\,b\,\cos\left(c+d\,x\right)+a^5\,b^2\right)}-\frac{\cos\left(c+d\,x\right)\,\left(\frac{1}{a^3}-\frac{6\,b^2}{a^5}\right)}{d}-\frac{3\,b\,{\cos\left(c+d\,x\right)}^2}{2\,a^4\,d}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(3\,a^2\,b-10\,b^3\right)}{a^6\,d}","Not used",1,"cos(c + d*x)^3/(3*a^3*d) - (cos(c + d*x)*(5*b^4 - 3*a^2*b^2) + (9*b^5 - 5*a^2*b^3)/(2*a))/(d*(a^7*cos(c + d*x)^2 + a^5*b^2 + 2*a^6*b*cos(c + d*x))) - (cos(c + d*x)*(1/a^3 - (6*b^2)/a^5))/d - (3*b*cos(c + d*x)^2)/(2*a^4*d) + (log(b + a*cos(c + d*x))*(3*a^2*b - 10*b^3))/(a^6*d)","B"
224,1,93,83,1.073463,"\text{Not used}","int(sin(c + d*x)/(a + b/cos(c + d*x))^3,x)","\frac{3\,b^2\,\cos\left(c+d\,x\right)+\frac{5\,b^3}{2\,a}}{d\,\left(a^5\,{\cos\left(c+d\,x\right)}^2+2\,a^4\,b\,\cos\left(c+d\,x\right)+a^3\,b^2\right)}-\frac{\cos\left(c+d\,x\right)}{a^3\,d}+\frac{3\,b\,\ln\left(b+a\,\cos\left(c+d\,x\right)\right)}{a^4\,d}","Not used",1,"(3*b^2*cos(c + d*x) + (5*b^3)/(2*a))/(d*(a^5*cos(c + d*x)^2 + a^3*b^2 + 2*a^4*b*cos(c + d*x))) - cos(c + d*x)/(a^3*d) + (3*b*log(b + a*cos(c + d*x)))/(a^4*d)","B"
225,1,182,163,1.394453,"\text{Not used}","int(1/(sin(c + d*x)*(a + b/cos(c + d*x))^3),x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)}{2\,d\,{\left(a+b\right)}^3}-\frac{\frac{\cos\left(c+d\,x\right)\,\left(b^4-3\,a^2\,b^2\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,\left(b^4-5\,a^2\,b^2\right)}{2\,a^2\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(a^2\,{\cos\left(c+d\,x\right)}^2+2\,a\,b\,\cos\left(c+d\,x\right)+b^2\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)}{2\,d\,{\left(a-b\right)}^3}-\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(\frac{1}{2\,{\left(a+b\right)}^3}-\frac{1}{2\,{\left(a-b\right)}^3}\right)}{d}","Not used",1,"log(cos(c + d*x) - 1)/(2*d*(a + b)^3) - ((cos(c + d*x)*(b^4 - 3*a^2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (b*(b^4 - 5*a^2*b^2))/(2*a^2*(a^4 + b^4 - 2*a^2*b^2)))/(d*(b^2 + a^2*cos(c + d*x)^2 + 2*a*b*cos(c + d*x))) - log(cos(c + d*x) + 1)/(2*d*(a - b)^3) - (log(b + a*cos(c + d*x))*(1/(2*(a + b)^3) - 1/(2*(a - b)^3)))/d","B"
226,1,378,229,1.701901,"\text{Not used}","int(1/(sin(c + d*x)^3*(a + b/cos(c + d*x))^3),x)","\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(\frac{3\,b}{4\,{\left(a+b\right)}^4}-\frac{1}{4\,{\left(a+b\right)}^3}+\frac{3\,b}{4\,{\left(a-b\right)}^4}+\frac{1}{4\,{\left(a-b\right)}^3}\right)}{d}-\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{3\,b}{4\,{\left(a+b\right)}^4}-\frac{1}{4\,{\left(a+b\right)}^3}\right)}{d}-\frac{\frac{{\cos\left(c+d\,x\right)}^3\,\left(a^5+9\,a^3\,b^2+2\,a\,b^4\right)}{2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{{\cos\left(c+d\,x\right)}^2\,\left(-a^4\,b+10\,a^2\,b^3+3\,b^5\right)}{2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,b\,\left(2\,a^2\,b^2+b^4\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{a\,\cos\left(c+d\,x\right)\,\left(11\,a^2\,b^2+b^4\right)}{2\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left({\cos\left(c+d\,x\right)}^2\,\left(a^2-b^2\right)+b^2-a^2\,{\cos\left(c+d\,x\right)}^4+2\,a\,b\,\cos\left(c+d\,x\right)-2\,a\,b\,{\cos\left(c+d\,x\right)}^3\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(a+2\,b\right)}{4\,d\,{\left(a-b\right)}^4}","Not used",1,"(log(b + a*cos(c + d*x))*((3*b)/(4*(a + b)^4) - 1/(4*(a + b)^3) + (3*b)/(4*(a - b)^4) + 1/(4*(a - b)^3)))/d - (log(cos(c + d*x) - 1)*((3*b)/(4*(a + b)^4) - 1/(4*(a + b)^3)))/d - ((cos(c + d*x)^3*(2*a*b^4 + a^5 + 9*a^3*b^2))/(2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (cos(c + d*x)^2*(3*b^5 - a^4*b + 10*a^2*b^3))/(2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*b*(b^4 + 2*a^2*b^2))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (a*cos(c + d*x)*(b^4 + 11*a^2*b^2))/(2*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)))/(d*(cos(c + d*x)^2*(a^2 - b^2) + b^2 - a^2*cos(c + d*x)^4 + 2*a*b*cos(c + d*x) - 2*a*b*cos(c + d*x)^3)) - (log(cos(c + d*x) + 1)*(a + 2*b))/(4*d*(a - b)^4)","B"
227,1,673,313,2.554167,"\text{Not used}","int(1/(sin(c + d*x)^5*(a + b/cos(c + d*x))^3),x)","\frac{\ln\left(\cos\left(c+d\,x\right)-1\right)\,\left(\frac{3}{16\,{\left(a+b\right)}^3}-\frac{15\,b}{16\,{\left(a+b\right)}^4}+\frac{3\,b^2}{4\,{\left(a+b\right)}^5}\right)}{d}+\frac{\frac{19\,a^4\,b^3+28\,a^2\,b^5+b^7}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{{\cos\left(c+d\,x\right)}^2\,\left(-2\,a^6\,b+23\,a^4\,b^3+26\,a^2\,b^5+b^7\right)}{2\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{3\,{\cos\left(c+d\,x\right)}^4\,\left(-a^6\,b+8\,a^4\,b^3+9\,a^2\,b^5\right)}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{3\,{\cos\left(c+d\,x\right)}^5\,\left(a^7+18\,a^5\,b^2+13\,a^3\,b^4\right)}{8\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{a\,\cos\left(c+d\,x\right)\,\left(55\,a^4\,b^2+46\,a^2\,b^4-5\,b^6\right)}{8\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{a\,{\cos\left(c+d\,x\right)}^3\,\left(5\,a^6+103\,a^4\,b^2+91\,a^2\,b^4-7\,b^6\right)}{8\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}}{d\,\left({\cos\left(c+d\,x\right)}^2\,\left(a^2-2\,b^2\right)-{\cos\left(c+d\,x\right)}^4\,\left(2\,a^2-b^2\right)+b^2+a^2\,{\cos\left(c+d\,x\right)}^6+2\,a\,b\,\cos\left(c+d\,x\right)-4\,a\,b\,{\cos\left(c+d\,x\right)}^3+2\,a\,b\,{\cos\left(c+d\,x\right)}^5\right)}-\frac{\ln\left(\cos\left(c+d\,x\right)+1\right)\,\left(\frac{3\,b^2}{4\,{\left(a-b\right)}^5}+\frac{15\,b}{16\,{\left(a-b\right)}^4}+\frac{3}{16\,{\left(a-b\right)}^3}\right)}{d}+\frac{\ln\left(b+a\,\cos\left(c+d\,x\right)\right)\,\left(3\,a^6\,b+15\,a^4\,b^3+6\,a^2\,b^5\right)}{d\,\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)}","Not used",1,"(log(cos(c + d*x) - 1)*(3/(16*(a + b)^3) - (15*b)/(16*(a + b)^4) + (3*b^2)/(4*(a + b)^5)))/d + ((b^7 + 28*a^2*b^5 + 19*a^4*b^3)/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (cos(c + d*x)^2*(b^7 - 2*a^6*b + 26*a^2*b^5 + 23*a^4*b^3))/(2*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (3*cos(c + d*x)^4*(9*a^2*b^5 - a^6*b + 8*a^4*b^3))/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (3*cos(c + d*x)^5*(a^7 + 13*a^3*b^4 + 18*a^5*b^2))/(8*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (a*cos(c + d*x)*(46*a^2*b^4 - 5*b^6 + 55*a^4*b^2))/(8*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (a*cos(c + d*x)^3*(5*a^6 - 7*b^6 + 91*a^2*b^4 + 103*a^4*b^2))/(8*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)))/(d*(cos(c + d*x)^2*(a^2 - 2*b^2) - cos(c + d*x)^4*(2*a^2 - b^2) + b^2 + a^2*cos(c + d*x)^6 + 2*a*b*cos(c + d*x) - 4*a*b*cos(c + d*x)^3 + 2*a*b*cos(c + d*x)^5)) - (log(cos(c + d*x) + 1)*((3*b^2)/(4*(a - b)^5) + (15*b)/(16*(a - b)^4) + 3/(16*(a - b)^3)))/d + (log(b + a*cos(c + d*x))*(3*a^6*b + 6*a^2*b^5 + 15*a^4*b^3))/(d*(a^10 - b^10 + 5*a^2*b^8 - 10*a^4*b^6 + 10*a^6*b^4 - 5*a^8*b^2))","B"
228,1,3975,539,5.710108,"\text{Not used}","int(sin(c + d*x)^6/(a + b/cos(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-55\,a^7+454\,a^6\,b+2969\,a^5\,b^2+608\,a^4\,b^3-12212\,a^3\,b^4-9688\,a^2\,b^5+10080\,a\,b^6+9408\,b^7\right)}{24\,a^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\left(55\,a^7+454\,a^6\,b-2969\,a^5\,b^2+608\,a^4\,b^3+12212\,a^3\,b^4-9688\,a^2\,b^5-10080\,a\,b^6+9408\,b^7\right)}{24\,a^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-215\,a^7+2154\,a^6\,b+22673\,a^5\,b^2+32224\,a^4\,b^3-107220\,a^3\,b^4-163240\,a^2\,b^5+90720\,a\,b^6+141120\,b^7\right)}{120\,a^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(215\,a^7+2154\,a^6\,b-22673\,a^5\,b^2+32224\,a^4\,b^3+107220\,a^3\,b^4-163240\,a^2\,b^5-90720\,a\,b^6+141120\,b^7\right)}{120\,a^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2545\,a^7-4994\,a^6\,b+11173\,a^5\,b^2+74752\,a^4\,b^3-58820\,a^3\,b^4-287000\,a^2\,b^5+50400\,a\,b^6+235200\,b^7\right)}{120\,a^8}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(2545\,a^7+4994\,a^6\,b+11173\,a^5\,b^2-74752\,a^4\,b^3-58820\,a^3\,b^4+287000\,a^2\,b^5+50400\,a\,b^6-235200\,b^7\right)}{120\,a^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}\,\left(a-b\right)\,\left(5\,a^6+43\,a^5\,b-180\,a^4\,b^2-244\,a^3\,b^3+600\,a^2\,b^4+224\,a\,b^5-448\,b^6\right)}{8\,a^8}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,a\,b+b^2\right)\,\left(5\,a^5-48\,a^4\,b-132\,a^3\,b^2+376\,a^2\,b^3+224\,a\,b^4-448\,b^5\right)}{8\,a^8}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(10\,a^2-70\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2+12\,a\,b+8\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}\,\left(4\,a^2-12\,a\,b+8\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^2+28\,a\,b+28\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(4\,a^2-28\,a\,b+28\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-4\,a^2+28\,a\,b+56\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(4\,a^2+28\,a\,b-56\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{128\,a^{25}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{16\,a^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,a^9}-\frac{\left(\frac{\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{128\,a^{25}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{16\,a^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)\,1{}\mathrm{i}}{16\,a^9}}{\frac{\frac{75\,a^{19}\,b}{4}+\frac{285\,a^{18}\,b^2}{2}-\frac{13415\,a^{17}\,b^3}{8}-\frac{26515\,a^{16}\,b^4}{4}+\frac{196765\,a^{15}\,b^5}{4}+\frac{296845\,a^{14}\,b^6}{4}-\frac{4466945\,a^{13}\,b^7}{8}-297558\,a^{12}\,b^8+3099308\,a^{11}\,b^9+163573\,a^{10}\,b^{10}-9486373\,a^9\,b^{11}+2126380\,a^8\,b^{12}+16804748\,a^7\,b^{13}-6722456\,a^6\,b^{14}-17144736\,a^5\,b^{15}+8902208\,a^4\,b^{16}+9345280\,a^3\,b^{17}-5644800\,a^2\,b^{18}-2107392\,a\,b^{19}+1404928\,b^{20}}{a^{24}}+\frac{\left(\frac{\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{128\,a^{25}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{16\,a^9}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{16\,a^9}+\frac{\left(\frac{\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{128\,a^{25}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{16\,a^9}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)}{16\,a^9}}\right)\,\left(a^6\,5{}\mathrm{i}-a^4\,b^2\,180{}\mathrm{i}+a^2\,b^4\,600{}\mathrm{i}-b^6\,448{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,a^9\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)}{16\,a^{25}}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)}{2\,a^9}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)\,1{}\mathrm{i}}{2\,a^9}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)}{16\,a^{25}}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)}{2\,a^9}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)\,1{}\mathrm{i}}{2\,a^9}}{\frac{\frac{75\,a^{19}\,b}{4}+\frac{285\,a^{18}\,b^2}{2}-\frac{13415\,a^{17}\,b^3}{8}-\frac{26515\,a^{16}\,b^4}{4}+\frac{196765\,a^{15}\,b^5}{4}+\frac{296845\,a^{14}\,b^6}{4}-\frac{4466945\,a^{13}\,b^7}{8}-297558\,a^{12}\,b^8+3099308\,a^{11}\,b^9+163573\,a^{10}\,b^{10}-9486373\,a^9\,b^{11}+2126380\,a^8\,b^{12}+16804748\,a^7\,b^{13}-6722456\,a^6\,b^{14}-17144736\,a^5\,b^{15}+8902208\,a^4\,b^{16}+9345280\,a^3\,b^{17}-5644800\,a^2\,b^{18}-2107392\,a\,b^{19}+1404928\,b^{20}}{a^{24}}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)}{16\,a^{25}}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)}{2\,a^9}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)}{2\,a^9}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(25\,a^{15}-75\,a^{14}\,b+579\,a^{13}\,b^2+3071\,a^{12}\,b^3-7704\,a^{11}\,b^4-72696\,a^{10}\,b^5+153600\,a^9\,b^6+364160\,a^8\,b^7-881920\,a^7\,b^8-601600\,a^6\,b^9+2085120\,a^5\,b^{10}+32640\,a^4\,b^{11}-2150400\,a^3\,b^{12}+673792\,a^2\,b^{13}+802816\,a\,b^{14}-401408\,b^{15}\right)}{8\,a^{16}}-\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-10\,a^{26}+106\,a^{25}\,b+178\,a^{24}\,b^2-1122\,a^{23}\,b^3+136\,a^{22}\,b^4+2360\,a^{21}\,b^5-1200\,a^{20}\,b^6-1344\,a^{19}\,b^7+896\,a^{18}\,b^8}{a^{24}}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)\,\left(512\,a^{20}\,b-1024\,a^{19}\,b^2+512\,a^{18}\,b^3\right)}{16\,a^{25}}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)}{2\,a^9}\right)\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)}{2\,a^9}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(6\,a^4-47\,a^2\,b^2+56\,b^4\right)\,1{}\mathrm{i}}{a^9\,d}","Not used",1,"((tan(c/2 + (d*x)/2)^3*(10080*a*b^6 + 454*a^6*b - 55*a^7 + 9408*b^7 - 9688*a^2*b^5 - 12212*a^3*b^4 + 608*a^4*b^3 + 2969*a^5*b^2))/(24*a^8) + (tan(c/2 + (d*x)/2)^13*(454*a^6*b - 10080*a*b^6 + 55*a^7 + 9408*b^7 - 9688*a^2*b^5 + 12212*a^3*b^4 + 608*a^4*b^3 - 2969*a^5*b^2))/(24*a^8) + (tan(c/2 + (d*x)/2)^5*(90720*a*b^6 + 2154*a^6*b - 215*a^7 + 141120*b^7 - 163240*a^2*b^5 - 107220*a^3*b^4 + 32224*a^4*b^3 + 22673*a^5*b^2))/(120*a^8) + (tan(c/2 + (d*x)/2)^11*(2154*a^6*b - 90720*a*b^6 + 215*a^7 + 141120*b^7 - 163240*a^2*b^5 + 107220*a^3*b^4 + 32224*a^4*b^3 - 22673*a^5*b^2))/(120*a^8) + (tan(c/2 + (d*x)/2)^7*(50400*a*b^6 - 4994*a^6*b + 2545*a^7 + 235200*b^7 - 287000*a^2*b^5 - 58820*a^3*b^4 + 74752*a^4*b^3 + 11173*a^5*b^2))/(120*a^8) - (tan(c/2 + (d*x)/2)^9*(50400*a*b^6 + 4994*a^6*b + 2545*a^7 - 235200*b^7 + 287000*a^2*b^5 - 58820*a^3*b^4 - 74752*a^4*b^3 + 11173*a^5*b^2))/(120*a^8) + (tan(c/2 + (d*x)/2)^15*(a - b)*(224*a*b^5 + 43*a^5*b + 5*a^6 - 448*b^6 + 600*a^2*b^4 - 244*a^3*b^3 - 180*a^4*b^2))/(8*a^8) - (tan(c/2 + (d*x)/2)*(2*a*b + a^2 + b^2)*(224*a*b^4 - 48*a^4*b + 5*a^5 - 448*b^5 + 376*a^2*b^3 - 132*a^3*b^2))/(8*a^8))/(d*(2*a*b - tan(c/2 + (d*x)/2)^8*(10*a^2 - 70*b^2) + tan(c/2 + (d*x)/2)^2*(12*a*b + 4*a^2 + 8*b^2) + tan(c/2 + (d*x)/2)^14*(4*a^2 - 12*a*b + 8*b^2) + tan(c/2 + (d*x)/2)^4*(28*a*b + 4*a^2 + 28*b^2) + tan(c/2 + (d*x)/2)^12*(4*a^2 - 28*a*b + 28*b^2) + tan(c/2 + (d*x)/2)^6*(28*a*b - 4*a^2 + 56*b^2) - tan(c/2 + (d*x)/2)^10*(28*a*b + 4*a^2 - 56*b^2) + tan(c/2 + (d*x)/2)^16*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan(((((((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 - (tan(c/2 + (d*x)/2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2)*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(128*a^25))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(16*a^9) + (tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i)*1i)/(16*a^9) - (((((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 + (tan(c/2 + (d*x)/2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2)*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(128*a^25))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(16*a^9) - (tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i)*1i)/(16*a^9))/(((75*a^19*b)/4 - 2107392*a*b^19 + 1404928*b^20 - 5644800*a^2*b^18 + 9345280*a^3*b^17 + 8902208*a^4*b^16 - 17144736*a^5*b^15 - 6722456*a^6*b^14 + 16804748*a^7*b^13 + 2126380*a^8*b^12 - 9486373*a^9*b^11 + 163573*a^10*b^10 + 3099308*a^11*b^9 - 297558*a^12*b^8 - (4466945*a^13*b^7)/8 + (296845*a^14*b^6)/4 + (196765*a^15*b^5)/4 - (26515*a^16*b^4)/4 - (13415*a^17*b^3)/8 + (285*a^18*b^2)/2)/a^24 + (((((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 - (tan(c/2 + (d*x)/2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2)*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(128*a^25))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(16*a^9) + (tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(16*a^9) + (((((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 + (tan(c/2 + (d*x)/2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2)*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(128*a^25))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(16*a^9) - (tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i))/(16*a^9)))*(a^6*5i - b^6*448i + a^2*b^4*600i - a^4*b^2*180i)*1i)/(8*a^9*d) + (b*atan(((b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16) + (b*((a + b)*(a - b))^(1/2)*((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 - (b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(6*a^4 + 56*b^4 - 47*a^2*b^2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2))/(16*a^25))*(6*a^4 + 56*b^4 - 47*a^2*b^2))/(2*a^9))*(6*a^4 + 56*b^4 - 47*a^2*b^2)*1i)/(2*a^9) + (b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16) - (b*((a + b)*(a - b))^(1/2)*((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 + (b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(6*a^4 + 56*b^4 - 47*a^2*b^2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2))/(16*a^25))*(6*a^4 + 56*b^4 - 47*a^2*b^2))/(2*a^9))*(6*a^4 + 56*b^4 - 47*a^2*b^2)*1i)/(2*a^9))/(((75*a^19*b)/4 - 2107392*a*b^19 + 1404928*b^20 - 5644800*a^2*b^18 + 9345280*a^3*b^17 + 8902208*a^4*b^16 - 17144736*a^5*b^15 - 6722456*a^6*b^14 + 16804748*a^7*b^13 + 2126380*a^8*b^12 - 9486373*a^9*b^11 + 163573*a^10*b^10 + 3099308*a^11*b^9 - 297558*a^12*b^8 - (4466945*a^13*b^7)/8 + (296845*a^14*b^6)/4 + (196765*a^15*b^5)/4 - (26515*a^16*b^4)/4 - (13415*a^17*b^3)/8 + (285*a^18*b^2)/2)/a^24 + (b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16) + (b*((a + b)*(a - b))^(1/2)*((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 - (b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(6*a^4 + 56*b^4 - 47*a^2*b^2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2))/(16*a^25))*(6*a^4 + 56*b^4 - 47*a^2*b^2))/(2*a^9))*(6*a^4 + 56*b^4 - 47*a^2*b^2))/(2*a^9) - (b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(802816*a*b^14 - 75*a^14*b + 25*a^15 - 401408*b^15 + 673792*a^2*b^13 - 2150400*a^3*b^12 + 32640*a^4*b^11 + 2085120*a^5*b^10 - 601600*a^6*b^9 - 881920*a^7*b^8 + 364160*a^8*b^7 + 153600*a^9*b^6 - 72696*a^10*b^5 - 7704*a^11*b^4 + 3071*a^12*b^3 + 579*a^13*b^2))/(8*a^16) - (b*((a + b)*(a - b))^(1/2)*((106*a^25*b - 10*a^26 + 896*a^18*b^8 - 1344*a^19*b^7 - 1200*a^20*b^6 + 2360*a^21*b^5 + 136*a^22*b^4 - 1122*a^23*b^3 + 178*a^24*b^2)/a^24 + (b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(6*a^4 + 56*b^4 - 47*a^2*b^2)*(512*a^20*b + 512*a^18*b^3 - 1024*a^19*b^2))/(16*a^25))*(6*a^4 + 56*b^4 - 47*a^2*b^2))/(2*a^9))*(6*a^4 + 56*b^4 - 47*a^2*b^2))/(2*a^9)))*((a + b)*(a - b))^(1/2)*(6*a^4 + 56*b^4 - 47*a^2*b^2)*1i)/(a^9*d)","B"
229,1,3255,333,5.761040,"\text{Not used}","int(sin(c + d*x)^4/(a + b/cos(c + d*x))^3,x)","-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-15\,a^5+26\,a^4\,b-73\,a^3\,b^2-300\,a^2\,b^3+180\,a\,b^4+600\,b^5\right)}{2\,a^6}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(a^5+6\,a^4\,b-31\,a^3\,b^2+4\,a^2\,b^3+60\,a\,b^4-40\,b^5\right)}{4\,a^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(15\,a^5+26\,a^4\,b+73\,a^3\,b^2-300\,a^2\,b^3-180\,a\,b^4+600\,b^5\right)}{2\,a^6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a^5-34\,a^4\,b-239\,a^3\,b^2-220\,a^2\,b^3+540\,a\,b^4+600\,b^5\right)}{4\,a^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(5\,a^5+34\,a^4\,b-239\,a^3\,b^2+220\,a^2\,b^3+540\,a\,b^4-600\,b^5\right)}{4\,a^6}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)\,\left(a^4-7\,a^3\,b-24\,a^2\,b^2+20\,a\,b^3+40\,b^4\right)}{4\,a^6}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2-20\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+8\,a\,b+6\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(2\,a^2-8\,a\,b+6\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-a^2+10\,a\,b+15\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2+10\,a\,b-15\,b^2\right)\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{3\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{16\,a^{19}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,3{}\mathrm{i}}{8\,a^7}-\frac{\left(\frac{3\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{16\,a^{19}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^7}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,3{}\mathrm{i}}{8\,a^7}}{\frac{27\,a^{13}\,b+162\,a^{12}\,b^2-\frac{3267\,a^{11}\,b^3}{2}-4671\,a^{10}\,b^4+\frac{62181\,a^9\,b^5}{2}+24408\,a^8\,b^6-205119\,a^7\,b^7-4104\,a^6\,b^8+576720\,a^5\,b^9-195480\,a^4\,b^{10}-718200\,a^3\,b^{11}+388800\,a^2\,b^{12}+324000\,a\,b^{13}-216000\,b^{14}}{a^{18}}+\frac{3\,\left(\frac{3\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{16\,a^{19}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^7}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^7}+\frac{3\,\left(\frac{3\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{16\,a^{19}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^7}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)}{8\,a^7}}\right)\,\left(a^4\,1{}\mathrm{i}-a^2\,b^2\,24{}\mathrm{i}+b^4\,40{}\mathrm{i}\right)\,3{}\mathrm{i}}{4\,a^7\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}+\frac{3\,b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}-\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{4\,a^{12}\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,3{}\mathrm{i}}{2\,\left(a^9-a^7\,b^2\right)}+\frac{b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}-\frac{3\,b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}+\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{4\,a^{12}\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,3{}\mathrm{i}}{2\,\left(a^9-a^7\,b^2\right)}}{\frac{27\,a^{13}\,b+162\,a^{12}\,b^2-\frac{3267\,a^{11}\,b^3}{2}-4671\,a^{10}\,b^4+\frac{62181\,a^9\,b^5}{2}+24408\,a^8\,b^6-205119\,a^7\,b^7-4104\,a^6\,b^8+576720\,a^5\,b^9-195480\,a^4\,b^{10}-718200\,a^3\,b^{11}+388800\,a^2\,b^{12}+324000\,a\,b^{13}-216000\,b^{14}}{a^{18}}+\frac{3\,b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}+\frac{3\,b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}-\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{4\,a^{12}\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}-\frac{3\,b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(9\,a^{11}-27\,a^{10}\,b+171\,a^9\,b^2+711\,a^8\,b^3-1728\,a^7\,b^4-10944\,a^6\,b^5+23616\,a^5\,b^6+22752\,a^4\,b^7-69120\,a^3\,b^8+5760\,a^2\,b^9+57600\,a\,b^{10}-28800\,b^{11}\right)}{2\,a^{12}}-\frac{3\,b\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(\frac{-12\,a^{20}+108\,a^{19}\,b+108\,a^{18}\,b^2-732\,a^{17}\,b^3+288\,a^{16}\,b^4+720\,a^{15}\,b^5-480\,a^{14}\,b^6}{a^{18}}+\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,\left(128\,a^{16}\,b-256\,a^{15}\,b^2+128\,a^{14}\,b^3\right)}{4\,a^{12}\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}\right)\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)}{2\,\left(a^9-a^7\,b^2\right)}}\right)\,\sqrt{\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^4-11\,a^2\,b^2+10\,b^4\right)\,3{}\mathrm{i}}{d\,\left(a^9-a^7\,b^2\right)}","Not used",1,"(atan(((((3*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 - (3*tan(c/2 + (d*x)/2)*(a^4*1i + b^4*40i - a^2*b^2*24i)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(16*a^19))*(a^4*1i + b^4*40i - a^2*b^2*24i))/(8*a^7) + (tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12))*(a^4*1i + b^4*40i - a^2*b^2*24i)*3i)/(8*a^7) - (((3*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 + (3*tan(c/2 + (d*x)/2)*(a^4*1i + b^4*40i - a^2*b^2*24i)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(16*a^19))*(a^4*1i + b^4*40i - a^2*b^2*24i))/(8*a^7) - (tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12))*(a^4*1i + b^4*40i - a^2*b^2*24i)*3i)/(8*a^7))/((324000*a*b^13 + 27*a^13*b - 216000*b^14 + 388800*a^2*b^12 - 718200*a^3*b^11 - 195480*a^4*b^10 + 576720*a^5*b^9 - 4104*a^6*b^8 - 205119*a^7*b^7 + 24408*a^8*b^6 + (62181*a^9*b^5)/2 - 4671*a^10*b^4 - (3267*a^11*b^3)/2 + 162*a^12*b^2)/a^18 + (3*((3*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 - (3*tan(c/2 + (d*x)/2)*(a^4*1i + b^4*40i - a^2*b^2*24i)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(16*a^19))*(a^4*1i + b^4*40i - a^2*b^2*24i))/(8*a^7) + (tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12))*(a^4*1i + b^4*40i - a^2*b^2*24i))/(8*a^7) + (3*((3*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 + (3*tan(c/2 + (d*x)/2)*(a^4*1i + b^4*40i - a^2*b^2*24i)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(16*a^19))*(a^4*1i + b^4*40i - a^2*b^2*24i))/(8*a^7) - (tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12))*(a^4*1i + b^4*40i - a^2*b^2*24i))/(8*a^7)))*(a^4*1i + b^4*40i - a^2*b^2*24i)*3i)/(4*a^7*d) - ((tan(c/2 + (d*x)/2)^5*(180*a*b^4 + 26*a^4*b - 15*a^5 + 600*b^5 - 300*a^2*b^3 - 73*a^3*b^2))/(2*a^6) - (3*tan(c/2 + (d*x)/2)^11*(60*a*b^4 + 6*a^4*b + a^5 - 40*b^5 + 4*a^2*b^3 - 31*a^3*b^2))/(4*a^6) + (tan(c/2 + (d*x)/2)^7*(26*a^4*b - 180*a*b^4 + 15*a^5 + 600*b^5 - 300*a^2*b^3 + 73*a^3*b^2))/(2*a^6) + (tan(c/2 + (d*x)/2)^3*(540*a*b^4 - 34*a^4*b + 5*a^5 + 600*b^5 - 220*a^2*b^3 - 239*a^3*b^2))/(4*a^6) - (tan(c/2 + (d*x)/2)^9*(540*a*b^4 + 34*a^4*b + 5*a^5 - 600*b^5 + 220*a^2*b^3 - 239*a^3*b^2))/(4*a^6) + (3*tan(c/2 + (d*x)/2)*(a + b)*(20*a*b^3 - 7*a^3*b + a^4 + 40*b^4 - 24*a^2*b^2))/(4*a^6))/(d*(2*a*b - tan(c/2 + (d*x)/2)^6*(4*a^2 - 20*b^2) + tan(c/2 + (d*x)/2)^2*(8*a*b + 2*a^2 + 6*b^2) + tan(c/2 + (d*x)/2)^10*(2*a^2 - 8*a*b + 6*b^2) + tan(c/2 + (d*x)/2)^4*(10*a*b - a^2 + 15*b^2) + tan(c/2 + (d*x)/2)^12*(a^2 - 2*a*b + b^2) + a^2 + b^2 - tan(c/2 + (d*x)/2)^8*(10*a*b + a^2 - 15*b^2))) + (b*atan(((b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12) + (3*b*((a + b)*(a - b))^(1/2)*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 - (3*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^4 + 10*b^4 - 11*a^2*b^2)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(4*a^12*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2)*3i)/(2*(a^9 - a^7*b^2)) + (b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12) - (3*b*((a + b)*(a - b))^(1/2)*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 + (3*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^4 + 10*b^4 - 11*a^2*b^2)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(4*a^12*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2)*3i)/(2*(a^9 - a^7*b^2)))/((324000*a*b^13 + 27*a^13*b - 216000*b^14 + 388800*a^2*b^12 - 718200*a^3*b^11 - 195480*a^4*b^10 + 576720*a^5*b^9 - 4104*a^6*b^8 - 205119*a^7*b^7 + 24408*a^8*b^6 + (62181*a^9*b^5)/2 - 4671*a^10*b^4 - (3267*a^11*b^3)/2 + 162*a^12*b^2)/a^18 + (3*b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12) + (3*b*((a + b)*(a - b))^(1/2)*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 - (3*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^4 + 10*b^4 - 11*a^2*b^2)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(4*a^12*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)) - (3*b*((a + b)*(a - b))^(1/2)*((tan(c/2 + (d*x)/2)*(57600*a*b^10 - 27*a^10*b + 9*a^11 - 28800*b^11 + 5760*a^2*b^9 - 69120*a^3*b^8 + 22752*a^4*b^7 + 23616*a^5*b^6 - 10944*a^6*b^5 - 1728*a^7*b^4 + 711*a^8*b^3 + 171*a^9*b^2))/(2*a^12) - (3*b*((a + b)*(a - b))^(1/2)*((108*a^19*b - 12*a^20 - 480*a^14*b^6 + 720*a^15*b^5 + 288*a^16*b^4 - 732*a^17*b^3 + 108*a^18*b^2)/a^18 + (3*b*tan(c/2 + (d*x)/2)*((a + b)*(a - b))^(1/2)*(2*a^4 + 10*b^4 - 11*a^2*b^2)*(128*a^16*b + 128*a^14*b^3 - 256*a^15*b^2))/(4*a^12*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2)))*(2*a^4 + 10*b^4 - 11*a^2*b^2))/(2*(a^9 - a^7*b^2))))*((a + b)*(a - b))^(1/2)*(2*a^4 + 10*b^4 - 11*a^2*b^2)*3i)/(d*(a^9 - a^7*b^2))","B"
230,1,4026,267,9.095006,"\text{Not used}","int(sin(c + d*x)^2/(a + b/cos(c + d*x))^3,x)","\frac{\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^4-5\,a^3\,b-13\,a^2\,b^2+6\,a\,b^3+12\,b^4\right)}{a^4\,b-a^5}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-3\,a^5+4\,a^4\,b-14\,a^3\,b^2-37\,a^2\,b^3+18\,a\,b^4+36\,b^5\right)}{\left(a^4\,b-a^5\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^5+4\,a^4\,b+14\,a^3\,b^2-37\,a^2\,b^3-18\,a\,b^4+36\,b^5\right)}{\left(a^4\,b-a^5\right)\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^4+5\,a^3\,b-13\,a^2\,b^2-6\,a\,b^3+12\,b^4\right)}{a^4\,\left(a+b\right)}}{d\,\left(2\,a\,b-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2-6\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,b^2+4\,a\,b\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a\,b-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-2\,a\,b+b^2\right)+a^2+b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)}{2\,a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,1{}\mathrm{i}}{2\,a^5}-\frac{\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)}{2\,a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)\,1{}\mathrm{i}}{2\,a^5}}{\frac{8\,\left(6\,a^{10}\,b+30\,a^9\,b^2-169\,a^8\,b^3-491\,a^7\,b^4+1495\,a^6\,b^5+1746\,a^5\,b^6-4356\,a^4\,b^7-2160\,a^3\,b^8+4752\,a^2\,b^9+864\,a\,b^{10}-1728\,b^{11}\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)}{2\,a^5}+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)}{2\,a^5}+\frac{\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(\frac{\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{a^5\,\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)}{2\,a^5}-\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}\right)}{2\,a^5}}\right)\,\left(a^2\,1{}\mathrm{i}-b^2\,12{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^5\,d}+\frac{b\,\mathrm{atan}\left(\frac{\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}}{\frac{8\,\left(6\,a^{10}\,b+30\,a^9\,b^2-169\,a^8\,b^3-491\,a^7\,b^4+1495\,a^6\,b^5+1746\,a^5\,b^6-4356\,a^4\,b^7-2160\,a^3\,b^8+4752\,a^2\,b^9+864\,a\,b^{10}-1728\,b^{11}\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}+\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}-\frac{b\,\left(\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^{10}-2\,a^9\,b+11\,a^8\,b^2+52\,a^7\,b^3-61\,a^6\,b^4-386\,a^5\,b^5+386\,a^4\,b^6+624\,a^3\,b^7-624\,a^2\,b^8-288\,a\,b^9+288\,b^{10}\right)}{a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3}-\frac{b\,\left(\frac{4\,\left(-4\,a^{17}+24\,a^{16}\,b+36\,a^{15}\,b^2-100\,a^{14}\,b^3-56\,a^{13}\,b^4+124\,a^{12}\,b^5+24\,a^{11}\,b^6-48\,a^{10}\,b^7\right)}{a^{15}+a^{14}\,b-a^{13}\,b^2-a^{12}\,b^3}+\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,\left(8\,a^{15}\,b-8\,a^{14}\,b^2-16\,a^{13}\,b^3+16\,a^{12}\,b^4+8\,a^{11}\,b^5-8\,a^{10}\,b^6\right)}{\left(a^{11}+a^{10}\,b-a^9\,b^2-a^8\,b^3\right)\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)}{2\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(6\,a^4-19\,a^2\,b^2+12\,b^4\right)\,1{}\mathrm{i}}{d\,\left(a^{11}-3\,a^9\,b^2+3\,a^7\,b^4-a^5\,b^6\right)}","Not used",1,"((tan(c/2 + (d*x)/2)*(6*a*b^3 - 5*a^3*b + a^4 + 12*b^4 - 13*a^2*b^2))/(a^4*b - a^5) + (tan(c/2 + (d*x)/2)^3*(18*a*b^4 + 4*a^4*b - 3*a^5 + 36*b^5 - 37*a^2*b^3 - 14*a^3*b^2))/((a^4*b - a^5)*(a + b)) + (tan(c/2 + (d*x)/2)^5*(4*a^4*b - 18*a*b^4 + 3*a^5 + 36*b^5 - 37*a^2*b^3 + 14*a^3*b^2))/((a^4*b - a^5)*(a + b)) + (tan(c/2 + (d*x)/2)^7*(5*a^3*b - 6*a*b^3 + a^4 + 12*b^4 - 13*a^2*b^2))/(a^4*(a + b)))/(d*(2*a*b - tan(c/2 + (d*x)/2)^4*(2*a^2 - 6*b^2) + tan(c/2 + (d*x)/2)^2*(4*a*b + 4*b^2) - tan(c/2 + (d*x)/2)^6*(4*a*b - 4*b^2) + tan(c/2 + (d*x)/2)^8*(a^2 - 2*a*b + b^2) + a^2 + b^2)) + (atan((((a^2*1i - b^2*12i)*((((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2*1i - b^2*12i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2*1i - b^2*12i))/(2*a^5) + (8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*1i)/(2*a^5) - ((a^2*1i - b^2*12i)*((((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2*1i - b^2*12i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2*1i - b^2*12i))/(2*a^5) - (8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2))*1i)/(2*a^5))/((8*(864*a*b^10 + 6*a^10*b - 1728*b^11 + 4752*a^2*b^9 - 2160*a^3*b^8 - 4356*a^4*b^7 + 1746*a^5*b^6 + 1495*a^6*b^5 - 491*a^7*b^4 - 169*a^8*b^3 + 30*a^9*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + ((a^2*1i - b^2*12i)*((((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*tan(c/2 + (d*x)/2)*(a^2*1i - b^2*12i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2*1i - b^2*12i))/(2*a^5) + (8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))/(2*a^5) + ((a^2*1i - b^2*12i)*((((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*tan(c/2 + (d*x)/2)*(a^2*1i - b^2*12i)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/(a^5*(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))*(a^2*1i - b^2*12i))/(2*a^5) - (8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2)))/(2*a^5)))*(a^2*1i - b^2*12i)*1i)/(a^5*d) + (b*atan(((b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*1i)/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)) + (b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*1i)/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))/((8*(864*a*b^10 + 6*a^10*b - 1728*b^11 + 4752*a^2*b^9 - 2160*a^3*b^8 - 4356*a^4*b^7 + 1746*a^5*b^6 + 1495*a^6*b^5 - 491*a^7*b^4 - 169*a^8*b^3 + 30*a^9*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) + (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) - (4*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)) - (b*((8*tan(c/2 + (d*x)/2)*(a^10 - 2*a^9*b - 288*a*b^9 + 288*b^10 - 624*a^2*b^8 + 624*a^3*b^7 + 386*a^4*b^6 - 386*a^5*b^5 - 61*a^6*b^4 + 52*a^7*b^3 + 11*a^8*b^2))/(a^10*b + a^11 - a^8*b^3 - a^9*b^2) - (b*((4*(24*a^16*b - 4*a^17 - 48*a^10*b^7 + 24*a^11*b^6 + 124*a^12*b^5 - 56*a^13*b^4 - 100*a^14*b^3 + 36*a^15*b^2))/(a^14*b + a^15 - a^12*b^3 - a^13*b^2) + (4*b*tan(c/2 + (d*x)/2)*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*(8*a^15*b - 8*a^10*b^6 + 8*a^11*b^5 + 16*a^12*b^4 - 16*a^13*b^3 - 8*a^14*b^2))/((a^10*b + a^11 - a^8*b^3 - a^9*b^2)*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2))/(2*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))))*((a + b)^3*(a - b)^3)^(1/2)*(6*a^4 + 12*b^4 - 19*a^2*b^2)*1i)/(d*(a^11 - a^5*b^6 + 3*a^7*b^4 - 3*a^9*b^2))","B"
231,1,423,376,2.858284,"\text{Not used}","int(1/(sin(c + d*x)^2*(a + b/cos(c + d*x))^3),x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d\,{\left(a-b\right)}^3}-\frac{\frac{a^3-3\,a^2\,b+3\,a\,b^2-b^3}{a+b}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^5-5\,a^4\,b+22\,a^3\,b^2-20\,a^2\,b^3+7\,a\,b^4-5\,b^5\right)}{{\left(a+b\right)}^3}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4-4\,a^3\,b+12\,a^2\,b^2-5\,a\,b^3+3\,b^4\right)}{{\left(a+b\right)}^2}}{d\,\left(\left(2\,a^5-10\,a^4\,b+20\,a^3\,b^2-20\,a^2\,b^3+10\,a\,b^4-2\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-4\,a^5+12\,a^4\,b-8\,a^3\,b^2-8\,a^2\,b^3+12\,a\,b^4-4\,b^5\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^5-2\,a^4\,b-4\,a^3\,b^2+4\,a^2\,b^3+2\,a\,b^4-2\,b^5\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a\,b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6-3{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^2+3{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^4-1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^6}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{5/2}}\right)\,\left(2\,a^2+3\,b^2\right)\,3{}\mathrm{i}}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"tan(c/2 + (d*x)/2)/(2*d*(a - b)^3) - ((3*a*b^2 - 3*a^2*b + a^3 - b^3)/(a + b) + (tan(c/2 + (d*x)/2)^4*(7*a*b^4 - 5*a^4*b + a^5 - 5*b^5 - 20*a^2*b^3 + 22*a^3*b^2))/(a + b)^3 - (2*tan(c/2 + (d*x)/2)^2*(a^4 - 4*a^3*b - 5*a*b^3 + 3*b^4 + 12*a^2*b^2))/(a + b)^2)/(d*(tan(c/2 + (d*x)/2)*(2*a*b^4 - 2*a^4*b + 2*a^5 - 2*b^5 + 4*a^2*b^3 - 4*a^3*b^2) - tan(c/2 + (d*x)/2)^3*(4*a^5 - 12*a^4*b - 12*a*b^4 + 4*b^5 + 8*a^2*b^3 + 8*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(10*a*b^4 - 10*a^4*b + 2*a^5 - 2*b^5 - 20*a^2*b^3 + 20*a^3*b^2))) + (a*b*atan((a^6*tan(c/2 + (d*x)/2)*1i - b^6*tan(c/2 + (d*x)/2)*1i + a^2*b^4*tan(c/2 + (d*x)/2)*3i - a^4*b^2*tan(c/2 + (d*x)/2)*3i)/((a + b)^(7/2)*(a - b)^(5/2)))*(2*a^2 + 3*b^2)*3i)/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
232,1,588,515,1.780594,"\text{Not used}","int(1/(sin(c + d*x)^4*(a + b/cos(c + d*x))^3),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d\,{\left(a-b\right)}^3}+\frac{\frac{a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4}{3\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^7-21\,a^6\,b+111\,a^5\,b^2-145\,a^4\,b^3+145\,a^3\,b^4-111\,a^2\,b^5+21\,a\,b^6-3\,b^7\right)}{{\left(a+b\right)}^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(17\,a^6-102\,a^5\,b+399\,a^4\,b^2-364\,a^3\,b^3+399\,a^2\,b^4-102\,a\,b^5+17\,b^6\right)}{3\,{\left(a+b\right)}^3}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a-b\right)\,\left(a^4-4\,a^3\,b+6\,a^2\,b^2-4\,a\,b^3+b^4\right)}{3\,{\left(a+b\right)}^2}}{d\,\left(\left(-8\,a^6+48\,a^5\,b-120\,a^4\,b^2+160\,a^3\,b^3-120\,a^2\,b^4+48\,a\,b^5-8\,b^6\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(16\,a^6-64\,a^5\,b+80\,a^4\,b^2-80\,a^2\,b^4+64\,a\,b^5-16\,b^6\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(-8\,a^6+16\,a^5\,b+8\,a^4\,b^2-32\,a^3\,b^3+8\,a^2\,b^4+16\,a\,b^5-8\,b^6\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a+b\right)}{8\,d\,{\left(a-b\right)}^4}+\frac{a\,b\,\mathrm{atan}\left(\frac{1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8-4{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^2+6{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^4-4{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^6+1{}\mathrm{i}\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^8}{{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{7/2}}\right)\,\left(6\,a^4+23\,a^2\,b^2+6\,b^4\right)\,1{}\mathrm{i}}{d\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*d*(a - b)^3) + ((a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2)/(3*(a + b)) + (tan(c/2 + (d*x)/2)^6*(21*a*b^6 - 21*a^6*b + 3*a^7 - 3*b^7 - 111*a^2*b^5 + 145*a^3*b^4 - 145*a^4*b^3 + 111*a^5*b^2))/(a + b)^4 - (tan(c/2 + (d*x)/2)^4*(17*a^6 - 102*a^5*b - 102*a*b^5 + 17*b^6 + 399*a^2*b^4 - 364*a^3*b^3 + 399*a^4*b^2))/(3*(a + b)^3) + (7*tan(c/2 + (d*x)/2)^2*(a - b)*(a^4 - 4*a^3*b - 4*a*b^3 + b^4 + 6*a^2*b^2))/(3*(a + b)^2))/(d*(tan(c/2 + (d*x)/2)^3*(16*a*b^5 + 16*a^5*b - 8*a^6 - 8*b^6 + 8*a^2*b^4 - 32*a^3*b^3 + 8*a^4*b^2) - tan(c/2 + (d*x)/2)^7*(8*a^6 - 48*a^5*b - 48*a*b^5 + 8*b^6 + 120*a^2*b^4 - 160*a^3*b^3 + 120*a^4*b^2) + tan(c/2 + (d*x)/2)^5*(64*a*b^5 - 64*a^5*b + 16*a^6 - 16*b^6 - 80*a^2*b^4 + 80*a^4*b^2))) + (3*tan(c/2 + (d*x)/2)*(a + b))/(8*d*(a - b)^4) + (a*b*atan((a^8*tan(c/2 + (d*x)/2)*1i + b^8*tan(c/2 + (d*x)/2)*1i - a^2*b^6*tan(c/2 + (d*x)/2)*4i + a^4*b^4*tan(c/2 + (d*x)/2)*6i - a^6*b^2*tan(c/2 + (d*x)/2)*4i)/((a + b)^(9/2)*(a - b)^(7/2)))*(6*a^4 + 6*b^4 + 23*a^2*b^2)*1i)/(d*(a + b)^(9/2)*(a - b)^(9/2))","B"
233,0,-1,516,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}}{b+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*sin(c + d*x))^(7/2))/(b + a*cos(c + d*x)), x)","F"
234,0,-1,430,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\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*sin(c + d*x))^(5/2))/(b + a*cos(c + d*x)), x)","F"
235,0,-1,444,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\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*sin(c + d*x))^(3/2))/(b + a*cos(c + d*x)), x)","F"
236,0,-1,356,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,\sqrt{e\,\sin\left(c+d\,x\right)}}{b+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*sin(c + d*x))^(1/2))/(b + a*cos(c + d*x)), x)","F"
237,0,-1,370,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(1/2)*(a + b/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{\sqrt{e\,\sin\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*sin(c + d*x))^(1/2)*(b + a*cos(c + d*x))), x)","F"
238,0,-1,430,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(3/2)*(a + b/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(e\,\sin\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*sin(c + d*x))^(3/2)*(b + a*cos(c + d*x))), x)","F"
239,0,-1,452,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(5/2)*(a + b/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(e\,\sin\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*sin(c + d*x))^(5/2)*(b + a*cos(c + d*x))), x)","F"
240,0,-1,511,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(7/2)*(a + b/cos(c + d*x))),x)","\int \frac{\cos\left(c+d\,x\right)}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}\,\left(b+a\,\cos\left(c+d\,x\right)\right)} \,d x","Not used",1,"int(cos(c + d*x)/((e*sin(c + d*x))^(7/2)*(b + a*cos(c + d*x))), x)","F"
241,0,-1,1070,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(9/2)/(a + b/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\left(c+d\,x\right)\right)}^{9/2}}{{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*sin(c + d*x))^(9/2))/(b + a*cos(c + d*x))^2, x)","F"
242,0,-1,1101,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(7/2)/(a + b/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\left(c+d\,x\right)\right)}^{7/2}}{{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*sin(c + d*x))^(7/2))/(b + a*cos(c + d*x))^2, x)","F"
243,0,-1,850,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(5/2)/(a + b/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}}{{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*sin(c + d*x))^(5/2))/(b + a*cos(c + d*x))^2, x)","F"
244,0,-1,882,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(3/2)/(a + b/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}}{{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*sin(c + d*x))^(3/2))/(b + a*cos(c + d*x))^2, x)","F"
245,0,-1,809,0.000000,"\text{Not used}","int((e*sin(c + d*x))^(1/2)/(a + b/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{e\,\sin\left(c+d\,x\right)}}{{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*sin(c + d*x))^(1/2))/(b + a*cos(c + d*x))^2, x)","F"
246,0,-1,838,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(1/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{\sqrt{e\,\sin\left(c+d\,x\right)}\,{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/((e*sin(c + d*x))^(1/2)*(b + a*cos(c + d*x))^2), x)","F"
247,0,-1,1054,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(3/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{3/2}\,{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/((e*sin(c + d*x))^(3/2)*(b + a*cos(c + d*x))^2), x)","F"
248,0,-1,1089,0.000000,"\text{Not used}","int(1/((e*sin(c + d*x))^(5/2)*(a + b/cos(c + d*x))^2),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{{\left(e\,\sin\left(c+d\,x\right)\right)}^{5/2}\,{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int(cos(c + d*x)^2/((e*sin(c + d*x))^(5/2)*(b + a*cos(c + d*x))^2), x)","F"
249,0,-1,125,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^(1/2),x)","\int \sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}} \,d x","Not used",1,"int((a + b/cos(e + f*x))^(1/2), x)","F"
250,0,-1,121,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^(1/2)/sin(e + f*x)^2,x)","\int \frac{\sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}}}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b/cos(e + f*x))^(1/2)/sin(e + f*x)^2, x)","F"
251,0,-1,309,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^(3/2),x)","\int {\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + b/cos(e + f*x))^(3/2), x)","F"
252,0,-1,228,0.000000,"\text{Not used}","int((a + b/cos(e + f*x))^(3/2)/sin(e + f*x)^2,x)","\int \frac{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^{3/2}}{{\sin\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b/cos(e + f*x))^(3/2)/sin(e + f*x)^2, x)","F"
253,0,-1,106,0.000000,"\text{Not used}","int(1/(a + b/cos(e + f*x))^(1/2),x)","\int \frac{1}{\sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int(1/(a + b/cos(e + f*x))^(1/2), x)","F"
254,0,-1,255,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(a + b/cos(e + f*x))^(1/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,\sqrt{a+\frac{b}{\cos\left(e+f\,x\right)}}} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(a + b/cos(e + f*x))^(1/2)), x)","F"
255,0,-1,347,0.000000,"\text{Not used}","int(1/(a + b/cos(e + f*x))^(3/2),x)","\int \frac{1}{{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b/cos(e + f*x))^(3/2), x)","F"
256,0,-1,318,0.000000,"\text{Not used}","int(1/(sin(e + f*x)^2*(a + b/cos(e + f*x))^(3/2)),x)","\int \frac{1}{{\sin\left(e+f\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(e+f\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int(1/(sin(e + f*x)^2*(a + b/cos(e + f*x))^(3/2)), x)","F"
257,0,-1,249,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^3,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^3 \,d x","Not used",1,"int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^3, x)","F"
258,0,-1,190,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^2,x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^m\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^2 \,d x","Not used",1,"int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^2, x)","F"
259,0,-1,119,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + b/cos(c + d*x)),x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^m\,\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right) \,d x","Not used",1,"int((e*sin(c + d*x))^m*(a + b/cos(c + d*x)), x)","F"
260,0,-1,232,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + b/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(e\,\sin\left(c+d\,x\right)\right)}^m}{b+a\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((cos(c + d*x)*(e*sin(c + d*x))^m)/(b + a*cos(c + d*x)), x)","F"
261,0,-1,405,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + b/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(e\,\sin\left(c+d\,x\right)\right)}^m}{{\left(b+a\,\cos\left(c+d\,x\right)\right)}^2} \,d x","Not used",1,"int((cos(c + d*x)^2*(e*sin(c + d*x))^m)/(b + a*cos(c + d*x))^2, x)","F"
262,0,-1,580,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + b/cos(c + d*x))^3,x)","\int \frac{{\cos\left(c+d\,x\right)}^3\,{\left(e\,\sin\left(c+d\,x\right)\right)}^m}{{\left(b+a\,\cos\left(c+d\,x\right)\right)}^3} \,d x","Not used",1,"int((cos(c + d*x)^3*(e*sin(c + d*x))^m)/(b + a*cos(c + d*x))^3, x)","F"
263,0,-1,28,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^(3/2),x)","\int {\left(e\,\sin\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*sin(c + d*x))^m*(a + b/cos(c + d*x))^(3/2), x)","F"
264,0,-1,28,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^(1/2),x)","\int {\left(e\,\sin\left(c+d\,x\right)\right)}^m\,\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}} \,d x","Not used",0,"int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^(1/2), x)","F"
265,0,-1,28,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + b/cos(c + d*x))^(1/2),x)","\int \frac{{\left(e\,\sin\left(c+d\,x\right)\right)}^m}{\sqrt{a+\frac{b}{\cos\left(c+d\,x\right)}}} \,d x","Not used",0,"int((e*sin(c + d*x))^m/(a + b/cos(c + d*x))^(1/2), x)","F"
266,0,-1,28,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m/(a + b/cos(c + d*x))^(3/2),x)","\int \frac{{\left(e\,\sin\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*sin(c + d*x))^m/(a + b/cos(c + d*x))^(3/2), x)","F"
267,0,-1,26,0.000000,"\text{Not used}","int((e*sin(c + d*x))^m*(a + b/cos(c + d*x))^n,x)","\int {\left(e\,\sin\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*sin(c + d*x))^m*(a + b/cos(c + d*x))^n, x)","F"
268,0,-1,150,0.000000,"\text{Not used}","int(sin(c + d*x)^5*(a + b/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^5\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^5*(a + b/cos(c + d*x))^n, x)","F"
269,0,-1,121,0.000000,"\text{Not used}","int(sin(c + d*x)^3*(a + b/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^3\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",1,"int(sin(c + d*x)^3*(a + b/cos(c + d*x))^n, x)","F"
270,1,73,48,1.386439,"\text{Not used}","int(sin(c + d*x)*(a + b/cos(c + d*x))^n,x)","\frac{\cos\left(c+d\,x\right)\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n\,{{}}_2{\mathrm{F}}_1\left(1-n,-n;\ 2-n;\ -\frac{a\,\cos\left(c+d\,x\right)}{b}\right)}{d\,{\left(\frac{a\,\cos\left(c+d\,x\right)}{b}+1\right)}^n\,\left(n-1\right)}","Not used",1,"(cos(c + d*x)*(a + b/cos(c + d*x))^n*hypergeom([1 - n, -n], 2 - n, -(a*cos(c + d*x))/b))/(d*((a*cos(c + d*x))/b + 1)^n*(n - 1))","B"
271,0,-1,115,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/sin(c + d*x),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{\sin\left(c+d\,x\right)} \,d x","Not used",1,"int((a + b/cos(c + d*x))^n/sin(c + d*x), x)","F"
272,0,-1,231,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/sin(c + d*x)^3,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^3} \,d x","Not used",1,"int((a + b/cos(c + d*x))^n/sin(c + d*x)^3, x)","F"
273,0,-1,24,0.000000,"\text{Not used}","int(sin(c + d*x)^4*(a + b/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^4\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(sin(c + d*x)^4*(a + b/cos(c + d*x))^n, x)","F"
274,0,-1,24,0.000000,"\text{Not used}","int(sin(c + d*x)^2*(a + b/cos(c + d*x))^n,x)","\int {\sin\left(c+d\,x\right)}^2\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(sin(c + d*x)^2*(a + b/cos(c + d*x))^n, x)","F"
275,0,-1,136,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/sin(c + d*x)^2,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^2} \,d x","Not used",1,"int((a + b/cos(c + d*x))^n/sin(c + d*x)^2, x)","F"
276,0,-1,424,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/sin(c + d*x)^4,x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^4} \,d x","Not used",1,"int((a + b/cos(c + d*x))^n/sin(c + d*x)^4, x)","F"
277,0,-1,26,0.000000,"\text{Not used}","int(sin(c + d*x)^(3/2)*(a + b/cos(c + d*x))^n,x)","\int {\sin\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(sin(c + d*x)^(3/2)*(a + b/cos(c + d*x))^n, x)","F"
278,0,-1,26,0.000000,"\text{Not used}","int(sin(c + d*x)^(1/2)*(a + b/cos(c + d*x))^n,x)","\int \sqrt{\sin\left(c+d\,x\right)}\,{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n \,d x","Not used",0,"int(sin(c + d*x)^(1/2)*(a + b/cos(c + d*x))^n, x)","F"
279,0,-1,26,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/sin(c + d*x)^(1/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{\sqrt{\sin\left(c+d\,x\right)}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^n/sin(c + d*x)^(1/2), x)","F"
280,0,-1,26,0.000000,"\text{Not used}","int((a + b/cos(c + d*x))^n/sin(c + d*x)^(3/2),x)","\int \frac{{\left(a+\frac{b}{\cos\left(c+d\,x\right)}\right)}^n}{{\sin\left(c+d\,x\right)}^{3/2}} \,d x","Not used",0,"int((a + b/cos(c + d*x))^n/sin(c + d*x)^(3/2), x)","F"
281,0,-1,190,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(e/sin(c + d*x))^(5/2),x)","\int \left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))*(e/sin(c + d*x))^(5/2), x)","F"
282,0,-1,169,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(e/sin(c + d*x))^(3/2),x)","\int \left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))*(e/sin(c + d*x))^(3/2), x)","F"
283,0,-1,121,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))*(e/sin(c + d*x))^(1/2),x)","\int \left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)\,\sqrt{\frac{e}{\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))*(e/sin(c + d*x))^(1/2), x)","F"
284,0,-1,122,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e/sin(c + d*x))^(1/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{\sqrt{\frac{e}{\sin\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e/sin(c + d*x))^(1/2), x)","F"
285,0,-1,182,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e/sin(c + d*x))^(3/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e/sin(c + d*x))^(3/2), x)","F"
286,0,-1,197,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))/(e/sin(c + d*x))^(5/2),x)","\int \frac{a+\frac{a}{\cos\left(c+d\,x\right)}}{{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))/(e/sin(c + d*x))^(5/2), x)","F"
287,0,-1,270,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(5/2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{5/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(5/2), x)","F"
288,0,-1,240,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(3/2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{3/2} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(3/2), x)","F"
289,0,-1,154,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(1/2),x)","\int {\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2\,\sqrt{\frac{e}{\sin\left(c+d\,x\right)}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(1/2), x)","F"
290,0,-1,153,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e/sin(c + d*x))^(1/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{\sqrt{\frac{e}{\sin\left(c+d\,x\right)}}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e/sin(c + d*x))^(1/2), x)","F"
291,0,-1,222,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e/sin(c + d*x))^(3/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{3/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e/sin(c + d*x))^(3/2), x)","F"
292,0,-1,236,0.000000,"\text{Not used}","int((a + a/cos(c + d*x))^2/(e/sin(c + d*x))^(5/2),x)","\int \frac{{\left(a+\frac{a}{\cos\left(c+d\,x\right)}\right)}^2}{{\left(\frac{e}{\sin\left(c+d\,x\right)}\right)}^{5/2}} \,d x","Not used",1,"int((a + a/cos(c + d*x))^2/(e/sin(c + d*x))^(5/2), x)","F"
293,0,-1,155,0.000000,"\text{Not used}","int((e/sin(c + d*x))^(5/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(5/2))/(a*(cos(c + d*x) + 1)), x)","F"
294,0,-1,145,0.000000,"\text{Not used}","int((e/sin(c + d*x))^(3/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(3/2))/(a*(cos(c + d*x) + 1)), x)","F"
295,0,-1,105,0.000000,"\text{Not used}","int((e/sin(c + d*x))^(1/2)/(a + a/cos(c + d*x)),x)","\int \frac{\cos\left(c+d\,x\right)\,\sqrt{\frac{e}{\sin\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/sin(c + d*x))^(1/2))/(a*(cos(c + d*x) + 1)), x)","F"
296,0,-1,99,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))*(e/sin(c + d*x))^(1/2)),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,\sqrt{\frac{e}{\sin\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/sin(c + d*x))^(1/2)*(cos(c + d*x) + 1)), x)","F"
297,0,-1,106,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))*(e/sin(c + d*x))^(3/2)),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(3/2)*(cos(c + d*x) + 1)), x)","F"
298,0,-1,120,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))*(e/sin(c + d*x))^(5/2)),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(5/2)*(cos(c + d*x) + 1)), x)","F"
299,0,-1,149,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))*(e/sin(c + d*x))^(7/2)),x)","\int \frac{\cos\left(c+d\,x\right)}{a\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(7/2)*(cos(c + d*x) + 1)), x)","F"
300,0,-1,268,0.000000,"\text{Not used}","int((e/sin(c + d*x))^(5/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(5/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
301,0,-1,250,0.000000,"\text{Not used}","int((e/sin(c + d*x))^(3/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(3/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
302,0,-1,201,0.000000,"\text{Not used}","int((e/sin(c + d*x))^(1/2)/(a + a/cos(c + d*x))^2,x)","\int \frac{{\cos\left(c+d\,x\right)}^2\,\sqrt{\frac{e}{\sin\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/sin(c + d*x))^(1/2))/(a^2*(cos(c + d*x) + 1)^2), x)","F"
303,0,-1,199,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(1/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,\sqrt{\frac{e}{\sin\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/sin(c + d*x))^(1/2)*(cos(c + d*x) + 1)^2), x)","F"
304,0,-1,213,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(3/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(3/2)*(cos(c + d*x) + 1)^2), x)","F"
305,0,-1,215,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(5/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(5/2)*(cos(c + d*x) + 1)^2), x)","F"
306,0,-1,172,0.000000,"\text{Not used}","int(1/((a + a/cos(c + d*x))^2*(e/sin(c + d*x))^(7/2)),x)","\int \frac{{\cos\left(c+d\,x\right)}^2}{a^2\,{\left(\frac{e}{\sin\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/sin(c + d*x))^(7/2)*(cos(c + d*x) + 1)^2), x)","F"