1,1,235,115,6.627642,"\text{Not used}","int(tan(c + d*x)^5*(a + a*sin(c + d*x)),x)","\frac{-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{15\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{23\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{8\,d}+\frac{7\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{8\,d}+\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"((11*a*tan(c/2 + (d*x)/2)^2)/2 - (15*a*tan(c/2 + (d*x)/2))/4 + (11*a*tan(c/2 + (d*x)/2)^3)/4 - 5*a*tan(c/2 + (d*x)/2)^4 + (11*a*tan(c/2 + (d*x)/2)^5)/4 + (11*a*tan(c/2 + (d*x)/2)^6)/2 - (15*a*tan(c/2 + (d*x)/2)^7)/4)/(d*(2*tan(c/2 + (d*x)/2)^3 - 2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^4 + 2*tan(c/2 + (d*x)/2)^5 - 2*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8 + 1)) - (23*a*log(tan(c/2 + (d*x)/2) - 1))/(8*d) + (7*a*log(tan(c/2 + (d*x)/2) + 1))/(8*d) + (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
2,1,154,71,6.469430,"\text{Not used}","int(tan(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{5\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{2\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{2\,d}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{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)}^3+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(5*a*log(tan(c/2 + (d*x)/2) - 1))/(2*d) - (a*log(tan(c/2 + (d*x)/2) + 1))/(2*d) + (3*a*tan(c/2 + (d*x)/2) - 4*a*tan(c/2 + (d*x)/2)^2 + 3*a*tan(c/2 + (d*x)/2)^3)/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^3 + tan(c/2 + (d*x)/2)^4 + 1)) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
3,1,43,30,6.623092,"\text{Not used}","int(tan(c + d*x)*(a + a*sin(c + d*x)),x)","-\frac{a\,\left(\sin\left(c+d\,x\right)+2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"-(a*(sin(c + d*x) + 2*log(tan(c/2 + (d*x)/2) - 1) - log(tan(c/2 + (d*x)/2)^2 + 1)))/d","B"
4,1,38,24,6.578424,"\text{Not used}","int(cot(c + d*x)*(a + a*sin(c + d*x)),x)","\frac{a\,\left(\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\sin\left(c+d\,x\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"(a*(log(tan(c/2 + (d*x)/2)) + sin(c + d*x) - log(tan(c/2 + (d*x)/2)^2 + 1)))/d","B"
5,1,146,54,6.540158,"\text{Not used}","int(cot(c + d*x)^3*(a + a*sin(c + d*x)),x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{10\,a\,{\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)}^2}{2}+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(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\right)}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + 2*a*tan(c/2 + (d*x)/2) + (a*tan(c/2 + (d*x)/2)^2)/2 + 10*a*tan(c/2 + (d*x)/2)^3)/(d*(4*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^4)) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*log(tan(c/2 + (d*x)/2)))/d","B"
6,1,207,81,6.696724,"\text{Not used}","int(cot(c + d*x)^5*(a + a*sin(c + d*x)),x)","\frac{7\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{46\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,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)}^4}{64\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(7*a*tan(c/2 + (d*x)/2))/(8*d) + ((11*a*tan(c/2 + (d*x)/2)^2)/4 - (2*a*tan(c/2 + (d*x)/2))/3 - a/4 + (40*a*tan(c/2 + (d*x)/2)^3)/3 + 3*a*tan(c/2 + (d*x)/2)^4 + 46*a*tan(c/2 + (d*x)/2)^5)/(d*(16*tan(c/2 + (d*x)/2)^4 + 16*tan(c/2 + (d*x)/2)^6)) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (3*a*tan(c/2 + (d*x)/2)^2)/(16*d) - (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (a*log(tan(c/2 + (d*x)/2)))/d","B"
7,1,267,115,7.367739,"\text{Not used}","int(cot(c + d*x)^7*(a + a*sin(c + d*x)),x)","\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,d}-\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,d}-\frac{19\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,d}-\frac{a\,\left(1920\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-1920\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{1920\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{51\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{29\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{128}+\frac{35\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{32}+\frac{25\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{128}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{80}-\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{384}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{160}+\frac{a}{384}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"(3*a*tan(c/2 + (d*x)/2)^3)/(32*d) - (29*a*tan(c/2 + (d*x)/2)^2)/(128*d) - (19*a*tan(c/2 + (d*x)/2))/(16*d) + (a*tan(c/2 + (d*x)/2)^4)/(32*d) - (a*tan(c/2 + (d*x)/2)^5)/(160*d) - (a*tan(c/2 + (d*x)/2)^6)/(384*d) - (a*(1920*log(tan(c/2 + (d*x)/2)) - 1920*log(tan(c/2 + (d*x)/2)^2 + 1)))/(1920*d) - (cot(c/2 + (d*x)/2)^6*(a/384 + (a*tan(c/2 + (d*x)/2))/160 - (11*a*tan(c/2 + (d*x)/2)^2)/384 - (7*a*tan(c/2 + (d*x)/2)^3)/80 + (25*a*tan(c/2 + (d*x)/2)^4)/128 + (35*a*tan(c/2 + (d*x)/2)^5)/32 + (29*a*tan(c/2 + (d*x)/2)^6)/128 + (51*a*tan(c/2 + (d*x)/2)^7)/16))/(d*(tan(c/2 + (d*x)/2)^2 + 1))","B"
8,1,351,101,11.222893,"\text{Not used}","int(tan(c + d*x)^6*(a + a*sin(c + d*x)),x)","\frac{\left(\frac{a\,\left(30\,c+30\,d\,x-30\right)}{15}-2\,a\,\left(c+d\,x\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{a\,\left(15\,c+15\,d\,x+60\right)}{15}-a\,\left(c+d\,x\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(4\,a\,\left(c+d\,x\right)-\frac{a\,\left(60\,c+60\,d\,x-40\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{a\,\left(30\,c+30\,d\,x-140\right)}{15}-2\,a\,\left(c+d\,x\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{44\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{15}+\left(2\,a\,\left(c+d\,x\right)-\frac{a\,\left(30\,c+30\,d\,x-52\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(\frac{a\,\left(60\,c+60\,d\,x-344\right)}{15}-4\,a\,\left(c+d\,x\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(a\,\left(c+d\,x\right)-\frac{a\,\left(15\,c+15\,d\,x-156\right)}{15}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(2\,a\,\left(c+d\,x\right)-\frac{a\,\left(30\,c+30\,d\,x-162\right)}{15}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\left(15\,c+15\,d\,x-96\right)}{15}-a\,\left(c+d\,x\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^5\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-a\,x","Not used",1,"((a*(15*c + 15*d*x - 96))/15 - tan(c/2 + (d*x)/2)*((a*(30*c + 30*d*x - 162))/15 - 2*a*(c + d*x)) - a*(c + d*x) + tan(c/2 + (d*x)/2)^8*((a*(15*c + 15*d*x + 60))/15 - a*(c + d*x)) + tan(c/2 + (d*x)/2)^9*((a*(30*c + 30*d*x - 30))/15 - 2*a*(c + d*x)) - tan(c/2 + (d*x)/2)^4*((a*(30*c + 30*d*x - 52))/15 - 2*a*(c + d*x)) - tan(c/2 + (d*x)/2)^7*((a*(60*c + 60*d*x - 40))/15 - 4*a*(c + d*x)) - tan(c/2 + (d*x)/2)^2*((a*(15*c + 15*d*x - 156))/15 - a*(c + d*x)) + tan(c/2 + (d*x)/2)^6*((a*(30*c + 30*d*x - 140))/15 - 2*a*(c + d*x)) + tan(c/2 + (d*x)/2)^3*((a*(60*c + 60*d*x - 344))/15 - 4*a*(c + d*x)) + (44*a*tan(c/2 + (d*x)/2)^5)/15)/(d*(tan(c/2 + (d*x)/2) - 1)^5*(tan(c/2 + (d*x)/2) + 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)) - a*x","B"
9,1,231,72,9.418272,"\text{Not used}","int(tan(c + d*x)^4*(a + a*sin(c + d*x)),x)","a\,x+\frac{\left(\frac{2\,a\,\left(3\,c+3\,d\,x\right)}{3}-\frac{a\,\left(6\,c+6\,d\,x-6\right)}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(\frac{a\,\left(3\,c+3\,d\,x-12\right)}{3}-\frac{a\,\left(3\,c+3\,d\,x\right)}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\left(\frac{a\,\left(3\,c+3\,d\,x\right)}{3}-\frac{a\,\left(3\,c+3\,d\,x-4\right)}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(\frac{a\,\left(6\,c+6\,d\,x-26\right)}{3}-\frac{2\,a\,\left(3\,c+3\,d\,x\right)}{3}\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a\,\left(3\,c+3\,d\,x\right)}{3}-\frac{a\,\left(3\,c+3\,d\,x-16\right)}{3}}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"a*x + ((a*(3*c + 3*d*x))/3 - (a*(3*c + 3*d*x - 16))/3 + tan(c/2 + (d*x)/2)^2*((a*(3*c + 3*d*x))/3 - (a*(3*c + 3*d*x - 4))/3) - tan(c/2 + (d*x)/2)^4*((a*(3*c + 3*d*x))/3 - (a*(3*c + 3*d*x - 12))/3) + tan(c/2 + (d*x)/2)^5*((2*a*(3*c + 3*d*x))/3 - (a*(6*c + 6*d*x - 6))/3) - tan(c/2 + (d*x)/2)*((2*a*(3*c + 3*d*x))/3 - (a*(6*c + 6*d*x - 26))/3) + (4*a*tan(c/2 + (d*x)/2)^3)/3)/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1))","B"
10,1,111,39,6.768189,"\text{Not used}","int(tan(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{\left(a\,\left(c+d\,x-2\right)-a\,\left(c+d\,x\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(a\,\left(c+d\,x\right)-a\,\left(c+d\,x-2\right)\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a\,\left(c+d\,x\right)+a\,\left(c+d\,x-4\right)}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-a\,x","Not used",1,"(tan(c/2 + (d*x)/2)*(a*(c + d*x) - a*(c + d*x - 2)) - tan(c/2 + (d*x)/2)^2*(a*(c + d*x) - a*(c + d*x - 2)) - a*(c + d*x) + a*(c + d*x - 4))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)) - a*x","B"
11,1,108,41,6.905613,"\text{Not used}","int(cot(c + d*x)^2*(a + a*sin(c + d*x)),x)","\frac{2\,a\,\mathrm{atan}\left(\frac{\sqrt{2}\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,\cos\left(\frac{c}{2}-\frac{\pi }{4}+\frac{d\,x}{2}\right)}\right)+a\,\ln\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\,\cos\left(c+d\,x\right)-\frac{a\,\sin\left(2\,c+2\,d\,x\right)}{2}}{d\,\sin\left(c+d\,x\right)}","Not used",1,"(2*a*atan((2^(1/2)*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2)))/(2*cos(c/2 - pi/4 + (d*x)/2))) + a*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a*cos(c + d*x) - (a*sin(2*c + 2*d*x))/2)/(d*sin(c + d*x))","B"
12,1,228,82,6.601790,"\text{Not used}","int(cot(c + d*x)^4*(a + a*sin(c + d*x)),x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+17\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{3}}{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)}^3\right)}-\frac{5\,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}{24\,d}-\frac{3\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{6\,a^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{6\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a/3 + a*tan(c/2 + (d*x)/2) - (14*a*tan(c/2 + (d*x)/2)^2)/3 + 17*a*tan(c/2 + (d*x)/2)^3 - 5*a*tan(c/2 + (d*x)/2)^4)/(d*(8*tan(c/2 + (d*x)/2)^3 + 8*tan(c/2 + (d*x)/2)^5)) - (5*a*tan(c/2 + (d*x)/2))/(8*d) + (a*tan(c/2 + (d*x)/2)^3)/(24*d) - (3*a*log(tan(c/2 + (d*x)/2)))/(2*d) - (2*a*atan((4*a^2)/(6*a^2 + 4*a^2*tan(c/2 + (d*x)/2)) - (6*a^2*tan(c/2 + (d*x)/2))/(6*a^2 + 4*a^2*tan(c/2 + (d*x)/2))))/d","B"
13,1,291,122,6.672848,"\text{Not used}","int(cot(c + d*x)^6*(a + a*sin(c + d*x)),x)","\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{22\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-72\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{59\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{15\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}}{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)}^5\right)}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{15\,a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}+\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{\frac{15\,a^2}{2}+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{15\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(\frac{15\,a^2}{2}+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}\right)}{d}","Not used",1,"(11*a*tan(c/2 + (d*x)/2))/(16*d) - (a/5 + (a*tan(c/2 + (d*x)/2))/2 - (32*a*tan(c/2 + (d*x)/2)^2)/15 - (15*a*tan(c/2 + (d*x)/2)^3)/2 + (59*a*tan(c/2 + (d*x)/2)^4)/3 - 72*a*tan(c/2 + (d*x)/2)^5 + 22*a*tan(c/2 + (d*x)/2)^6)/(d*(32*tan(c/2 + (d*x)/2)^5 + 32*tan(c/2 + (d*x)/2)^7)) - (a*tan(c/2 + (d*x)/2)^2)/(4*d) - (7*a*tan(c/2 + (d*x)/2)^3)/(96*d) + (a*tan(c/2 + (d*x)/2)^4)/(64*d) + (a*tan(c/2 + (d*x)/2)^5)/(160*d) + (15*a*log(tan(c/2 + (d*x)/2)))/(8*d) + (2*a*atan((4*a^2)/((15*a^2)/2 + 4*a^2*tan(c/2 + (d*x)/2)) - (15*a^2*tan(c/2 + (d*x)/2))/(2*((15*a^2)/2 + 4*a^2*tan(c/2 + (d*x)/2)))))/d","B"
14,1,283,119,6.566728,"\text{Not used}","int(tan(c + d*x)^5*(a + a*sin(c + d*x))^2,x)","\frac{4\,a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{4\,d}-\frac{\frac{15\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}-22\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{61\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}-36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{61\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-22\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{15\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+14\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{31\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{4\,d}","Not used",1,"(4*a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (a^2*log(tan(c/2 + (d*x)/2) + 1))/(4*d) - ((61*a^2*tan(c/2 + (d*x)/2)^3)/2 - 22*a^2*tan(c/2 + (d*x)/2)^2 - 36*a^2*tan(c/2 + (d*x)/2)^4 + (61*a^2*tan(c/2 + (d*x)/2)^5)/2 - 22*a^2*tan(c/2 + (d*x)/2)^6 + (15*a^2*tan(c/2 + (d*x)/2)^7)/2 + (15*a^2*tan(c/2 + (d*x)/2))/2)/(d*(8*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 12*tan(c/2 + (d*x)/2)^3 + 14*tan(c/2 + (d*x)/2)^4 - 12*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^6 - 4*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8 + 1)) - (31*a^2*log(tan(c/2 + (d*x)/2) - 1))/(4*d)","B"
15,1,204,72,7.110775,"\text{Not used}","int(tan(c + d*x)^3*(a + a*sin(c + d*x))^2,x)","\frac{6\,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)}^4+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}+\frac{6\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d}-\frac{3\,a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(8*a^2*tan(c/2 + (d*x)/2)^3 - 6*a^2*tan(c/2 + (d*x)/2)^2 - 6*a^2*tan(c/2 + (d*x)/2)^4 + 6*a^2*tan(c/2 + (d*x)/2)^5 + 6*a^2*tan(c/2 + (d*x)/2))/(d*(3*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) - 4*tan(c/2 + (d*x)/2)^3 + 3*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^6 + 1)) + (6*a^2*log(tan(c/2 + (d*x)/2) - 1))/d - (3*a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
16,1,178,52,6.669399,"\text{Not used}","int(tan(c + d*x)*(a + a*sin(c + d*x))^2,x)","-\frac{4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a^2\,\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)-2\,a^2\,\left(4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+1\right)\right)+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}-\frac{2\,a^2\,\left(2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{d}","Not used",1,"- (4*a^2*tan(c/2 + (d*x)/2)^3 - tan(c/2 + (d*x)/2)^2*(4*a^2*(2*log(tan(c/2 + (d*x)/2) - 1) - log(tan(c/2 + (d*x)/2)^2 + 1)) - 2*a^2*(4*log(tan(c/2 + (d*x)/2) - 1) - 2*log(tan(c/2 + (d*x)/2)^2 + 1) + 1)) + 4*a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^2) - (2*a^2*(2*log(tan(c/2 + (d*x)/2) - 1) - log(tan(c/2 + (d*x)/2)^2 + 1)))/d","B"
17,1,56,30,6.669266,"\text{Not used}","int(cot(c + d*x)^3*(a + a*sin(c + d*x))^2,x)","-\frac{a^2\,\left(2\,{\sin\left(c+d\,x\right)}^4+8\,{\sin\left(c+d\,x\right)}^3-{\sin\left(c+d\,x\right)}^2+8\,\sin\left(c+d\,x\right)+2\right)}{4\,d\,{\sin\left(c+d\,x\right)}^2}","Not used",1,"-(a^2*(8*sin(c + d*x) - sin(c + d*x)^2 + 8*sin(c + d*x)^3 + 2*sin(c + d*x)^4 + 2))/(4*d*sin(c + d*x)^2)","B"
18,1,392,132,11.181717,"\text{Not used}","int(cot(c + d*x)^7*(a + a*sin(c + d*x))^2,x)","-\frac{a^2\,\left(24\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-312\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-220\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3864\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-360\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+21000\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+3510\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+21000\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-360\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+3864\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-220\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-312\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+3840\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+7680\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+3840\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)-3840\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-7680\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-3840\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+5\right)}{1920\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"-(a^2*(24*tan(c/2 + (d*x)/2) - 20*tan(c/2 + (d*x)/2)^2 - 312*tan(c/2 + (d*x)/2)^3 - 220*tan(c/2 + (d*x)/2)^4 + 3864*tan(c/2 + (d*x)/2)^5 - 360*tan(c/2 + (d*x)/2)^6 + 21000*tan(c/2 + (d*x)/2)^7 + 3510*tan(c/2 + (d*x)/2)^8 + 21000*tan(c/2 + (d*x)/2)^9 - 360*tan(c/2 + (d*x)/2)^10 + 3864*tan(c/2 + (d*x)/2)^11 - 220*tan(c/2 + (d*x)/2)^12 - 312*tan(c/2 + (d*x)/2)^13 - 20*tan(c/2 + (d*x)/2)^14 + 24*tan(c/2 + (d*x)/2)^15 + 5*tan(c/2 + (d*x)/2)^16 + 3840*tan(c/2 + (d*x)/2)^6*log(tan(c/2 + (d*x)/2)^2 + 1) + 7680*tan(c/2 + (d*x)/2)^8*log(tan(c/2 + (d*x)/2)^2 + 1) + 3840*tan(c/2 + (d*x)/2)^10*log(tan(c/2 + (d*x)/2)^2 + 1) - 3840*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^6 - 7680*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^8 - 3840*log(tan(c/2 + (d*x)/2))*tan(c/2 + (d*x)/2)^10 + 5))/(1920*d*tan(c/2 + (d*x)/2)^6*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
19,1,392,149,10.917098,"\text{Not used}","int(tan(c + d*x)^6*(a + a*sin(c + d*x))^2,x)","-\frac{9\,a^2\,x}{2}-\frac{\frac{9\,a^2\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(18\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(180\,c+180\,d\,x-422\right)}{10}\right)+\frac{174\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}-\frac{a^2\,\left(45\,c+45\,d\,x-128\right)}{10}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(18\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(180\,c+180\,d\,x-90\right)}{10}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(27\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(270\,c+270\,d\,x-168\right)}{10}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{63\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(315\,c+315\,d\,x-360\right)}{10}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(27\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(270\,c+270\,d\,x-600\right)}{10}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(360\,c+360\,d\,x-424\right)}{10}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{63\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(315\,c+315\,d\,x-536\right)}{10}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(36\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(360\,c+360\,d\,x-600\right)}{10}\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^5\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"- (9*a^2*x)/2 - ((9*a^2*(c + d*x))/2 - tan(c/2 + (d*x)/2)*(18*a^2*(c + d*x) - (a^2*(180*c + 180*d*x - 422))/10) + (174*a^2*tan(c/2 + (d*x)/2)^5)/5 - (a^2*(45*c + 45*d*x - 128))/10 + tan(c/2 + (d*x)/2)^9*(18*a^2*(c + d*x) - (a^2*(180*c + 180*d*x - 90))/10) + tan(c/2 + (d*x)/2)^4*(27*a^2*(c + d*x) - (a^2*(270*c + 270*d*x - 168))/10) - tan(c/2 + (d*x)/2)^8*((63*a^2*(c + d*x))/2 - (a^2*(315*c + 315*d*x - 360))/10) - tan(c/2 + (d*x)/2)^6*(27*a^2*(c + d*x) - (a^2*(270*c + 270*d*x - 600))/10) - tan(c/2 + (d*x)/2)^3*(36*a^2*(c + d*x) - (a^2*(360*c + 360*d*x - 424))/10) + tan(c/2 + (d*x)/2)^2*((63*a^2*(c + d*x))/2 - (a^2*(315*c + 315*d*x - 536))/10) + tan(c/2 + (d*x)/2)^7*(36*a^2*(c + d*x) - (a^2*(360*c + 360*d*x - 600))/10))/(d*(tan(c/2 + (d*x)/2) - 1)^5*(tan(c/2 + (d*x)/2) + 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
20,1,287,120,10.071673,"\text{Not used}","int(tan(c + d*x)^4*(a + a*sin(c + d*x))^2,x)","\frac{7\,a^2\,x}{2}+\frac{\frac{7\,a^2\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{21\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(63\,c+63\,d\,x-150\right)}{6}\right)-\frac{a^2\,\left(21\,c+21\,d\,x-64\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{21\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(63\,c+63\,d\,x-42\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{35\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(105\,c+105\,d\,x-126\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{35\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(105\,c+105\,d\,x-194\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{49\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(147\,c+147\,d\,x-196\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{49\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(147\,c+147\,d\,x-252\right)}{6}\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(7*a^2*x)/2 + ((7*a^2*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((21*a^2*(c + d*x))/2 - (a^2*(63*c + 63*d*x - 150))/6) - (a^2*(21*c + 21*d*x - 64))/6 + tan(c/2 + (d*x)/2)^6*((21*a^2*(c + d*x))/2 - (a^2*(63*c + 63*d*x - 42))/6) - tan(c/2 + (d*x)/2)^5*((35*a^2*(c + d*x))/2 - (a^2*(105*c + 105*d*x - 126))/6) + tan(c/2 + (d*x)/2)^2*((35*a^2*(c + d*x))/2 - (a^2*(105*c + 105*d*x - 194))/6) + tan(c/2 + (d*x)/2)^4*((49*a^2*(c + d*x))/2 - (a^2*(147*c + 147*d*x - 196))/6) - tan(c/2 + (d*x)/2)^3*((49*a^2*(c + d*x))/2 - (a^2*(147*c + 147*d*x - 252))/6))/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
21,1,213,71,8.692958,"\text{Not used}","int(tan(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","-\frac{5\,a^2\,x}{2}-\frac{\frac{5\,a^2\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{5\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(5\,c+5\,d\,x-6\right)}{2}\right)-\frac{a^2\,\left(5\,c+5\,d\,x-16\right)}{2}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{5\,a^2\,\left(c+d\,x\right)}{2}-\frac{a^2\,\left(5\,c+5\,d\,x-10\right)}{2}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(5\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(10\,c+10\,d\,x-10\right)}{2}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(5\,a^2\,\left(c+d\,x\right)-\frac{a^2\,\left(10\,c+10\,d\,x-22\right)}{2}\right)}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"- (5*a^2*x)/2 - ((5*a^2*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((5*a^2*(c + d*x))/2 - (a^2*(5*c + 5*d*x - 6))/2) - (a^2*(5*c + 5*d*x - 16))/2 + tan(c/2 + (d*x)/2)^4*((5*a^2*(c + d*x))/2 - (a^2*(5*c + 5*d*x - 10))/2) - tan(c/2 + (d*x)/2)^3*(5*a^2*(c + d*x) - (a^2*(10*c + 10*d*x - 10))/2) + tan(c/2 + (d*x)/2)^2*(5*a^2*(c + d*x) - (a^2*(10*c + 10*d*x - 22))/2))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
22,1,123,45,6.582623,"\text{Not used}","int((a + a*sin(c + d*x))^2,x)","\frac{3\,a^2\,x}{2}-\frac{a^2\,\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)-a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-a^2\,\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}-4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2\,\left(\frac{3\,c}{2}+\frac{3\,d\,x}{2}\right)-a^2\,\left(3\,c+3\,d\,x-4\right)\right)+a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^2}","Not used",1,"(3*a^2*x)/2 - (a^2*((3*c)/2 + (3*d*x)/2) - a^2*tan(c/2 + (d*x)/2)^3 - a^2*((3*c)/2 + (3*d*x)/2 - 4) + tan(c/2 + (d*x)/2)^2*(2*a^2*((3*c)/2 + (3*d*x)/2) - a^2*(3*c + 3*d*x - 4)) + a^2*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^2)","B"
23,1,201,74,6.520321,"\text{Not used}","int(cot(c + d*x)^2*(a + a*sin(c + d*x))^2,x)","\frac{2\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{-3\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-a^2}{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{a^2\,\mathrm{atan}\left(\frac{a^4}{4\,a^4+a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}-\frac{4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^4+a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(2*a^2*log(tan(c/2 + (d*x)/2)))/d + (8*a^2*tan(c/2 + (d*x)/2)^3 - 3*a^2*tan(c/2 + (d*x)/2)^4 - a^2 + 8*a^2*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2) + 4*tan(c/2 + (d*x)/2)^3 + 2*tan(c/2 + (d*x)/2)^5)) + (a^2*atan(a^4/(4*a^4 + a^4*tan(c/2 + (d*x)/2)) - (4*a^4*tan(c/2 + (d*x)/2))/(4*a^4 + a^4*tan(c/2 + (d*x)/2))))/d + (a^2*tan(c/2 + (d*x)/2))/(2*d)","B"
24,1,293,98,6.516710,"\text{Not used}","int(cot(c + d*x)^4*(a + a*sin(c + d*x))^2,x)","\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{3\,a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^2\,\mathrm{atan}\left(\frac{a^4}{6\,a^4-a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{6\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^4-a^4\,\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)}^6+34\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{19\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^2}{3}}{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{a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}","Not used",1,"(a^2*tan(c/2 + (d*x)/2)^2)/(4*d) + (a^2*tan(c/2 + (d*x)/2)^3)/(24*d) - (3*a^2*log(tan(c/2 + (d*x)/2)))/d - (a^2*atan(a^4/(6*a^4 - a^4*tan(c/2 + (d*x)/2)) + (6*a^4*tan(c/2 + (d*x)/2))/(6*a^4 - a^4*tan(c/2 + (d*x)/2))))/d - (36*a^2*tan(c/2 + (d*x)/2)^3 - (a^2*tan(c/2 + (d*x)/2)^2)/3 + (19*a^2*tan(c/2 + (d*x)/2)^4)/3 + 34*a^2*tan(c/2 + (d*x)/2)^5 - 9*a^2*tan(c/2 + (d*x)/2)^6 + a^2/3 + 2*a^2*tan(c/2 + (d*x)/2))/(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)) - (a^2*tan(c/2 + (d*x)/2))/(8*d)","B"
25,1,398,160,6.469114,"\text{Not used}","int(tan(c + d*x)^7*(a + a*sin(c + d*x))^3,x)","\frac{\frac{105\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{4}-\frac{263\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{2}+\frac{1301\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{4}-582\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{1657\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2}-\frac{2767\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{1657\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{2}-582\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{1301\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-\frac{263\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{105\,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}-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-38\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+63\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+92\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-84\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+63\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-38\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+18\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}+\frac{209\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{8\,d}-\frac{a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{8\,d}-\frac{13\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"((1301*a^3*tan(c/2 + (d*x)/2)^3)/4 - (263*a^3*tan(c/2 + (d*x)/2)^2)/2 - 582*a^3*tan(c/2 + (d*x)/2)^4 + (1657*a^3*tan(c/2 + (d*x)/2)^5)/2 - (2767*a^3*tan(c/2 + (d*x)/2)^6)/3 + (1657*a^3*tan(c/2 + (d*x)/2)^7)/2 - 582*a^3*tan(c/2 + (d*x)/2)^8 + (1301*a^3*tan(c/2 + (d*x)/2)^9)/4 - (263*a^3*tan(c/2 + (d*x)/2)^10)/2 + (105*a^3*tan(c/2 + (d*x)/2)^11)/4 + (105*a^3*tan(c/2 + (d*x)/2))/4)/(d*(18*tan(c/2 + (d*x)/2)^2 - 6*tan(c/2 + (d*x)/2) - 38*tan(c/2 + (d*x)/2)^3 + 63*tan(c/2 + (d*x)/2)^4 - 84*tan(c/2 + (d*x)/2)^5 + 92*tan(c/2 + (d*x)/2)^6 - 84*tan(c/2 + (d*x)/2)^7 + 63*tan(c/2 + (d*x)/2)^8 - 38*tan(c/2 + (d*x)/2)^9 + 18*tan(c/2 + (d*x)/2)^10 - 6*tan(c/2 + (d*x)/2)^11 + tan(c/2 + (d*x)/2)^12 + 1)) + (209*a^3*log(tan(c/2 + (d*x)/2) - 1))/(8*d) - (a^3*log(tan(c/2 + (d*x)/2) + 1))/(8*d) - (13*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
26,1,262,91,7.460054,"\text{Not used}","int(tan(c + d*x)^3*(a + a*sin(c + d*x))^3,x)","\frac{14\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d}+\frac{14\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-14\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{98\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{100\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{98\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-14\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+14\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+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)}^5+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{7\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(14*a^3*log(tan(c/2 + (d*x)/2) - 1))/d + ((98*a^3*tan(c/2 + (d*x)/2)^3)/3 - 14*a^3*tan(c/2 + (d*x)/2)^2 - (100*a^3*tan(c/2 + (d*x)/2)^4)/3 + (98*a^3*tan(c/2 + (d*x)/2)^5)/3 - 14*a^3*tan(c/2 + (d*x)/2)^6 + 14*a^3*tan(c/2 + (d*x)/2)^7 + 14*a^3*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) - 6*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^4 - 6*tan(c/2 + (d*x)/2)^5 + 4*tan(c/2 + (d*x)/2)^6 - 2*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^8 + 1)) - (7*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
27,1,281,70,7.264818,"\text{Not used}","int(tan(c + d*x)*(a + a*sin(c + d*x))^3,x)","-\frac{\frac{56\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^3\,\left(12\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-6\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)-\frac{2\,a^3\,\left(36\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-18\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+9\right)}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^3\,\left(12\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-6\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)-\frac{2\,a^3\,\left(36\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-18\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)+9\right)}{3}\right)+8\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}-\frac{2\,a^3\,\left(12\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)-6\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\right)}{3\,d}","Not used",1,"- ((56*a^3*tan(c/2 + (d*x)/2)^3)/3 + 8*a^3*tan(c/2 + (d*x)/2)^5 - tan(c/2 + (d*x)/2)^2*(2*a^3*(12*log(tan(c/2 + (d*x)/2) - 1) - 6*log(tan(c/2 + (d*x)/2)^2 + 1)) - (2*a^3*(36*log(tan(c/2 + (d*x)/2) - 1) - 18*log(tan(c/2 + (d*x)/2)^2 + 1) + 9))/3) - tan(c/2 + (d*x)/2)^4*(2*a^3*(12*log(tan(c/2 + (d*x)/2) - 1) - 6*log(tan(c/2 + (d*x)/2)^2 + 1)) - (2*a^3*(36*log(tan(c/2 + (d*x)/2) - 1) - 18*log(tan(c/2 + (d*x)/2)^2 + 1) + 9))/3) + 8*a^3*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^3) - (2*a^3*(12*log(tan(c/2 + (d*x)/2) - 1) - 6*log(tan(c/2 + (d*x)/2)^2 + 1)))/(3*d)","B"
28,1,253,98,6.759747,"\text{Not used}","int(cot(c + d*x)^3*(a + a*sin(c + d*x))^3,x)","\frac{2\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{22\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{49\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+\frac{182\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+\frac{51\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+34\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^3}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,{\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\right)}-\frac{3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{2\,a^3\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(2*a^3*log(tan(c/2 + (d*x)/2)))/d - (a^3*tan(c/2 + (d*x)/2)^2)/(8*d) - ((3*a^3*tan(c/2 + (d*x)/2)^2)/2 + 34*a^3*tan(c/2 + (d*x)/2)^3 + (51*a^3*tan(c/2 + (d*x)/2)^4)/2 + (182*a^3*tan(c/2 + (d*x)/2)^5)/3 + (49*a^3*tan(c/2 + (d*x)/2)^6)/2 + 22*a^3*tan(c/2 + (d*x)/2)^7 + a^3/2 + 6*a^3*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^4 + 12*tan(c/2 + (d*x)/2)^6 + 4*tan(c/2 + (d*x)/2)^8)) - (3*a^3*tan(c/2 + (d*x)/2))/(2*d) - (2*a^3*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
29,1,438,180,11.047357,"\text{Not used}","int(tan(c + d*x)^6*(a + a*sin(c + d*x))^3,x)","-\frac{23\,a^3\,x}{2}-\frac{\frac{23\,a^3\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{115\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(1725\,c+1725\,d\,x-4750\right)}{30}\right)-\frac{a^3\,\left(345\,c+345\,d\,x-1088\right)}{30}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{115\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(1725\,c+1725\,d\,x-690\right)}{30}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{299\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(4485\,c+4485\,d\,x-3450\right)}{30}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{299\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(4485\,c+4485\,d\,x-10694\right)}{30}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{575\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(8625\,c+8625\,d\,x-8740\right)}{30}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{575\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(8625\,c+8625\,d\,x-18460\right)}{30}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(437\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(13110\,c+13110\,d\,x-16100\right)}{30}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(437\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(13110\,c+13110\,d\,x-25244\right)}{30}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(529\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(15870\,c+15870\,d\,x-23368\right)}{30}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(529\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(15870\,c+15870\,d\,x-26680\right)}{30}\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^5\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"- (23*a^3*x)/2 - ((23*a^3*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((115*a^3*(c + d*x))/2 - (a^3*(1725*c + 1725*d*x - 4750))/30) - (a^3*(345*c + 345*d*x - 1088))/30 + tan(c/2 + (d*x)/2)^10*((115*a^3*(c + d*x))/2 - (a^3*(1725*c + 1725*d*x - 690))/30) - tan(c/2 + (d*x)/2)^9*((299*a^3*(c + d*x))/2 - (a^3*(4485*c + 4485*d*x - 3450))/30) + tan(c/2 + (d*x)/2)^2*((299*a^3*(c + d*x))/2 - (a^3*(4485*c + 4485*d*x - 10694))/30) + tan(c/2 + (d*x)/2)^8*((575*a^3*(c + d*x))/2 - (a^3*(8625*c + 8625*d*x - 8740))/30) - tan(c/2 + (d*x)/2)^3*((575*a^3*(c + d*x))/2 - (a^3*(8625*c + 8625*d*x - 18460))/30) - tan(c/2 + (d*x)/2)^7*(437*a^3*(c + d*x) - (a^3*(13110*c + 13110*d*x - 16100))/30) + tan(c/2 + (d*x)/2)^4*(437*a^3*(c + d*x) - (a^3*(13110*c + 13110*d*x - 25244))/30) + tan(c/2 + (d*x)/2)^6*(529*a^3*(c + d*x) - (a^3*(15870*c + 15870*d*x - 23368))/30) - tan(c/2 + (d*x)/2)^5*(529*a^3*(c + d*x) - (a^3*(15870*c + 15870*d*x - 26680))/30))/(d*(tan(c/2 + (d*x)/2) - 1)^5*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
30,1,371,119,10.500410,"\text{Not used}","int(tan(c + d*x)^4*(a + a*sin(c + d*x))^3,x)","\frac{17\,a^3\,x}{2}+\frac{\frac{17\,a^3\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(153\,c+153\,d\,x-378\right)}{6}\right)-\frac{a^3\,\left(51\,c+51\,d\,x-160\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{51\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(153\,c+153\,d\,x-102\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(51\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(306\,c+306\,d\,x-306\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(51\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(306\,c+306\,d\,x-654\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(85\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(510\,c+510\,d\,x-578\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(85\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(510\,c+510\,d\,x-1022\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(102\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(612\,c+612\,d\,x-918\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(102\,a^3\,\left(c+d\,x\right)-\frac{a^3\,\left(612\,c+612\,d\,x-1002\right)}{6}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3}","Not used",1,"(17*a^3*x)/2 + ((17*a^3*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((51*a^3*(c + d*x))/2 - (a^3*(153*c + 153*d*x - 378))/6) - (a^3*(51*c + 51*d*x - 160))/6 + tan(c/2 + (d*x)/2)^8*((51*a^3*(c + d*x))/2 - (a^3*(153*c + 153*d*x - 102))/6) - tan(c/2 + (d*x)/2)^7*(51*a^3*(c + d*x) - (a^3*(306*c + 306*d*x - 306))/6) + tan(c/2 + (d*x)/2)^2*(51*a^3*(c + d*x) - (a^3*(306*c + 306*d*x - 654))/6) + tan(c/2 + (d*x)/2)^6*(85*a^3*(c + d*x) - (a^3*(510*c + 510*d*x - 578))/6) - tan(c/2 + (d*x)/2)^3*(85*a^3*(c + d*x) - (a^3*(510*c + 510*d*x - 1022))/6) - tan(c/2 + (d*x)/2)^5*(102*a^3*(c + d*x) - (a^3*(612*c + 612*d*x - 918))/6) + tan(c/2 + (d*x)/2)^4*(102*a^3*(c + d*x) - (a^3*(612*c + 612*d*x - 1002))/6))/(d*(tan(c/2 + (d*x)/2) - tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^3 - 1)^3)","B"
31,1,288,89,10.331458,"\text{Not used}","int(tan(c + d*x)^2*(a + a*sin(c + d*x))^3,x)","-\frac{11\,a^3\,x}{2}-\frac{\frac{11\,a^3\,\left(c+d\,x\right)}{2}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{11\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(33\,c+33\,d\,x-38\right)}{6}\right)-\frac{a^3\,\left(33\,c+33\,d\,x-104\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{11\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(33\,c+33\,d\,x-66\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-66\right)}{6}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-120\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-192\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{33\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(99\,c+99\,d\,x-246\right)}{6}\right)}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"- (11*a^3*x)/2 - ((11*a^3*(c + d*x))/2 - tan(c/2 + (d*x)/2)*((11*a^3*(c + d*x))/2 - (a^3*(33*c + 33*d*x - 38))/6) - (a^3*(33*c + 33*d*x - 104))/6 + tan(c/2 + (d*x)/2)^6*((11*a^3*(c + d*x))/2 - (a^3*(33*c + 33*d*x - 66))/6) - tan(c/2 + (d*x)/2)^5*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 66))/6) - tan(c/2 + (d*x)/2)^3*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 120))/6) + tan(c/2 + (d*x)/2)^4*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 192))/6) + tan(c/2 + (d*x)/2)^2*((33*a^3*(c + d*x))/2 - (a^3*(99*c + 99*d*x - 246))/6))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
32,1,156,63,8.918604,"\text{Not used}","int((a + a*sin(c + d*x))^3,x)","\frac{5\,a^3\,x}{2}-\frac{\frac{5\,a^3\,\left(c+d\,x\right)}{2}-3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{a^3\,\left(15\,c+15\,d\,x-44\right)}{6}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{15\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(45\,c+45\,d\,x-36\right)}{6}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{15\,a^3\,\left(c+d\,x\right)}{2}-\frac{a^3\,\left(45\,c+45\,d\,x-96\right)}{6}\right)+3\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^3}","Not used",1,"(5*a^3*x)/2 - ((5*a^3*(c + d*x))/2 - 3*a^3*tan(c/2 + (d*x)/2)^5 - (a^3*(15*c + 15*d*x - 44))/6 + tan(c/2 + (d*x)/2)^4*((15*a^3*(c + d*x))/2 - (a^3*(45*c + 45*d*x - 36))/6) + tan(c/2 + (d*x)/2)^2*((15*a^3*(c + d*x))/2 - (a^3*(45*c + 45*d*x - 96))/6) + 3*a^3*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^2 + 1)^3)","B"
33,1,264,92,6.773878,"\text{Not used}","int(cot(c + d*x)^2*(a + a*sin(c + d*x))^3,x)","\frac{3\,a^3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{a^3\,\mathrm{atan}\left(\frac{a^6}{6\,a^6-a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}+\frac{6\,a^6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6\,a^6-a^6\,\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)}{2\,d}+\frac{-7\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{32\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-a^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,{\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)}","Not used",1,"(3*a^3*log(tan(c/2 + (d*x)/2)))/d + (a^3*atan(a^6/(6*a^6 - a^6*tan(c/2 + (d*x)/2)) + (6*a^6*tan(c/2 + (d*x)/2))/(6*a^6 - a^6*tan(c/2 + (d*x)/2))))/d + (a^3*tan(c/2 + (d*x)/2))/(2*d) + (3*a^3*tan(c/2 + (d*x)/2)^2 + 24*a^3*tan(c/2 + (d*x)/2)^3 - 3*a^3*tan(c/2 + (d*x)/2)^4 + 8*a^3*tan(c/2 + (d*x)/2)^5 - 7*a^3*tan(c/2 + (d*x)/2)^6 - a^3 + (32*a^3*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^5 + 2*tan(c/2 + (d*x)/2)^7))","B"
34,1,379,129,7.880270,"\text{Not used}","int(tan(c + d*x)^5*(a + a*sin(c + d*x))^4,x)","\frac{25\,a^4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{50\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d}-\frac{50\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-150\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+\frac{950\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{3}-\frac{1700\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}+\frac{2180\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{2452\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{2180\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{1700\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{950\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-150\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+50\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+31\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+44\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-40\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+31\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"(25*a^4*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (50*a^4*log(tan(c/2 + (d*x)/2) - 1))/d - ((950*a^4*tan(c/2 + (d*x)/2)^3)/3 - 150*a^4*tan(c/2 + (d*x)/2)^2 - (1700*a^4*tan(c/2 + (d*x)/2)^4)/3 + (2180*a^4*tan(c/2 + (d*x)/2)^5)/3 - (2452*a^4*tan(c/2 + (d*x)/2)^6)/3 + (2180*a^4*tan(c/2 + (d*x)/2)^7)/3 - (1700*a^4*tan(c/2 + (d*x)/2)^8)/3 + (950*a^4*tan(c/2 + (d*x)/2)^9)/3 - 150*a^4*tan(c/2 + (d*x)/2)^10 + 50*a^4*tan(c/2 + (d*x)/2)^11 + 50*a^4*tan(c/2 + (d*x)/2))/(d*(10*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2) - 20*tan(c/2 + (d*x)/2)^3 + 31*tan(c/2 + (d*x)/2)^4 - 40*tan(c/2 + (d*x)/2)^5 + 44*tan(c/2 + (d*x)/2)^6 - 40*tan(c/2 + (d*x)/2)^7 + 31*tan(c/2 + (d*x)/2)^8 - 20*tan(c/2 + (d*x)/2)^9 + 10*tan(c/2 + (d*x)/2)^10 - 4*tan(c/2 + (d*x)/2)^11 + tan(c/2 + (d*x)/2)^12 + 1))","B"
35,1,320,107,7.564321,"\text{Not used}","int(tan(c + d*x)^3*(a + a*sin(c + d*x))^4,x)","\frac{32\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d}+\frac{32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\frac{320\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{340\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{424\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{340\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{320\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+32\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}-\frac{16\,a^4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(32*a^4*log(tan(c/2 + (d*x)/2) - 1))/d + ((320*a^4*tan(c/2 + (d*x)/2)^3)/3 - 32*a^4*tan(c/2 + (d*x)/2)^2 - (340*a^4*tan(c/2 + (d*x)/2)^4)/3 + (424*a^4*tan(c/2 + (d*x)/2)^5)/3 - (340*a^4*tan(c/2 + (d*x)/2)^6)/3 + (320*a^4*tan(c/2 + (d*x)/2)^7)/3 - 32*a^4*tan(c/2 + (d*x)/2)^8 + 32*a^4*tan(c/2 + (d*x)/2)^9 + 32*a^4*tan(c/2 + (d*x)/2))/(d*(5*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2) - 8*tan(c/2 + (d*x)/2)^3 + 10*tan(c/2 + (d*x)/2)^4 - 12*tan(c/2 + (d*x)/2)^5 + 10*tan(c/2 + (d*x)/2)^6 - 8*tan(c/2 + (d*x)/2)^7 + 5*tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^9 + tan(c/2 + (d*x)/2)^10 + 1)) - (16*a^4*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
36,1,131,88,6.632736,"\text{Not used}","int(tan(c + d*x)*(a + a*sin(c + d*x))^4,x)","\frac{8\,a^4\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}-\frac{28\,a^4\,\sin\left(c+d\,x\right)}{3\,d}-\frac{16\,a^4\,\ln\left(\frac{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{d}+\frac{4\,a^4\,{\cos\left(c+d\,x\right)}^2}{d}-\frac{a^4\,{\cos\left(c+d\,x\right)}^4}{4\,d}+\frac{4\,a^4\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}","Not used",1,"(8*a^4*log(1/cos(c/2 + (d*x)/2)^2))/d - (28*a^4*sin(c + d*x))/(3*d) - (16*a^4*log((cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))/cos(c/2 + (d*x)/2)))/d + (4*a^4*cos(c + d*x)^2)/d - (a^4*cos(c + d*x)^4)/(4*d) + (4*a^4*cos(c + d*x)^2*sin(c + d*x))/(3*d)","B"
37,1,298,102,6.397769,"\text{Not used}","int(cot(c + d*x)^3*(a + a*sin(c + d*x))^4,x)","\frac{5\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{81\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}+\frac{224\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}+98\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{272\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+43\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^4}{2}}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\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\right)}-\frac{2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}-\frac{5\,a^4\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(5*a^4*log(tan(c/2 + (d*x)/2)))/d - (a^4*tan(c/2 + (d*x)/2)^2)/(8*d) - (2*a^4*tan(c/2 + (d*x)/2)^2 + 32*a^4*tan(c/2 + (d*x)/2)^3 + 43*a^4*tan(c/2 + (d*x)/2)^4 + (272*a^4*tan(c/2 + (d*x)/2)^5)/3 + 98*a^4*tan(c/2 + (d*x)/2)^6 + (224*a^4*tan(c/2 + (d*x)/2)^7)/3 + (81*a^4*tan(c/2 + (d*x)/2)^8)/2 + 8*a^4*tan(c/2 + (d*x)/2)^9 + a^4/2 + 8*a^4*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 16*tan(c/2 + (d*x)/2)^4 + 24*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8 + 4*tan(c/2 + (d*x)/2)^10)) - (2*a^4*tan(c/2 + (d*x)/2))/d - (5*a^4*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
38,1,437,143,11.050167,"\text{Not used}","int(tan(c + d*x)^4*(a + a*sin(c + d*x))^4,x)","\frac{163\,a^4\,x}{8}+\frac{\frac{163\,a^4\,\left(c+d\,x\right)}{8}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{489\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(1467\,c+1467\,d\,x-3630\right)}{24}\right)-\frac{a^4\,\left(489\,c+489\,d\,x-1536\right)}{24}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(\frac{489\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(1467\,c+1467\,d\,x-978\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{1141\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(3423\,c+3423\,d\,x-2934\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{1141\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(3423\,c+3423\,d\,x-7818\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{2119\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(6357\,c+6357\,d\,x-6520\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2119\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(6357\,c+6357\,d\,x-13448\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{1467\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(8802\,c+8802\,d\,x-11736\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{1467\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(8802\,c+8802\,d\,x-15912\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{1793\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(10758\,c+10758\,d\,x-15364\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{1793\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(10758\,c+10758\,d\,x-18428\right)}{24}\right)}{d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(163*a^4*x)/8 + ((163*a^4*(c + d*x))/8 - tan(c/2 + (d*x)/2)*((489*a^4*(c + d*x))/8 - (a^4*(1467*c + 1467*d*x - 3630))/24) - (a^4*(489*c + 489*d*x - 1536))/24 + tan(c/2 + (d*x)/2)^10*((489*a^4*(c + d*x))/8 - (a^4*(1467*c + 1467*d*x - 978))/24) - tan(c/2 + (d*x)/2)^9*((1141*a^4*(c + d*x))/8 - (a^4*(3423*c + 3423*d*x - 2934))/24) + tan(c/2 + (d*x)/2)^2*((1141*a^4*(c + d*x))/8 - (a^4*(3423*c + 3423*d*x - 7818))/24) + tan(c/2 + (d*x)/2)^8*((2119*a^4*(c + d*x))/8 - (a^4*(6357*c + 6357*d*x - 6520))/24) - tan(c/2 + (d*x)/2)^3*((2119*a^4*(c + d*x))/8 - (a^4*(6357*c + 6357*d*x - 13448))/24) - tan(c/2 + (d*x)/2)^7*((1467*a^4*(c + d*x))/4 - (a^4*(8802*c + 8802*d*x - 11736))/24) + tan(c/2 + (d*x)/2)^4*((1467*a^4*(c + d*x))/4 - (a^4*(8802*c + 8802*d*x - 15912))/24) + tan(c/2 + (d*x)/2)^6*((1793*a^4*(c + d*x))/4 - (a^4*(10758*c + 10758*d*x - 15364))/24) - tan(c/2 + (d*x)/2)^5*((1793*a^4*(c + d*x))/4 - (a^4*(10758*c + 10758*d*x - 18428))/24))/(d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
39,1,363,113,10.255104,"\text{Not used}","int(tan(c + d*x)^2*(a + a*sin(c + d*x))^4,x)","-\frac{95\,a^4\,x}{8}-\frac{\frac{95\,a^4\,\left(c+d\,x\right)}{8}-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{95\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(285\,c+285\,d\,x-326\right)}{24}\right)-\frac{a^4\,\left(285\,c+285\,d\,x-896\right)}{24}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(\frac{95\,a^4\,\left(c+d\,x\right)}{8}-\frac{a^4\,\left(285\,c+285\,d\,x-570\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{95\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(1140\,c+1140\,d\,x-570\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{95\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(1140\,c+1140\,d\,x-1430\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{95\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(1140\,c+1140\,d\,x-2154\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{95\,a^4\,\left(c+d\,x\right)}{2}-\frac{a^4\,\left(1140\,c+1140\,d\,x-3014\right)}{24}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{285\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(1710\,c+1710\,d\,x-1770\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{285\,a^4\,\left(c+d\,x\right)}{4}-\frac{a^4\,\left(1710\,c+1710\,d\,x-3606\right)}{24}\right)}{d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"- (95*a^4*x)/8 - ((95*a^4*(c + d*x))/8 - tan(c/2 + (d*x)/2)*((95*a^4*(c + d*x))/8 - (a^4*(285*c + 285*d*x - 326))/24) - (a^4*(285*c + 285*d*x - 896))/24 + tan(c/2 + (d*x)/2)^8*((95*a^4*(c + d*x))/8 - (a^4*(285*c + 285*d*x - 570))/24) - tan(c/2 + (d*x)/2)^7*((95*a^4*(c + d*x))/2 - (a^4*(1140*c + 1140*d*x - 570))/24) - tan(c/2 + (d*x)/2)^3*((95*a^4*(c + d*x))/2 - (a^4*(1140*c + 1140*d*x - 1430))/24) + tan(c/2 + (d*x)/2)^6*((95*a^4*(c + d*x))/2 - (a^4*(1140*c + 1140*d*x - 2154))/24) + tan(c/2 + (d*x)/2)^2*((95*a^4*(c + d*x))/2 - (a^4*(1140*c + 1140*d*x - 3014))/24) - tan(c/2 + (d*x)/2)^5*((285*a^4*(c + d*x))/4 - (a^4*(1710*c + 1710*d*x - 1770))/24) + tan(c/2 + (d*x)/2)^4*((285*a^4*(c + d*x))/4 - (a^4*(1710*c + 1710*d*x - 3606))/24))/(d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
40,1,237,87,8.590820,"\text{Not used}","int((a + a*sin(c + d*x))^4,x)","\frac{35\,a^4\,x}{8}-\frac{\frac{35\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{4}-\frac{35\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{27\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+\frac{a^4\,\left(105\,c+105\,d\,x\right)}{24}-\frac{a^4\,\left(105\,c+105\,d\,x-320\right)}{24}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^4\,\left(105\,c+105\,d\,x\right)}{6}-\frac{a^4\,\left(420\,c+420\,d\,x-192\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^4\,\left(105\,c+105\,d\,x\right)}{6}-\frac{a^4\,\left(420\,c+420\,d\,x-1088\right)}{24}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^4\,\left(105\,c+105\,d\,x\right)}{4}-\frac{a^4\,\left(630\,c+630\,d\,x-960\right)}{24}\right)+\frac{27\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}^4}","Not used",1,"(35*a^4*x)/8 - ((35*a^4*tan(c/2 + (d*x)/2)^3)/4 - (35*a^4*tan(c/2 + (d*x)/2)^5)/4 - (27*a^4*tan(c/2 + (d*x)/2)^7)/4 + (a^4*(105*c + 105*d*x))/24 - (a^4*(105*c + 105*d*x - 320))/24 + tan(c/2 + (d*x)/2)^6*((a^4*(105*c + 105*d*x))/6 - (a^4*(420*c + 420*d*x - 192))/24) + tan(c/2 + (d*x)/2)^2*((a^4*(105*c + 105*d*x))/6 - (a^4*(420*c + 420*d*x - 1088))/24) + tan(c/2 + (d*x)/2)^4*((a^4*(105*c + 105*d*x))/4 - (a^4*(630*c + 630*d*x - 960))/24) + (27*a^4*tan(c/2 + (d*x)/2))/4)/(d*(tan(c/2 + (d*x)/2)^2 + 1)^4)","B"
41,1,295,116,6.779028,"\text{Not used}","int(cot(c + d*x)^2*(a + a*sin(c + d*x))^4,x)","\frac{4\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{17\,a^4\,\mathrm{atan}\left(\frac{289\,a^8}{16\,\left(34\,a^8-\frac{289\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{34\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{34\,a^8-\frac{289\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}}\right)}{4\,d}+\frac{-\frac{25\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{2}-\frac{39\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{2}+32\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{19\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{128\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{15\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{32\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-a^4}{d\,\left(2\,{\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+12\,{\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+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(4*a^4*log(tan(c/2 + (d*x)/2)))/d + (17*a^4*atan((289*a^8)/(16*(34*a^8 - (289*a^8*tan(c/2 + (d*x)/2))/16)) + (34*a^8*tan(c/2 + (d*x)/2))/(34*a^8 - (289*a^8*tan(c/2 + (d*x)/2))/16)))/(4*d) + ((15*a^4*tan(c/2 + (d*x)/2)^2)/2 + (128*a^4*tan(c/2 + (d*x)/2)^3)/3 + (19*a^4*tan(c/2 + (d*x)/2)^4)/2 + 32*a^4*tan(c/2 + (d*x)/2)^5 - (39*a^4*tan(c/2 + (d*x)/2)^6)/2 - (25*a^4*tan(c/2 + (d*x)/2)^8)/2 - a^4 + (32*a^4*tan(c/2 + (d*x)/2))/3)/(d*(2*tan(c/2 + (d*x)/2) + 8*tan(c/2 + (d*x)/2)^3 + 12*tan(c/2 + (d*x)/2)^5 + 8*tan(c/2 + (d*x)/2)^7 + 2*tan(c/2 + (d*x)/2)^9)) + (a^4*tan(c/2 + (d*x)/2))/(2*d)","B"
42,1,384,140,6.709322,"\text{Not used}","int(cot(c + d*x)^4*(a + a*sin(c + d*x))^4,x)","\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}+\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{2\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{61\,a^4\,\mathrm{atan}\left(\frac{3721\,a^8}{16\,\left(61\,a^8-\frac{3721\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}+\frac{61\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{61\,a^8-\frac{3721\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}}\right)}{4\,d}+\frac{19\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}-\frac{-19\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-60\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\frac{67\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-48\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\frac{508\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+116\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-\frac{16\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{61\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+4\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^4}{3}}{d\,\left(8\,{\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+48\,{\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+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}","Not used",1,"(a^4*tan(c/2 + (d*x)/2)^2)/(2*d) + (a^4*tan(c/2 + (d*x)/2)^3)/(24*d) - (2*a^4*log(tan(c/2 + (d*x)/2)))/d - (61*a^4*atan((3721*a^8)/(16*(61*a^8 - (3721*a^8*tan(c/2 + (d*x)/2))/16)) + (61*a^8*tan(c/2 + (d*x)/2))/(61*a^8 - (3721*a^8*tan(c/2 + (d*x)/2))/16)))/(4*d) + (19*a^4*tan(c/2 + (d*x)/2))/(8*d) - ((61*a^4*tan(c/2 + (d*x)/2)^2)/3 - (16*a^4*tan(c/2 + (d*x)/2)^3)/3 + 116*a^4*tan(c/2 + (d*x)/2)^4 + (8*a^4*tan(c/2 + (d*x)/2)^5)/3 + (508*a^4*tan(c/2 + (d*x)/2)^6)/3 - 48*a^4*tan(c/2 + (d*x)/2)^7 + (67*a^4*tan(c/2 + (d*x)/2)^8)/3 - 60*a^4*tan(c/2 + (d*x)/2)^9 - 19*a^4*tan(c/2 + (d*x)/2)^10 + a^4/3 + 4*a^4*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 32*tan(c/2 + (d*x)/2)^5 + 48*tan(c/2 + (d*x)/2)^7 + 32*tan(c/2 + (d*x)/2)^9 + 8*tan(c/2 + (d*x)/2)^11))","B"
43,1,454,198,6.853207,"\text{Not used}","int(cot(c + d*x)^6*(a + a*sin(c + d*x))^4,x)","\frac{17\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}-\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,d}+\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16\,d}+\frac{a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{5\,a^4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{97\,a^4\,\mathrm{atan}\left(\frac{9409\,a^8}{16\,\left(\frac{485\,a^8}{4}+\frac{9409\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}-\frac{485\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\left(\frac{485\,a^8}{4}+\frac{9409\,a^8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}\right)}\right)}{4\,d}-\frac{-58\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+496\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-\frac{1567\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{3}+962\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-\frac{18437\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{15}+\frac{2296\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{3986\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{868\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{2312\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}-8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{97\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a^4}{5}}{d\,\left(32\,{\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}+192\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+128\,{\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{89\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}","Not used",1,"(17*a^4*tan(c/2 + (d*x)/2)^3)/(96*d) - (a^4*tan(c/2 + (d*x)/2)^2)/(2*d) + (a^4*tan(c/2 + (d*x)/2)^4)/(16*d) + (a^4*tan(c/2 + (d*x)/2)^5)/(160*d) - (5*a^4*log(tan(c/2 + (d*x)/2)))/(2*d) - (97*a^4*atan((9409*a^8)/(16*((485*a^8)/4 + (9409*a^8*tan(c/2 + (d*x)/2))/16)) - (485*a^8*tan(c/2 + (d*x)/2))/(4*((485*a^8)/4 + (9409*a^8*tan(c/2 + (d*x)/2))/16))))/(4*d) - ((97*a^4*tan(c/2 + (d*x)/2)^2)/15 - 8*a^4*tan(c/2 + (d*x)/2)^3 - (2312*a^4*tan(c/2 + (d*x)/2)^4)/15 + (868*a^4*tan(c/2 + (d*x)/2)^5)/3 - (3986*a^4*tan(c/2 + (d*x)/2)^6)/5 + (2296*a^4*tan(c/2 + (d*x)/2)^7)/3 - (18437*a^4*tan(c/2 + (d*x)/2)^8)/15 + 962*a^4*tan(c/2 + (d*x)/2)^9 - (1567*a^4*tan(c/2 + (d*x)/2)^10)/3 + 496*a^4*tan(c/2 + (d*x)/2)^11 - 58*a^4*tan(c/2 + (d*x)/2)^12 + a^4/5 + 2*a^4*tan(c/2 + (d*x)/2))/(d*(32*tan(c/2 + (d*x)/2)^5 + 128*tan(c/2 + (d*x)/2)^7 + 192*tan(c/2 + (d*x)/2)^9 + 128*tan(c/2 + (d*x)/2)^11 + 32*tan(c/2 + (d*x)/2)^13)) - (89*a^4*tan(c/2 + (d*x)/2))/(16*d)","B"
44,1,388,130,10.740145,"\text{Not used}","int(tan(c + d*x)^7/(a + a*sin(c + d*x)),x)","\frac{\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}-\frac{245\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}-\frac{595\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{96}+\frac{791\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{231\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{16}-\frac{25\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{16}+\frac{231\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{16}+\frac{791\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{192}-\frac{595\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{96}-\frac{245\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}+\frac{35\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-40\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+30\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+9\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{35\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a\,d}","Not used",1,"((35*tan(c/2 + (d*x)/2))/64 + (35*tan(c/2 + (d*x)/2)^2)/32 - (245*tan(c/2 + (d*x)/2)^3)/96 - (595*tan(c/2 + (d*x)/2)^4)/96 + (791*tan(c/2 + (d*x)/2)^5)/192 + (231*tan(c/2 + (d*x)/2)^6)/16 - (25*tan(c/2 + (d*x)/2)^7)/16 + (231*tan(c/2 + (d*x)/2)^8)/16 + (791*tan(c/2 + (d*x)/2)^9)/192 - (595*tan(c/2 + (d*x)/2)^10)/96 - (245*tan(c/2 + (d*x)/2)^11)/96 + (35*tan(c/2 + (d*x)/2)^12)/32 + (35*tan(c/2 + (d*x)/2)^13)/64)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 5*a*tan(c/2 + (d*x)/2)^2 - 12*a*tan(c/2 + (d*x)/2)^3 + 9*a*tan(c/2 + (d*x)/2)^4 + 30*a*tan(c/2 + (d*x)/2)^5 - 5*a*tan(c/2 + (d*x)/2)^6 - 40*a*tan(c/2 + (d*x)/2)^7 - 5*a*tan(c/2 + (d*x)/2)^8 + 30*a*tan(c/2 + (d*x)/2)^9 + 9*a*tan(c/2 + (d*x)/2)^10 - 12*a*tan(c/2 + (d*x)/2)^11 - 5*a*tan(c/2 + (d*x)/2)^12 + 2*a*tan(c/2 + (d*x)/2)^13 + a*tan(c/2 + (d*x)/2)^14)) - (35*atanh(tan(c/2 + (d*x)/2)))/(64*a*d)","B"
45,1,281,106,10.425274,"\text{Not used}","int(tan(c + d*x)^5/(a + a*sin(c + d*x)),x)","\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}-\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{8}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}-\frac{55\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{12}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}-\frac{55\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{12}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-8\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,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)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(5*atanh(tan(c/2 + (d*x)/2)))/(8*a*d) - ((5*tan(c/2 + (d*x)/2))/8 + (5*tan(c/2 + (d*x)/2)^2)/4 - (5*tan(c/2 + (d*x)/2)^3)/3 - (55*tan(c/2 + (d*x)/2)^4)/12 + (3*tan(c/2 + (d*x)/2)^5)/4 - (55*tan(c/2 + (d*x)/2)^6)/12 - (5*tan(c/2 + (d*x)/2)^7)/3 + (5*tan(c/2 + (d*x)/2)^8)/4 + (5*tan(c/2 + (d*x)/2)^9)/8)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - 3*a*tan(c/2 + (d*x)/2)^2 - 8*a*tan(c/2 + (d*x)/2)^3 + 2*a*tan(c/2 + (d*x)/2)^4 + 12*a*tan(c/2 + (d*x)/2)^5 + 2*a*tan(c/2 + (d*x)/2)^6 - 8*a*tan(c/2 + (d*x)/2)^7 - 3*a*tan(c/2 + (d*x)/2)^8 + 2*a*tan(c/2 + (d*x)/2)^9 + a*tan(c/2 + (d*x)/2)^10))","B"
46,1,172,82,9.111090,"\text{Not used}","int(tan(c + d*x)^3/(a + a*sin(c + d*x)),x)","\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{3\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a\,d}","Not used",1,"((3*tan(c/2 + (d*x)/2))/4 + (3*tan(c/2 + (d*x)/2)^2)/2 - tan(c/2 + (d*x)/2)^3/2 + (3*tan(c/2 + (d*x)/2)^4)/2 + (3*tan(c/2 + (d*x)/2)^5)/4)/(d*(a + 2*a*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2 - 4*a*tan(c/2 + (d*x)/2)^3 - a*tan(c/2 + (d*x)/2)^4 + 2*a*tan(c/2 + (d*x)/2)^5 + a*tan(c/2 + (d*x)/2)^6)) - (3*atanh(tan(c/2 + (d*x)/2)))/(4*a*d)","B"
47,1,61,37,6.658292,"\text{Not used}","int(tan(c + d*x)/(a + a*sin(c + d*x)),x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"atanh(tan(c/2 + (d*x)/2))/(a*d) - tan(c/2 + (d*x)/2)/(d*(a + 2*a*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))","B"
48,1,32,32,6.530779,"\text{Not used}","int(cot(c + d*x)/(a + a*sin(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)) - 2*log(tan(c/2 + (d*x)/2) + 1))/(a*d)","B"
49,1,23,32,6.576219,"\text{Not used}","int(cot(c + d*x)^3/(a + a*sin(c + d*x)),x)","\frac{\sin\left(c+d\,x\right)-\frac{1}{2}}{a\,d\,{\sin\left(c+d\,x\right)}^2}","Not used",1,"(sin(c + d*x) - 1/2)/(a*d*sin(c + d*x)^2)","B"
50,1,45,51,6.560305,"\text{Not used}","int(cot(c + d*x)^5/(a + a*sin(c + d*x)),x)","\frac{-{\sin\left(c+d\,x\right)}^3+\frac{{\sin\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)}{3}-\frac{1}{4}}{a\,d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"(sin(c + d*x)/3 + sin(c + d*x)^2/2 - sin(c + d*x)^3 - 1/4)/(a*d*sin(c + d*x)^4)","B"
51,1,63,68,6.794563,"\text{Not used}","int(cot(c + d*x)^7/(a + a*sin(c + d*x)),x)","\frac{{\sin\left(c+d\,x\right)}^5-\frac{{\sin\left(c+d\,x\right)}^4}{2}-\frac{2\,{\sin\left(c+d\,x\right)}^3}{3}+\frac{{\sin\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)}{5}-\frac{1}{6}}{a\,d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"(sin(c + d*x)/5 + sin(c + d*x)^2/2 - (2*sin(c + d*x)^3)/3 - sin(c + d*x)^4/2 + sin(c + d*x)^5 - 1/6)/(a*d*sin(c + d*x)^6)","B"
52,1,83,84,6.766912,"\text{Not used}","int(cot(c + d*x)^9/(a + a*sin(c + d*x)),x)","\frac{-{\sin\left(c+d\,x\right)}^7+\frac{{\sin\left(c+d\,x\right)}^6}{2}+{\sin\left(c+d\,x\right)}^5-\frac{3\,{\sin\left(c+d\,x\right)}^4}{4}-\frac{3\,{\sin\left(c+d\,x\right)}^3}{5}+\frac{{\sin\left(c+d\,x\right)}^2}{2}+\frac{\sin\left(c+d\,x\right)}{7}-\frac{1}{8}}{a\,d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"(sin(c + d*x)/7 + sin(c + d*x)^2/2 - (3*sin(c + d*x)^3)/5 - (3*sin(c + d*x)^4)/4 + sin(c + d*x)^5 + sin(c + d*x)^6/2 - sin(c + d*x)^7 - 1/8)/(a*d*sin(c + d*x)^8)","B"
53,1,99,84,8.485567,"\text{Not used}","int(tan(c + d*x)^6/(a + a*sin(c + d*x)),x)","-\frac{32\,\left(20\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{35\,a\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^5\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^7}","Not used",1,"-(32*(2*tan(c/2 + (d*x)/2) - 4*tan(c/2 + (d*x)/2)^2 - 10*tan(c/2 + (d*x)/2)^3 + 5*tan(c/2 + (d*x)/2)^4 + 20*tan(c/2 + (d*x)/2)^5 + 1))/(35*a*d*(tan(c/2 + (d*x)/2) - 1)^5*(tan(c/2 + (d*x)/2) + 1)^7)","B"
54,1,73,69,6.732080,"\text{Not used}","int(tan(c + d*x)^4/(a + a*sin(c + d*x)),x)","\frac{16\,\left(-6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{15\,a\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}^3\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^5}","Not used",1,"(16*(2*tan(c/2 + (d*x)/2) - 2*tan(c/2 + (d*x)/2)^2 - 6*tan(c/2 + (d*x)/2)^3 + 1))/(15*a*d*(tan(c/2 + (d*x)/2) - 1)^3*(tan(c/2 + (d*x)/2) + 1)^5)","B"
55,1,47,50,6.401864,"\text{Not used}","int(tan(c + d*x)^2/(a + a*sin(c + d*x)),x)","-\frac{4\,\left(2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{3\,a\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3}","Not used",1,"-(4*(2*tan(c/2 + (d*x)/2) + 1))/(3*a*d*(tan(c/2 + (d*x)/2) - 1)*(tan(c/2 + (d*x)/2) + 1)^3)","B"
56,1,21,23,6.428412,"\text{Not used}","int(1/(a + a*sin(c + d*x)),x)","-\frac{2}{a\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"-2/(a*d*(tan(c/2 + (d*x)/2) + 1))","B"
57,1,25,29,6.636182,"\text{Not used}","int(cot(c + d*x)^2/(a + a*sin(c + d*x)),x)","-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)+\mathrm{cot}\left(c+d\,x\right)}{a\,d}","Not used",1,"-(log(tan(c/2 + (d*x)/2)) + cot(c + d*x))/(a*d)","B"
58,1,115,58,6.634818,"\text{Not used}","int(cot(c + d*x)^4/(a + a*sin(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{3}\right)}{8\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) + log(tan(c/2 + (d*x)/2))/(2*a*d) - tan(c/2 + (d*x)/2)/(8*a*d) + (cot(c/2 + (d*x)/2)^3*(tan(c/2 + (d*x)/2) + tan(c/2 + (d*x)/2)^2 - 1/3))/(8*a*d)","B"
59,1,183,82,6.661800,"\text{Not used}","int(cot(c + d*x)^6/(a + a*sin(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,a\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{1}{5}\right)}{32\,a\,d}","Not used",1,"tan(c/2 + (d*x)/2)^2/(8*a*d) - tan(c/2 + (d*x)/2)^3/(32*a*d) - tan(c/2 + (d*x)/2)^4/(64*a*d) + tan(c/2 + (d*x)/2)^5/(160*a*d) - (3*log(tan(c/2 + (d*x)/2)))/(8*a*d) + tan(c/2 + (d*x)/2)/(16*a*d) - (cot(c/2 + (d*x)/2)^5*(4*tan(c/2 + (d*x)/2)^3 - tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)/2 + 2*tan(c/2 + (d*x)/2)^4 + 1/5))/(32*a*d)","B"
60,1,387,106,8.220850,"\text{Not used}","int(cot(c + d*x)^8/(a + a*sin(c + d*x)),x)","\frac{3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-3\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}-7\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+7\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)-21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+105\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+315\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-63\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+21\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+840\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{2688\,a\,d\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}","Not used",1,"(3*sin(c/2 + (d*x)/2)^14 - 3*cos(c/2 + (d*x)/2)^14 - 7*cos(c/2 + (d*x)/2)*sin(c/2 + (d*x)/2)^13 + 7*cos(c/2 + (d*x)/2)^13*sin(c/2 + (d*x)/2) - 21*cos(c/2 + (d*x)/2)^2*sin(c/2 + (d*x)/2)^12 + 63*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^11 + 63*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^10 - 315*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^9 - 105*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^8 + 105*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^6 + 315*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2)^5 - 63*cos(c/2 + (d*x)/2)^10*sin(c/2 + (d*x)/2)^4 - 63*cos(c/2 + (d*x)/2)^11*sin(c/2 + (d*x)/2)^3 + 21*cos(c/2 + (d*x)/2)^12*sin(c/2 + (d*x)/2)^2 + 840*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)/(2688*a*d*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^7)","B"
61,1,444,189,10.464225,"\text{Not used}","int(tan(c + d*x)^7/(a + a*sin(c + d*x))^2,x)","\frac{\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{16}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}-\frac{49\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{24}-\frac{693\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{320}+\frac{791\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{240}+\frac{1207\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{192}+\frac{123\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{4}+\frac{1207\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{192}+\frac{791\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{240}-\frac{693\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320}-\frac{49\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{24}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16}+\frac{7\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+64\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-90\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+64\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+36\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-20\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\right)}-\frac{7\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a^2\,d}","Not used",1,"((7*tan(c/2 + (d*x)/2))/64 + (7*tan(c/2 + (d*x)/2)^2)/16 + (7*tan(c/2 + (d*x)/2)^3)/192 - (49*tan(c/2 + (d*x)/2)^4)/24 - (693*tan(c/2 + (d*x)/2)^5)/320 + (791*tan(c/2 + (d*x)/2)^6)/240 + (1207*tan(c/2 + (d*x)/2)^7)/192 + (123*tan(c/2 + (d*x)/2)^8)/4 + (1207*tan(c/2 + (d*x)/2)^9)/192 + (791*tan(c/2 + (d*x)/2)^10)/240 - (693*tan(c/2 + (d*x)/2)^11)/320 - (49*tan(c/2 + (d*x)/2)^12)/24 + (7*tan(c/2 + (d*x)/2)^13)/192 + (7*tan(c/2 + (d*x)/2)^14)/16 + (7*tan(c/2 + (d*x)/2)^15)/64)/(d*(36*a^2*tan(c/2 + (d*x)/2)^5 - 20*a^2*tan(c/2 + (d*x)/2)^4 - 20*a^2*tan(c/2 + (d*x)/2)^3 + 64*a^2*tan(c/2 + (d*x)/2)^6 - 20*a^2*tan(c/2 + (d*x)/2)^7 - 90*a^2*tan(c/2 + (d*x)/2)^8 - 20*a^2*tan(c/2 + (d*x)/2)^9 + 64*a^2*tan(c/2 + (d*x)/2)^10 + 36*a^2*tan(c/2 + (d*x)/2)^11 - 20*a^2*tan(c/2 + (d*x)/2)^12 - 20*a^2*tan(c/2 + (d*x)/2)^13 + 4*a^2*tan(c/2 + (d*x)/2)^15 + a^2*tan(c/2 + (d*x)/2)^16 + a^2 + 4*a^2*tan(c/2 + (d*x)/2))) - (7*atanh(tan(c/2 + (d*x)/2)))/(64*a^2*d)","B"
62,1,361,146,10.504458,"\text{Not used}","int(tan(c + d*x)^5/(a + a*sin(c + d*x))^2,x)","\frac{5\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{32\,a^2\,d}-\frac{\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{32}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{8}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{96}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{3}-\frac{121\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{48}-\frac{119\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{12}-\frac{121\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{48}-\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{35\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8}+\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{32}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-17\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+28\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-17\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-12\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\right)}","Not used",1,"(5*atanh(tan(c/2 + (d*x)/2)))/(32*a^2*d) - ((5*tan(c/2 + (d*x)/2))/32 + (5*tan(c/2 + (d*x)/2)^2)/8 + (35*tan(c/2 + (d*x)/2)^3)/96 - (5*tan(c/2 + (d*x)/2)^4)/3 - (121*tan(c/2 + (d*x)/2)^5)/48 - (119*tan(c/2 + (d*x)/2)^6)/12 - (121*tan(c/2 + (d*x)/2)^7)/48 - (5*tan(c/2 + (d*x)/2)^8)/3 + (35*tan(c/2 + (d*x)/2)^9)/96 + (5*tan(c/2 + (d*x)/2)^10)/8 + (5*tan(c/2 + (d*x)/2)^11)/32)/(d*(2*a^2*tan(c/2 + (d*x)/2)^2 - 12*a^2*tan(c/2 + (d*x)/2)^3 - 17*a^2*tan(c/2 + (d*x)/2)^4 + 8*a^2*tan(c/2 + (d*x)/2)^5 + 28*a^2*tan(c/2 + (d*x)/2)^6 + 8*a^2*tan(c/2 + (d*x)/2)^7 - 17*a^2*tan(c/2 + (d*x)/2)^8 - 12*a^2*tan(c/2 + (d*x)/2)^9 + 2*a^2*tan(c/2 + (d*x)/2)^10 + 4*a^2*tan(c/2 + (d*x)/2)^11 + a^2*tan(c/2 + (d*x)/2)^12 + a^2 + 4*a^2*tan(c/2 + (d*x)/2)))","B"
63,1,240,104,10.052312,"\text{Not used}","int(tan(c + d*x)^3/(a + a*sin(c + d*x))^2,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{12}+\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{13\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-10\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a^2\,d}","Not used",1,"(tan(c/2 + (d*x)/2)/4 + tan(c/2 + (d*x)/2)^2 + (13*tan(c/2 + (d*x)/2)^3)/12 + (10*tan(c/2 + (d*x)/2)^4)/3 + (13*tan(c/2 + (d*x)/2)^5)/12 + tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^7/4)/(d*(4*a^2*tan(c/2 + (d*x)/2)^2 - 4*a^2*tan(c/2 + (d*x)/2)^3 - 10*a^2*tan(c/2 + (d*x)/2)^4 - 4*a^2*tan(c/2 + (d*x)/2)^5 + 4*a^2*tan(c/2 + (d*x)/2)^6 + 4*a^2*tan(c/2 + (d*x)/2)^7 + a^2*tan(c/2 + (d*x)/2)^8 + a^2 + 4*a^2*tan(c/2 + (d*x)/2))) - atanh(tan(c/2 + (d*x)/2))/(4*a^2*d)","B"
64,1,116,60,7.639622,"\text{Not used}","int(tan(c + d*x)/(a + a*sin(c + d*x))^2,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^2\,d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\right)}","Not used",1,"atanh(tan(c/2 + (d*x)/2))/(2*a^2*d) - (tan(c/2 + (d*x)/2)/2 + tan(c/2 + (d*x)/2)^3/2)/(d*(6*a^2*tan(c/2 + (d*x)/2)^2 + 4*a^2*tan(c/2 + (d*x)/2)^3 + a^2*tan(c/2 + (d*x)/2)^4 + a^2 + 4*a^2*tan(c/2 + (d*x)/2)))","B"
65,1,87,52,6.589943,"\text{Not used}","int(cot(c + d*x)/(a + a*sin(c + d*x))^2,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^2\,d}-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - (2*log(tan(c/2 + (d*x)/2) + 1))/(a^2*d) - (2*tan(c/2 + (d*x)/2))/(d*(a^2*tan(c/2 + (d*x)/2)^2 + a^2 + 2*a^2*tan(c/2 + (d*x)/2)))","B"
66,1,103,65,6.527831,"\text{Not used}","int(cot(c + d*x)^3/(a + a*sin(c + d*x))^2,x)","\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{8}\right)}{a^2\,d}","Not used",1,"(2*log(tan(c/2 + (d*x)/2)))/(a^2*d) - tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (4*log(tan(c/2 + (d*x)/2) + 1))/(a^2*d) + tan(c/2 + (d*x)/2)/(a^2*d) + (cot(c/2 + (d*x)/2)^2*(tan(c/2 + (d*x)/2) - 1/8))/(a^2*d)","B"
67,1,36,55,6.334949,"\text{Not used}","int(cot(c + d*x)^5/(a + a*sin(c + d*x))^2,x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^2}{2}-\frac{2\,\sin\left(c+d\,x\right)}{3}+\frac{1}{4}}{a^2\,d\,{\sin\left(c+d\,x\right)}^4}","Not used",1,"-(sin(c + d*x)^2/2 - (2*sin(c + d*x))/3 + 1/4)/(a^2*d*sin(c + d*x)^4)","B"
68,1,46,73,6.374820,"\text{Not used}","int(cot(c + d*x)^7/(a + a*sin(c + d*x))^2,x)","\frac{15\,{\sin\left(c+d\,x\right)}^4-20\,{\sin\left(c+d\,x\right)}^3+12\,\sin\left(c+d\,x\right)-5}{30\,a^2\,d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"(12*sin(c + d*x) - 20*sin(c + d*x)^3 + 15*sin(c + d*x)^4 - 5)/(30*a^2*d*sin(c + d*x)^6)","B"
69,1,76,127,6.542386,"\text{Not used}","int(cot(c + d*x)^9/(a + a*sin(c + d*x))^2,x)","\frac{-420\,{\sin\left(c+d\,x\right)}^6+560\,{\sin\left(c+d\,x\right)}^5+210\,{\sin\left(c+d\,x\right)}^4-672\,{\sin\left(c+d\,x\right)}^3+140\,{\sin\left(c+d\,x\right)}^2+240\,\sin\left(c+d\,x\right)-105}{840\,a^2\,d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"(240*sin(c + d*x) + 140*sin(c + d*x)^2 - 672*sin(c + d*x)^3 + 210*sin(c + d*x)^4 + 560*sin(c + d*x)^5 - 420*sin(c + d*x)^6 - 105)/(840*a^2*d*sin(c + d*x)^8)","B"
70,1,85,145,6.632722,"\text{Not used}","int(cot(c + d*x)^11/(a + a*sin(c + d*x))^2,x)","\frac{\frac{{\sin\left(c+d\,x\right)}^8}{2}-\frac{2\,{\sin\left(c+d\,x\right)}^7}{3}-\frac{{\sin\left(c+d\,x\right)}^6}{2}+\frac{6\,{\sin\left(c+d\,x\right)}^5}{5}-\frac{6\,{\sin\left(c+d\,x\right)}^3}{7}+\frac{{\sin\left(c+d\,x\right)}^2}{4}+\frac{2\,\sin\left(c+d\,x\right)}{9}-\frac{1}{10}}{a^2\,d\,{\sin\left(c+d\,x\right)}^{10}}","Not used",1,"((2*sin(c + d*x))/9 + sin(c + d*x)^2/4 - (6*sin(c + d*x)^3)/7 + (6*sin(c + d*x)^5)/5 - sin(c + d*x)^6/2 - (2*sin(c + d*x)^7)/3 + sin(c + d*x)^8/2 - 1/10)/(a^2*d*sin(c + d*x)^10)","B"
71,1,116,199,6.849278,"\text{Not used}","int(cot(c + d*x)^13/(a + a*sin(c + d*x))^2,x)","-\frac{\frac{{\sin\left(c+d\,x\right)}^{10}}{2}-\frac{2\,{\sin\left(c+d\,x\right)}^9}{3}-\frac{3\,{\sin\left(c+d\,x\right)}^8}{4}+\frac{8\,{\sin\left(c+d\,x\right)}^7}{5}+\frac{{\sin\left(c+d\,x\right)}^6}{3}-\frac{12\,{\sin\left(c+d\,x\right)}^5}{7}+\frac{{\sin\left(c+d\,x\right)}^4}{4}+\frac{8\,{\sin\left(c+d\,x\right)}^3}{9}-\frac{3\,{\sin\left(c+d\,x\right)}^2}{10}-\frac{2\,\sin\left(c+d\,x\right)}{11}+\frac{1}{12}}{a^2\,d\,{\sin\left(c+d\,x\right)}^{12}}","Not used",1,"-((8*sin(c + d*x)^3)/9 - (3*sin(c + d*x)^2)/10 - (2*sin(c + d*x))/11 + sin(c + d*x)^4/4 - (12*sin(c + d*x)^5)/7 + sin(c + d*x)^6/3 + (8*sin(c + d*x)^7)/5 - (3*sin(c + d*x)^8)/4 - (2*sin(c + d*x)^9)/3 + sin(c + d*x)^10/2 + 1/12)/(a^2*d*sin(c + d*x)^12)","B"
72,1,418,171,10.050974,"\text{Not used}","int(tan(c + d*x)^5/(a + a*sin(c + d*x))^3,x)","\frac{-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{64}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{32}-\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{96}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{32}+\frac{527\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{960}+\frac{901\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{80}+\frac{711\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{80}+\frac{901\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{80}+\frac{527\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{960}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32}-\frac{17\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}+11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-39\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-38\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+27\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+72\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+27\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-38\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-39\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+11\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^3\right)}+\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^4/32 - (3*tan(c/2 + (d*x)/2)^2)/32 - (17*tan(c/2 + (d*x)/2)^3)/96 - tan(c/2 + (d*x)/2)/64 + (527*tan(c/2 + (d*x)/2)^5)/960 + (901*tan(c/2 + (d*x)/2)^6)/80 + (711*tan(c/2 + (d*x)/2)^7)/80 + (901*tan(c/2 + (d*x)/2)^8)/80 + (527*tan(c/2 + (d*x)/2)^9)/960 + tan(c/2 + (d*x)/2)^10/32 - (17*tan(c/2 + (d*x)/2)^11)/96 - (3*tan(c/2 + (d*x)/2)^12)/32 - tan(c/2 + (d*x)/2)^13/64)/(d*(11*a^3*tan(c/2 + (d*x)/2)^2 - 4*a^3*tan(c/2 + (d*x)/2)^3 - 39*a^3*tan(c/2 + (d*x)/2)^4 - 38*a^3*tan(c/2 + (d*x)/2)^5 + 27*a^3*tan(c/2 + (d*x)/2)^6 + 72*a^3*tan(c/2 + (d*x)/2)^7 + 27*a^3*tan(c/2 + (d*x)/2)^8 - 38*a^3*tan(c/2 + (d*x)/2)^9 - 39*a^3*tan(c/2 + (d*x)/2)^10 - 4*a^3*tan(c/2 + (d*x)/2)^11 + 11*a^3*tan(c/2 + (d*x)/2)^12 + 6*a^3*tan(c/2 + (d*x)/2)^13 + a^3*tan(c/2 + (d*x)/2)^14 + a^3 + 6*a^3*tan(c/2 + (d*x)/2))) + atanh(tan(c/2 + (d*x)/2))/(64*a^3*d)","B"
73,1,302,126,9.925399,"\text{Not used}","int(tan(c + d*x)^3/(a + a*sin(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{16}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{8}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{6}+\frac{37\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{8}+\frac{101\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}+\frac{37\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{8}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-14\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-28\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-14\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+13\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^3\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{16\,a^3\,d}","Not used",1,"(tan(c/2 + (d*x)/2)/16 + (3*tan(c/2 + (d*x)/2)^2)/8 + (5*tan(c/2 + (d*x)/2)^3)/6 + (37*tan(c/2 + (d*x)/2)^4)/8 + (101*tan(c/2 + (d*x)/2)^5)/24 + (37*tan(c/2 + (d*x)/2)^6)/8 + (5*tan(c/2 + (d*x)/2)^7)/6 + (3*tan(c/2 + (d*x)/2)^8)/8 + tan(c/2 + (d*x)/2)^9/16)/(d*(13*a^3*tan(c/2 + (d*x)/2)^2 + 8*a^3*tan(c/2 + (d*x)/2)^3 - 14*a^3*tan(c/2 + (d*x)/2)^4 - 28*a^3*tan(c/2 + (d*x)/2)^5 - 14*a^3*tan(c/2 + (d*x)/2)^6 + 8*a^3*tan(c/2 + (d*x)/2)^7 + 13*a^3*tan(c/2 + (d*x)/2)^8 + 6*a^3*tan(c/2 + (d*x)/2)^9 + a^3*tan(c/2 + (d*x)/2)^10 + a^3 + 6*a^3*tan(c/2 + (d*x)/2))) - atanh(tan(c/2 + (d*x)/2))/(16*a^3*d)","B"
74,1,186,82,8.819291,"\text{Not used}","int(tan(c + d*x)/(a + a*sin(c + d*x))^3,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{4\,a^3\,d}+\frac{-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{6}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4}}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+20\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+15\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^3\right)}","Not used",1,"atanh(tan(c/2 + (d*x)/2))/(4*a^3*d) + (tan(c/2 + (d*x)/2)^2/2 - tan(c/2 + (d*x)/2)/4 + tan(c/2 + (d*x)/2)^3/6 + tan(c/2 + (d*x)/2)^4/2 - tan(c/2 + (d*x)/2)^5/4)/(d*(15*a^3*tan(c/2 + (d*x)/2)^2 + 20*a^3*tan(c/2 + (d*x)/2)^3 + 15*a^3*tan(c/2 + (d*x)/2)^4 + 6*a^3*tan(c/2 + (d*x)/2)^5 + a^3*tan(c/2 + (d*x)/2)^6 + a^3 + 6*a^3*tan(c/2 + (d*x)/2)))","B"
75,1,148,74,6.647667,"\text{Not used}","int(cot(c + d*x)/(a + a*sin(c + d*x))^3,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+6\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^3\right)}-\frac{2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) - (4*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^3)/(d*(6*a^3*tan(c/2 + (d*x)/2)^2 + 4*a^3*tan(c/2 + (d*x)/2)^3 + a^3*tan(c/2 + (d*x)/2)^4 + a^3 + 4*a^3*tan(c/2 + (d*x)/2))) - (2*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d)","B"
76,1,169,86,6.700564,"\text{Not used}","int(cot(c + d*x)^3/(a + a*sin(c + d*x))^3,x)","\frac{5\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^3\,d}-\frac{10\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}+\frac{-10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{23\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{2}}{d\,\left(4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+8\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}+\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}","Not used",1,"(5*log(tan(c/2 + (d*x)/2)))/(a^3*d) - tan(c/2 + (d*x)/2)^2/(8*a^3*d) - (10*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) + (5*tan(c/2 + (d*x)/2) + (23*tan(c/2 + (d*x)/2)^2)/2 - 10*tan(c/2 + (d*x)/2)^3 - 1/2)/(d*(4*a^3*tan(c/2 + (d*x)/2)^2 + 8*a^3*tan(c/2 + (d*x)/2)^3 + 4*a^3*tan(c/2 + (d*x)/2)^4)) + (3*tan(c/2 + (d*x)/2))/(2*a^3*d)","B"
77,1,171,96,6.716671,"\text{Not used}","int(cot(c + d*x)^5/(a + a*sin(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^3\,d}-\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^3\,d}+\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^3\,d}+\frac{19\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^3\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(38\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{1}{4}\right)}{16\,a^3\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(8*a^3*d) - (9*tan(c/2 + (d*x)/2)^2)/(16*a^3*d) - tan(c/2 + (d*x)/2)^4/(64*a^3*d) + (4*log(tan(c/2 + (d*x)/2)))/(a^3*d) - (8*log(tan(c/2 + (d*x)/2) + 1))/(a^3*d) + (19*tan(c/2 + (d*x)/2))/(8*a^3*d) + (cot(c/2 + (d*x)/2)^4*(2*tan(c/2 + (d*x)/2) - 9*tan(c/2 + (d*x)/2)^2 + 38*tan(c/2 + (d*x)/2)^3 - 1/4))/(16*a^3*d)","B"
78,1,46,73,6.693377,"\text{Not used}","int(cot(c + d*x)^7/(a + a*sin(c + d*x))^3,x)","\frac{20\,{\sin\left(c+d\,x\right)}^3-45\,{\sin\left(c+d\,x\right)}^2+36\,\sin\left(c+d\,x\right)-10}{60\,a^3\,d\,{\sin\left(c+d\,x\right)}^6}","Not used",1,"(36*sin(c + d*x) - 45*sin(c + d*x)^2 + 20*sin(c + d*x)^3 - 10)/(60*a^3*d*sin(c + d*x)^6)","B"
79,1,66,109,6.629187,"\text{Not used}","int(cot(c + d*x)^9/(a + a*sin(c + d*x))^3,x)","-\frac{280\,{\sin\left(c+d\,x\right)}^5-630\,{\sin\left(c+d\,x\right)}^4+336\,{\sin\left(c+d\,x\right)}^3+280\,{\sin\left(c+d\,x\right)}^2-360\,\sin\left(c+d\,x\right)+105}{840\,a^3\,d\,{\sin\left(c+d\,x\right)}^8}","Not used",1,"-(280*sin(c + d*x)^2 - 360*sin(c + d*x) + 336*sin(c + d*x)^3 - 630*sin(c + d*x)^4 + 280*sin(c + d*x)^5 + 105)/(840*a^3*d*sin(c + d*x)^8)","B"
80,1,86,145,6.810581,"\text{Not used}","int(cot(c + d*x)^11/(a + a*sin(c + d*x))^3,x)","\frac{280\,{\sin\left(c+d\,x\right)}^7-630\,{\sin\left(c+d\,x\right)}^6+168\,{\sin\left(c+d\,x\right)}^5+700\,{\sin\left(c+d\,x\right)}^4-600\,{\sin\left(c+d\,x\right)}^3-105\,{\sin\left(c+d\,x\right)}^2+280\,\sin\left(c+d\,x\right)-84}{840\,a^3\,d\,{\sin\left(c+d\,x\right)}^{10}}","Not used",1,"(280*sin(c + d*x) - 105*sin(c + d*x)^2 - 600*sin(c + d*x)^3 + 700*sin(c + d*x)^4 + 168*sin(c + d*x)^5 - 630*sin(c + d*x)^6 + 280*sin(c + d*x)^7 - 84)/(840*a^3*d*sin(c + d*x)^10)","B"
81,1,85,145,6.821547,"\text{Not used}","int(cot(c + d*x)^13/(a + a*sin(c + d*x))^3,x)","\frac{-\frac{{\sin\left(c+d\,x\right)}^9}{3}+\frac{3\,{\sin\left(c+d\,x\right)}^8}{4}-\frac{4\,{\sin\left(c+d\,x\right)}^6}{3}+\frac{6\,{\sin\left(c+d\,x\right)}^5}{7}+\frac{3\,{\sin\left(c+d\,x\right)}^4}{4}-\frac{8\,{\sin\left(c+d\,x\right)}^3}{9}+\frac{3\,\sin\left(c+d\,x\right)}{11}-\frac{1}{12}}{a^3\,d\,{\sin\left(c+d\,x\right)}^{12}}","Not used",1,"((3*sin(c + d*x))/11 - (8*sin(c + d*x)^3)/9 + (3*sin(c + d*x)^4)/4 + (6*sin(c + d*x)^5)/7 - (4*sin(c + d*x)^6)/3 + (3*sin(c + d*x)^8)/4 - sin(c + d*x)^9/3 - 1/12)/(a^3*d*sin(c + d*x)^12)","B"
82,1,476,195,10.661374,"\text{Not used}","int(tan(c + d*x)^5/(a + a*sin(c + d*x))^4,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}}{64}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}}{8}+\frac{73\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}}{192}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}}{12}-\frac{139\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}}{320}+\frac{1073\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{120}+\frac{10277\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9}{960}+\frac{237\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{10}+\frac{10277\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{960}+\frac{1073\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{120}-\frac{139\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{320}+\frac{5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{12}+\frac{73\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{192}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{64}}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{16}+8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{15}+24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{14}+24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{13}-36\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-120\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}-88\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+88\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+198\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+88\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-88\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-120\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-36\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^4\right)}-\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{64\,a^4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)/64 + tan(c/2 + (d*x)/2)^2/8 + (73*tan(c/2 + (d*x)/2)^3)/192 + (5*tan(c/2 + (d*x)/2)^4)/12 - (139*tan(c/2 + (d*x)/2)^5)/320 + (1073*tan(c/2 + (d*x)/2)^6)/120 + (10277*tan(c/2 + (d*x)/2)^7)/960 + (237*tan(c/2 + (d*x)/2)^8)/10 + (10277*tan(c/2 + (d*x)/2)^9)/960 + (1073*tan(c/2 + (d*x)/2)^10)/120 - (139*tan(c/2 + (d*x)/2)^11)/320 + (5*tan(c/2 + (d*x)/2)^12)/12 + (73*tan(c/2 + (d*x)/2)^13)/192 + tan(c/2 + (d*x)/2)^14/8 + tan(c/2 + (d*x)/2)^15/64)/(d*(24*a^4*tan(c/2 + (d*x)/2)^2 + 24*a^4*tan(c/2 + (d*x)/2)^3 - 36*a^4*tan(c/2 + (d*x)/2)^4 - 120*a^4*tan(c/2 + (d*x)/2)^5 - 88*a^4*tan(c/2 + (d*x)/2)^6 + 88*a^4*tan(c/2 + (d*x)/2)^7 + 198*a^4*tan(c/2 + (d*x)/2)^8 + 88*a^4*tan(c/2 + (d*x)/2)^9 - 88*a^4*tan(c/2 + (d*x)/2)^10 - 120*a^4*tan(c/2 + (d*x)/2)^11 - 36*a^4*tan(c/2 + (d*x)/2)^12 + 24*a^4*tan(c/2 + (d*x)/2)^13 + 24*a^4*tan(c/2 + (d*x)/2)^14 + 8*a^4*tan(c/2 + (d*x)/2)^15 + a^4*tan(c/2 + (d*x)/2)^16 + a^4 + 8*a^4*tan(c/2 + (d*x)/2))) - atanh(tan(c/2 + (d*x)/2))/(64*a^4*d)","B"
83,1,172,132,7.507699,"\text{Not used}","int(tan(c + d*x)^3/(a + a*sin(c + d*x))^4,x)","\frac{4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+\frac{56\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{5}+\frac{32\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{5}+4\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8}{a^4\,d\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^2\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^{10}}","Not used",1,"(4*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^8 + (32*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^7)/5 + (56*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^6)/5 + (32*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^5)/5 + 4*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^4)/(a^4*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))^2*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^10)","B"
84,1,240,105,10.069616,"\text{Not used}","int(tan(c + d*x)/(a + a*sin(c + d*x))^4,x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,a^4\,d}+\frac{-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{8}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{24}+\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\frac{43\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+8\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+28\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+56\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+70\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+56\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+28\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a^4\right)}","Not used",1,"atanh(tan(c/2 + (d*x)/2))/(8*a^4*d) + (tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)/8 + (43*tan(c/2 + (d*x)/2)^3)/24 + (10*tan(c/2 + (d*x)/2)^4)/3 + (43*tan(c/2 + (d*x)/2)^5)/24 + tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^7/8)/(d*(28*a^4*tan(c/2 + (d*x)/2)^2 + 56*a^4*tan(c/2 + (d*x)/2)^3 + 70*a^4*tan(c/2 + (d*x)/2)^4 + 56*a^4*tan(c/2 + (d*x)/2)^5 + 28*a^4*tan(c/2 + (d*x)/2)^6 + 8*a^4*tan(c/2 + (d*x)/2)^7 + a^4*tan(c/2 + (d*x)/2)^8 + a^4 + 8*a^4*tan(c/2 + (d*x)/2)))","B"
85,1,228,106,6.610434,"\text{Not used}","int(cot(c + d*x)^3/(a + a*sin(c + d*x))^4,x)","\frac{9\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^4\,d}-\frac{48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{129\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-29\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-6\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{1}{2}}{d\,\left(4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+24\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+16\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{18\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^4\,d}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4\,d}","Not used",1,"(9*log(tan(c/2 + (d*x)/2)))/(a^4*d) - tan(c/2 + (d*x)/2)^2/(8*a^4*d) - (10*tan(c/2 + (d*x)/2)^3 - 29*tan(c/2 + (d*x)/2)^2 - 6*tan(c/2 + (d*x)/2) + (129*tan(c/2 + (d*x)/2)^4)/2 + 48*tan(c/2 + (d*x)/2)^5 + 1/2)/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 + 16*a^4*tan(c/2 + (d*x)/2)^3 + 24*a^4*tan(c/2 + (d*x)/2)^4 + 16*a^4*tan(c/2 + (d*x)/2)^5 + 4*a^4*tan(c/2 + (d*x)/2)^6)) - (18*log(tan(c/2 + (d*x)/2) + 1))/(a^4*d) + (2*tan(c/2 + (d*x)/2))/(a^4*d)","B"
86,1,235,135,6.807442,"\text{Not used}","int(cot(c + d*x)^7/(a + a*sin(c + d*x))^4,x)","\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^4\,d}-\frac{189\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{128\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{8\,a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{40\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{384\,a^4\,d}+\frac{8\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{16\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{a^4\,d}+\frac{21\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^4\,d}+\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(336\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-\frac{189\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{2}+\frac{88\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{8\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}-\frac{1}{6}\right)}{64\,a^4\,d}","Not used",1,"(11*tan(c/2 + (d*x)/2)^3)/(24*a^4*d) - (189*tan(c/2 + (d*x)/2)^2)/(128*a^4*d) - tan(c/2 + (d*x)/2)^4/(8*a^4*d) + tan(c/2 + (d*x)/2)^5/(40*a^4*d) - tan(c/2 + (d*x)/2)^6/(384*a^4*d) + (8*log(tan(c/2 + (d*x)/2)))/(a^4*d) - (16*log(tan(c/2 + (d*x)/2) + 1))/(a^4*d) + (21*tan(c/2 + (d*x)/2))/(4*a^4*d) + (cot(c/2 + (d*x)/2)^6*((8*tan(c/2 + (d*x)/2))/5 - 8*tan(c/2 + (d*x)/2)^2 + (88*tan(c/2 + (d*x)/2)^3)/3 - (189*tan(c/2 + (d*x)/2)^4)/2 + 336*tan(c/2 + (d*x)/2)^5 - 1/6))/(64*a^4*d)","B"
87,1,231,127,7.576639,"\text{Not used}","int(tan(c + d*x)^2/(a + a*sin(c + d*x))^4,x)","\frac{\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}}{315}+\frac{128\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{315}+\frac{48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{35}+\frac{536\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{105}+\frac{112\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{15}+\frac{48\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{5}+\frac{16\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{3}+\frac{8\,{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7}{3}}{a^4\,d\,\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,{\left(\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}^9}","Not used",1,"((16*cos(c/2 + (d*x)/2)^10)/315 + (128*cos(c/2 + (d*x)/2)^9*sin(c/2 + (d*x)/2))/315 + (8*cos(c/2 + (d*x)/2)^3*sin(c/2 + (d*x)/2)^7)/3 + (16*cos(c/2 + (d*x)/2)^4*sin(c/2 + (d*x)/2)^6)/3 + (48*cos(c/2 + (d*x)/2)^5*sin(c/2 + (d*x)/2)^5)/5 + (112*cos(c/2 + (d*x)/2)^6*sin(c/2 + (d*x)/2)^4)/15 + (536*cos(c/2 + (d*x)/2)^7*sin(c/2 + (d*x)/2)^3)/105 + (48*cos(c/2 + (d*x)/2)^8*sin(c/2 + (d*x)/2)^2)/35)/(a^4*d*(cos(c/2 + (d*x)/2) - sin(c/2 + (d*x)/2))*(cos(c/2 + (d*x)/2) + sin(c/2 + (d*x)/2))^9)","B"
88,1,203,108,12.051782,"\text{Not used}","int(cot(c + d*x)^2/(a + a*sin(c + d*x))^4,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}-\frac{37\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+121\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{514\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{338\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\frac{491\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{15}+1}{d\,\left(2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+10\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+20\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+20\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+10\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{4\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^4*d) - ((491*tan(c/2 + (d*x)/2))/15 + (338*tan(c/2 + (d*x)/2)^2)/3 + (514*tan(c/2 + (d*x)/2)^3)/3 + 121*tan(c/2 + (d*x)/2)^4 + 37*tan(c/2 + (d*x)/2)^5 + 1)/(d*(10*a^4*tan(c/2 + (d*x)/2)^2 + 20*a^4*tan(c/2 + (d*x)/2)^3 + 20*a^4*tan(c/2 + (d*x)/2)^4 + 10*a^4*tan(c/2 + (d*x)/2)^5 + 2*a^4*tan(c/2 + (d*x)/2)^6 + 2*a^4*tan(c/2 + (d*x)/2))) - (4*log(tan(c/2 + (d*x)/2)))/(a^4*d)","B"
89,1,171,120,7.825645,"\text{Not used}","int(cot(c + d*x)^4/(a + a*sin(c + d*x))^4,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,a^4\,d}-\frac{14\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}+\frac{35\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a^4\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{291\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{8}+\frac{549\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{8}+41\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-\frac{3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8}+\frac{1}{24}\right)}{a^4\,d\,{\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}^3}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^4*d) - tan(c/2 + (d*x)/2)^2/(2*a^4*d) - (14*log(tan(c/2 + (d*x)/2)))/(a^4*d) + (35*tan(c/2 + (d*x)/2))/(8*a^4*d) - (cot(c/2 + (d*x)/2)^3*(3*tan(c/2 + (d*x)/2)^2 - (3*tan(c/2 + (d*x)/2))/8 + 41*tan(c/2 + (d*x)/2)^3 + (549*tan(c/2 + (d*x)/2)^4)/8 + (291*tan(c/2 + (d*x)/2)^5)/8 + 1/24))/(a^4*d*(tan(c/2 + (d*x)/2) + 1)^3)","B"
90,1,209,133,7.672068,"\text{Not used}","int(cot(c + d*x)^6/(a + a*sin(c + d*x))^4,x)","\frac{11\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32\,a^4\,d}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2\,a^4\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16\,a^4\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^4\,d}-\frac{27\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,a^4\,d}+\frac{111\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,a^4\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{367\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{16}+\frac{87\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{16}-\frac{37\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{32}+\frac{9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{32}-\frac{9\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{160}+\frac{1}{160}\right)}{a^4\,d\,\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}","Not used",1,"(11*tan(c/2 + (d*x)/2)^3)/(32*a^4*d) - (3*tan(c/2 + (d*x)/2)^2)/(2*a^4*d) - tan(c/2 + (d*x)/2)^4/(16*a^4*d) + tan(c/2 + (d*x)/2)^5/(160*a^4*d) - (27*log(tan(c/2 + (d*x)/2)))/(2*a^4*d) + (111*tan(c/2 + (d*x)/2))/(16*a^4*d) - (cot(c/2 + (d*x)/2)^5*((9*tan(c/2 + (d*x)/2)^2)/32 - (9*tan(c/2 + (d*x)/2))/160 - (37*tan(c/2 + (d*x)/2)^3)/32 + (87*tan(c/2 + (d*x)/2)^4)/16 + (367*tan(c/2 + (d*x)/2)^5)/16 + 1/160))/(a^4*d*(tan(c/2 + (d*x)/2) + 1))","B"
91,0,-1,162,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(1/2), x)","F"
92,0,-1,101,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(1/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(1/2), x)","F"
93,0,-1,89,0.000000,"\text{Not used}","int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(1/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^2\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(1/2), x)","F"
94,0,-1,163,0.000000,"\text{Not used}","int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(1/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^4\,\sqrt{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(1/2), x)","F"
95,0,-1,167,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(3/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(3/2), x)","F"
96,0,-1,88,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(3/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(3/2), x)","F"
97,0,-1,121,0.000000,"\text{Not used}","int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(3/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(3/2), x)","F"
98,0,-1,197,0.000000,"\text{Not used}","int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(3/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(3/2), x)","F"
99,0,-1,151,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(5/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(5/2), x)","F"
100,0,-1,118,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(5/2),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(5/2), x)","F"
101,0,-1,151,0.000000,"\text{Not used}","int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(5/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(5/2), x)","F"
102,0,-1,227,0.000000,"\text{Not used}","int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(5/2),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2} \,d x","Not used",1,"int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(5/2), x)","F"
103,0,-1,150,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(1/2), x)","F"
104,0,-1,107,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(1/2), x)","F"
105,0,-1,62,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(1/2), x)","F"
106,0,-1,135,0.000000,"\text{Not used}","int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(1/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^4}{\sqrt{a+a\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(1/2), x)","F"
107,0,-1,177,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(3/2), x)","F"
108,0,-1,134,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(3/2), x)","F"
109,0,-1,113,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(3/2), x)","F"
110,0,-1,144,0.000000,"\text{Not used}","int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(3/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^4}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(3/2), x)","F"
111,0,-1,207,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(5/2), x)","F"
112,0,-1,167,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(5/2), x)","F"
113,0,-1,141,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(5/2), x)","F"
114,0,-1,191,0.000000,"\text{Not used}","int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(5/2),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^4}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(5/2), x)","F"
115,0,-1,982,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(1/3),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3} \,d x","Not used",1,"int(tan(e + f*x)^4*(a + a*sin(e + f*x))^(1/3), x)","F"
116,0,-1,123,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(1/3),x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3} \,d x","Not used",1,"int(tan(e + f*x)^2*(a + a*sin(e + f*x))^(1/3), x)","F"
117,0,-1,80,0.000000,"\text{Not used}","int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(1/3),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3} \,d x","Not used",1,"int(cot(e + f*x)^2*(a + a*sin(e + f*x))^(1/3), x)","F"
118,0,-1,80,0.000000,"\text{Not used}","int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(1/3),x)","\int {\mathrm{cot}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3} \,d x","Not used",1,"int(cot(e + f*x)^4*(a + a*sin(e + f*x))^(1/3), x)","F"
119,0,-1,551,0.000000,"\text{Not used}","int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(1/3),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^4}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(tan(e + f*x)^4/(a + a*sin(e + f*x))^(1/3), x)","F"
120,0,-1,126,0.000000,"\text{Not used}","int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(1/3),x)","\int \frac{{\mathrm{tan}\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(tan(e + f*x)^2/(a + a*sin(e + f*x))^(1/3), x)","F"
121,0,-1,80,0.000000,"\text{Not used}","int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(1/3),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^2}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(cot(e + f*x)^2/(a + a*sin(e + f*x))^(1/3), x)","F"
122,0,-1,80,0.000000,"\text{Not used}","int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(1/3),x)","\int \frac{{\mathrm{cot}\left(e+f\,x\right)}^4}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^{1/3}} \,d x","Not used",1,"int(cot(e + f*x)^4/(a + a*sin(e + f*x))^(1/3), x)","F"
123,0,-1,269,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + a*sin(e + f*x))^3,x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((g*tan(e + f*x))^p*(a + a*sin(e + f*x))^3, x)","F"
124,0,-1,187,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + a*sin(e + f*x))^2,x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((g*tan(e + f*x))^p*(a + a*sin(e + f*x))^2, x)","F"
125,0,-1,129,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + a*sin(e + f*x)),x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,\left(a+a\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((g*tan(e + f*x))^p*(a + a*sin(e + f*x)), x)","F"
126,0,-1,108,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p/(a + a*sin(e + f*x)),x)","\int \frac{{\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p}{a+a\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((g*tan(e + f*x))^p/(a + a*sin(e + f*x)), x)","F"
127,0,-1,138,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p/(a + a*sin(e + f*x))^2,x)","\int \frac{{\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((g*tan(e + f*x))^p/(a + a*sin(e + f*x))^2, x)","F"
128,0,-1,248,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p/(a + a*sin(e + f*x))^3,x)","\int \frac{{\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p}{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^3} \,d x","Not used",1,"int((g*tan(e + f*x))^p/(a + a*sin(e + f*x))^3, x)","F"
129,0,-1,111,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + a*sin(e + f*x))^m,x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((g*tan(e + f*x))^p*(a + a*sin(e + f*x))^m, x)","F"
130,0,-1,163,0.000000,"\text{Not used}","int(tan(e + f*x)^3*(a + a*sin(e + f*x))^m,x)","\int {\mathrm{tan}\left(e+f\,x\right)}^3\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(tan(e + f*x)^3*(a + a*sin(e + f*x))^m, x)","F"
131,0,-1,72,0.000000,"\text{Not used}","int(tan(e + f*x)*(a + a*sin(e + f*x))^m,x)","\int \mathrm{tan}\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(tan(e + f*x)*(a + a*sin(e + f*x))^m, x)","F"
132,0,-1,43,0.000000,"\text{Not used}","int(cot(e + f*x)*(a + a*sin(e + f*x))^m,x)","\int \mathrm{cot}\left(e+f\,x\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cot(e + f*x)*(a + a*sin(e + f*x))^m, x)","F"
133,0,-1,83,0.000000,"\text{Not used}","int(cot(e + f*x)^3*(a + a*sin(e + f*x))^m,x)","\int {\mathrm{cot}\left(e+f\,x\right)}^3\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cot(e + f*x)^3*(a + a*sin(e + f*x))^m, x)","F"
134,0,-1,123,0.000000,"\text{Not used}","int(cot(e + f*x)^5*(a + a*sin(e + f*x))^m,x)","\int {\mathrm{cot}\left(e+f\,x\right)}^5\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cot(e + f*x)^5*(a + a*sin(e + f*x))^m, x)","F"
135,0,-1,311,0.000000,"\text{Not used}","int(tan(e + f*x)^4*(a + a*sin(e + f*x))^m,x)","\int {\mathrm{tan}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(tan(e + f*x)^4*(a + a*sin(e + f*x))^m, x)","F"
136,0,-1,157,0.000000,"\text{Not used}","int(tan(e + f*x)^2*(a + a*sin(e + f*x))^m,x)","\int {\mathrm{tan}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(tan(e + f*x)^2*(a + a*sin(e + f*x))^m, x)","F"
137,0,-1,74,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m,x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int((a + a*sin(e + f*x))^m, x)","F"
138,0,-1,89,0.000000,"\text{Not used}","int(cot(e + f*x)^2*(a + a*sin(e + f*x))^m,x)","\int {\mathrm{cot}\left(e+f\,x\right)}^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cot(e + f*x)^2*(a + a*sin(e + f*x))^m, x)","F"
139,0,-1,89,0.000000,"\text{Not used}","int(cot(e + f*x)^4*(a + a*sin(e + f*x))^m,x)","\int {\mathrm{cot}\left(e+f\,x\right)}^4\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",1,"int(cot(e + f*x)^4*(a + a*sin(e + f*x))^m, x)","F"
140,1,176,88,6.734726,"\text{Not used}","int(tan(c + d*x)^3*(a + b*sin(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a+\frac{3\,b}{2}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-\frac{3\,b}{2}\right)}{d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{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,"(log(tan(c/2 + (d*x)/2) - 1)*(a + (3*b)/2))/d + (log(tan(c/2 + (d*x)/2) + 1)*(a - (3*b)/2))/d - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (3*b*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^2 + 2*a*tan(c/2 + (d*x)/2)^4 - 2*b*tan(c/2 + (d*x)/2)^3 + 3*b*tan(c/2 + (d*x)/2)^5)/(d*(tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 - 1))","B"
141,1,74,55,6.635569,"\text{Not used}","int(tan(c + d*x)*(a + b*sin(c + d*x)),x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-b\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a+b\right)}{d}-\frac{b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (log(tan(c/2 + (d*x)/2) + 1)*(a - b))/d - (log(tan(c/2 + (d*x)/2) - 1)*(a + b))/d - (b*sin(c + d*x))/d","B"
142,1,47,24,6.564478,"\text{Not used}","int(cot(c + d*x)*(a + b*sin(c + d*x)),x)","\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)))/d - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (b*sin(c + d*x))/d","B"
143,1,146,54,6.631333,"\text{Not used}","int(cot(c + d*x)^3*(a + b*sin(c + d*x)),x)","\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{10\,b\,{\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)}^2}{2}+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{2}}{d\,\left(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\right)}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(a*log(tan(c/2 + (d*x)/2)^2 + 1))/d - (b*tan(c/2 + (d*x)/2))/(2*d) - (a/2 + 2*b*tan(c/2 + (d*x)/2) + (a*tan(c/2 + (d*x)/2)^2)/2 + 10*b*tan(c/2 + (d*x)/2)^3)/(d*(4*tan(c/2 + (d*x)/2)^2 + 4*tan(c/2 + (d*x)/2)^4)) - (a*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*log(tan(c/2 + (d*x)/2)))/d","B"
144,1,207,81,6.669745,"\text{Not used}","int(cot(c + d*x)^5*(a + b*sin(c + d*x)),x)","\frac{7\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{46\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\frac{40\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{11\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4}-\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}-\frac{a}{4}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{a\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}+\frac{3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{16\,d}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}","Not used",1,"(7*b*tan(c/2 + (d*x)/2))/(8*d) + ((11*a*tan(c/2 + (d*x)/2)^2)/4 - (2*b*tan(c/2 + (d*x)/2))/3 - a/4 + 3*a*tan(c/2 + (d*x)/2)^4 + (40*b*tan(c/2 + (d*x)/2)^3)/3 + 46*b*tan(c/2 + (d*x)/2)^5)/(d*(16*tan(c/2 + (d*x)/2)^4 + 16*tan(c/2 + (d*x)/2)^6)) - (a*log(tan(c/2 + (d*x)/2)^2 + 1))/d + (3*a*tan(c/2 + (d*x)/2)^2)/(16*d) - (a*tan(c/2 + (d*x)/2)^4)/(64*d) - (b*tan(c/2 + (d*x)/2)^3)/(24*d) + (a*log(tan(c/2 + (d*x)/2)))/d","B"
145,1,110,72,10.182692,"\text{Not used}","int(tan(c + d*x)^4*(a + b*sin(c + d*x)),x)","a\,x+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}-\frac{14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}-\frac{32\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{16\,b}{3}}{d\,{\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}^3\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}","Not used",1,"a*x + ((16*b)/3 + 2*a*tan(c/2 + (d*x)/2) - (14*a*tan(c/2 + (d*x)/2)^3)/3 - (14*a*tan(c/2 + (d*x)/2)^5)/3 + 2*a*tan(c/2 + (d*x)/2)^7 - (32*b*tan(c/2 + (d*x)/2)^2)/3)/(d*(tan(c/2 + (d*x)/2)^2 - 1)^3*(tan(c/2 + (d*x)/2)^2 + 1))","B"
146,1,55,38,6.595192,"\text{Not used}","int(tan(c + d*x)^2*(a + b*sin(c + d*x)),x)","-a\,x-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,b}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}","Not used",1,"- a*x - (4*b + 2*a*tan(c/2 + (d*x)/2) + 2*a*tan(c/2 + (d*x)/2)^3)/(d*(tan(c/2 + (d*x)/2)^4 - 1))","B"
147,1,158,41,6.597232,"\text{Not used}","int(cot(c + d*x)^2*(a + b*sin(c + d*x)),x)","\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}+\frac{b\,\ln\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)}^2-4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a}{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)\right)}+\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,b\,a}-\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,b\,a}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2))/(2*d) + (b*log(tan(c/2 + (d*x)/2)))/d - (a - 4*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)/(d*(2*tan(c/2 + (d*x)/2) + 2*tan(c/2 + (d*x)/2)^3)) + (2*a*atan((4*a^2)/(4*a*b + 4*a^2*tan(c/2 + (d*x)/2)) - (4*a*b*tan(c/2 + (d*x)/2))/(4*a*b + 4*a^2*tan(c/2 + (d*x)/2))))/d","B"
148,1,225,82,6.294193,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x)),x)","\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{-5\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+17\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-\frac{14\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{a}{3}}{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)}^3\right)}-\frac{5\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{2\,d}-\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,b\,a}-\frac{6\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,b\,a}\right)}{d}","Not used",1,"(a*tan(c/2 + (d*x)/2)^3)/(24*d) - (a/3 + b*tan(c/2 + (d*x)/2) - (14*a*tan(c/2 + (d*x)/2)^2)/3 - 5*a*tan(c/2 + (d*x)/2)^4 + 17*b*tan(c/2 + (d*x)/2)^3)/(d*(8*tan(c/2 + (d*x)/2)^3 + 8*tan(c/2 + (d*x)/2)^5)) - (5*a*tan(c/2 + (d*x)/2))/(8*d) + (b*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*b*log(tan(c/2 + (d*x)/2)))/(2*d) - (2*a*atan((4*a^2)/(6*a*b + 4*a^2*tan(c/2 + (d*x)/2)) - (6*a*b*tan(c/2 + (d*x)/2))/(6*a*b + 4*a^2*tan(c/2 + (d*x)/2))))/d","B"
149,1,288,122,6.299328,"\text{Not used}","int(cot(c + d*x)^6*(a + b*sin(c + d*x)),x)","\frac{11\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{16\,d}-\frac{22\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-72\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{59\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}-\frac{15\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{2}-\frac{32\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{15}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}+\frac{a}{5}}{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)}^5\right)}-\frac{7\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{96\,d}+\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{15\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{8\,d}+\frac{2\,a\,\mathrm{atan}\left(\frac{4\,a^2}{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+\frac{15\,b\,a}{2}}-\frac{15\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,\left(4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+\frac{15\,b\,a}{2}\right)}\right)}{d}","Not used",1,"(11*a*tan(c/2 + (d*x)/2))/(16*d) - (a/5 + (b*tan(c/2 + (d*x)/2))/2 - (32*a*tan(c/2 + (d*x)/2)^2)/15 + (59*a*tan(c/2 + (d*x)/2)^4)/3 + 22*a*tan(c/2 + (d*x)/2)^6 - (15*b*tan(c/2 + (d*x)/2)^3)/2 - 72*b*tan(c/2 + (d*x)/2)^5)/(d*(32*tan(c/2 + (d*x)/2)^5 + 32*tan(c/2 + (d*x)/2)^7)) - (7*a*tan(c/2 + (d*x)/2)^3)/(96*d) + (a*tan(c/2 + (d*x)/2)^5)/(160*d) - (b*tan(c/2 + (d*x)/2)^2)/(4*d) + (b*tan(c/2 + (d*x)/2)^4)/(64*d) + (15*b*log(tan(c/2 + (d*x)/2)))/(8*d) + (2*a*atan((4*a^2)/((15*a*b)/2 + 4*a^2*tan(c/2 + (d*x)/2)) - (15*a*b*tan(c/2 + (d*x)/2))/(2*((15*a*b)/2 + 4*a^2*tan(c/2 + (d*x)/2)))))/d","B"
150,1,232,111,6.722146,"\text{Not used}","int(tan(c + d*x)^3*(a + b*sin(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2+4\,b^2\right)+4\,a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+1\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2+2\,b^2\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(a+b\right)\,\left(a+2\,b\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(a-b\right)\,\left(a-2\,b\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(2*a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^6*(2*a^2 + 4*b^2) + 4*a^2*tan(c/2 + (d*x)/2)^4 + 2*a*b*tan(c/2 + (d*x)/2)^3 + 2*a*b*tan(c/2 + (d*x)/2)^5 + 6*a*b*tan(c/2 + (d*x)/2)^7 + 6*a*b*tan(c/2 + (d*x)/2))/(d*(tan(c/2 + (d*x)/2)^8 - 2*tan(c/2 + (d*x)/2)^4 + 1)) - (log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 + 2*b^2))/d + (log(tan(c/2 + (d*x)/2) - 1)*(a + b)*(a + 2*b))/d + (log(tan(c/2 + (d*x)/2) + 1)*(a - b)*(a - 2*b))/d","B"
151,1,150,78,6.366115,"\text{Not used}","int(tan(c + d*x)*(a + b*sin(c + d*x))^2,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2+b^2\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left(a+b\right)}^2}{d}-\frac{2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,{\left(a-b\right)}^2}{d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 + b^2))/d - (log(tan(c/2 + (d*x)/2) - 1)*(a + b)^2)/d - (2*b^2*tan(c/2 + (d*x)/2)^2 + 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (log(tan(c/2 + (d*x)/2) + 1)*(a - b)^2)/d","B"
152,1,117,46,6.436385,"\text{Not used}","int(cot(c + d*x)*(a + b*sin(c + d*x))^2,x)","\frac{a^2\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}+\frac{2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^2\,\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}{d}","Not used",1,"(a^2*log(tan(c/2 + (d*x)/2)))/d + (2*b^2*tan(c/2 + (d*x)/2)^2 + 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(2*tan(c/2 + (d*x)/2)^2 + tan(c/2 + (d*x)/2)^4 + 1)) - (a^2*log(tan(c/2 + (d*x)/2)^2 + 1))/d","B"
153,1,221,84,6.385201,"\text{Not used}","int(cot(c + d*x)^3*(a + b*sin(c + d*x))^2,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2-b^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{a^2}{2}+8\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\frac{a^2}{2}+24\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+20\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-b^2\right)}{d}-\frac{a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 - b^2))/d - (tan(c/2 + (d*x)/2)^4*(a^2/2 + 8*b^2) + a^2*tan(c/2 + (d*x)/2)^2 + a^2/2 + 24*a*b*tan(c/2 + (d*x)/2)^3 + 20*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 8*tan(c/2 + (d*x)/2)^4 + 4*tan(c/2 + (d*x)/2)^6)) - (a^2*tan(c/2 + (d*x)/2)^2)/(8*d) - (log(tan(c/2 + (d*x)/2))*(a^2 - b^2))/d - (a*b*tan(c/2 + (d*x)/2))/d","B"
154,1,310,126,6.444303,"\text{Not used}","int(cot(c + d*x)^5*(a + b*sin(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^2}{2}-2\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{23\,a^2}{4}-4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^2+30\,b^2\right)-\frac{a^2}{4}+\frac{76\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{3}+\frac{356\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{3}+92\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-\frac{4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^2-2\,b^2\right)}{d}-\frac{a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-2\,b^2\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a^2}{16}-\frac{b^2}{8}\right)}{d}-\frac{a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,d}+\frac{7\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*((5*a^2)/2 - 2*b^2) + tan(c/2 + (d*x)/2)^4*((23*a^2)/4 - 4*b^2) + tan(c/2 + (d*x)/2)^6*(3*a^2 + 30*b^2) - a^2/4 + (76*a*b*tan(c/2 + (d*x)/2)^3)/3 + (356*a*b*tan(c/2 + (d*x)/2)^5)/3 + 92*a*b*tan(c/2 + (d*x)/2)^7 - (4*a*b*tan(c/2 + (d*x)/2))/3)/(d*(16*tan(c/2 + (d*x)/2)^4 + 32*tan(c/2 + (d*x)/2)^6 + 16*tan(c/2 + (d*x)/2)^8)) - (log(tan(c/2 + (d*x)/2)^2 + 1)*(a^2 - 2*b^2))/d - (a^2*tan(c/2 + (d*x)/2)^4)/(64*d) + (log(tan(c/2 + (d*x)/2))*(a^2 - 2*b^2))/d + (tan(c/2 + (d*x)/2)^2*((3*a^2)/16 - b^2/8))/d - (a*b*tan(c/2 + (d*x)/2)^3)/(12*d) + (7*a*b*tan(c/2 + (d*x)/2))/(4*d)","B"
155,1,235,149,10.036372,"\text{Not used}","int(tan(c + d*x)^4*(a + b*sin(c + d*x))^2,x)","\frac{x\,\left(2\,a^2+5\,b^2\right)}{2}-\frac{\left(-2\,a^2-5\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(\frac{8\,a^2}{3}+\frac{20\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(\frac{28\,a^2}{3}+\frac{22\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\frac{64\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{3}+\left(\frac{8\,a^2}{3}+\frac{20\,b^2}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\frac{32\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{3}+\left(-2\,a^2-5\,b^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{32\,a\,b}{3}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-{\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+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}","Not used",1,"(x*(2*a^2 + 5*b^2))/2 - (tan(c/2 + (d*x)/2)^3*((8*a^2)/3 + (20*b^2)/3) - tan(c/2 + (d*x)/2)^9*(2*a^2 + 5*b^2) - (32*a*b)/3 + tan(c/2 + (d*x)/2)^7*((8*a^2)/3 + (20*b^2)/3) + tan(c/2 + (d*x)/2)^5*((28*a^2)/3 + (22*b^2)/3) - tan(c/2 + (d*x)/2)*(2*a^2 + 5*b^2) + (32*a*b*tan(c/2 + (d*x)/2)^2)/3 + (64*a*b*tan(c/2 + (d*x)/2)^4)/3)/(d*(tan(c/2 + (d*x)/2)^2 + 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 - 1))","B"
156,1,147,94,9.286726,"\text{Not used}","int(tan(c + d*x)^2*(a + b*sin(c + d*x))^2,x)","\frac{\left(2\,a^2+3\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(4\,a^2+2\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(2\,a^2+3\,b^2\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,a\,b}{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)}-\frac{x\,\left(2\,a^2+3\,b^2\right)}{2}","Not used",1,"(8*a*b + tan(c/2 + (d*x)/2)^3*(4*a^2 + 2*b^2) + tan(c/2 + (d*x)/2)^5*(2*a^2 + 3*b^2) + tan(c/2 + (d*x)/2)*(2*a^2 + 3*b^2) + 8*a*b*tan(c/2 + (d*x)/2)^2)/(d*(tan(c/2 + (d*x)/2)^2 - tan(c/2 + (d*x)/2)^4 - tan(c/2 + (d*x)/2)^6 + 1)) - (x*(2*a^2 + 3*b^2))/2","B"
157,1,277,78,7.273037,"\text{Not used}","int(cot(c + d*x)^2*(a + b*sin(c + d*x))^2,x)","\frac{b^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)-2\,a^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)+2\,a\,b\,\ln\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)-\frac{b^2\,\cos\left(c+d\,x\right)}{8}+\frac{b^2\,\cos\left(3\,c+3\,d\,x\right)}{8}-a\,b\,\sin\left(2\,c+2\,d\,x\right)}{d\,\sin\left(c+d\,x\right)}","Not used",1,"(b^2*atan((b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 4*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - b^2*sin(c/2 + (d*x)/2) + 4*a*b*cos(c/2 + (d*x)/2))) - 2*a^2*atan((b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 4*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - b^2*sin(c/2 + (d*x)/2) + 4*a*b*cos(c/2 + (d*x)/2))) + 2*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (a^2*cos(c + d*x) - (b^2*cos(c + d*x))/8 + (b^2*cos(3*c + 3*d*x))/8 - a*b*sin(2*c + 2*d*x))/(d*sin(c + d*x))","B"
158,1,584,133,8.997163,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x))^2,x)","-\frac{\frac{5\,b^2\,\cos\left(c+d\,x\right)}{16}+\frac{a^2\,\cos\left(3\,c+3\,d\,x\right)}{3}-\frac{11\,b^2\,\cos\left(3\,c+3\,d\,x\right)}{32}+\frac{b^2\,\cos\left(5\,c+5\,d\,x\right)}{32}+\frac{a^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{2}-\frac{3\,b^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{4}+\frac{3\,a\,b\,\sin\left(c+d\,x\right)}{2}-\frac{3\,a^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{2}+\frac{9\,b^2\,\mathrm{atan}\left(\frac{-2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{2\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+6\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{4}+a\,b\,\sin\left(2\,c+2\,d\,x\right)-\frac{a\,b\,\sin\left(3\,c+3\,d\,x\right)}{2}-\frac{a\,b\,\sin\left(4\,c+4\,d\,x\right)}{4}+\frac{9\,a\,b\,\sin\left(c+d\,x\right)\,\ln\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{3\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{4}}{d\,{\sin\left(c+d\,x\right)}^3}","Not used",1,"-((5*b^2*cos(c + d*x))/16 + (a^2*cos(3*c + 3*d*x))/3 - (11*b^2*cos(3*c + 3*d*x))/32 + (b^2*cos(5*c + 5*d*x))/32 + (a^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/2 - (3*b^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/4 + (3*a*b*sin(c + d*x))/2 - (3*a^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/2 + (9*b^2*atan((3*b^2*cos(c/2 + (d*x)/2) - 2*a^2*cos(c/2 + (d*x)/2) + 6*a*b*sin(c/2 + (d*x)/2))/(2*a^2*sin(c/2 + (d*x)/2) - 3*b^2*sin(c/2 + (d*x)/2) + 6*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/4 + a*b*sin(2*c + 2*d*x) - (a*b*sin(3*c + 3*d*x))/2 - (a*b*sin(4*c + 4*d*x))/4 + (9*a*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/4 - (3*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/4)/(d*sin(c + d*x)^3)","B"
159,1,888,202,11.280202,"\text{Not used}","int(cot(c + d*x)^6*(a + b*sin(c + d*x))^2,x)","\frac{\frac{95\,b^2\,\cos\left(c+d\,x\right)}{384}-\frac{5\,a^2\,\cos\left(c+d\,x\right)}{24}+\frac{5\,a^2\,\cos\left(3\,c+3\,d\,x\right)}{48}-\frac{23\,a^2\,\cos\left(5\,c+5\,d\,x\right)}{240}-\frac{163\,b^2\,\cos\left(3\,c+3\,d\,x\right)}{384}+\frac{71\,b^2\,\cos\left(5\,c+5\,d\,x\right)}{384}-\frac{b^2\,\cos\left(7\,c+7\,d\,x\right)}{128}+\frac{5\,a^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{8}-\frac{a^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(5\,c+5\,d\,x\right)}{8}-\frac{25\,b^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(3\,c+3\,d\,x\right)}{16}+\frac{5\,b^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(5\,c+5\,d\,x\right)}{16}+\frac{5\,a\,b\,\sin\left(c+d\,x\right)}{4}-\frac{5\,a^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{4}+\frac{25\,b^2\,\mathrm{atan}\left(\frac{-4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b+10\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}{4\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2+15\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b-10\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^2}\right)\,\sin\left(c+d\,x\right)}{8}+\frac{5\,a\,b\,\sin\left(2\,c+2\,d\,x\right)}{8}-\frac{5\,a\,b\,\sin\left(3\,c+3\,d\,x\right)}{8}-\frac{17\,a\,b\,\sin\left(4\,c+4\,d\,x\right)}{32}+\frac{a\,b\,\sin\left(5\,c+5\,d\,x\right)}{8}+\frac{a\,b\,\sin\left(6\,c+6\,d\,x\right)}{16}+\frac{75\,a\,b\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{32}-\frac{75\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(3\,c+3\,d\,x\right)}{64}+\frac{15\,a\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\sin\left(5\,c+5\,d\,x\right)}{64}}{d\,{\sin\left(c+d\,x\right)}^5}","Not used",1,"((95*b^2*cos(c + d*x))/384 - (5*a^2*cos(c + d*x))/24 + (5*a^2*cos(3*c + 3*d*x))/48 - (23*a^2*cos(5*c + 5*d*x))/240 - (163*b^2*cos(3*c + 3*d*x))/384 + (71*b^2*cos(5*c + 5*d*x))/384 - (b^2*cos(7*c + 7*d*x))/128 + (5*a^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/8 - (a^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(5*c + 5*d*x))/8 - (25*b^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(3*c + 3*d*x))/16 + (5*b^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(5*c + 5*d*x))/16 + (5*a*b*sin(c + d*x))/4 - (5*a^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/4 + (25*b^2*atan((10*b^2*cos(c/2 + (d*x)/2) - 4*a^2*cos(c/2 + (d*x)/2) + 15*a*b*sin(c/2 + (d*x)/2))/(4*a^2*sin(c/2 + (d*x)/2) - 10*b^2*sin(c/2 + (d*x)/2) + 15*a*b*cos(c/2 + (d*x)/2)))*sin(c + d*x))/8 + (5*a*b*sin(2*c + 2*d*x))/8 - (5*a*b*sin(3*c + 3*d*x))/8 - (17*a*b*sin(4*c + 4*d*x))/32 + (a*b*sin(5*c + 5*d*x))/8 + (a*b*sin(6*c + 6*d*x))/16 + (75*a*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/32 - (75*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(3*c + 3*d*x))/64 + (15*a*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*sin(5*c + 5*d*x))/64)/(d*sin(c + d*x)^5)","B"
160,1,366,150,6.981292,"\text{Not used}","int(tan(c + d*x)^3*(a + b*sin(c + d*x))^3,x)","\frac{\left(9\,a^2\,b+5\,b^3\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+\left(2\,a^3+12\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+\left(12\,a^2\,b+\frac{20\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+\left(6\,a^3+12\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+\left(6\,a^2\,b-\frac{22\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+\left(6\,a^3+12\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+\left(12\,a^2\,b+\frac{20\,b^3}{3}\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+\left(2\,a^3+12\,a\,b^2\right)\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+\left(9\,a^2\,b+5\,b^3\right)\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+{\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+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^3+6\,a\,b^2\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,{\left(a-b\right)}^2\,\left(a-\frac{5\,b}{2}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left(a+b\right)}^2\,\left(a+\frac{5\,b}{2}\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(9*a^2*b + 5*b^3) + tan(c/2 + (d*x)/2)^2*(12*a*b^2 + 2*a^3) + tan(c/2 + (d*x)/2)^4*(12*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^8*(12*a*b^2 + 2*a^3) + tan(c/2 + (d*x)/2)^6*(12*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^9*(9*a^2*b + 5*b^3) + tan(c/2 + (d*x)/2)^5*(6*a^2*b - (22*b^3)/3) + tan(c/2 + (d*x)/2)^3*(12*a^2*b + (20*b^3)/3) + tan(c/2 + (d*x)/2)^7*(12*a^2*b + (20*b^3)/3))/(d*(tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^10 + 1)) - (log(tan(c/2 + (d*x)/2)^2 + 1)*(6*a*b^2 + a^3))/d + (log(tan(c/2 + (d*x)/2) + 1)*(a - b)^2*(a - (5*b)/2))/d + (log(tan(c/2 + (d*x)/2) - 1)*(a + b)^2*(a + (5*b)/2))/d","B"
161,1,226,105,6.745606,"\text{Not used}","int(tan(c + d*x)*(a + b*sin(c + d*x))^3,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(a^3+3\,a\,b^2\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^2\,b+2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^2\,b+2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(12\,a^2\,b+\frac{20\,b^3}{3}\right)+6\,a\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+6\,a\,b^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)}^6+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,{\left(a-b\right)}^3}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,{\left(a+b\right)}^3}{d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(3*a*b^2 + a^3))/d - (tan(c/2 + (d*x)/2)*(6*a^2*b + 2*b^3) + tan(c/2 + (d*x)/2)^5*(6*a^2*b + 2*b^3) + tan(c/2 + (d*x)/2)^3*(12*a^2*b + (20*b^3)/3) + 6*a*b^2*tan(c/2 + (d*x)/2)^2 + 6*a*b^2*tan(c/2 + (d*x)/2)^4)/(d*(3*tan(c/2 + (d*x)/2)^2 + 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 + 1)) - (log(tan(c/2 + (d*x)/2) + 1)*(a - b)^3)/d - (log(tan(c/2 + (d*x)/2) - 1)*(a + b)^3)/d","B"
162,1,118,67,6.677868,"\text{Not used}","int(cot(c + d*x)*(a + b*sin(c + d*x))^3,x)","\frac{b^3\,\sin\left(c+d\,x\right)}{3\,d}-\frac{a^3\,\ln\left(\frac{1}{{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}\right)}{d}+\frac{a^3\,\ln\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)}^2}{2\,d}-\frac{b^3\,{\cos\left(c+d\,x\right)}^2\,\sin\left(c+d\,x\right)}{3\,d}+\frac{3\,a^2\,b\,\sin\left(c+d\,x\right)}{d}","Not used",1,"(b^3*sin(c + d*x))/(3*d) - (a^3*log(1/cos(c/2 + (d*x)/2)^2))/d + (a^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/d - (3*a*b^2*cos(c + d*x)^2)/(2*d) - (b^3*cos(c + d*x)^2*sin(c + d*x))/(3*d) + (3*a^2*b*sin(c + d*x))/d","B"
163,1,312,116,6.945959,"\text{Not used}","int(cot(c + d*x)^3*(a + b*sin(c + d*x))^3,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a\,b^2-a^3\right)}{d}-\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(3\,a\,b^2-a^3\right)}{d}-\frac{\frac{3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{2}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{3\,a^3}{2}+24\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{a^3}{2}+24\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(30\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(42\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(66\,a^2\,b-\frac{16\,b^3}{3}\right)+\frac{a^3}{2}+6\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+12\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,{\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\right)}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2))*(3*a*b^2 - a^3))/d - (log(tan(c/2 + (d*x)/2)^2 + 1)*(3*a*b^2 - a^3))/d - ((3*a^3*tan(c/2 + (d*x)/2)^2)/2 + tan(c/2 + (d*x)/2)^4*(24*a*b^2 + (3*a^3)/2) + tan(c/2 + (d*x)/2)^6*(24*a*b^2 + a^3/2) + tan(c/2 + (d*x)/2)^7*(30*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^3*(42*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^5*(66*a^2*b - (16*b^3)/3) + a^3/2 + 6*a^2*b*tan(c/2 + (d*x)/2))/(d*(4*tan(c/2 + (d*x)/2)^2 + 12*tan(c/2 + (d*x)/2)^4 + 12*tan(c/2 + (d*x)/2)^6 + 4*tan(c/2 + (d*x)/2)^8)) - (a^3*tan(c/2 + (d*x)/2)^2)/(8*d) - (3*a^2*b*tan(c/2 + (d*x)/2))/(2*d)","B"
164,1,424,165,6.969113,"\text{Not used}","int(cot(c + d*x)^5*(a + b*sin(c + d*x))^3,x)","\frac{\ln\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)\,\left(6\,a\,b^2-a^3\right)}{d}-\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a\,b^2}{8}-\frac{3\,a^3}{16}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(6\,a\,b^2-a^3\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(3\,a^3+90\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(18\,a\,b^2-\frac{33\,a^3}{4}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a\,b^2-\frac{9\,a^3}{4}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{35\,a^3}{4}+78\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(36\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(138\,a^2\,b-72\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(216\,a^2\,b-88\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(316\,a^2\,b-\frac{328\,b^3}{3}\right)-\frac{a^3}{4}-2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+48\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{21\,a^2\,b}{8}-\frac{b^3}{2}\right)}{d}-\frac{a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)^2 + 1)*(6*a*b^2 - a^3))/d - (a^3*tan(c/2 + (d*x)/2)^4)/(64*d) - (tan(c/2 + (d*x)/2)^2*((3*a*b^2)/8 - (3*a^3)/16))/d - (log(tan(c/2 + (d*x)/2))*(6*a*b^2 - a^3))/d + (tan(c/2 + (d*x)/2)^8*(90*a*b^2 + 3*a^3) - tan(c/2 + (d*x)/2)^4*(18*a*b^2 - (33*a^3)/4) - tan(c/2 + (d*x)/2)^2*(6*a*b^2 - (9*a^3)/4) + tan(c/2 + (d*x)/2)^6*(78*a*b^2 + (35*a^3)/4) + tan(c/2 + (d*x)/2)^3*(36*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^9*(138*a^2*b - 72*b^3) + tan(c/2 + (d*x)/2)^5*(216*a^2*b - 88*b^3) + tan(c/2 + (d*x)/2)^7*(316*a^2*b - (328*b^3)/3) - a^3/4 - 2*a^2*b*tan(c/2 + (d*x)/2))/(d*(16*tan(c/2 + (d*x)/2)^4 + 48*tan(c/2 + (d*x)/2)^6 + 48*tan(c/2 + (d*x)/2)^8 + 16*tan(c/2 + (d*x)/2)^10)) + (tan(c/2 + (d*x)/2)*((21*a^2*b)/8 - b^3/2))/d - (a^2*b*tan(c/2 + (d*x)/2)^3)/(8*d)","B"
165,1,297,220,9.196700,"\text{Not used}","int(tan(c + d*x)^4*(a + b*sin(c + d*x))^3,x)","\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+15\,b^2\right)}{2\,a^3+15\,a\,b^2}\right)\,\left(2\,a^2+15\,b^2\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{2\,a^3}{3}+5\,a\,b^2\right)-16\,a^2\,b-\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^3+15\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(\frac{2\,a^3}{3}+5\,a\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(2\,a^3+15\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,a^3+42\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(12\,a^3+42\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(48\,a^2\,b+32\,b^3\right)-\frac{32\,b^3}{3}+32\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-1\right)}","Not used",1,"(a*atan((a*tan(c/2 + (d*x)/2)*(2*a^2 + 15*b^2))/(15*a*b^2 + 2*a^3))*(2*a^2 + 15*b^2))/d - (tan(c/2 + (d*x)/2)^3*(5*a*b^2 + (2*a^3)/3) - 16*a^2*b - tan(c/2 + (d*x)/2)*(15*a*b^2 + 2*a^3) + tan(c/2 + (d*x)/2)^9*(5*a*b^2 + (2*a^3)/3) - tan(c/2 + (d*x)/2)^11*(15*a*b^2 + 2*a^3) + tan(c/2 + (d*x)/2)^5*(42*a*b^2 + 12*a^3) + tan(c/2 + (d*x)/2)^7*(42*a*b^2 + 12*a^3) + tan(c/2 + (d*x)/2)^4*(48*a^2*b + 32*b^3) - (32*b^3)/3 + 32*a^2*b*tan(c/2 + (d*x)/2)^6)/(d*(3*tan(c/2 + (d*x)/2)^4 - 3*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^12 - 1))","B"
166,1,249,146,9.151889,"\text{Not used}","int(tan(c + d*x)^2*(a + b*sin(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^3+9\,a\,b^2\right)+12\,a^2\,b+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^3+9\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^3+15\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(6\,a^3+15\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(24\,a^2\,b+\frac{32\,b^3}{3}\right)+\frac{16\,b^3}{3}+12\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{d\,\left(-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a\,\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^2+9\,b^2\right)}{2\,a^3+9\,a\,b^2}\right)\,\left(2\,a^2+9\,b^2\right)}{d}","Not used",1,"(tan(c/2 + (d*x)/2)*(9*a*b^2 + 2*a^3) + 12*a^2*b + tan(c/2 + (d*x)/2)^7*(9*a*b^2 + 2*a^3) + tan(c/2 + (d*x)/2)^3*(15*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^5*(15*a*b^2 + 6*a^3) + tan(c/2 + (d*x)/2)^2*(24*a^2*b + (32*b^3)/3) + (16*b^3)/3 + 12*a^2*b*tan(c/2 + (d*x)/2)^4)/(d*(2*tan(c/2 + (d*x)/2)^2 - 2*tan(c/2 + (d*x)/2)^6 - tan(c/2 + (d*x)/2)^8 + 1)) - (a*atan((a*tan(c/2 + (d*x)/2)*(2*a^2 + 9*b^2))/(9*a*b^2 + 2*a^3))*(2*a^2 + 9*b^2))/d","B"
167,1,289,102,6.856667,"\text{Not used}","int(cot(c + d*x)^2*(a + b*sin(c + d*x))^3,x)","\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(\frac{a\,b^2\,3{}\mathrm{i}}{2}-a^3\,1{}\mathrm{i}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^2\,b-\frac{4\,b^3}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^3+6\,a\,b^2\right)-3\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(6\,a\,b^2-3\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(12\,a^2\,b-4\,b^3\right)-a^3+24\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+6\,{\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{3\,a^2\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(2\,a^2-3\,b^2\right)\,1{}\mathrm{i}}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2))/(2*d) - (log(tan(c/2 + (d*x)/2) - 1i)*((a*b^2*3i)/2 - a^3*1i))/d + (tan(c/2 + (d*x)/2)*(12*a^2*b - (4*b^3)/3) - tan(c/2 + (d*x)/2)^6*(6*a*b^2 + a^3) - 3*a^3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^2*(6*a*b^2 - 3*a^3) + tan(c/2 + (d*x)/2)^5*(12*a^2*b - 4*b^3) - a^3 + 24*a^2*b*tan(c/2 + (d*x)/2)^3)/(d*(2*tan(c/2 + (d*x)/2) + 6*tan(c/2 + (d*x)/2)^3 + 6*tan(c/2 + (d*x)/2)^5 + 2*tan(c/2 + (d*x)/2)^7)) + (3*a^2*b*log(tan(c/2 + (d*x)/2)))/d - (a*log(tan(c/2 + (d*x)/2) + 1i)*(2*a^2 - 3*b^2)*1i)/(2*d)","B"
168,1,405,194,6.808505,"\text{Not used}","int(cot(c + d*x)^4*(a + b*sin(c + d*x))^3,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{9\,a^2\,b}{2}-b^3\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(\frac{a\,b^2\,9{}\mathrm{i}}{2}-a^3\,1{}\mathrm{i}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,a\,b^2}{2}-\frac{5\,a^3}{8}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(12\,a\,b^2-4\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(5\,a^3+12\,a\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(60\,a\,b^2-14\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(36\,a\,b^2-\frac{44\,a^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(51\,a^2\,b-32\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(57\,a^2\,b-\frac{64\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(105\,a^2\,b-32\,b^3\right)+\frac{a^3}{3}+3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+24\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+24\,{\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{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(2\,a^2-9\,b^2\right)\,1{}\mathrm{i}}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^3)/(24*d) - (log(tan(c/2 + (d*x)/2))*((9*a^2*b)/2 - b^3))/d - (log(tan(c/2 + (d*x)/2) + 1i)*((a*b^2*9i)/2 - a^3*1i))/d + (tan(c/2 + (d*x)/2)*((3*a*b^2)/2 - (5*a^3)/8))/d - (tan(c/2 + (d*x)/2)^2*(12*a*b^2 - 4*a^3) - tan(c/2 + (d*x)/2)^8*(12*a*b^2 + 5*a^3) + tan(c/2 + (d*x)/2)^4*(60*a*b^2 - 14*a^3) + tan(c/2 + (d*x)/2)^6*(36*a*b^2 - (44*a^3)/3) + tan(c/2 + (d*x)/2)^7*(51*a^2*b - 32*b^3) + tan(c/2 + (d*x)/2)^3*(57*a^2*b - (64*b^3)/3) + tan(c/2 + (d*x)/2)^5*(105*a^2*b - 32*b^3) + a^3/3 + 3*a^2*b*tan(c/2 + (d*x)/2))/(d*(8*tan(c/2 + (d*x)/2)^3 + 24*tan(c/2 + (d*x)/2)^5 + 24*tan(c/2 + (d*x)/2)^7 + 8*tan(c/2 + (d*x)/2)^9)) + (3*a^2*b*tan(c/2 + (d*x)/2)^2)/(8*d) - (a*log(tan(c/2 + (d*x)/2) - 1i)*(2*a^2 - 9*b^2)*1i)/(2*d)","B"
169,1,507,291,7.057585,"\text{Not used}","int(cot(c + d*x)^6*(a + b*sin(c + d*x))^3,x)","\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(12\,a\,b^2-22\,a^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(4\,a\,b^2-\frac{26\,a^3}{15}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(96\,a\,b^2-\frac{78\,a^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(320\,a\,b^2-\frac{191\,a^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(408\,a\,b^2-\frac{296\,a^3}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{39\,a^2\,b}{2}-4\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(216\,a^2\,b-196\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{519\,a^2\,b}{2}-\frac{484\,b^3}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(\frac{909\,a^2\,b}{2}-268\,b^3\right)-\frac{a^3}{5}-\frac{3\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{d\,\left(32\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+96\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+96\,{\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)}^3\,\left(\frac{a\,b^2}{8}-\frac{7\,a^3}{96}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,a^2\,b}{4}-\frac{b^3}{8}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{45\,a^2\,b}{8}-\frac{5\,b^3}{2}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\mathrm{i}\right)\,\left(\frac{a\,b^2\,15{}\mathrm{i}}{2}-a^3\,1{}\mathrm{i}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{27\,a\,b^2}{8}-\frac{11\,a^3}{16}\right)}{d}+\frac{3\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,d}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1{}\mathrm{i}\right)\,\left(2\,a^2-15\,b^2\right)\,1{}\mathrm{i}}{2\,d}","Not used",1,"(a^3*tan(c/2 + (d*x)/2)^5)/(160*d) + (tan(c/2 + (d*x)/2)^10*(12*a*b^2 - 22*a^3) - tan(c/2 + (d*x)/2)^2*(4*a*b^2 - (26*a^3)/15) + tan(c/2 + (d*x)/2)^4*(96*a*b^2 - (78*a^3)/5) + tan(c/2 + (d*x)/2)^8*(320*a*b^2 - (191*a^3)/3) + tan(c/2 + (d*x)/2)^6*(408*a*b^2 - (296*a^3)/5) + tan(c/2 + (d*x)/2)^3*((39*a^2*b)/2 - 4*b^3) + tan(c/2 + (d*x)/2)^9*(216*a^2*b - 196*b^3) + tan(c/2 + (d*x)/2)^5*((519*a^2*b)/2 - (484*b^3)/3) + tan(c/2 + (d*x)/2)^7*((909*a^2*b)/2 - 268*b^3) - a^3/5 - (3*a^2*b*tan(c/2 + (d*x)/2))/2)/(d*(32*tan(c/2 + (d*x)/2)^5 + 96*tan(c/2 + (d*x)/2)^7 + 96*tan(c/2 + (d*x)/2)^9 + 32*tan(c/2 + (d*x)/2)^11)) + (tan(c/2 + (d*x)/2)^3*((a*b^2)/8 - (7*a^3)/96))/d - (tan(c/2 + (d*x)/2)^2*((3*a^2*b)/4 - b^3/8))/d + (log(tan(c/2 + (d*x)/2))*((45*a^2*b)/8 - (5*b^3)/2))/d - (log(tan(c/2 + (d*x)/2) - 1i)*((a*b^2*15i)/2 - a^3*1i))/d - (tan(c/2 + (d*x)/2)*((27*a*b^2)/8 - (11*a^3)/16))/d + (3*a^2*b*tan(c/2 + (d*x)/2)^4)/(64*d) - (a*log(tan(c/2 + (d*x)/2) + 1i)*(2*a^2 - 15*b^2)*1i)/(2*d)","B"
170,1,498,204,7.426271,"\text{Not used}","int(tan(c + d*x)^5/(a + b*sin(c + d*x)),x)","\frac{a^5\,\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{1}{a+b}-\frac{7\,b}{8\,{\left(a+b\right)}^2}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}+\frac{7\,b}{8\,{\left(a-b\right)}^2}+\frac{1}{a-b}\right)}{d}-\frac{\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a\,b^2-2\,a^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(7\,a^2\,b-3\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(15\,a^2\,b-11\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(15\,a^2\,b-11\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^2-3\,b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\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,"(a^5*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (log(tan(c/2 + (d*x)/2) - 1)*(1/(a + b) - (7*b)/(8*(a + b)^2) + b^2/(4*(a + b)^3)))/d - (log(tan(c/2 + (d*x)/2) + 1)*(b^2/(4*(a - b)^3) + (7*b)/(8*(a - b)^2) + 1/(a - b)))/d - ((2*a^3*tan(c/2 + (d*x)/2)^2)/(a^4 + b^4 - 2*a^2*b^2) + (2*a^3*tan(c/2 + (d*x)/2)^6)/(a^4 + b^4 - 2*a^2*b^2) + (4*tan(c/2 + (d*x)/2)^4*(a*b^2 - 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) - (tan(c/2 + (d*x)/2)^7*(7*a^2*b - 3*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^3*(15*a^2*b - 11*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (tan(c/2 + (d*x)/2)^5*(15*a^2*b - 11*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (b*tan(c/2 + (d*x)/2)*(7*a^2 - 3*b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(d*(6*tan(c/2 + (d*x)/2)^4 - 4*tan(c/2 + (d*x)/2)^2 - 4*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^8 + 1))","B"
171,1,217,126,7.035050,"\text{Not used}","int(tan(c + d*x)^3/(a + b*sin(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(2\,a-b\right)}{2\,d\,{\left(a-b\right)}^2}-\frac{\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2-b^2}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2-b^2}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a^2-b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+1\right)}-\frac{a^3\,\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(2\,a+b\right)}{2\,d\,{\left(a+b\right)}^2}","Not used",1,"(log(tan(c/2 + (d*x)/2) + 1)*(2*a - b))/(2*d*(a - b)^2) - ((b*tan(c/2 + (d*x)/2))/(a^2 - b^2) - (2*a*tan(c/2 + (d*x)/2)^2)/(a^2 - b^2) + (b*tan(c/2 + (d*x)/2)^3)/(a^2 - b^2))/(d*(tan(c/2 + (d*x)/2)^4 - 2*tan(c/2 + (d*x)/2)^2 + 1)) - (a^3*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^4 + b^4 - 2*a^2*b^2)) + (log(tan(c/2 + (d*x)/2) - 1)*(2*a + b))/(2*d*(a + b)^2)","B"
172,1,91,74,6.731655,"\text{Not used}","int(tan(c + d*x)/(a + b*sin(c + d*x)),x)","\frac{a\,\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{d\,\left(a^2-b^2\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{d\,\left(a-b\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d\,\left(a+b\right)}","Not used",1,"(a*log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(d*(a^2 - b^2)) - log(tan(c/2 + (d*x)/2) + 1)/(d*(a - b)) - log(tan(c/2 + (d*x)/2) - 1)/(d*(a + b))","B"
173,1,48,34,6.361881,"\text{Not used}","int(cot(c + d*x)/(a + b*sin(c + d*x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)-\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{a\,d}","Not used",1,"(log(tan(c/2 + (d*x)/2)) - log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))/(a*d)","B"
174,1,144,84,6.632133,"\text{Not used}","int(cot(c + d*x)^3/(a + b*sin(c + d*x)),x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^2\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-b^2\right)}{a^3\,d}-\frac{\frac{a}{2}-2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{4\,a^2\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}+\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^2-b^2\right)}{a^3\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(2*a^2*d) - tan(c/2 + (d*x)/2)^2/(8*a*d) - (log(tan(c/2 + (d*x)/2))*(a^2 - b^2))/(a^3*d) - (a/2 - 2*b*tan(c/2 + (d*x)/2))/(4*a^2*d*tan(c/2 + (d*x)/2)^2) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 - b^2))/(a^3*d)","B"
175,1,281,148,6.408665,"\text{Not used}","int(cot(c + d*x)^5/(a + b*sin(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3}{16\,a}-\frac{b^2}{8\,a^3}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b}{8\,a^2}+\frac{2\,b\,\left(\frac{3}{8\,a}-\frac{b^2}{4\,a^3}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a\,b^2-3\,a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(14\,a^2\,b-8\,b^3\right)+\frac{a^3}{4}-\frac{2\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{16\,a^4\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}-\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{a^5\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(3/(16*a) - b^2/(8*a^3)))/d - tan(c/2 + (d*x)/2)^4/(64*a*d) - (tan(c/2 + (d*x)/2)*(b/(8*a^2) + (2*b*(3/(8*a) - b^2/(4*a^3)))/a))/d - (tan(c/2 + (d*x)/2)^2*(2*a*b^2 - 3*a^3) + tan(c/2 + (d*x)/2)^3*(14*a^2*b - 8*b^3) + a^3/4 - (2*a^2*b*tan(c/2 + (d*x)/2))/3)/(16*a^4*d*tan(c/2 + (d*x)/2)^4) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 + b^4 - 2*a^2*b^2))/(a^5*d) + (b*tan(c/2 + (d*x)/2)^3)/(24*a^2*d) + (log(tan(c/2 + (d*x)/2))*(a^4 + b^4 - 2*a^2*b^2))/(a^5*d)","B"
176,1,372,177,9.546876,"\text{Not used}","int(tan(c + d*x)^4/(a + b*sin(c + d*x)),x)","\frac{\frac{2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,\left(5\,a^2\,b-2\,b^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a\,b^2-5\,a^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2\,b-b^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^4-2\,a^2\,b^2+b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}+\frac{2\,a^4\,\mathrm{atan}\left(\frac{\frac{a^4\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}+\frac{2\,a^5\,\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)}^{5/2}}}{2\,a^4}\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"((2*a^3*tan(c/2 + (d*x)/2))/(a^4 + b^4 - 2*a^2*b^2) - (2*(5*a^2*b - 2*b^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*a^3*tan(c/2 + (d*x)/2)^5)/(a^4 + b^4 - 2*a^2*b^2) + (4*tan(c/2 + (d*x)/2)^3*(2*a*b^2 - 5*a^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (4*tan(c/2 + (d*x)/2)^2*(2*a^2*b - b^3))/(a^4 + b^4 - 2*a^2*b^2) - (2*a^2*b*tan(c/2 + (d*x)/2)^4)/(a^4 + b^4 - 2*a^2*b^2))/(d*(3*tan(c/2 + (d*x)/2)^2 - 3*tan(c/2 + (d*x)/2)^4 + tan(c/2 + (d*x)/2)^6 - 1)) + (2*a^4*atan(((a^4*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a^5*tan(c/2 + (d*x)/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(2*a^4)))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
177,1,148,96,6.368758,"\text{Not used}","int(tan(c + d*x)^2/(a + b*sin(c + d*x)),x)","\frac{\frac{2\,b}{a^2-b^2}-\frac{2\,a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^2-b^2}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2-1\right)}-\frac{2\,a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(2\,a^2\,b-2\,b^3\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}+\frac{2\,a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2-b^2\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}}{2\,a^2}\right)}{d\,{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}","Not used",1,"((2*b)/(a^2 - b^2) - (2*a*tan(c/2 + (d*x)/2))/(a^2 - b^2))/(d*(tan(c/2 + (d*x)/2)^2 - 1)) - (2*a^2*atan(((a^2*(2*a^2*b - 2*b^3))/((a + b)^(3/2)*(a - b)^(3/2)) + (2*a^3*tan(c/2 + (d*x)/2)*(a^2 - b^2))/((a + b)^(3/2)*(a - b)^(3/2)))/(2*a^2)))/(d*(a + b)^(3/2)*(a - b)^(3/2))","B"
178,1,204,80,6.999879,"\text{Not used}","int(cot(c + d*x)^2/(a + b*sin(c + d*x)),x)","-\frac{\mathrm{cot}\left(c+d\,x\right)}{a\,d}-\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}+\frac{\mathrm{atan}\left(\frac{a^3\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a\,b^2\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-b^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,3{}\mathrm{i}}{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-2\,a^3\,b-5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+2\,a\,b^3+4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}}{a^2\,d}","Not used",1,"(atan((a^3*(b^2 - a^2)^(1/2)*1i - a*b^2*(b^2 - a^2)^(1/2)*2i - b^3*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*tan(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*3i)/(2*a*b^3 - 2*a^3*b + a^4*tan(c/2 + (d*x)/2) + 4*b^4*tan(c/2 + (d*x)/2) - 5*a^2*b^2*tan(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i)/(a^2*d) - cot(c + d*x)/(a*d) - (b*log(tan(c/2 + (d*x)/2)))/(a^2*d)","B"
179,1,654,154,7.143697,"\text{Not used}","int(cot(c + d*x)^4/(a + b*sin(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}-\frac{{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a\,d}+\frac{5\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}-\frac{5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{8\,a\,d}+\frac{3\,b\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{2\,a^2\,d}-\frac{b^3\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)}{a^4\,d}+\frac{b\,{\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{b^2\,\mathrm{cot}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}+\frac{b^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}+\frac{\mathrm{atan}\left(\frac{2\,a^5\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}+8\,b^5\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}-7\,a^3\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}-16\,a^2\,b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}+4\,a\,b^4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}+7\,a^4\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{2{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^8-5{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^7\,b-16{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^6\,b^2+14{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^5\,b^3+34{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4\,b^4-13{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b^5-28{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^6+4{}\mathrm{i}\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^7+8{}\mathrm{i}\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^8}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^4\,d}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a*d) - cot(c/2 + (d*x)/2)^3/(24*a*d) + (5*cot(c/2 + (d*x)/2))/(8*a*d) - (5*tan(c/2 + (d*x)/2))/(8*a*d) + (3*b*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(2*a^2*d) - (b^3*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)))/(a^4*d) + (b*cot(c/2 + (d*x)/2)^2)/(8*a^2*d) - (b^2*cot(c/2 + (d*x)/2))/(2*a^3*d) - (b*tan(c/2 + (d*x)/2)^2)/(8*a^2*d) + (b^2*tan(c/2 + (d*x)/2))/(2*a^3*d) + (atan((2*a^5*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 8*b^5*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 7*a^3*b^2*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) - 16*a^2*b^3*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 4*a*b^4*cos(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2) + 7*a^4*b*sin(c/2 + (d*x)/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(a^8*sin(c/2 + (d*x)/2)*2i + b^8*sin(c/2 + (d*x)/2)*8i + a*b^7*cos(c/2 + (d*x)/2)*4i - a^7*b*cos(c/2 + (d*x)/2)*5i - a^3*b^5*cos(c/2 + (d*x)/2)*13i + a^5*b^3*cos(c/2 + (d*x)/2)*14i - a^2*b^6*sin(c/2 + (d*x)/2)*28i + a^4*b^4*sin(c/2 + (d*x)/2)*34i - a^6*b^2*sin(c/2 + (d*x)/2)*16i))*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^4*d)","B"
180,1,1099,307,7.129573,"\text{Not used}","int(cot(c + d*x)^6/(a + b*sin(c + d*x)),x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b}{32\,a^2}+\frac{b\,\left(\frac{7}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b^2}{8\,a^3}-\frac{11}{16\,a}+\frac{2\,b\,\left(\frac{b}{16\,a^2}+\frac{2\,b\,\left(\frac{7}{32\,a}-\frac{b^2}{8\,a^3}\right)}{a}\right)}{a}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{7}{96\,a}-\frac{b^2}{24\,a^3}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(\frac{15\,a^4\,b}{8}-\frac{5\,a^2\,b^3}{2}+b^5\right)}{a^6\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{7\,a^4}{3}-\frac{4\,a^2\,b^2}{3}\right)-\frac{a^4}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(22\,a^4-36\,a^2\,b^2+16\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a\,b^3-8\,a^3\,b\right)+\frac{a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2}}{32\,a^5\,d\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)\,1{}\mathrm{i}}{a^6}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)\,1{}\mathrm{i}}{a^6}}{\frac{15\,a^{10}\,b-65\,a^8\,b^3+113\,a^6\,b^5-99\,a^4\,b^7+44\,a^2\,b^9-8\,b^{11}}{2\,a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}-66\,a^8\,b^2+110\,a^6\,b^4-94\,a^4\,b^6+42\,a^2\,b^8-8\,b^{10}\right)}{2\,a^9}-\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)}{a^6}+\frac{\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{8\,a^{12}-39\,a^{10}\,b^2+44\,a^8\,b^4-16\,a^6\,b^6}{4\,a^{10}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{12}-32\,a^{10}\,b^2\right)}{4\,a^9}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a^6}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(31\,a^{10}\,b-98\,a^8\,b^3+96\,a^6\,b^5-32\,a^4\,b^7\right)}{4\,a^9}\right)}{a^6}}\right)\,\sqrt{-{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a^6\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a*d) + (tan(c/2 + (d*x)/2)^2*(b/(32*a^2) + (b*(7/(32*a) - b^2/(8*a^3)))/a))/d - (tan(c/2 + (d*x)/2)*(b^2/(8*a^3) - 11/(16*a) + (2*b*(b/(16*a^2) + (2*b*(7/(32*a) - b^2/(8*a^3)))/a))/a))/d - (tan(c/2 + (d*x)/2)^3*(7/(96*a) - b^2/(24*a^3)))/d - (b*tan(c/2 + (d*x)/2)^4)/(64*a^2*d) - (log(tan(c/2 + (d*x)/2))*((15*a^4*b)/8 + b^5 - (5*a^2*b^3)/2))/(a^6*d) + (tan(c/2 + (d*x)/2)^2*((7*a^4)/3 - (4*a^2*b^2)/3) - a^4/5 - tan(c/2 + (d*x)/2)^4*(22*a^4 + 16*b^4 - 36*a^2*b^2) + tan(c/2 + (d*x)/2)^3*(4*a*b^3 - 8*a^3*b) + (a^3*b*tan(c/2 + (d*x)/2))/2)/(32*a^5*d*tan(c/2 + (d*x)/2)^5) - (atan((((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9))*1i)/a^6 + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9))*1i)/a^6)/((15*a^10*b - 8*b^11 + 44*a^2*b^9 - 99*a^4*b^7 + 113*a^6*b^5 - 65*a^8*b^3)/(2*a^10) + (tan(c/2 + (d*x)/2)*(16*a^10 - 8*b^10 + 42*a^2*b^8 - 94*a^4*b^6 + 110*a^6*b^4 - 66*a^8*b^2))/(2*a^9) - ((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9)))/a^6 + ((-(a + b)^5*(a - b)^5)^(1/2)*((8*a^12 - 16*a^6*b^6 + 44*a^8*b^4 - 39*a^10*b^2)/(4*a^10) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^12 - 32*a^10*b^2))/(4*a^9))*(-(a + b)^5*(a - b)^5)^(1/2))/a^6 + (tan(c/2 + (d*x)/2)*(31*a^10*b - 32*a^4*b^7 + 96*a^6*b^5 - 98*a^8*b^3))/(4*a^9)))/a^6))*(-(a + b)^5*(a - b)^5)^(1/2)*2i)/(a^6*d)","B"
181,1,755,242,7.781689,"\text{Not used}","int(tan(c + d*x)^5/(a + b*sin(c + d*x))^2,x)","\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^6+5\,a^4\,b^2\right)}{d\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{1}{{\left(a+b\right)}^2}-\frac{7\,b}{4\,{\left(a+b\right)}^3}+\frac{3\,b^2}{4\,{\left(a+b\right)}^4}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{3\,b^2}{4\,{\left(a-b\right)}^4}+\frac{7\,b}{4\,{\left(a-b\right)}^3}+\frac{1}{{\left(a-b\right)}^2}\right)}{d}-\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^3+a\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a\,b^2-2\,a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a\,b^2-2\,a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(2\,a^3+a\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(11\,a^4+a^2\,b^2\right)}{2\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^4+a^2\,b^2\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^4+a^2\,b^2\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(13\,a^4+31\,a^2\,b^2-8\,b^4\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(11\,a^4+a^2\,b^2\right)}{2\,\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-3\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+12\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-8\,b\,{\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)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^6 + 5*a^4*b^2))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (log(tan(c/2 + (d*x)/2) - 1)*(1/(a + b)^2 - (7*b)/(4*(a + b)^3) + (3*b^2)/(4*(a + b)^4)))/d - (log(tan(c/2 + (d*x)/2) + 1)*((3*b^2)/(4*(a - b)^4) + (7*b)/(4*(a - b)^3) + 1/(a - b)^2))/d - ((tan(c/2 + (d*x)/2)^2*(a*b^2 + 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) + (3*tan(c/2 + (d*x)/2)^4*(a*b^2 - 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) + (3*tan(c/2 + (d*x)/2)^6*(a*b^2 - 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) + (tan(c/2 + (d*x)/2)^8*(a*b^2 + 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) - (b*tan(c/2 + (d*x)/2)^9*(11*a^4 + a^2*b^2))/(2*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (8*b*tan(c/2 + (d*x)/2)^3*(2*a^4 + a^2*b^2))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (8*b*tan(c/2 + (d*x)/2)^7*(2*a^4 + a^2*b^2))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b*tan(c/2 + (d*x)/2)^5*(13*a^4 - 8*b^4 + 31*a^2*b^2))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) - (b*tan(c/2 + (d*x)/2)*(11*a^4 + a^2*b^2))/(2*(a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - 3*a*tan(c/2 + (d*x)/2)^2 + 2*a*tan(c/2 + (d*x)/2)^4 + 2*a*tan(c/2 + (d*x)/2)^6 - 3*a*tan(c/2 + (d*x)/2)^8 + a*tan(c/2 + (d*x)/2)^10 - 8*b*tan(c/2 + (d*x)/2)^3 + 12*b*tan(c/2 + (d*x)/2)^5 - 8*b*tan(c/2 + (d*x)/2)^7 + 2*b*tan(c/2 + (d*x)/2)^9))","B"
182,1,351,161,7.245076,"\text{Not used}","int(tan(c + d*x)^3/(a + b*sin(c + d*x))^2,x)","\frac{\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{a^2-b^2}+\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{a^2-b^2}+\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+b^2\right)}{{\left(a^2-b^2\right)}^2}-\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{a^4-2\,a^2\,b^2+b^4}-\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{{\left(a^2-b^2\right)}^2}}{d\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{d\,{\left(a-b\right)}^3}-\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^4+3\,a^2\,b^2\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{a\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d\,{\left(a+b\right)}^3}","Not used",1,"((2*a*tan(c/2 + (d*x)/2)^2)/(a^2 - b^2) + (2*a*tan(c/2 + (d*x)/2)^4)/(a^2 - b^2) + (4*b*tan(c/2 + (d*x)/2)^3*(a^2 + b^2))/(a^2 - b^2)^2 - (4*a^2*b*tan(c/2 + (d*x)/2)^5)/(a^4 + b^4 - 2*a^2*b^2) - (4*a^2*b*tan(c/2 + (d*x)/2))/(a^2 - b^2)^2)/(d*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^2 - a*tan(c/2 + (d*x)/2)^4 + a*tan(c/2 + (d*x)/2)^6 - 4*b*tan(c/2 + (d*x)/2)^3 + 2*b*tan(c/2 + (d*x)/2)^5)) + (a*log(tan(c/2 + (d*x)/2) + 1))/(d*(a - b)^3) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 + 3*a^2*b^2))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (a*log(tan(c/2 + (d*x)/2) - 1))/(d*(a + b)^3)","B"
183,1,158,109,6.757767,"\text{Not used}","int(tan(c + d*x)/(a + b*sin(c + d*x))^2,x)","\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^2+b^2\right)}{d\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{d\,{\left(a-b\right)}^2}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d\,{\left(a+b\right)}^2}+\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^2-b^2\right)\,\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}","Not used",1,"(log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 + b^2))/(d*(a^4 + b^4 - 2*a^2*b^2)) - log(tan(c/2 + (d*x)/2) + 1)/(d*(a - b)^2) - log(tan(c/2 + (d*x)/2) - 1)/(d*(a + b)^2) + (2*b*tan(c/2 + (d*x)/2))/(d*(a^2 - b^2)*(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2))","B"
184,1,105,53,6.376052,"\text{Not used}","int(cot(c + d*x)/(a + b*sin(c + d*x))^2,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^2\,d}-\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{a^2\,d}-\frac{2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^3+2\,b\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^2*d) - log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)/(a^2*d) - (2*b*tan(c/2 + (d*x)/2))/(d*(a^3*tan(c/2 + (d*x)/2)^2 + a^3 + 2*a^2*b*tan(c/2 + (d*x)/2)))","B"
185,1,235,114,6.378514,"\text{Not used}","int(cot(c + d*x)^3/(a + b*sin(c + d*x))^2,x)","\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{a^2}{2}-8\,b^2\right)+\frac{a^2}{2}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^2\,b-2\,b^3\right)}{a}-3\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+4\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,b\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\right)}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^2\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-3\,b^2\right)}{a^4\,d}+\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^2-3\,b^2\right)}{a^4\,d}","Not used",1,"(b*tan(c/2 + (d*x)/2))/(a^3*d) - (tan(c/2 + (d*x)/2)^2*(a^2/2 - 8*b^2) + a^2/2 - (4*tan(c/2 + (d*x)/2)^3*(3*a^2*b - 2*b^3))/a - 3*a*b*tan(c/2 + (d*x)/2))/(d*(4*a^4*tan(c/2 + (d*x)/2)^2 + 4*a^4*tan(c/2 + (d*x)/2)^4 + 8*a^3*b*tan(c/2 + (d*x)/2)^3)) - tan(c/2 + (d*x)/2)^2/(8*a^2*d) - (log(tan(c/2 + (d*x)/2))*(a^2 - 3*b^2))/(a^4*d) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 - 3*b^2))/(a^4*d)","B"
186,1,439,188,6.899979,"\text{Not used}","int(cot(c + d*x)^5/(a + b*sin(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(3\,a^4-62\,a^2\,b^2+64\,b^4\right)-\frac{a^4}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{11\,a^4}{4}-\frac{10\,a^2\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(20\,a\,b^3-\frac{62\,a^3\,b}{3}\right)-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(60\,a^4\,b-96\,a^2\,b^3+32\,b^5\right)}{a}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{6}}{d\,\left(16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+16\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,b\,a^5\,{\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)}^4}{64\,a^2\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{\frac{a^2}{16}+\frac{b^2}{8}}{a^4}+\frac{1}{8\,a^2}-\frac{b^2}{2\,a^4}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{b\,\left(32\,a^2+64\,b^2\right)}{64\,a^5}-\frac{b}{4\,a^3}+\frac{4\,b\,\left(\frac{\frac{a^2}{8}+\frac{b^2}{4}}{a^4}+\frac{1}{4\,a^2}-\frac{b^2}{a^4}\right)}{a}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4-6\,a^2\,b^2+5\,b^4\right)}{a^6\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{12\,a^3\,d}-\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^4-6\,a^2\,b^2+5\,b^4\right)}{a^6\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^4*(3*a^4 + 64*b^4 - 62*a^2*b^2) - a^4/4 + tan(c/2 + (d*x)/2)^2*((11*a^4)/4 - (10*a^2*b^2)/3) + tan(c/2 + (d*x)/2)^3*(20*a*b^3 - (62*a^3*b)/3) - (tan(c/2 + (d*x)/2)^5*(60*a^4*b + 32*b^5 - 96*a^2*b^3))/a + (5*a^3*b*tan(c/2 + (d*x)/2))/6)/(d*(16*a^6*tan(c/2 + (d*x)/2)^4 + 16*a^6*tan(c/2 + (d*x)/2)^6 + 32*a^5*b*tan(c/2 + (d*x)/2)^5)) - tan(c/2 + (d*x)/2)^4/(64*a^2*d) + (tan(c/2 + (d*x)/2)^2*((a^2/16 + b^2/8)/a^4 + 1/(8*a^2) - b^2/(2*a^4)))/d - (tan(c/2 + (d*x)/2)*((b*(32*a^2 + 64*b^2))/(64*a^5) - b/(4*a^3) + (4*b*((a^2/8 + b^2/4)/a^4 + 1/(4*a^2) - b^2/a^4))/a))/d + (log(tan(c/2 + (d*x)/2))*(a^4 + 5*b^4 - 6*a^2*b^2))/(a^6*d) + (b*tan(c/2 + (d*x)/2)^3)/(12*a^3*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 + 5*b^4 - 6*a^2*b^2))/(a^6*d)","B"
187,1,722,333,9.895389,"\text{Not used}","int(tan(c + d*x)^4/(a + b*sin(c + d*x))^2,x)","\frac{\frac{2\,\left(13\,a^4\,b+2\,a^2\,b^3\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-3\,a^5+14\,a^3\,b^2+4\,a\,b^4\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(a^4\,b+4\,a^2\,b^3\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(29\,a^4\,b+16\,a^2\,b^3\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(7\,a^5+30\,a^3\,b^2+8\,a\,b^4\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-7\,a^5+48\,a^3\,b^2+4\,a\,b^4\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(11\,a^4\,b+42\,a^2\,b^3-8\,b^5\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(a^2+4\,b^2\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}+\frac{2\,a^3\,\mathrm{atan}\left(\frac{\frac{a^3\,\left(a^2+4\,b^2\right)\,\left(2\,a^6\,b-6\,a^4\,b^3+6\,a^2\,b^5-2\,b^7\right)}{{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}+\frac{2\,a^4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+4\,b^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)}^{7/2}}}{2\,a^5+8\,a^3\,b^2}\right)\,\left(a^2+4\,b^2\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((2*(13*a^4*b + 2*a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)*(4*a*b^4 - 3*a^5 + 14*a^3*b^2))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^6*(a^4*b + 4*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (2*tan(c/2 + (d*x)/2)^2*(29*a^4*b + 16*a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^5*(8*a*b^4 + 7*a^5 + 30*a^3*b^2))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^3*(4*a*b^4 - 7*a^5 + 48*a^3*b^2))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^4*(11*a^4*b - 8*b^5 + 42*a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*a^3*tan(c/2 + (d*x)/2)^7*(a^2 + 4*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/(d*(a + 2*b*tan(c/2 + (d*x)/2) - 2*a*tan(c/2 + (d*x)/2)^2 + 2*a*tan(c/2 + (d*x)/2)^6 - a*tan(c/2 + (d*x)/2)^8 - 6*b*tan(c/2 + (d*x)/2)^3 + 6*b*tan(c/2 + (d*x)/2)^5 - 2*b*tan(c/2 + (d*x)/2)^7)) + (2*a^3*atan(((a^3*(a^2 + 4*b^2)*(2*a^6*b - 2*b^7 + 6*a^2*b^5 - 6*a^4*b^3))/((a + b)^(7/2)*(a - b)^(7/2)) + (2*a^4*tan(c/2 + (d*x)/2)*(a^2 + 4*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/((a + b)^(7/2)*(a - b)^(7/2)))/(2*a^5 + 8*a^3*b^2))*(a^2 + 4*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
188,1,313,200,8.675187,"\text{Not used}","int(tan(c + d*x)^2/(a + b*sin(c + d*x))^2,x)","-\frac{\frac{6\,a^2\,b}{{\left(a^2-b^2\right)}^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a\,b^2-a^3\right)}{{\left(a^2-b^2\right)}^2}-\frac{2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+2\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(a^2+2\,b^2\right)}{{\left(a^2-b^2\right)}^2}}{d\,\left(-a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4-2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}-\frac{2\,a\,\mathrm{atan}\left(\frac{\frac{a\,\left(a^2+2\,b^2\right)\,\left(2\,a^4\,b-4\,a^2\,b^3+2\,b^5\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}+\frac{2\,a^2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(a^2+2\,b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}}{2\,a^3+4\,a\,b^2}\right)\,\left(a^2+2\,b^2\right)}{d\,{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"- ((6*a^2*b)/(a^2 - b^2)^2 + (2*tan(c/2 + (d*x)/2)*(4*a*b^2 - a^3))/(a^2 - b^2)^2 - (2*b*tan(c/2 + (d*x)/2)^2*(a^2 + 2*b^2))/(a^4 + b^4 - 2*a^2*b^2) - (2*a*tan(c/2 + (d*x)/2)^3*(a^2 + 2*b^2))/(a^2 - b^2)^2)/(d*(a + 2*b*tan(c/2 + (d*x)/2) - a*tan(c/2 + (d*x)/2)^4 - 2*b*tan(c/2 + (d*x)/2)^3)) - (2*a*atan(((a*(a^2 + 2*b^2)*(2*a^4*b + 2*b^5 - 4*a^2*b^3))/((a + b)^(5/2)*(a - b)^(5/2)) + (2*a^2*tan(c/2 + (d*x)/2)*(a^2 + 2*b^2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(5/2)))/(4*a*b^2 + 2*a^3))*(a^2 + 2*b^2))/(d*(a + b)^(5/2)*(a - b)^(5/2))","B"
189,1,1616,115,8.316783,"\text{Not used}","int(cot(c + d*x)^2/(a + b*sin(c + d*x))^2,x)","-\frac{a^4\,\cos\left(c+d\,x\right)-\frac{b^4}{2}-b^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+\frac{a^2\,b^2}{2}+\frac{b^4\,\cos\left(2\,c+2\,d\,x\right)}{2}-a^2\,b^2\,\cos\left(c+d\,x\right)-a\,b^3\,\sin\left(2\,c+2\,d\,x\right)+a^3\,b\,\sin\left(2\,c+2\,d\,x\right)+a^2\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+b^4\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)+b^3\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-\frac{a^2\,b^2\,\cos\left(2\,c+2\,d\,x\right)}{2}-a\,b^3\,\sin\left(c+d\,x\right)+a^3\,b\,\sin\left(c+d\,x\right)-a^2\,b\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-a^3\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-a^2\,b^2\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)\,\cos\left(2\,c+2\,d\,x\right)-b^3\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,2{}\mathrm{i}-2\,a\,b^3\,\sin\left(c+d\,x\right)\,\ln\left(\frac{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)}\right)+2\,a^3\,b\,\sin\left(c+d\,x\right)\,\ln\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^2\,\sin\left(c+d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\cos\left(2\,c+2\,d\,x\right)\,\mathrm{atan}\left(\frac{a^3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}-b^3\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,8{}\mathrm{i}-a\,b^2\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}+a^2\,b\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\sqrt{b^2-a^2}\,4{}\mathrm{i}}{\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^4-3\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^3\,b-8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a^2\,b^2+4\,\cos\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,a\,b^3+8\,\sin\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,b^4}\right)\,\sqrt{b^2-a^2}\,1{}\mathrm{i}}{2\,a^3\,d\,\left(a^2-b^2\right)\,\left(\frac{b}{4}+\frac{a\,\sin\left(c+d\,x\right)}{2}-\frac{b\,\cos\left(2\,c+2\,d\,x\right)}{4}\right)}","Not used",1,"-(a^4*cos(c + d*x) - b^4/2 - b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + (a^2*b^2)/2 + (b^4*cos(2*c + 2*d*x))/2 - a^2*b^2*cos(c + d*x) - a*b^3*sin(2*c + 2*d*x) + a^3*b*sin(2*c + 2*d*x) + a^2*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + b^4*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) + b^3*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i - (a^2*b^2*cos(2*c + 2*d*x))/2 - a*b^3*sin(c + d*x) + a^3*b*sin(c + d*x) - a^2*b*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*1i - a^3*sin(c + d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i - a^2*b^2*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2))*cos(2*c + 2*d*x) - b^3*cos(2*c + 2*d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*2i - 2*a*b^3*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + 2*a^3*b*sin(c + d*x)*log(sin(c/2 + (d*x)/2)/cos(c/2 + (d*x)/2)) + a*b^2*sin(c + d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*4i + a^2*b*cos(2*c + 2*d*x)*atan((a^3*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*1i - b^3*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*8i - a*b^2*cos(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i + a^2*b*sin(c/2 + (d*x)/2)*(b^2 - a^2)^(1/2)*4i)/(a^4*sin(c/2 + (d*x)/2) + 8*b^4*sin(c/2 + (d*x)/2) + 4*a*b^3*cos(c/2 + (d*x)/2) - 3*a^3*b*cos(c/2 + (d*x)/2) - 8*a^2*b^2*sin(c/2 + (d*x)/2)))*(b^2 - a^2)^(1/2)*1i)/(2*a^3*d*(a^2 - b^2)*(b/4 + (a*sin(c + d*x))/2 - (b*cos(2*c + 2*d*x))/4))","B"
190,1,973,238,6.830175,"\text{Not used}","int(cot(c + d*x)^4/(a + b*sin(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(28\,a^2\,b-40\,b^3\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(8\,a\,b^2-\frac{14\,a^3}{3}\right)-\frac{a^3}{3}+\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(5\,a^4+4\,a^2\,b^2-16\,b^4\right)}{a}}{d\,\left(8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,b\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^2\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{16\,a^2+32\,b^2}{64\,a^4}+\frac{3}{8\,a^2}-\frac{2\,b^2}{a^4}\right)}{d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{4\,a^3\,d}+\frac{b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(3\,a^2-4\,b^2\right)}{a^5\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}+\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}+\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}-\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)\,1{}\mathrm{i}}{a^5}}{\frac{4\,\left(3\,a^6\,b-19\,a^4\,b^3+32\,a^2\,b^5-16\,b^7\right)}{a^8}+\frac{4\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^6-14\,a^4\,b^2+28\,a^2\,b^4-16\,b^6\right)}{a^7}-\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}+\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)}{a^5}+\frac{\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,\left(\frac{2\,\left(a^9-8\,a^7\,b^2+8\,a^5\,b^4\right)}{a^8}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(5\,a^7\,b-20\,a^5\,b^3+16\,a^3\,b^5\right)}{a^7}-\frac{\left(2\,a^2\,b-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(3\,a^{10}-4\,a^8\,b^2\right)}{a^7}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)}{a^5}\right)}{a^5}}\right)\,\sqrt{b^2-a^2}\,\left(a^2-4\,b^2\right)\,2{}\mathrm{i}}{a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^3*(28*a^2*b - 40*b^3) - tan(c/2 + (d*x)/2)^2*(8*a*b^2 - (14*a^3)/3) - a^3/3 + (4*a^2*b*tan(c/2 + (d*x)/2))/3 + (tan(c/2 + (d*x)/2)^4*(5*a^4 - 16*b^4 + 4*a^2*b^2))/a)/(d*(8*a^5*tan(c/2 + (d*x)/2)^3 + 8*a^5*tan(c/2 + (d*x)/2)^5 + 16*a^4*b*tan(c/2 + (d*x)/2)^4)) + tan(c/2 + (d*x)/2)^3/(24*a^2*d) - (tan(c/2 + (d*x)/2)*((16*a^2 + 32*b^2)/(64*a^4) + 3/(8*a^2) - (2*b^2)/a^4))/d - (b*tan(c/2 + (d*x)/2)^2)/(4*a^3*d) + (b*log(tan(c/2 + (d*x)/2))*(3*a^2 - 4*b^2))/(a^5*d) + (atan((((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 + ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5)*1i)/a^5 + ((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 - ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5)*1i)/a^5)/((4*(3*a^6*b - 16*b^7 + 32*a^2*b^5 - 19*a^4*b^3))/a^8 + (4*tan(c/2 + (d*x)/2)*(2*a^6 - 16*b^6 + 28*a^2*b^4 - 14*a^4*b^2))/a^7 - ((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 + ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5))/a^5 + ((b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*((2*(a^9 + 8*a^5*b^4 - 8*a^7*b^2))/a^8 + (2*tan(c/2 + (d*x)/2)*(5*a^7*b + 16*a^3*b^5 - 20*a^5*b^3))/a^7 - ((2*a^2*b - (2*tan(c/2 + (d*x)/2)*(3*a^10 - 4*a^8*b^2))/a^7)*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2))/a^5))/a^5))*(b^2 - a^2)^(1/2)*(a^2 - 4*b^2)*2i)/(a^5*d)","B"
191,1,1424,424,6.905247,"\text{Not used}","int(cot(c + d*x)^6/(a + b*sin(c + d*x))^2,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^2\,d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1}{4\,a^2}+\frac{b^2}{2\,a^4}-\frac{4\,b\,\left(\frac{b\,\left(64\,a^2+128\,b^2\right)}{256\,a^5}-\frac{b}{8\,a^3}+\frac{4\,b\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{5}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{a}\right)}{a}+\frac{\left(64\,a^2+128\,b^2\right)\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{5}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{32\,a^2}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{64\,a^2+128\,b^2}{3072\,a^4}+\frac{5}{96\,a^2}-\frac{b^2}{6\,a^4}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{31\,a^4\,b}{3}-8\,a^2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{59\,a^5}{3}-72\,a^3\,b^2+48\,a\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(124\,a^4\,b-360\,a^2\,b^3+224\,b^5\right)+\frac{a^5}{5}-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{32\,a^5}{15}-2\,a^3\,b^2\right)-\frac{3\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{5}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(11\,a^6-22\,a^4\,b^2-24\,a^2\,b^4+32\,b^6\right)}{a}}{d\,\left(32\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+32\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+64\,b\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{b\,\left(64\,a^2+128\,b^2\right)}{512\,a^5}-\frac{b}{16\,a^3}+\frac{2\,b\,\left(\frac{64\,a^2+128\,b^2}{1024\,a^4}+\frac{5}{32\,a^2}-\frac{b^2}{2\,a^4}\right)}{a}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(15\,a^4\,b-40\,a^2\,b^3+24\,b^5\right)}{4\,a^7\,d}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{32\,a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)\,1{}\mathrm{i}}{a^7}+\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)\,1{}\mathrm{i}}{a^7}}{\frac{15\,a^{10}\,b-160\,a^8\,b^3+539\,a^6\,b^5-802\,a^4\,b^7+552\,a^2\,b^9-144\,b^{11}}{a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(8\,a^{10}-98\,a^8\,b^2+400\,a^6\,b^4-682\,a^4\,b^6+516\,a^2\,b^8-144\,b^{10}\right)}{a^{11}}-\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}+\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)}{a^7}+\frac{\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\frac{4\,a^{13}-47\,a^{11}\,b^2+92\,a^9\,b^4-48\,a^7\,b^6}{2\,a^{12}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(23\,a^{11}\,b-134\,a^9\,b^3+208\,a^7\,b^5-96\,a^5\,b^7\right)}{2\,a^{11}}-\frac{\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(12\,a^{14}-16\,a^{12}\,b^2\right)}{2\,a^{11}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^7}\right)}{a^7}}\right)\,\left(a^2-6\,b^2\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{a^7\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a^2*d) + (tan(c/2 + (d*x)/2)*(1/(4*a^2) + b^2/(2*a^4) - (4*b*((b*(64*a^2 + 128*b^2))/(256*a^5) - b/(8*a^3) + (4*b*((64*a^2 + 128*b^2)/(1024*a^4) + 5/(32*a^2) - b^2/(2*a^4)))/a))/a + ((64*a^2 + 128*b^2)*((64*a^2 + 128*b^2)/(1024*a^4) + 5/(32*a^2) - b^2/(2*a^4)))/(32*a^2)))/d - (tan(c/2 + (d*x)/2)^3*((64*a^2 + 128*b^2)/(3072*a^4) + 5/(96*a^2) - b^2/(6*a^4)))/d - (tan(c/2 + (d*x)/2)^3*((31*a^4*b)/3 - 8*a^2*b^3) + tan(c/2 + (d*x)/2)^4*(48*a*b^4 + (59*a^5)/3 - 72*a^3*b^2) + tan(c/2 + (d*x)/2)^5*(124*a^4*b + 224*b^5 - 360*a^2*b^3) + a^5/5 - tan(c/2 + (d*x)/2)^2*((32*a^5)/15 - 2*a^3*b^2) - (3*a^4*b*tan(c/2 + (d*x)/2))/5 + (2*tan(c/2 + (d*x)/2)^6*(11*a^6 + 32*b^6 - 24*a^2*b^4 - 22*a^4*b^2))/a)/(d*(32*a^7*tan(c/2 + (d*x)/2)^5 + 32*a^7*tan(c/2 + (d*x)/2)^7 + 64*a^6*b*tan(c/2 + (d*x)/2)^6)) + (tan(c/2 + (d*x)/2)^2*((b*(64*a^2 + 128*b^2))/(512*a^5) - b/(16*a^3) + (2*b*((64*a^2 + 128*b^2)/(1024*a^4) + 5/(32*a^2) - b^2/(2*a^4)))/a))/d - (log(tan(c/2 + (d*x)/2))*(15*a^4*b + 24*b^5 - 40*a^2*b^3))/(4*a^7*d) - (b*tan(c/2 + (d*x)/2)^4)/(32*a^3*d) - (atan((((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7)*1i)/a^7 + ((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7)*1i)/a^7)/((15*a^10*b - 144*b^11 + 552*a^2*b^9 - 802*a^4*b^7 + 539*a^6*b^5 - 160*a^8*b^3)/a^12 + (tan(c/2 + (d*x)/2)*(8*a^10 - 144*b^10 + 516*a^2*b^8 - 682*a^4*b^6 + 400*a^6*b^4 - 98*a^8*b^2))/a^11 - ((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) + ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7))/a^7 + ((a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*((4*a^13 - 48*a^7*b^6 + 92*a^9*b^4 - 47*a^11*b^2)/(2*a^12) + (tan(c/2 + (d*x)/2)*(23*a^11*b - 96*a^5*b^7 + 208*a^7*b^5 - 134*a^9*b^3))/(2*a^11) - ((2*a^2*b - (tan(c/2 + (d*x)/2)*(12*a^14 - 16*a^12*b^2))/(2*a^11))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2))/a^7))/a^7))*(a^2 - 6*b^2)*(-(a + b)^3*(a - b)^3)^(1/2)*2i)/(a^7*d)","B"
192,1,1229,321,10.735225,"\text{Not used}","int(tan(c + d*x)^5/(a + b*sin(c + d*x))^3,x)","\frac{\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-2\,a^7+11\,a^5\,b^2+38\,a^3\,b^4+a\,b^6\right)}{a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(-a^7+12\,a^5\,b^2+33\,a^3\,b^4+4\,a\,b^6\right)}{a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(-a^7+12\,a^5\,b^2+33\,a^3\,b^4+4\,a\,b^6\right)}{a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(-2\,a^7+11\,a^5\,b^2+38\,a^3\,b^4+a\,b^6\right)}{a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(6\,a^7+13\,a^5\,b^2+118\,a^3\,b^4+7\,a\,b^6\right)}{a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}\,\left(37\,a^6+58\,a^4\,b^2+a^2\,b^4\right)}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(7\,a^6+132\,a^4\,b^2-57\,a^2\,b^4+14\,b^6\right)}{2\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(7\,a^6+132\,a^4\,b^2-57\,a^2\,b^4+14\,b^6\right)}{2\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(83\,a^6+226\,a^4\,b^2-17\,a^2\,b^4-4\,b^6\right)}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(83\,a^6+226\,a^4\,b^2-17\,a^2\,b^4-4\,b^6\right)}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}+\frac{b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(37\,a^6+58\,a^4\,b^2+a^2\,b^4\right)}{4\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(4\,a^2+24\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}\,\left(2\,a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2-4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{12}+a^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+16\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2+16\,b^2\right)-12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7-12\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{11}+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(\frac{3\,b^2}{2\,{\left(a-b\right)}^5}+\frac{21\,b}{8\,{\left(a-b\right)}^4}+\frac{1}{{\left(a-b\right)}^3}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(\frac{1}{{\left(a+b\right)}^3}-\frac{21\,b}{8\,{\left(a+b\right)}^4}+\frac{3\,b^2}{2\,{\left(a+b\right)}^5}\right)}{d}+\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^7+13\,a^5\,b^2+10\,a^3\,b^4\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,"((tan(c/2 + (d*x)/2)^2*(a*b^6 - 2*a^7 + 38*a^3*b^4 + 11*a^5*b^2))/(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2) - (4*tan(c/2 + (d*x)/2)^4*(4*a*b^6 - a^7 + 33*a^3*b^4 + 12*a^5*b^2))/(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2) - (4*tan(c/2 + (d*x)/2)^8*(4*a*b^6 - a^7 + 33*a^3*b^4 + 12*a^5*b^2))/(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2) + (tan(c/2 + (d*x)/2)^10*(a*b^6 - 2*a^7 + 38*a^3*b^4 + 11*a^5*b^2))/(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2) + (2*tan(c/2 + (d*x)/2)^6*(7*a*b^6 + 6*a^7 + 118*a^3*b^4 + 13*a^5*b^2))/(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2) + (b*tan(c/2 + (d*x)/2)^11*(37*a^6 + a^2*b^4 + 58*a^4*b^2))/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (b*tan(c/2 + (d*x)/2)^5*(7*a^6 + 14*b^6 - 57*a^2*b^4 + 132*a^4*b^2))/(2*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (b*tan(c/2 + (d*x)/2)^7*(7*a^6 + 14*b^6 - 57*a^2*b^4 + 132*a^4*b^2))/(2*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (b*tan(c/2 + (d*x)/2)^3*(83*a^6 - 4*b^6 - 17*a^2*b^4 + 226*a^4*b^2))/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (b*tan(c/2 + (d*x)/2)^9*(83*a^6 - 4*b^6 - 17*a^2*b^4 + 226*a^4*b^2))/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) + (b*tan(c/2 + (d*x)/2)*(37*a^6 + a^2*b^4 + 58*a^4*b^2))/(4*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)))/(d*(tan(c/2 + (d*x)/2)^6*(4*a^2 + 24*b^2) - tan(c/2 + (d*x)/2)^10*(2*a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^2*(2*a^2 - 4*b^2) + a^2*tan(c/2 + (d*x)/2)^12 + a^2 - tan(c/2 + (d*x)/2)^4*(a^2 + 16*b^2) - tan(c/2 + (d*x)/2)^8*(a^2 + 16*b^2) - 12*a*b*tan(c/2 + (d*x)/2)^3 + 8*a*b*tan(c/2 + (d*x)/2)^5 + 8*a*b*tan(c/2 + (d*x)/2)^7 - 12*a*b*tan(c/2 + (d*x)/2)^9 + 4*a*b*tan(c/2 + (d*x)/2)^11 + 4*a*b*tan(c/2 + (d*x)/2))) - (log(tan(c/2 + (d*x)/2) + 1)*((3*b^2)/(2*(a - b)^5) + (21*b)/(8*(a - b)^4) + 1/(a - b)^3))/d - (log(tan(c/2 + (d*x)/2) - 1)*(1/(a + b)^3 - (21*b)/(8*(a + b)^4) + (3*b^2)/(2*(a + b)^5)))/d + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^7 + 10*a^3*b^4 + 13*a^5*b^2))/(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"
193,1,690,232,7.463574,"\text{Not used}","int(tan(c + d*x)^3/(a + b*sin(c + d*x))^3,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)\,\left(2\,a-b\right)}{2\,d\,{\left(a+b\right)}^4}-\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(-a^5+6\,a^3\,b^2+7\,a\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^5+2\,a^3\,b^2+9\,a\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(3\,a^4\,b+13\,a^2\,b^3-4\,b^5\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(-a^5+6\,a^3\,b^2+7\,a\,b^4\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(7\,a^4+5\,a^2\,b^2\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(3\,a^4+13\,a^2\,b^2-4\,b^4\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a^3\,b+5\,a\,b^3\right)}{\left(a^2-b^2\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2+8\,b^2\right)+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+a^2-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)\,\left(2\,a+b\right)}{2\,d\,{\left(a-b\right)}^4}-\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^5+8\,a^3\,b^2+3\,a\,b^4\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(tan(c/2 + (d*x)/2) - 1)*(2*a - b))/(2*d*(a + b)^4) - ((2*tan(c/2 + (d*x)/2)^6*(7*a*b^4 - a^5 + 6*a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (4*tan(c/2 + (d*x)/2)^4*(9*a*b^4 + a^5 + 2*a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (tan(c/2 + (d*x)/2)^5*(3*a^4*b - 4*b^5 + 13*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)^2*(7*a*b^4 - a^5 + 6*a^3*b^2))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(c/2 + (d*x)/2)^7*(7*a^4 + 5*a^2*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (b*tan(c/2 + (d*x)/2)^3*(3*a^4 - 4*b^4 + 13*a^2*b^2))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)) + (a*tan(c/2 + (d*x)/2)*(5*a*b^3 + 7*a^3*b))/((a^2 - b^2)*(a^4 + b^4 - 2*a^2*b^2)))/(d*(a^2*tan(c/2 + (d*x)/2)^8 - tan(c/2 + (d*x)/2)^4*(2*a^2 + 8*b^2) + 4*b^2*tan(c/2 + (d*x)/2)^2 + 4*b^2*tan(c/2 + (d*x)/2)^6 + a^2 - 4*a*b*tan(c/2 + (d*x)/2)^3 - 4*a*b*tan(c/2 + (d*x)/2)^5 + 4*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2))) + (log(tan(c/2 + (d*x)/2) + 1)*(2*a + b))/(2*d*(a - b)^4) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(3*a*b^4 + a^5 + 8*a^3*b^2))/(d*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))","B"
194,1,304,149,6.853929,"\text{Not used}","int(tan(c + d*x)/(a + b*sin(c + d*x))^3,x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(3\,a^2\,b^2+b^4\right)}{a\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{4\,a^2\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{a^4-2\,a^2\,b^2+b^4}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^2+4\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+a^2+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-1\right)}{d\,{\left(a+b\right)}^3}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+1\right)}{d\,{\left(a-b\right)}^3}+\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^3+3\,a\,b^2\right)}{d\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}","Not used",1,"((2*tan(c/2 + (d*x)/2)^2*(b^4 + 3*a^2*b^2))/(a*(a^4 + b^4 - 2*a^2*b^2)) + (4*a^2*b*tan(c/2 + (d*x)/2))/(a^4 + b^4 - 2*a^2*b^2) + (4*a^2*b*tan(c/2 + (d*x)/2)^3)/(a^4 + b^4 - 2*a^2*b^2))/(d*(tan(c/2 + (d*x)/2)^2*(2*a^2 + 4*b^2) + a^2*tan(c/2 + (d*x)/2)^4 + a^2 + 4*a*b*tan(c/2 + (d*x)/2)^3 + 4*a*b*tan(c/2 + (d*x)/2))) - log(tan(c/2 + (d*x)/2) - 1)/(d*(a + b)^3) - log(tan(c/2 + (d*x)/2) + 1)/(d*(a - b)^3) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(3*a*b^2 + a^3))/(d*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))","B"
195,1,369,75,6.537311,"\text{Not used}","int(cot(c + d*x)/(a + b*sin(c + d*x))^3,x)","\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^3\,d}-\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)}{a^3\,d}-\frac{6\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{d\,\left(a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^5+4\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,a^3\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4+4\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,a^2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}-\frac{4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{d\,\left(a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+2\,a^4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+a^4+4\,a^3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+4\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+4\,a^2\,b^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\right)}","Not used",1,"log(tan(c/2 + (d*x)/2))/(a^3*d) - log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)/(a^3*d) - (6*b^2*tan(c/2 + (d*x)/2)^2)/(d*(2*a^5*tan(c/2 + (d*x)/2)^2 + a^5*tan(c/2 + (d*x)/2)^4 + a^5 + 4*a^3*b^2*tan(c/2 + (d*x)/2)^2 + 4*a^4*b*tan(c/2 + (d*x)/2) + 4*a^4*b*tan(c/2 + (d*x)/2)^3)) - (4*b*tan(c/2 + (d*x)/2))/(d*(2*a^4*tan(c/2 + (d*x)/2)^2 + a^4*tan(c/2 + (d*x)/2)^4 + a^4 + 4*a^2*b^2*tan(c/2 + (d*x)/2)^2 + 4*a^3*b*tan(c/2 + (d*x)/2) + 4*a^3*b*tan(c/2 + (d*x)/2)^3)) - (4*b*tan(c/2 + (d*x)/2)^3)/(d*(2*a^4*tan(c/2 + (d*x)/2)^2 + a^4*tan(c/2 + (d*x)/2)^4 + a^4 + 4*a^2*b^2*tan(c/2 + (d*x)/2)^2 + 4*a^3*b*tan(c/2 + (d*x)/2) + 4*a^3*b*tan(c/2 + (d*x)/2)^3))","B"
196,1,334,145,6.789743,"\text{Not used}","int(cot(c + d*x)^3/(a + b*sin(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(22\,a\,b^2-a^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(26\,a^2\,b-8\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(22\,a^2\,b-32\,b^3\right)-\frac{a^3}{2}+4\,a^2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^4-96\,a^2\,b^2+112\,b^4\right)}{2\,a}}{d\,\left(4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+4\,a^6\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(8\,a^6+16\,a^4\,b^2\right)+16\,a^5\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+16\,a^5\,b\,{\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)}^2}{8\,a^3\,d}+\frac{3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^4\,d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^2-6\,b^2\right)}{a^5\,d}+\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^2-6\,b^2\right)}{a^5\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^2*(22*a*b^2 - a^3) + tan(c/2 + (d*x)/2)^3*(26*a^2*b - 8*b^3) + tan(c/2 + (d*x)/2)^5*(22*a^2*b - 32*b^3) - a^3/2 + 4*a^2*b*tan(c/2 + (d*x)/2) - (tan(c/2 + (d*x)/2)^4*(a^4 + 112*b^4 - 96*a^2*b^2))/(2*a))/(d*(4*a^6*tan(c/2 + (d*x)/2)^2 + 4*a^6*tan(c/2 + (d*x)/2)^6 + tan(c/2 + (d*x)/2)^4*(8*a^6 + 16*a^4*b^2) + 16*a^5*b*tan(c/2 + (d*x)/2)^3 + 16*a^5*b*tan(c/2 + (d*x)/2)^5)) - tan(c/2 + (d*x)/2)^2/(8*a^3*d) + (3*b*tan(c/2 + (d*x)/2))/(2*a^4*d) - (log(tan(c/2 + (d*x)/2))*(a^2 - 6*b^2))/(a^5*d) + (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^2 - 6*b^2))/(a^5*d)","B"
197,1,563,221,7.261835,"\text{Not used}","int(cot(c + d*x)^5/(a + b*sin(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{23\,a^5}{4}-172\,a^3\,b^2+272\,a\,b^4\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(27\,a^4\,b-40\,a^2\,b^3\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-134\,a^4\,b+200\,a^2\,b^3+128\,b^5\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(106\,a^4\,b-336\,a^2\,b^3+192\,b^5\right)-\frac{a^5}{4}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{5\,a^5}{2}-5\,a^3\,b^2\right)+a^4\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(3\,a^6-276\,a^4\,b^2+768\,a^2\,b^4-352\,b^6\right)}{a}}{d\,\left(16\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+16\,a^8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(32\,a^8+64\,a^6\,b^2\right)+64\,a^7\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+64\,a^7\,b\,{\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)}^4}{64\,a^3\,d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{3}{32\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{16\,a^5}+\frac{3}{16\,a^3}-\frac{9\,b^2}{4\,a^5}\right)}{a}-\frac{192\,a^2\,b+128\,b^3}{256\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{8\,a^6}\right)}{d}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(a^4-12\,a^2\,b^2+15\,b^4\right)}{a^7\,d}+\frac{b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{8\,a^4\,d}-\frac{\ln\left(a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+2\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+a\right)\,\left(a^4-12\,a^2\,b^2+15\,b^4\right)}{a^7\,d}","Not used",1,"(tan(c/2 + (d*x)/2)^4*(272*a*b^4 + (23*a^5)/4 - 172*a^3*b^2) - tan(c/2 + (d*x)/2)^3*(27*a^4*b - 40*a^2*b^3) + tan(c/2 + (d*x)/2)^5*(128*b^5 - 134*a^4*b + 200*a^2*b^3) - tan(c/2 + (d*x)/2)^7*(106*a^4*b + 192*b^5 - 336*a^2*b^3) - a^5/4 + tan(c/2 + (d*x)/2)^2*((5*a^5)/2 - 5*a^3*b^2) + a^4*b*tan(c/2 + (d*x)/2) + (tan(c/2 + (d*x)/2)^6*(3*a^6 - 352*b^6 + 768*a^2*b^4 - 276*a^4*b^2))/a)/(d*(16*a^8*tan(c/2 + (d*x)/2)^4 + 16*a^8*tan(c/2 + (d*x)/2)^8 + tan(c/2 + (d*x)/2)^6*(32*a^8 + 64*a^6*b^2) + 64*a^7*b*tan(c/2 + (d*x)/2)^5 + 64*a^7*b*tan(c/2 + (d*x)/2)^7)) - tan(c/2 + (d*x)/2)^4/(64*a^3*d) + (tan(c/2 + (d*x)/2)^2*((3*(a^2 + 4*b^2))/(32*a^5) + 3/(32*a^3) - (9*b^2)/(8*a^5)))/d - (tan(c/2 + (d*x)/2)*((6*b*((3*(a^2 + 4*b^2))/(16*a^5) + 3/(16*a^3) - (9*b^2)/(4*a^5)))/a - (192*a^2*b + 128*b^3)/(256*a^6) + (9*b*(a^2 + 4*b^2))/(8*a^6)))/d + (log(tan(c/2 + (d*x)/2))*(a^4 + 15*b^4 - 12*a^2*b^2))/(a^7*d) + (b*tan(c/2 + (d*x)/2)^3)/(8*a^4*d) - (log(a + 2*b*tan(c/2 + (d*x)/2) + a*tan(c/2 + (d*x)/2)^2)*(a^4 + 15*b^4 - 12*a^2*b^2))/(a^7*d)","B"
198,1,1099,474,11.220260,"\text{Not used}","int(tan(c + d*x)^4/(a + b*sin(c + d*x))^3,x)","\frac{\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(2\,a^6\,b+21\,a^4\,b^3+12\,a^2\,b^5\right)}{a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(14\,a^7+23\,a^5\,b^2+242\,a^3\,b^4+36\,a\,b^6\right)}{3\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}-\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(2\,a^5+21\,a^3\,b^2+12\,a\,b^4\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(30\,a^4\,b+71\,a^2\,b^3+4\,b^5\right)}{3\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{a^2\,\left(42\,a^4\,b+61\,a^2\,b^3+2\,b^5\right)}{3\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{10\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(4\,a^6\,b+16\,a^4\,b^3+43\,a^2\,b^5\right)}{3\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{4\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(-2\,a^7+65\,a^5\,b^2+131\,a^3\,b^4+16\,a\,b^6\right)}{3\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(22\,a^6\,b+233\,a^4\,b^3+153\,a^2\,b^5+12\,b^7\right)}{3\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}+\frac{a^3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9\,\left(2\,a^4+21\,a^2\,b^2+12\,b^4\right)}{a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8}-\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-6\,a^6+105\,a^4\,b^2+208\,a^2\,b^4+8\,b^6\right)}{3\,\left(a^2-b^2\right)\,\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}}{d\,\left({\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^2+12\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(2\,a^2+12\,b^2\right)+a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^{10}-a^2+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2-4\,b^2\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(a^2-4\,b^2\right)+8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3-8\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}+\frac{a^2\,\mathrm{atan}\left(\frac{\frac{a^2\,\left(2\,a^4+21\,a^2\,b^2+12\,b^4\right)\,\left(2\,a^8\,b-8\,a^6\,b^3+12\,a^4\,b^5-8\,a^2\,b^7+2\,b^9\right)}{2\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}+\frac{a^3\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4+21\,a^2\,b^2+12\,b^4\right)\,\left(a^8-4\,a^6\,b^2+6\,a^4\,b^4-4\,a^2\,b^6+b^8\right)}{{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}}{2\,a^6+21\,a^4\,b^2+12\,a^2\,b^4}\right)\,\left(2\,a^4+21\,a^2\,b^2+12\,b^4\right)}{d\,{\left(a+b\right)}^{9/2}\,{\left(a-b\right)}^{9/2}}","Not used",1,"((3*tan(c/2 + (d*x)/2)^8*(2*a^6*b + 12*a^2*b^5 + 21*a^4*b^3))/(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2) - (2*tan(c/2 + (d*x)/2)^5*(36*a*b^6 + 14*a^7 + 242*a^3*b^4 + 23*a^5*b^2))/(3*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2)) - (4*tan(c/2 + (d*x)/2)^7*(12*a*b^4 + 2*a^5 + 21*a^3*b^2))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (2*tan(c/2 + (d*x)/2)^2*(30*a^4*b + 4*b^5 + 71*a^2*b^3))/(3*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (a^2*(42*a^4*b + 2*b^5 + 61*a^2*b^3))/(3*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (10*tan(c/2 + (d*x)/2)^4*(4*a^6*b + 43*a^2*b^5 + 16*a^4*b^3))/(3*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (4*tan(c/2 + (d*x)/2)^3*(16*a*b^6 - 2*a^7 + 131*a^3*b^4 + 65*a^5*b^2))/(3*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) - (2*tan(c/2 + (d*x)/2)^6*(22*a^6*b + 12*b^7 + 153*a^2*b^5 + 233*a^4*b^3))/(3*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)) + (a^3*tan(c/2 + (d*x)/2)^9*(2*a^4 + 12*b^4 + 21*a^2*b^2))/(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2) - (a*tan(c/2 + (d*x)/2)*(8*b^6 - 6*a^6 + 208*a^2*b^4 + 105*a^4*b^2))/(3*(a^2 - b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)))/(d*(tan(c/2 + (d*x)/2)^4*(2*a^2 + 12*b^2) - tan(c/2 + (d*x)/2)^6*(2*a^2 + 12*b^2) + a^2*tan(c/2 + (d*x)/2)^10 - a^2 + tan(c/2 + (d*x)/2)^2*(a^2 - 4*b^2) - tan(c/2 + (d*x)/2)^8*(a^2 - 4*b^2) + 8*a*b*tan(c/2 + (d*x)/2)^3 - 8*a*b*tan(c/2 + (d*x)/2)^7 + 4*a*b*tan(c/2 + (d*x)/2)^9 - 4*a*b*tan(c/2 + (d*x)/2))) + (a^2*atan(((a^2*(2*a^4 + 12*b^4 + 21*a^2*b^2)*(2*a^8*b + 2*b^9 - 8*a^2*b^7 + 12*a^4*b^5 - 8*a^6*b^3))/(2*(a + b)^(9/2)*(a - b)^(9/2)) + (a^3*tan(c/2 + (d*x)/2)*(2*a^4 + 12*b^4 + 21*a^2*b^2)*(a^8 + b^8 - 4*a^2*b^6 + 6*a^4*b^4 - 4*a^6*b^2))/((a + b)^(9/2)*(a - b)^(9/2)))/(2*a^6 + 12*a^2*b^4 + 21*a^4*b^2))*(2*a^4 + 12*b^4 + 21*a^2*b^2))/(d*(a + b)^(9/2)*(a - b)^(9/2))","B"
199,1,627,350,10.357614,"\text{Not used}","int(tan(c + d*x)^2/(a + b*sin(c + d*x))^3,x)","\frac{\frac{5\,\left(2\,a^4\,b+a^2\,b^3\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(2\,a^5+a^3\,b^2+12\,a\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(2\,a^4\,b+6\,a^2\,b^3+7\,b^5\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{3\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(2\,a^4\,b+11\,a^2\,b^3+2\,b^5\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(-2\,a^4+29\,a^2\,b^2+18\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-\frac{a\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(2\,a^4+11\,a^2\,b^2+2\,b^4\right)}{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{d\,\left(a^2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6-a^2-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^2+4\,b^2\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^2+4\,b^2\right)+4\,a\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5-4\,a\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,a^4+11\,a^2\,b^2+2\,b^4\right)\,\left(2\,a^6\,b-6\,a^4\,b^3+6\,a^2\,b^5-2\,b^7\right)}{2\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}+\frac{a\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(2\,a^4+11\,a^2\,b^2+2\,b^4\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)}^{7/2}}}{2\,a^4+11\,a^2\,b^2+2\,b^4}\right)\,\left(2\,a^4+11\,a^2\,b^2+2\,b^4\right)}{d\,{\left(a+b\right)}^{7/2}\,{\left(a-b\right)}^{7/2}}","Not used",1,"((5*(2*a^4*b + a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (2*tan(c/2 + (d*x)/2)^3*(12*a*b^4 + 2*a^5 + a^3*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (2*tan(c/2 + (d*x)/2)^2*(2*a^4*b + 7*b^5 + 6*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (3*tan(c/2 + (d*x)/2)^4*(2*a^4*b + 2*b^5 + 11*a^2*b^3))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) + (a*tan(c/2 + (d*x)/2)*(18*b^4 - 2*a^4 + 29*a^2*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2) - (a*tan(c/2 + (d*x)/2)^5*(2*a^4 + 2*b^4 + 11*a^2*b^2))/(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/(d*(a^2*tan(c/2 + (d*x)/2)^6 - a^2 - tan(c/2 + (d*x)/2)^2*(a^2 + 4*b^2) + tan(c/2 + (d*x)/2)^4*(a^2 + 4*b^2) + 4*a*b*tan(c/2 + (d*x)/2)^5 - 4*a*b*tan(c/2 + (d*x)/2))) - (atan((((2*a^4 + 2*b^4 + 11*a^2*b^2)*(2*a^6*b - 2*b^7 + 6*a^2*b^5 - 6*a^4*b^3))/(2*(a + b)^(7/2)*(a - b)^(7/2)) + (a*tan(c/2 + (d*x)/2)*(2*a^4 + 2*b^4 + 11*a^2*b^2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2))/((a + b)^(7/2)*(a - b)^(7/2)))/(2*a^4 + 2*b^4 + 11*a^2*b^2))*(2*a^4 + 2*b^4 + 11*a^2*b^2))/(d*(a + b)^(7/2)*(a - b)^(7/2))","B"
200,1,1762,202,7.852548,"\text{Not used}","int(cot(c + d*x)^2/(a + b*sin(c + d*x))^3,x)","\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{2\,a^3\,d}-\frac{a^2-\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(7\,a\,b^3-6\,a^3\,b\right)}{a^2-b^2}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(a^4+9\,a^2\,b^2-12\,b^4\right)}{a^2-b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(a^4+12\,a^2\,b^2-16\,b^4\right)}{a^2-b^2}+\frac{2\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(6\,a^4\,b+a^2\,b^3-10\,b^5\right)}{a\,\left(a^2-b^2\right)}}{d\,\left(2\,a^5\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(4\,a^5+8\,a^3\,b^2\right)+2\,a^5\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2+8\,a^4\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\right)}-\frac{3\,b\,\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}+\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)\,1{}\mathrm{i}}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}{\frac{2\,\left(6\,a^4\,b-27\,a^2\,b^3+18\,b^5\right)}{a^8-a^6\,b^2}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-24\,a^4\,b^2+39\,a^2\,b^4-18\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}+\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}+\frac{\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,\left(\frac{2\,a^8-15\,a^6\,b^2+12\,a^4\,b^4}{a^8-a^6\,b^2}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(10\,a^8\,b-46\,a^6\,b^3+60\,a^4\,b^5-24\,a^2\,b^7\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}-\frac{\left(\frac{2\,a^{10}\,b-2\,a^8\,b^3}{a^8-a^6\,b^2}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-20\,a^{10}\,b^2+22\,a^8\,b^4-8\,a^6\,b^6\right)}{a^9-2\,a^7\,b^2+a^5\,b^4}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}\right)}{a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(a^4-\frac{9\,a^2\,b^2}{2}+3\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^{10}-3\,a^8\,b^2+3\,a^6\,b^4-a^4\,b^6\right)}","Not used",1,"tan(c/2 + (d*x)/2)/(2*a^3*d) - (a^2 - (2*tan(c/2 + (d*x)/2)*(7*a*b^3 - 6*a^3*b))/(a^2 - b^2) + (tan(c/2 + (d*x)/2)^4*(a^4 - 12*b^4 + 9*a^2*b^2))/(a^2 - b^2) + (2*tan(c/2 + (d*x)/2)^2*(a^4 - 16*b^4 + 12*a^2*b^2))/(a^2 - b^2) + (2*tan(c/2 + (d*x)/2)^3*(6*a^4*b - 10*b^5 + a^2*b^3))/(a*(a^2 - b^2)))/(d*(2*a^5*tan(c/2 + (d*x)/2)^5 + tan(c/2 + (d*x)/2)^3*(4*a^5 + 8*a^3*b^2) + 2*a^5*tan(c/2 + (d*x)/2) + 8*a^4*b*tan(c/2 + (d*x)/2)^2 + 8*a^4*b*tan(c/2 + (d*x)/2)^4)) - (3*b*log(tan(c/2 + (d*x)/2)))/(a^4*d) - (atan((((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) + (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + ((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) - (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))*1i)/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))/((2*(6*a^4*b + 18*b^5 - 27*a^2*b^3))/(a^8 - a^6*b^2) + (2*tan(c/2 + (d*x)/2)*(4*a^6 - 18*b^6 + 39*a^2*b^4 - 24*a^4*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2) - ((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) + (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2) + ((-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*((2*a^8 + 12*a^4*b^4 - 15*a^6*b^2)/(a^8 - a^6*b^2) + (tan(c/2 + (d*x)/2)*(10*a^8*b - 24*a^2*b^7 + 60*a^4*b^5 - 46*a^6*b^3))/(a^9 + a^5*b^4 - 2*a^7*b^2) - (((2*a^10*b - 2*a^8*b^3)/(a^8 - a^6*b^2) - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^6*b^6 + 22*a^8*b^4 - 20*a^10*b^2))/(a^9 + a^5*b^4 - 2*a^7*b^2))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))/(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2)))*(-(a + b)^3*(a - b)^3)^(1/2)*(a^4 + 3*b^4 - (9*a^2*b^2)/2)*2i)/(d*(a^10 - a^4*b^6 + 3*a^6*b^4 - 3*a^8*b^2))","B"
201,1,1261,289,7.311321,"\text{Not used}","int(cot(c + d*x)^4/(a + b*sin(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3}{24\,a^3\,d}-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{8\,a^5}+\frac{1}{4\,a^3}-\frac{9\,b^2}{2\,a^5}\right)}{d}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(5\,a^4+16\,a^2\,b^2-80\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{29\,a^4}{3}+72\,a^2\,b^2-304\,b^4\right)-\frac{a^4}{3}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{13\,a^4}{3}-\frac{40\,a^2\,b^2}{3}\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(156\,a\,b^3-\frac{170\,a^3\,b}{3}\right)-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(-55\,a^4\,b+104\,a^2\,b^3+144\,b^5\right)}{a}+\frac{5\,a^3\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{3}}{d\,\left(8\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3+8\,a^7\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(16\,a^7+32\,a^5\,b^2\right)+32\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4+32\,a^6\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\right)}+\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(9\,a^2\,b-20\,b^3\right)}{2\,a^6\,d}-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2}{8\,a^4\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)\,1{}\mathrm{i}}{a^8-a^6\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)\,1{}\mathrm{i}}{a^8-a^6\,b^2}}{\frac{18\,a^6\,b-211\,a^4\,b^3+560\,a^2\,b^5-400\,b^7}{a^{10}}+\frac{2\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(4\,a^6-58\,a^4\,b^2+230\,a^2\,b^4-200\,b^6\right)}{a^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)}{a^8-a^6\,b^2}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,\left(\frac{2\,a^{10}-28\,a^8\,b^2+40\,a^6\,b^4}{a^{10}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(13\,a^8\,b-76\,a^6\,b^3+80\,a^4\,b^5\right)}{a^9}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(6\,a^{12}-8\,a^{10}\,b^2\right)}{a^9}\right)\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)}{a^8-a^6\,b^2}\right)}{a^8-a^6\,b^2}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{19\,a^2\,b^2}{2}+10\,b^4\right)\,2{}\mathrm{i}}{d\,\left(a^8-a^6\,b^2\right)}","Not used",1,"tan(c/2 + (d*x)/2)^3/(24*a^3*d) - (tan(c/2 + (d*x)/2)*((3*(a^2 + 4*b^2))/(8*a^5) + 1/(4*a^3) - (9*b^2)/(2*a^5)))/d + (tan(c/2 + (d*x)/2)^6*(5*a^4 - 80*b^4 + 16*a^2*b^2) + tan(c/2 + (d*x)/2)^4*((29*a^4)/3 - 304*b^4 + 72*a^2*b^2) - a^4/3 + tan(c/2 + (d*x)/2)^2*((13*a^4)/3 - (40*a^2*b^2)/3) - tan(c/2 + (d*x)/2)^3*(156*a*b^3 - (170*a^3*b)/3) - (tan(c/2 + (d*x)/2)^5*(144*b^5 - 55*a^4*b + 104*a^2*b^3))/a + (5*a^3*b*tan(c/2 + (d*x)/2))/3)/(d*(8*a^7*tan(c/2 + (d*x)/2)^3 + 8*a^7*tan(c/2 + (d*x)/2)^7 + tan(c/2 + (d*x)/2)^5*(16*a^7 + 32*a^5*b^2) + 32*a^6*b*tan(c/2 + (d*x)/2)^4 + 32*a^6*b*tan(c/2 + (d*x)/2)^6)) + (log(tan(c/2 + (d*x)/2))*(9*a^2*b - 20*b^3))/(2*a^6*d) - (3*b*tan(c/2 + (d*x)/2)^2)/(8*a^4*d) + (atan((((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2))*1i)/(a^8 - a^6*b^2) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2))*1i)/(a^8 - a^6*b^2))/((18*a^6*b - 400*b^7 + 560*a^2*b^5 - 211*a^4*b^3)/a^10 + (2*tan(c/2 + (d*x)/2)*(4*a^6 - 200*b^6 + 230*a^2*b^4 - 58*a^4*b^2))/a^9 - ((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2)))/(a^8 - a^6*b^2) + ((-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*((2*a^10 + 40*a^6*b^4 - 28*a^8*b^2)/a^10 + (tan(c/2 + (d*x)/2)*(13*a^8*b + 80*a^4*b^5 - 76*a^6*b^3))/a^9 - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(6*a^12 - 8*a^10*b^2))/a^9)*(a^4 + 10*b^4 - (19*a^2*b^2)/2))/(a^8 - a^6*b^2)))/(a^8 - a^6*b^2)))*(-(a + b)*(a - b))^(1/2)*(a^4 + 10*b^4 - (19*a^2*b^2)/2)*2i)/(d*(a^8 - a^6*b^2))","B"
202,1,1614,492,7.300728,"\text{Not used}","int(cot(c + d*x)^6/(a + b*sin(c + d*x))^3,x)","\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5}{160\,a^3\,d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{a^2+4\,b^2}{32\,a^5}+\frac{1}{24\,a^3}-\frac{3\,b^2}{8\,a^5}\right)}{d}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(\frac{1}{8\,a^3}-\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}-\frac{6\,b\,\left(\frac{6\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{1}{8\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{a}-\frac{384\,a^2\,b+256\,b^3}{1024\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{16\,a^6}\right)}{a}+\frac{3\,\left(a^2+4\,b^2\right)\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{1}{8\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{a^2}+\frac{3\,b\,\left(384\,a^2\,b+256\,b^3\right)}{512\,a^7}\right)}{d}-\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^3\,\left(\frac{187\,a^5\,b}{15}-14\,a^3\,b^3\right)+\frac{a^6}{5}+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4\,\left(\frac{263\,a^6}{15}-\frac{358\,a^4\,b^2}{3}+112\,a^2\,b^4\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5\,\left(\frac{1519\,a^5\,b}{6}-1360\,a^3\,b^3+1216\,a\,b^5\right)-{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{29\,a^6}{15}-\frac{14\,a^4\,b^2}{5}\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\,\left(22\,a^6-56\,a^4\,b^2-368\,a^2\,b^4+448\,b^6\right)+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6\,\left(\frac{125\,a^6}{3}+112\,a^4\,b^2-2112\,a^2\,b^4+2176\,b^6\right)+\frac{8\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(30\,a^6\,b-149\,a^4\,b^3+36\,a^2\,b^5+104\,b^7\right)}{a}-\frac{7\,a^5\,b\,\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}{10}}{d\,\left(32\,a^9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^5+32\,a^9\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^9+{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^7\,\left(64\,a^9+128\,a^7\,b^2\right)+128\,a^8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^6+128\,a^8\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^8\right)}+\frac{{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^2\,\left(\frac{3\,b\,\left(\frac{3\,\left(a^2+4\,b^2\right)}{32\,a^5}+\frac{1}{8\,a^3}-\frac{9\,b^2}{8\,a^5}\right)}{a}-\frac{384\,a^2\,b+256\,b^3}{2048\,a^6}+\frac{9\,b\,\left(a^2+4\,b^2\right)}{32\,a^6}\right)}{d}-\frac{\ln\left(\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\right)\,\left(45\,a^4\,b-200\,a^2\,b^3+168\,b^5\right)}{8\,a^8\,d}-\frac{3\,b\,{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)}^4}{64\,a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)\,1{}\mathrm{i}}{a^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)\,1{}\mathrm{i}}{a^8}}{\frac{\frac{45\,a^{10}\,b}{2}-\frac{1795\,a^8\,b^3}{4}+\frac{9731\,a^6\,b^5}{4}-\frac{10649\,a^4\,b^7}{2}+5082\,a^2\,b^9-1764\,b^{11}}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(16\,a^{10}-406\,a^8\,b^2+3185\,a^6\,b^4-8549\,a^4\,b^6+9282\,a^2\,b^8-3528\,b^{10}\right)}{2\,a^{13}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)}{a^8}+\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,\left(\frac{2\,a^{14}-\frac{169\,a^{12}\,b^2}{4}+121\,a^{10}\,b^4-84\,a^8\,b^6}{a^{14}}+\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(61\,a^{12}\,b-538\,a^{10}\,b^3+1136\,a^8\,b^5-672\,a^6\,b^7\right)}{4\,a^{13}}-\frac{\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(2\,a^2\,b-\frac{\mathrm{tan}\left(\frac{c}{2}+\frac{d\,x}{2}\right)\,\left(24\,a^{16}-32\,a^{14}\,b^2\right)}{4\,a^{13}}\right)\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)}{a^8}\right)}{a^8}}\right)\,\sqrt{-\left(a+b\right)\,\left(a-b\right)}\,\left(a^4-\frac{29\,a^2\,b^2}{2}+21\,b^4\right)\,2{}\mathrm{i}}{a^8\,d}","Not used",1,"tan(c/2 + (d*x)/2)^5/(160*a^3*d) - (tan(c/2 + (d*x)/2)^3*((a^2 + 4*b^2)/(32*a^5) + 1/(24*a^3) - (3*b^2)/(8*a^5)))/d + (tan(c/2 + (d*x)/2)*(1/(8*a^3) - (3*(a^2 + 4*b^2))/(32*a^5) - (6*b*((6*b*((3*(a^2 + 4*b^2))/(32*a^5) + 1/(8*a^3) - (9*b^2)/(8*a^5)))/a - (384*a^2*b + 256*b^3)/(1024*a^6) + (9*b*(a^2 + 4*b^2))/(16*a^6)))/a + (3*(a^2 + 4*b^2)*((3*(a^2 + 4*b^2))/(32*a^5) + 1/(8*a^3) - (9*b^2)/(8*a^5)))/a^2 + (3*b*(384*a^2*b + 256*b^3))/(512*a^7)))/d - (tan(c/2 + (d*x)/2)^3*((187*a^5*b)/15 - 14*a^3*b^3) + a^6/5 + tan(c/2 + (d*x)/2)^4*((263*a^6)/15 + 112*a^2*b^4 - (358*a^4*b^2)/3) + tan(c/2 + (d*x)/2)^5*(1216*a*b^5 + (1519*a^5*b)/6 - 1360*a^3*b^3) - tan(c/2 + (d*x)/2)^2*((29*a^6)/15 - (14*a^4*b^2)/5) + tan(c/2 + (d*x)/2)^8*(22*a^6 + 448*b^6 - 368*a^2*b^4 - 56*a^4*b^2) + tan(c/2 + (d*x)/2)^6*((125*a^6)/3 + 2176*b^6 - 2112*a^2*b^4 + 112*a^4*b^2) + (8*tan(c/2 + (d*x)/2)^7*(30*a^6*b + 104*b^7 + 36*a^2*b^5 - 149*a^4*b^3))/a - (7*a^5*b*tan(c/2 + (d*x)/2))/10)/(d*(32*a^9*tan(c/2 + (d*x)/2)^5 + 32*a^9*tan(c/2 + (d*x)/2)^9 + tan(c/2 + (d*x)/2)^7*(64*a^9 + 128*a^7*b^2) + 128*a^8*b*tan(c/2 + (d*x)/2)^6 + 128*a^8*b*tan(c/2 + (d*x)/2)^8)) + (tan(c/2 + (d*x)/2)^2*((3*b*((3*(a^2 + 4*b^2))/(32*a^5) + 1/(8*a^3) - (9*b^2)/(8*a^5)))/a - (384*a^2*b + 256*b^3)/(2048*a^6) + (9*b*(a^2 + 4*b^2))/(32*a^6)))/d - (log(tan(c/2 + (d*x)/2))*(45*a^4*b + 168*b^5 - 200*a^2*b^3))/(8*a^8*d) - (3*b*tan(c/2 + (d*x)/2)^4)/(64*a^4*d) - (atan((((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8)*1i)/a^8 + ((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8)*1i)/a^8)/(((45*a^10*b)/2 - 1764*b^11 + 5082*a^2*b^9 - (10649*a^4*b^7)/2 + (9731*a^6*b^5)/4 - (1795*a^8*b^3)/4)/a^14 + (tan(c/2 + (d*x)/2)*(16*a^10 - 3528*b^10 + 9282*a^2*b^8 - 8549*a^4*b^6 + 3185*a^6*b^4 - 406*a^8*b^2))/(2*a^13) - ((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) + ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8))/a^8 + ((-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*((2*a^14 - 84*a^8*b^6 + 121*a^10*b^4 - (169*a^12*b^2)/4)/a^14 + (tan(c/2 + (d*x)/2)*(61*a^12*b - 672*a^6*b^7 + 1136*a^8*b^5 - 538*a^10*b^3))/(4*a^13) - ((-(a + b)*(a - b))^(1/2)*(2*a^2*b - (tan(c/2 + (d*x)/2)*(24*a^16 - 32*a^14*b^2))/(4*a^13))*(a^4 + 21*b^4 - (29*a^2*b^2)/2))/a^8))/a^8))*(-(a + b)*(a - b))^(1/2)*(a^4 + 21*b^4 - (29*a^2*b^2)/2)*2i)/(a^8*d)","B"
203,0,-1,271,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + b*sin(e + f*x))^3,x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^3 \,d x","Not used",1,"int((g*tan(e + f*x))^p*(a + b*sin(e + f*x))^3, x)","F"
204,0,-1,186,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + b*sin(e + f*x))^2,x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2 \,d x","Not used",1,"int((g*tan(e + f*x))^p*(a + b*sin(e + f*x))^2, x)","F"
205,0,-1,129,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + b*sin(e + f*x)),x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,\left(a+b\,\sin\left(e+f\,x\right)\right) \,d x","Not used",1,"int((g*tan(e + f*x))^p*(a + b*sin(e + f*x)), x)","F"
206,0,-1,284,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p/(a + b*sin(e + f*x)),x)","\int \frac{{\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p}{a+b\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((g*tan(e + f*x))^p/(a + b*sin(e + f*x)), x)","F"
207,0,-1,737,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p/(a + b*sin(e + f*x))^2,x)","\int \frac{{\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p}{{\left(a+b\,\sin\left(e+f\,x\right)\right)}^2} \,d x","Not used",1,"int((g*tan(e + f*x))^p/(a + b*sin(e + f*x))^2, x)","F"
208,0,-1,26,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + b*sin(e + f*x))^m,x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,{\left(a+b\,\sin\left(e+f\,x\right)\right)}^m \,d x","Not used",0,"int((g*tan(e + f*x))^p*(a + b*sin(e + f*x))^m, x)","F"