1,1,46,33,0.458117,"\text{Not used}","int(tan(x)^4/(a + a*cos(x)),x)","\frac{\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5+\frac{8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3}-\mathrm{tan}\left(\frac{x}{2}\right)}{a\,{\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}^3}","Not used",1,"atanh(tan(x/2))/a - ((8*tan(x/2)^3)/3 - tan(x/2) + tan(x/2)^5)/(a*(tan(x/2)^2 - 1)^3)","B"
2,1,13,19,0.335149,"\text{Not used}","int(tan(x)^3/(a + a*cos(x)),x)","-\frac{\cos\left(x\right)-\frac{1}{2}}{a\,{\cos\left(x\right)}^2}","Not used",1,"-(cos(x) - 1/2)/(a*cos(x)^2)","B"
3,1,30,15,0.351863,"\text{Not used}","int(tan(x)^2/(a + a*cos(x)),x)","-\frac{2\,\mathrm{atanh}\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{a\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}","Not used",1,"- (2*atanh(tan(x/2)))/a - (2*tan(x/2))/(a*(tan(x/2)^2 - 1))","B"
4,1,14,18,0.403811,"\text{Not used}","int(tan(x)/(a + a*cos(x)),x)","-\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}{a}","Not used",1,"-log(tan(x/2)^2 - 1)/a","B"
5,1,21,33,0.336232,"\text{Not used}","int(cot(x)/(a + a*cos(x)),x)","\frac{2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{4\,a}","Not used",1,"(2*log(tan(x/2)) - tan(x/2)^2)/(4*a)","B"
6,1,35,30,0.381691,"\text{Not used}","int(cot(x)^2/(a + a*cos(x)),x)","\frac{4\,{\cos\left(\frac{x}{2}\right)}^4-8\,{\cos\left(\frac{x}{2}\right)}^2+1}{12\,a\,{\cos\left(\frac{x}{2}\right)}^3\,\sin\left(\frac{x}{2}\right)}","Not used",1,"(4*cos(x/2)^4 - 8*cos(x/2)^2 + 1)/(12*a*cos(x/2)^3*sin(x/2))","B"
7,1,40,46,0.407582,"\text{Not used}","int(cot(x)^3/(a + a*cos(x)),x)","-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^6-6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+12\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)+2}{32\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}","Not used",1,"-(tan(x/2)^6 - 6*tan(x/2)^4 + 12*tan(x/2)^2*log(tan(x/2)) + 2)/(32*a*tan(x/2)^2)","B"
8,1,45,40,0.454898,"\text{Not used}","int(cot(x)^4/(a + a*cos(x)),x)","\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8-20\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+90\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+60\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-5}{240\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}","Not used",1,"(60*tan(x/2)^2 + 90*tan(x/2)^4 - 20*tan(x/2)^6 + 3*tan(x/2)^8 - 5)/(240*a*tan(x/2)^3)","B"
9,1,20,33,0.366350,"\text{Not used}","int(tan(3*x)/(cos(3*x) + 1)^2,x)","-\frac{\ln\left({\mathrm{tan}\left(\frac{3\,x}{2}\right)}^2-1\right)}{3}-\frac{{\mathrm{tan}\left(\frac{3\,x}{2}\right)}^2}{6}","Not used",1,"- log(tan((3*x)/2)^2 - 1)/3 - tan((3*x)/2)^2/6","B"
10,1,1666,113,1.096709,"\text{Not used}","int(tan(x)^4/(a + b*cos(x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{64\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{112\,a\,b^2+128\,a^2\,b-64\,a^3-352\,b^3+\frac{16\,b^4}{a}+\frac{320\,b^5}{a^2}-\frac{112\,b^6}{a^3}-\frac{96\,b^7}{a^4}+\frac{48\,b^8}{a^5}}+\frac{144\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{16\,a\,b^4+128\,a^4\,b-64\,a^5+320\,b^5-352\,a^2\,b^3+112\,a^3\,b^2-\frac{112\,b^6}{a}-\frac{96\,b^7}{a^2}+\frac{48\,b^8}{a^3}}+\frac{80\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{320\,a\,b^5+128\,a^5\,b-64\,a^6-112\,b^6+16\,a^2\,b^4-352\,a^3\,b^3+112\,a^4\,b^2-\frac{96\,b^7}{a}+\frac{48\,b^8}{a^2}}-\frac{144\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{128\,a^6\,b-112\,a\,b^6-64\,a^7-96\,b^7+320\,a^2\,b^5+16\,a^3\,b^4-352\,a^4\,b^3+112\,a^5\,b^2+\frac{48\,b^8}{a}}+\frac{48\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{-64\,a^8+128\,a^7\,b+112\,a^6\,b^2-352\,a^5\,b^3+16\,a^4\,b^4+320\,a^3\,b^5-112\,a^2\,b^6-96\,a\,b^7+48\,b^8}-\frac{192\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-a^6+3\,a^4\,b^2-3\,a^2\,b^4+b^6}}{128\,a^3\,b-352\,a\,b^3-64\,a^4+16\,b^4+112\,a^2\,b^2+\frac{320\,b^5}{a}-\frac{112\,b^6}{a^2}-\frac{96\,b^7}{a^3}+\frac{48\,b^8}{a^4}}\right)\,\sqrt{-{\left(a+b\right)}^3\,{\left(a-b\right)}^3}}{a^4}-\frac{\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(5\,a^2-3\,b^2\right)}{3\,a^3}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^2+a\,b-2\,b^2\right)}{a^3}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(-2\,a^2+a\,b+2\,b^2\right)}{a^3}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^6-3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-1}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{8\,\left(-4\,a^{13}+2\,a^{12}\,b+10\,a^{11}\,b^2-6\,a^{10}\,b^3-6\,a^9\,b^4+4\,a^8\,b^5\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^9-4\,a^8\,b-7\,a^7\,b^2-11\,a^6\,b^3+39\,a^5\,b^4+3\,a^4\,b^5-48\,a^3\,b^6+16\,a^2\,b^7+16\,a\,b^8-8\,b^9\right)}{a^6}\right)\,1{}\mathrm{i}}{a^4}-\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{8\,\left(-4\,a^{13}+2\,a^{12}\,b+10\,a^{11}\,b^2-6\,a^{10}\,b^3-6\,a^9\,b^4+4\,a^8\,b^5\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^9-4\,a^8\,b-7\,a^7\,b^2-11\,a^6\,b^3+39\,a^5\,b^4+3\,a^4\,b^5-48\,a^3\,b^6+16\,a^2\,b^7+16\,a\,b^8-8\,b^9\right)}{a^6}\right)\,1{}\mathrm{i}}{a^4}}{\frac{16\,\left(-6\,a^{10}\,b+15\,a^9\,b^2+10\,a^8\,b^3-49\,a^7\,b^4+8\,a^6\,b^5+59\,a^5\,b^6-26\,a^4\,b^7-31\,a^3\,b^8+18\,a^2\,b^9+6\,a\,b^{10}-4\,b^{11}\right)}{a^9}+\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{8\,\left(-4\,a^{13}+2\,a^{12}\,b+10\,a^{11}\,b^2-6\,a^{10}\,b^3-6\,a^9\,b^4+4\,a^8\,b^5\right)}{a^9}-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)}{a^4}-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^9-4\,a^8\,b-7\,a^7\,b^2-11\,a^6\,b^3+39\,a^5\,b^4+3\,a^4\,b^5-48\,a^3\,b^6+16\,a^2\,b^7+16\,a\,b^8-8\,b^9\right)}{a^6}\right)}{a^4}+\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(\frac{8\,\left(-4\,a^{13}+2\,a^{12}\,b+10\,a^{11}\,b^2-6\,a^{10}\,b^3-6\,a^9\,b^4+4\,a^8\,b^5\right)}{a^9}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{3\,a^2\,b}{2}-b^3\right)\,\left(8\,a^{10}\,b-16\,a^9\,b^2+8\,a^8\,b^3\right)}{a^{10}}\right)}{a^4}+\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(4\,a^9-4\,a^8\,b-7\,a^7\,b^2-11\,a^6\,b^3+39\,a^5\,b^4+3\,a^4\,b^5-48\,a^3\,b^6+16\,a^2\,b^7+16\,a\,b^8-8\,b^9\right)}{a^6}\right)}{a^4}}\right)\,\left(\frac{3\,a^2\,b}{2}-b^3\right)\,2{}\mathrm{i}}{a^4}","Not used",1,"(2*atanh((64*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(112*a*b^2 + 128*a^2*b - 64*a^3 - 352*b^3 + (16*b^4)/a + (320*b^5)/a^2 - (112*b^6)/a^3 - (96*b^7)/a^4 + (48*b^8)/a^5) + (144*b^2*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(16*a*b^4 + 128*a^4*b - 64*a^5 + 320*b^5 - 352*a^2*b^3 + 112*a^3*b^2 - (112*b^6)/a - (96*b^7)/a^2 + (48*b^8)/a^3) + (80*b^3*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(320*a*b^5 + 128*a^5*b - 64*a^6 - 112*b^6 + 16*a^2*b^4 - 352*a^3*b^3 + 112*a^4*b^2 - (96*b^7)/a + (48*b^8)/a^2) - (144*b^4*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a^6*b - 112*a*b^6 - 64*a^7 - 96*b^7 + 320*a^2*b^5 + 16*a^3*b^4 - 352*a^4*b^3 + 112*a^5*b^2 + (48*b^8)/a) + (48*b^5*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a^7*b - 96*a*b^7 - 64*a^8 + 48*b^8 - 112*a^2*b^6 + 320*a^3*b^5 + 16*a^4*b^4 - 352*a^5*b^3 + 112*a^6*b^2) - (192*b*tan(x/2)*(b^6 - a^6 - 3*a^2*b^4 + 3*a^4*b^2)^(1/2))/(128*a^3*b - 352*a*b^3 - 64*a^4 + 16*b^4 + 112*a^2*b^2 + (320*b^5)/a - (112*b^6)/a^2 - (96*b^7)/a^3 + (48*b^8)/a^4))*(-(a + b)^3*(a - b)^3)^(1/2))/a^4 - ((4*tan(x/2)^3*(5*a^2 - 3*b^2))/(3*a^3) - (tan(x/2)*(a*b + 2*a^2 - 2*b^2))/a^3 + (tan(x/2)^5*(a*b - 2*a^2 + 2*b^2))/a^3)/(3*tan(x/2)^2 - 3*tan(x/2)^4 + tan(x/2)^6 - 1) - (atan(((((3*a^2*b)/2 - b^3)*((((3*a^2*b)/2 - b^3)*((8*(2*a^12*b - 4*a^13 + 4*a^8*b^5 - 6*a^9*b^4 - 6*a^10*b^3 + 10*a^11*b^2))/a^9 - (8*tan(x/2)*((3*a^2*b)/2 - b^3)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10))/a^4 - (8*tan(x/2)*(16*a*b^8 - 4*a^8*b + 4*a^9 - 8*b^9 + 16*a^2*b^7 - 48*a^3*b^6 + 3*a^4*b^5 + 39*a^5*b^4 - 11*a^6*b^3 - 7*a^7*b^2))/a^6)*1i)/a^4 - (((3*a^2*b)/2 - b^3)*((((3*a^2*b)/2 - b^3)*((8*(2*a^12*b - 4*a^13 + 4*a^8*b^5 - 6*a^9*b^4 - 6*a^10*b^3 + 10*a^11*b^2))/a^9 + (8*tan(x/2)*((3*a^2*b)/2 - b^3)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10))/a^4 + (8*tan(x/2)*(16*a*b^8 - 4*a^8*b + 4*a^9 - 8*b^9 + 16*a^2*b^7 - 48*a^3*b^6 + 3*a^4*b^5 + 39*a^5*b^4 - 11*a^6*b^3 - 7*a^7*b^2))/a^6)*1i)/a^4)/((16*(6*a*b^10 - 6*a^10*b - 4*b^11 + 18*a^2*b^9 - 31*a^3*b^8 - 26*a^4*b^7 + 59*a^5*b^6 + 8*a^6*b^5 - 49*a^7*b^4 + 10*a^8*b^3 + 15*a^9*b^2))/a^9 + (((3*a^2*b)/2 - b^3)*((((3*a^2*b)/2 - b^3)*((8*(2*a^12*b - 4*a^13 + 4*a^8*b^5 - 6*a^9*b^4 - 6*a^10*b^3 + 10*a^11*b^2))/a^9 - (8*tan(x/2)*((3*a^2*b)/2 - b^3)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10))/a^4 - (8*tan(x/2)*(16*a*b^8 - 4*a^8*b + 4*a^9 - 8*b^9 + 16*a^2*b^7 - 48*a^3*b^6 + 3*a^4*b^5 + 39*a^5*b^4 - 11*a^6*b^3 - 7*a^7*b^2))/a^6))/a^4 + (((3*a^2*b)/2 - b^3)*((((3*a^2*b)/2 - b^3)*((8*(2*a^12*b - 4*a^13 + 4*a^8*b^5 - 6*a^9*b^4 - 6*a^10*b^3 + 10*a^11*b^2))/a^9 + (8*tan(x/2)*((3*a^2*b)/2 - b^3)*(8*a^10*b + 8*a^8*b^3 - 16*a^9*b^2))/a^10))/a^4 + (8*tan(x/2)*(16*a*b^8 - 4*a^8*b + 4*a^9 - 8*b^9 + 16*a^2*b^7 - 48*a^3*b^6 + 3*a^4*b^5 + 39*a^5*b^4 - 11*a^6*b^3 - 7*a^7*b^2))/a^6))/a^4))*((3*a^2*b)/2 - b^3)*2i)/a^4","B"
11,1,115,57,0.602868,"\text{Not used}","int(tan(x)^3/(a + b*cos(x)),x)","-\frac{2\,a^2\,\mathrm{atanh}\left(\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+a+b}\right)-2\,b^2\,\mathrm{atanh}\left(\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+a+b}\right)}{a^3}-\frac{2\,a\,b-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2+2\,b\,a\right)}{a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-2\,a^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+a^3}","Not used",1,"- (2*a^2*atanh((a*tan(x/2)^2)/(a + b - b*tan(x/2)^2)) - 2*b^2*atanh((a*tan(x/2)^2)/(a + b - b*tan(x/2)^2)))/a^3 - (2*a*b - tan(x/2)^2*(2*a*b + 2*a^2))/(a^3 - 2*a^3*tan(x/2)^2 + a^3*tan(x/2)^4)","B"
12,1,77,61,0.547580,"\text{Not used}","int(tan(x)^2/(a + b*cos(x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)\,\sqrt{b^2-a^2}}{a\,\cos\left(\frac{x}{2}\right)+b\,\cos\left(\frac{x}{2}\right)}\right)\,\sqrt{b^2-a^2}}{a^2}-\frac{2\,b\,\mathrm{atanh}\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{a^2}+\frac{\sin\left(x\right)}{a\,\cos\left(x\right)}","Not used",1,"(2*atanh((sin(x/2)*(b^2 - a^2)^(1/2))/(a*cos(x/2) + b*cos(x/2)))*(b^2 - a^2)^(1/2))/a^2 - (2*b*atanh(sin(x/2)/cos(x/2)))/a^2 + sin(x)/(a*cos(x))","B"
13,1,48,20,0.514142,"\text{Not used}","int(tan(x)/(a + b*cos(x)),x)","\frac{\mathrm{atan}\left(\frac{a\,{\sin\left(\frac{x}{2}\right)}^2}{a\,{\cos\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}+b\,{\cos\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}-b\,{\sin\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}}\right)\,2{}\mathrm{i}}{a}","Not used",1,"(atan((a*sin(x/2)^2)/(a*cos(x/2)^2*1i + b*cos(x/2)^2*1i - b*sin(x/2)^2*1i))*2i)/a","B"
14,1,47,54,0.502957,"\text{Not used}","int(cot(x)/(a + b*cos(x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a+b}-\frac{a\,\ln\left(a+b+a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\right)}{a^2-b^2}","Not used",1,"log(tan(x/2))/(a + b) - (a*log(a + b + a*tan(x/2)^2 - b*tan(x/2)^2))/(a^2 - b^2)","B"
15,1,86,77,0.537060,"\text{Not used}","int(cot(x)^2/(a + b*cos(x)),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a-2\,b}-\frac{2\,a^2\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-b^2\right)}{{\left(a+b\right)}^{3/2}\,\sqrt{a-b}}\right)}{{\left(a+b\right)}^{3/2}\,{\left(a-b\right)}^{3/2}}-\frac{a-b}{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a+b\right)\,\left(2\,a-2\,b\right)}","Not used",1,"tan(x/2)/(2*a - 2*b) - (2*a^2*atan((tan(x/2)*(a^2 - b^2))/((a + b)^(3/2)*(a - b)^(1/2))))/((a + b)^(3/2)*(a - b)^(3/2)) - (a - b)/(tan(x/2)*(a + b)*(2*a - 2*b))","B"
16,1,116,93,0.584473,"\text{Not used}","int(cot(x)^3/(a + b*cos(x)),x)","\frac{a^3\,\ln\left(a+b+a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{2\,\left(4\,a-4\,b\right)}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(2\,a+b\right)}{2\,a^2+4\,a\,b+2\,b^2}-\frac{a-b}{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a+b\right)\,\left(4\,a-4\,b\right)}","Not used",1,"(a^3*log(a + b + a*tan(x/2)^2 - b*tan(x/2)^2))/(a^4 + b^4 - 2*a^2*b^2) - tan(x/2)^2/(2*(4*a - 4*b)) - (log(tan(x/2))*(2*a + b))/(4*a*b + 2*a^2 + 2*b^2) - (a - b)/(2*tan(x/2)^2*(a + b)*(4*a - 4*b))","B"
17,1,183,138,0.626153,"\text{Not used}","int(cot(x)^4/(a + b*cos(x)),x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{3\,\left(8\,a-8\,b\right)}-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{4}{8\,a-8\,b}+\frac{8\,a+8\,b}{{\left(8\,a-8\,b\right)}^2}\right)-\frac{\frac{a^2-2\,a\,b+b^2}{3\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-5\,a^3+7\,a^2\,b+a\,b^2-3\,b^3\right)}{{\left(a+b\right)}^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(8\,a^2-16\,a\,b+8\,b^2\right)}+\frac{2\,a^4\,\mathrm{atan}\left(\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4-2\,a^2\,b^2+b^4\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{3/2}}\right)}{{\left(a+b\right)}^{5/2}\,{\left(a-b\right)}^{5/2}}","Not used",1,"tan(x/2)^3/(3*(8*a - 8*b)) - tan(x/2)*(4/(8*a - 8*b) + (8*a + 8*b)/(8*a - 8*b)^2) - ((a^2 - 2*a*b + b^2)/(3*(a + b)) + (tan(x/2)^2*(a*b^2 + 7*a^2*b - 5*a^3 - 3*b^3))/(a + b)^2)/(tan(x/2)^3*(8*a^2 - 16*a*b + 8*b^2)) + (2*a^4*atan((tan(x/2)*(a^4 + b^4 - 2*a^2*b^2))/((a + b)^(5/2)*(a - b)^(3/2))))/((a + b)^(5/2)*(a - b)^(5/2))","B"
18,0,-1,44,0.000000,"\text{Not used}","int(cot(x)/(3 - cos(x))^(1/2),x)","\int \frac{\mathrm{cot}\left(x\right)}{\sqrt{3-\cos\left(x\right)}} \,d x","Not used",1,"int(cot(x)/(3 - cos(x))^(1/2), x)","F"
19,0,-1,37,0.000000,"\text{Not used}","int(tan(x)*(a + b*cos(x))^(1/2),x)","\int \mathrm{tan}\left(x\right)\,\sqrt{a+b\,\cos\left(x\right)} \,d x","Not used",1,"int(tan(x)*(a + b*cos(x))^(1/2), x)","F"
20,0,-1,24,0.000000,"\text{Not used}","int(tan(x)/(a + b*cos(x))^(1/2),x)","\int \frac{\mathrm{tan}\left(x\right)}{\sqrt{a+b\,\cos\left(x\right)}} \,d x","Not used",1,"int(tan(x)/(a + b*cos(x))^(1/2), x)","F"
21,0,-1,204,0.000000,"\text{Not used}","int((e*tan(c + d*x))^(1/2)/(a + b*cos(c + d*x)),x)","\int \frac{\sqrt{e\,\mathrm{tan}\left(c+d\,x\right)}}{a+b\,\cos\left(c+d\,x\right)} \,d x","Not used",1,"int((e*tan(c + d*x))^(1/2)/(a + b*cos(c + d*x)), x)","F"
22,0,-1,49,0.000000,"\text{Not used}","int((g*tan(e + f*x))^p*(a + b*cos(e + f*x))^m,x)","\int {\left(g\,\mathrm{tan}\left(e+f\,x\right)\right)}^p\,{\left(a+b\,\cos\left(e+f\,x\right)\right)}^m \,d x","Not used",0,"int((g*tan(e + f*x))^p*(a + b*cos(e + f*x))^m, x)","F"