1,1,83,55,0.479207,"\text{Not used}","int(tan(x)^4/(a + a/sin(x)),x)","\frac{x}{a}-\frac{-2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+\frac{14\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{3}+\frac{40\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{3}-\frac{26\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{15}-\frac{92\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{15}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{15}+\frac{16}{15}}{a\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}^3\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^5}","Not used",1,"x/a - ((2*tan(x/2))/15 - (92*tan(x/2)^2)/15 - (26*tan(x/2)^3)/15 + (40*tan(x/2)^4)/3 + (14*tan(x/2)^5)/3 - 4*tan(x/2)^6 - 2*tan(x/2)^7 + 16/15)/(a*(tan(x/2) - 1)^3*(tan(x/2) + 1)^5)","B"
2,1,134,68,0.434862,"\text{Not used}","int(tan(x)^3/(a + a/sin(x)),x)","\frac{5\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}{8\,a}+\frac{11\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{8\,a}-\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}+\frac{-\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{4}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{2}+\frac{9\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{2}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{2}-\frac{3\,\mathrm{tan}\left(\frac{x}{2}\right)}{4}}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3-a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+a}","Not used",1,"(5*log(tan(x/2) - 1))/(8*a) + (11*log(tan(x/2) + 1))/(8*a) - log(tan(x/2)^2 + 1)/a + (tan(x/2)^2/2 - (3*tan(x/2))/4 + (9*tan(x/2)^3)/2 + tan(x/2)^4/2 - (3*tan(x/2)^5)/4)/(a + 2*a*tan(x/2) - a*tan(x/2)^2 - 4*a*tan(x/2)^3 - a*tan(x/2)^4 + 2*a*tan(x/2)^5 + a*tan(x/2)^6)","B"
3,1,51,39,0.290555,"\text{Not used}","int(tan(x)^2/(a + a/sin(x)),x)","\frac{-2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}+\frac{4}{3}}{a\,\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}^3}-\frac{x}{a}","Not used",1,"((2*tan(x/2))/3 - 4*tan(x/2)^2 - 2*tan(x/2)^3 + 4/3)/(a*(tan(x/2) - 1)*(tan(x/2) + 1)^3) - x/a","B"
4,1,62,40,0.338535,"\text{Not used}","int(tan(x)/(a + a/sin(x)),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+a}-\frac{3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{2\,a}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}{2\,a}+\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}","Not used",1,"tan(x/2)/(a + 2*a*tan(x/2) + a*tan(x/2)^2) - (3*log(tan(x/2) + 1))/(2*a) - log(tan(x/2) - 1)/(2*a) + log(tan(x/2)^2 + 1)/a","B"
5,1,25,9,0.293824,"\text{Not used}","int(cot(x)/(a + a/sin(x)),x)","\frac{2\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}","Not used",1,"(2*log(tan(x/2) + 1) - log(tan(x/2)^2 + 1))/a","B"
6,1,45,15,0.282237,"\text{Not used}","int(cot(x)^2/(a + a/sin(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{4}{4\,\mathrm{tan}\left(\frac{x}{2}\right)+4}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)}{4\,\mathrm{tan}\left(\frac{x}{2}\right)+4}\right)}{a}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}","Not used",1,"(2*atan(4/(4*tan(x/2) + 4) - (4*tan(x/2))/(4*tan(x/2) + 4)))/a + log(tan(x/2))/a","B"
7,1,36,16,0.304013,"\text{Not used}","int(cot(x)^3/(a + a/sin(x)),x)","-\frac{\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2}-\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)+\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)+\frac{1}{2\,\mathrm{tan}\left(\frac{x}{2}\right)}}{a}","Not used",1,"-(tan(x/2)/2 - log(tan(x/2)^2 + 1) + log(tan(x/2)) + 1/(2*tan(x/2)))/a","B"
8,1,85,31,0.297519,"\text{Not used}","int(cot(x)^4/(a + a/sin(x)),x)","\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}-\frac{2\,\mathrm{atan}\left(\frac{4}{4\,\mathrm{tan}\left(\frac{x}{2}\right)+2}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{4\,\mathrm{tan}\left(\frac{x}{2}\right)+2}\right)}{a}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,a}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{2\,a}+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)-\frac{1}{2}}{4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}","Not used",1,"tan(x/2)^2/(8*a) - (2*atan(4/(4*tan(x/2) + 2) - (2*tan(x/2))/(4*tan(x/2) + 2)))/a - tan(x/2)/(2*a) - log(tan(x/2))/(2*a) + (2*tan(x/2) - 1/2)/(4*a*tan(x/2)^2)","B"
9,1,80,36,0.296739,"\text{Not used}","int(cot(x)^5/(a + a/sin(x)),x)","\frac{3\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a}-\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,a}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{a}+\frac{3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\mathrm{tan}\left(\frac{x}{2}\right)-\frac{1}{3}}{8\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}","Not used",1,"(3*tan(x/2))/(8*a) - log(tan(x/2)^2 + 1)/a + tan(x/2)^2/(8*a) - tan(x/2)^3/(24*a) + log(tan(x/2))/a + (tan(x/2) + 3*tan(x/2)^2 - 1/3)/(8*a*tan(x/2)^3)","B"
10,1,123,49,0.333327,"\text{Not used}","int(cot(x)^6/(a + a/sin(x)),x)","\frac{5\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,a}+\frac{2\,\mathrm{atan}\left(\frac{4}{4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{3}{2}}-\frac{3\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,\left(4\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{3}{2}\right)}\right)}{a}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,a}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,a}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{64\,a}+\frac{3\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{8\,a}+\frac{-10\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3+2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}-\frac{1}{4}}{16\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}","Not used",1,"(5*tan(x/2))/(8*a) + (2*atan(4/(4*tan(x/2) + 3/2) - (3*tan(x/2))/(2*(4*tan(x/2) + 3/2))))/a - tan(x/2)^2/(8*a) - tan(x/2)^3/(24*a) + tan(x/2)^4/(64*a) + (3*log(tan(x/2)))/(8*a) + ((2*tan(x/2))/3 + 2*tan(x/2)^2 - 10*tan(x/2)^3 - 1/4)/(16*a*tan(x/2)^4)","B"
11,1,113,58,0.431326,"\text{Not used}","int(cot(x)^7/(a + a/sin(x)),x)","-\frac{180\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3-960\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)-50\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2-15\,\mathrm{tan}\left(\frac{x}{2}\right)+300\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4+300\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+180\,{\mathrm{tan}\left(\frac{x}{2}\right)}^7-50\,{\mathrm{tan}\left(\frac{x}{2}\right)}^8-15\,{\mathrm{tan}\left(\frac{x}{2}\right)}^9+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^{10}+960\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)+6}{960\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}","Not used",1,"-(180*tan(x/2)^3 - 960*tan(x/2)^5*log(tan(x/2)^2 + 1) - 50*tan(x/2)^2 - 15*tan(x/2) + 300*tan(x/2)^4 + 300*tan(x/2)^6 + 180*tan(x/2)^7 - 50*tan(x/2)^8 - 15*tan(x/2)^9 + 6*tan(x/2)^10 + 960*tan(x/2)^5*log(tan(x/2)) + 6)/(960*a*tan(x/2)^5)","B"
12,1,445,178,2.300024,"\text{Not used}","int(tan(x)^5/(a + b/sin(x)),x)","\frac{\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a\,b^2-a^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(3\,a\,b^2-2\,a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6\,\left(2\,a\,b^2-a^3\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^7\,\left(3\,a^2\,b-7\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(11\,a^2\,b-15\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(11\,a^2\,b-15\,b^3\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(3\,a^2-7\,b^2\right)}{4\,\left(a^4-2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^8-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^6+6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)\,\left(\frac{5\,b}{8\,{\left(a+b\right)}^2}+\frac{1}{a+b}+\frac{b^2}{4\,{\left(a+b\right)}^3}\right)-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)\,\left(\frac{b^2}{4\,{\left(a-b\right)}^3}-\frac{5\,b}{8\,{\left(a-b\right)}^2}+\frac{1}{a-b}\right)+\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}-\frac{b^6\,\ln\left(b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}","Not used",1,"((2*tan(x/2)^2*(2*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) - (4*tan(x/2)^4*(3*a*b^2 - 2*a^3))/(a^4 + b^4 - 2*a^2*b^2) + (2*tan(x/2)^6*(2*a*b^2 - a^3))/(a^4 + b^4 - 2*a^2*b^2) + (tan(x/2)^7*(3*a^2*b - 7*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (tan(x/2)^3*(11*a^2*b - 15*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) - (tan(x/2)^5*(11*a^2*b - 15*b^3))/(4*(a^4 + b^4 - 2*a^2*b^2)) + (b*tan(x/2)*(3*a^2 - 7*b^2))/(4*(a^4 + b^4 - 2*a^2*b^2)))/(6*tan(x/2)^4 - 4*tan(x/2)^2 - 4*tan(x/2)^6 + tan(x/2)^8 + 1) - log(tan(x/2) - 1)*((5*b)/(8*(a + b)^2) + 1/(a + b) + b^2/(4*(a + b)^3)) - log(tan(x/2) + 1)*(b^2/(4*(a - b)^3) - (5*b)/(8*(a - b)^2) + 1/(a - b)) + log(tan(x/2)^2 + 1)/a - (b^6*log(b + 2*a*tan(x/2) + b*tan(x/2)^2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)","B"
13,1,172,113,1.137395,"\text{Not used}","int(tan(x)^3/(a + b/sin(x)),x)","\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)\,\left(2\,a-3\,b\right)}{2\,{\left(a-b\right)}^2}-\frac{\frac{b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{a^2-b^2}-\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a^2-b^2}+\frac{b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2-b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^4-2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)\,\left(2\,a+3\,b\right)}{2\,{\left(a+b\right)}^2}+\frac{b^4\,\ln\left(b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)}{a\,{\left(a^2-b^2\right)}^2}","Not used",1,"(log(tan(x/2) + 1)*(2*a - 3*b))/(2*(a - b)^2) - ((b*tan(x/2)^3)/(a^2 - b^2) - (2*a*tan(x/2)^2)/(a^2 - b^2) + (b*tan(x/2))/(a^2 - b^2))/(tan(x/2)^4 - 2*tan(x/2)^2 + 1) - log(tan(x/2)^2 + 1)/a + (log(tan(x/2) - 1)*(2*a + 3*b))/(2*(a + b)^2) + (b^4*log(b + 2*a*tan(x/2) + b*tan(x/2)^2))/(a*(a^2 - b^2)^2)","B"
14,1,80,66,0.442366,"\text{Not used}","int(tan(x)/(a + b/sin(x)),x)","\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{a-b}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)-1\right)}{a+b}+\frac{b^2\,\ln\left(b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)}{a\,\left(a^2-b^2\right)}","Not used",1,"log(tan(x/2)^2 + 1)/a - log(tan(x/2) + 1)/(a - b) - log(tan(x/2) - 1)/(a + b) + (b^2*log(b + 2*a*tan(x/2) + b*tan(x/2)^2))/(a*(a^2 - b^2))","B"
15,1,55,19,0.417516,"\text{Not used}","int(cot(x)/(a + b/sin(x)),x)","\frac{2\,\mathrm{atanh}\left(\frac{a\,\left(2\,b^3\,\sin\left(x\right)+\frac{5\,a\,b^2}{2}-a^3-\frac{a\,b^2\,\cos\left(2\,x\right)}{2}\right)}{{\left(-a^2+\sin\left(x\right)\,a\,b+2\,b^2\right)}^2}\right)}{a}","Not used",1,"(2*atanh((a*(2*b^3*sin(x) + (5*a*b^2)/2 - a^3 - (a*b^2*cos(2*x))/2))/(2*b^2 - a^2 + a*b*sin(x))^2))/a","B"
16,1,75,38,0.459401,"\text{Not used}","int(cot(x)^3/(a + b/sin(x)),x)","\ln\left(b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)\,\left(\frac{a}{b^2}-\frac{1}{a}\right)-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2\,b}+\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}-\frac{1}{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{a\,\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{b^2}","Not used",1,"log(b + 2*a*tan(x/2) + b*tan(x/2)^2)*(a/b^2 - 1/a) - tan(x/2)/(2*b) + log(tan(x/2)^2 + 1)/a - 1/(2*b*tan(x/2)) - (a*log(tan(x/2)))/b^2","B"
17,1,157,72,0.566796,"\text{Not used}","int(cot(x)^5/(a + b/sin(x)),x)","\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{7}{8\,b}-\frac{a^2}{2\,b^3}\right)-\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,b}+\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{8\,b^2}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(4\,a^2-7\,b^2\right)+\frac{b^2}{3}-a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(2\,a\,b^2-a^3\right)}{b^4}+\frac{\ln\left(b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)\,{\left(a^2-b^2\right)}^2}{a\,b^4}","Not used",1,"tan(x/2)*(7/(8*b) - a^2/(2*b^3)) - log(tan(x/2)^2 + 1)/a - tan(x/2)^3/(24*b) + (a*tan(x/2)^2)/(8*b^2) - (tan(x/2)^2*(4*a^2 - 7*b^2) + b^2/3 - a*b*tan(x/2))/(8*b^3*tan(x/2)^3) + (log(tan(x/2))*(2*a*b^2 - a^3))/b^4 + (log(b + 2*a*tan(x/2) + b*tan(x/2)^2)*(a^2 - b^2)^2)/(a*b^4)","B"
18,1,284,122,0.869797,"\text{Not used}","int(cot(x)^7/(a + b/sin(x)),x)","{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(\frac{3}{32\,b}-\frac{a^2}{24\,b^3}\right)-\frac{19\,\mathrm{tan}\left(\frac{x}{2}\right)}{16\,b}+\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2+1\right)}{a}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{160\,b}-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(\frac{a}{32\,b^2}+\frac{a\,\left(\frac{9}{32\,b}-\frac{a^2}{8\,b^3}\right)}{b}\right)+\frac{11\,a^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{8\,b^3}+\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{64\,b^2}-\frac{a^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{2\,b^5}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(a^5-3\,a^3\,b^2+3\,a\,b^4\right)}{b^6}-\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^5\,\left({\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(10\,a\,b^3-4\,a^3\,b\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(3\,b^4-\frac{4\,a^2\,b^2}{3}\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,\left(16\,a^4-44\,a^2\,b^2+38\,b^4\right)+\frac{b^4}{5}-\frac{a\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{2}\right)}{32\,b^5}+\frac{\ln\left(b\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)+b\right)\,{\left(a^2-b^2\right)}^3}{a\,b^6}","Not used",1,"tan(x/2)^3*(3/(32*b) - a^2/(24*b^3)) - (19*tan(x/2))/(16*b) + log(tan(x/2)^2 + 1)/a - tan(x/2)^5/(160*b) - tan(x/2)^2*(a/(32*b^2) + (a*(9/(32*b) - a^2/(8*b^3)))/b) + (11*a^2*tan(x/2))/(8*b^3) + (a*tan(x/2)^4)/(64*b^2) - (a^4*tan(x/2))/(2*b^5) - (log(tan(x/2))*(3*a*b^4 + a^5 - 3*a^3*b^2))/b^6 - (cot(x/2)^5*(tan(x/2)^3*(10*a*b^3 - 4*a^3*b) - tan(x/2)^2*(3*b^4 - (4*a^2*b^2)/3) + tan(x/2)^4*(16*a^4 + 38*b^4 - 44*a^2*b^2) + b^4/5 - (a*b^3*tan(x/2))/2))/(32*b^5) + (log(b + 2*a*tan(x/2) + b*tan(x/2)^2)*(a^2 - b^2)^3)/(a*b^6)","B"
19,1,4468,159,7.376531,"\text{Not used}","int(tan(x)^4/(a + b/sin(x)),x)","\frac{\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(a^2\,b-2\,b^3\right)}{a^4-2\,a^2\,b^2+b^4}-\frac{2\,\left(2\,a^2\,b-5\,b^3\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{a^4-2\,a^2\,b^2+b^4}-\frac{4\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(5\,a^2-8\,b^2\right)}{3\,\left(a^4-2\,a^2\,b^2+b^4\right)}+\frac{2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2-2\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}+\frac{2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5\,\left(a^2-2\,b^2\right)}{a^4-2\,a^2\,b^2+b^4}}{{\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{2\,\mathrm{atan}\left(\frac{320\,a\,b^{21}\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}+\frac{64\,a^{21}\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}-\frac{2560\,a^3\,b^{19}\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}+\frac{9280\,a^5\,b^{17}\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}-\frac{20160\,a^7\,b^{15}\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}+\frac{29184\,a^9\,b^{13}\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}-\frac{29504\,a^{11}\,b^{11}\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}+\frac{21120\,a^{13}\,b^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}-\frac{10560\,a^{15}\,b^7\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}+\frac{3520\,a^{17}\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}-\frac{704\,a^{19}\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{64\,a^{21}\,b-704\,a^{19}\,b^3+3520\,a^{17}\,b^5-10560\,a^{15}\,b^7+21120\,a^{13}\,b^9-29504\,a^{11}\,b^{11}+29184\,a^9\,b^{13}-20160\,a^7\,b^{15}+9280\,a^5\,b^{17}-2560\,a^3\,b^{19}+320\,a\,b^{21}}\right)}{a}+\frac{b^5\,\mathrm{atan}\left(\frac{\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{22}\,b-672\,a^{20}\,b^3+3200\,a^{18}\,b^5-9120\,a^{16}\,b^7+17280\,a^{14}\,b^9-22880\,a^{12}\,b^{11}+21696\,a^{10}\,b^{13}-14880\,a^8\,b^{15}+7360\,a^6\,b^{17}-2560\,a^4\,b^{19}+576\,a^2\,b^{21}-64\,b^{23}\right)+32\,a\,b^{22}-320\,a^3\,b^{20}+1440\,a^5\,b^{18}-3840\,a^7\,b^{16}+6720\,a^9\,b^{14}-8064\,a^{11}\,b^{12}+6720\,a^{13}\,b^{10}-3840\,a^{15}\,b^8+1440\,a^{17}\,b^6-320\,a^{19}\,b^4+32\,a^{21}\,b^2+\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^{23}\,b+96\,a^3\,b^{21}-864\,a^5\,b^{19}+3488\,a^7\,b^{17}-8320\,a^9\,b^{15}+12992\,a^{11}\,b^{13}-13888\,a^{13}\,b^{11}+10304\,a^{15}\,b^9-5248\,a^{17}\,b^7+1760\,a^{19}\,b^5-352\,a^{21}\,b^3+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{18}\,b^6-512\,a^{16}\,b^8+1792\,a^{14}\,b^{10}-3584\,a^{12}\,b^{12}+4480\,a^{10}\,b^{14}-3584\,a^8\,b^{16}+1792\,a^6\,b^{18}-512\,a^4\,b^{20}+64\,a^2\,b^{22}\right)+\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{24}\,b-1024\,a^{22}\,b^3+4960\,a^{20}\,b^5-14400\,a^{18}\,b^7+27840\,a^{16}\,b^9-37632\,a^{14}\,b^{11}+36288\,a^{12}\,b^{13}-24960\,a^{10}\,b^{15}+12000\,a^8\,b^{17}-3840\,a^6\,b^{19}+736\,a^4\,b^{21}-64\,a^2\,b^{23}\right)+32\,a^3\,b^{22}-320\,a^5\,b^{20}+1440\,a^7\,b^{18}-3840\,a^9\,b^{16}+6720\,a^{11}\,b^{14}-8064\,a^{13}\,b^{12}+6720\,a^{15}\,b^{10}-3840\,a^{17}\,b^8+1440\,a^{19}\,b^6-320\,a^{21}\,b^4+32\,a^{23}\,b^2\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)\,1{}\mathrm{i}}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}+\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{22}\,b-672\,a^{20}\,b^3+3200\,a^{18}\,b^5-9120\,a^{16}\,b^7+17280\,a^{14}\,b^9-22880\,a^{12}\,b^{11}+21696\,a^{10}\,b^{13}-14880\,a^8\,b^{15}+7360\,a^6\,b^{17}-2560\,a^4\,b^{19}+576\,a^2\,b^{21}-64\,b^{23}\right)+32\,a\,b^{22}-320\,a^3\,b^{20}+1440\,a^5\,b^{18}-3840\,a^7\,b^{16}+6720\,a^9\,b^{14}-8064\,a^{11}\,b^{12}+6720\,a^{13}\,b^{10}-3840\,a^{15}\,b^8+1440\,a^{17}\,b^6-320\,a^{19}\,b^4+32\,a^{21}\,b^2-\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^{23}\,b+96\,a^3\,b^{21}-864\,a^5\,b^{19}+3488\,a^7\,b^{17}-8320\,a^9\,b^{15}+12992\,a^{11}\,b^{13}-13888\,a^{13}\,b^{11}+10304\,a^{15}\,b^9-5248\,a^{17}\,b^7+1760\,a^{19}\,b^5-352\,a^{21}\,b^3+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{18}\,b^6-512\,a^{16}\,b^8+1792\,a^{14}\,b^{10}-3584\,a^{12}\,b^{12}+4480\,a^{10}\,b^{14}-3584\,a^8\,b^{16}+1792\,a^6\,b^{18}-512\,a^4\,b^{20}+64\,a^2\,b^{22}\right)-\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{24}\,b-1024\,a^{22}\,b^3+4960\,a^{20}\,b^5-14400\,a^{18}\,b^7+27840\,a^{16}\,b^9-37632\,a^{14}\,b^{11}+36288\,a^{12}\,b^{13}-24960\,a^{10}\,b^{15}+12000\,a^8\,b^{17}-3840\,a^6\,b^{19}+736\,a^4\,b^{21}-64\,a^2\,b^{23}\right)+32\,a^3\,b^{22}-320\,a^5\,b^{20}+1440\,a^7\,b^{18}-3840\,a^9\,b^{16}+6720\,a^{11}\,b^{14}-8064\,a^{13}\,b^{12}+6720\,a^{15}\,b^{10}-3840\,a^{17}\,b^8+1440\,a^{19}\,b^6-320\,a^{21}\,b^4+32\,a^{23}\,b^2\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)\,1{}\mathrm{i}}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}}{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{16}\,b^6-512\,a^{14}\,b^8+1792\,a^{12}\,b^{10}-3584\,a^{10}\,b^{12}+4480\,a^8\,b^{14}-3584\,a^6\,b^{16}+1792\,a^4\,b^{18}-512\,a^2\,b^{20}+64\,b^{22}\right)-128\,a\,b^{21}+832\,a^3\,b^{19}-2304\,a^5\,b^{17}+3520\,a^7\,b^{15}-3200\,a^9\,b^{13}+1728\,a^{11}\,b^{11}-512\,a^{13}\,b^9+64\,a^{15}\,b^7+\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{22}\,b-672\,a^{20}\,b^3+3200\,a^{18}\,b^5-9120\,a^{16}\,b^7+17280\,a^{14}\,b^9-22880\,a^{12}\,b^{11}+21696\,a^{10}\,b^{13}-14880\,a^8\,b^{15}+7360\,a^6\,b^{17}-2560\,a^4\,b^{19}+576\,a^2\,b^{21}-64\,b^{23}\right)+32\,a\,b^{22}-320\,a^3\,b^{20}+1440\,a^5\,b^{18}-3840\,a^7\,b^{16}+6720\,a^9\,b^{14}-8064\,a^{11}\,b^{12}+6720\,a^{13}\,b^{10}-3840\,a^{15}\,b^8+1440\,a^{17}\,b^6-320\,a^{19}\,b^4+32\,a^{21}\,b^2+\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^{23}\,b+96\,a^3\,b^{21}-864\,a^5\,b^{19}+3488\,a^7\,b^{17}-8320\,a^9\,b^{15}+12992\,a^{11}\,b^{13}-13888\,a^{13}\,b^{11}+10304\,a^{15}\,b^9-5248\,a^{17}\,b^7+1760\,a^{19}\,b^5-352\,a^{21}\,b^3+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{18}\,b^6-512\,a^{16}\,b^8+1792\,a^{14}\,b^{10}-3584\,a^{12}\,b^{12}+4480\,a^{10}\,b^{14}-3584\,a^8\,b^{16}+1792\,a^6\,b^{18}-512\,a^4\,b^{20}+64\,a^2\,b^{22}\right)+\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{24}\,b-1024\,a^{22}\,b^3+4960\,a^{20}\,b^5-14400\,a^{18}\,b^7+27840\,a^{16}\,b^9-37632\,a^{14}\,b^{11}+36288\,a^{12}\,b^{13}-24960\,a^{10}\,b^{15}+12000\,a^8\,b^{17}-3840\,a^6\,b^{19}+736\,a^4\,b^{21}-64\,a^2\,b^{23}\right)+32\,a^3\,b^{22}-320\,a^5\,b^{20}+1440\,a^7\,b^{18}-3840\,a^9\,b^{16}+6720\,a^{11}\,b^{14}-8064\,a^{13}\,b^{12}+6720\,a^{15}\,b^{10}-3840\,a^{17}\,b^8+1440\,a^{19}\,b^6-320\,a^{21}\,b^4+32\,a^{23}\,b^2\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}-\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{22}\,b-672\,a^{20}\,b^3+3200\,a^{18}\,b^5-9120\,a^{16}\,b^7+17280\,a^{14}\,b^9-22880\,a^{12}\,b^{11}+21696\,a^{10}\,b^{13}-14880\,a^8\,b^{15}+7360\,a^6\,b^{17}-2560\,a^4\,b^{19}+576\,a^2\,b^{21}-64\,b^{23}\right)+32\,a\,b^{22}-320\,a^3\,b^{20}+1440\,a^5\,b^{18}-3840\,a^7\,b^{16}+6720\,a^9\,b^{14}-8064\,a^{11}\,b^{12}+6720\,a^{13}\,b^{10}-3840\,a^{15}\,b^8+1440\,a^{17}\,b^6-320\,a^{19}\,b^4+32\,a^{21}\,b^2-\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(32\,a^{23}\,b+96\,a^3\,b^{21}-864\,a^5\,b^{19}+3488\,a^7\,b^{17}-8320\,a^9\,b^{15}+12992\,a^{11}\,b^{13}-13888\,a^{13}\,b^{11}+10304\,a^{15}\,b^9-5248\,a^{17}\,b^7+1760\,a^{19}\,b^5-352\,a^{21}\,b^3+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{18}\,b^6-512\,a^{16}\,b^8+1792\,a^{14}\,b^{10}-3584\,a^{12}\,b^{12}+4480\,a^{10}\,b^{14}-3584\,a^8\,b^{16}+1792\,a^6\,b^{18}-512\,a^4\,b^{20}+64\,a^2\,b^{22}\right)-\frac{b^5\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{24}\,b-1024\,a^{22}\,b^3+4960\,a^{20}\,b^5-14400\,a^{18}\,b^7+27840\,a^{16}\,b^9-37632\,a^{14}\,b^{11}+36288\,a^{12}\,b^{13}-24960\,a^{10}\,b^{15}+12000\,a^8\,b^{17}-3840\,a^6\,b^{19}+736\,a^4\,b^{21}-64\,a^2\,b^{23}\right)+32\,a^3\,b^{22}-320\,a^5\,b^{20}+1440\,a^7\,b^{18}-3840\,a^9\,b^{16}+6720\,a^{11}\,b^{14}-8064\,a^{13}\,b^{12}+6720\,a^{15}\,b^{10}-3840\,a^{17}\,b^8+1440\,a^{19}\,b^6-320\,a^{21}\,b^4+32\,a^{23}\,b^2\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}\right)}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{-a^{11}+5\,a^9\,b^2-10\,a^7\,b^4+10\,a^5\,b^6-5\,a^3\,b^8+a\,b^{10}}","Not used",1,"((4*tan(x/2)^2*(a^2*b - 2*b^3))/(a^4 + b^4 - 2*a^2*b^2) - (2*(2*a^2*b - 5*b^3))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*b^3*tan(x/2)^4)/(a^4 + b^4 - 2*a^2*b^2) - (4*a*tan(x/2)^3*(5*a^2 - 8*b^2))/(3*(a^4 + b^4 - 2*a^2*b^2)) + (2*a*tan(x/2)*(a^2 - 2*b^2))/(a^4 + b^4 - 2*a^2*b^2) + (2*a*tan(x/2)^5*(a^2 - 2*b^2))/(a^4 + b^4 - 2*a^2*b^2))/(3*tan(x/2)^2 - 3*tan(x/2)^4 + tan(x/2)^6 - 1) + (2*atan((320*a*b^21*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) + (64*a^21*b*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) - (2560*a^3*b^19*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) + (9280*a^5*b^17*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) - (20160*a^7*b^15*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) + (29184*a^9*b^13*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) - (29504*a^11*b^11*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) + (21120*a^13*b^9*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) - (10560*a^15*b^7*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) + (3520*a^17*b^5*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3) - (704*a^19*b^3*tan(x/2))/(320*a*b^21 + 64*a^21*b - 2560*a^3*b^19 + 9280*a^5*b^17 - 20160*a^7*b^15 + 29184*a^9*b^13 - 29504*a^11*b^11 + 21120*a^13*b^9 - 10560*a^15*b^7 + 3520*a^17*b^5 - 704*a^19*b^3)))/a + (b^5*atan(((b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(64*a^22*b - 64*b^23 + 576*a^2*b^21 - 2560*a^4*b^19 + 7360*a^6*b^17 - 14880*a^8*b^15 + 21696*a^10*b^13 - 22880*a^12*b^11 + 17280*a^14*b^9 - 9120*a^16*b^7 + 3200*a^18*b^5 - 672*a^20*b^3) + 32*a*b^22 - 320*a^3*b^20 + 1440*a^5*b^18 - 3840*a^7*b^16 + 6720*a^9*b^14 - 8064*a^11*b^12 + 6720*a^13*b^10 - 3840*a^15*b^8 + 1440*a^17*b^6 - 320*a^19*b^4 + 32*a^21*b^2 + (b^5*((a + b)^5*(a - b)^5)^(1/2)*(32*a^23*b + 96*a^3*b^21 - 864*a^5*b^19 + 3488*a^7*b^17 - 8320*a^9*b^15 + 12992*a^11*b^13 - 13888*a^13*b^11 + 10304*a^15*b^9 - 5248*a^17*b^7 + 1760*a^19*b^5 - 352*a^21*b^3 + tan(x/2)*(64*a^2*b^22 - 512*a^4*b^20 + 1792*a^6*b^18 - 3584*a^8*b^16 + 4480*a^10*b^14 - 3584*a^12*b^12 + 1792*a^14*b^10 - 512*a^16*b^8 + 64*a^18*b^6) + (b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(96*a^24*b - 64*a^2*b^23 + 736*a^4*b^21 - 3840*a^6*b^19 + 12000*a^8*b^17 - 24960*a^10*b^15 + 36288*a^12*b^13 - 37632*a^14*b^11 + 27840*a^16*b^9 - 14400*a^18*b^7 + 4960*a^20*b^5 - 1024*a^22*b^3) + 32*a^3*b^22 - 320*a^5*b^20 + 1440*a^7*b^18 - 3840*a^9*b^16 + 6720*a^11*b^14 - 8064*a^13*b^12 + 6720*a^15*b^10 - 3840*a^17*b^8 + 1440*a^19*b^6 - 320*a^21*b^4 + 32*a^23*b^2))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2))*1i)/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2) + (b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(64*a^22*b - 64*b^23 + 576*a^2*b^21 - 2560*a^4*b^19 + 7360*a^6*b^17 - 14880*a^8*b^15 + 21696*a^10*b^13 - 22880*a^12*b^11 + 17280*a^14*b^9 - 9120*a^16*b^7 + 3200*a^18*b^5 - 672*a^20*b^3) + 32*a*b^22 - 320*a^3*b^20 + 1440*a^5*b^18 - 3840*a^7*b^16 + 6720*a^9*b^14 - 8064*a^11*b^12 + 6720*a^13*b^10 - 3840*a^15*b^8 + 1440*a^17*b^6 - 320*a^19*b^4 + 32*a^21*b^2 - (b^5*((a + b)^5*(a - b)^5)^(1/2)*(32*a^23*b + 96*a^3*b^21 - 864*a^5*b^19 + 3488*a^7*b^17 - 8320*a^9*b^15 + 12992*a^11*b^13 - 13888*a^13*b^11 + 10304*a^15*b^9 - 5248*a^17*b^7 + 1760*a^19*b^5 - 352*a^21*b^3 + tan(x/2)*(64*a^2*b^22 - 512*a^4*b^20 + 1792*a^6*b^18 - 3584*a^8*b^16 + 4480*a^10*b^14 - 3584*a^12*b^12 + 1792*a^14*b^10 - 512*a^16*b^8 + 64*a^18*b^6) - (b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(96*a^24*b - 64*a^2*b^23 + 736*a^4*b^21 - 3840*a^6*b^19 + 12000*a^8*b^17 - 24960*a^10*b^15 + 36288*a^12*b^13 - 37632*a^14*b^11 + 27840*a^16*b^9 - 14400*a^18*b^7 + 4960*a^20*b^5 - 1024*a^22*b^3) + 32*a^3*b^22 - 320*a^5*b^20 + 1440*a^7*b^18 - 3840*a^9*b^16 + 6720*a^11*b^14 - 8064*a^13*b^12 + 6720*a^15*b^10 - 3840*a^17*b^8 + 1440*a^19*b^6 - 320*a^21*b^4 + 32*a^23*b^2))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2))*1i)/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2))/(2*tan(x/2)*(64*b^22 - 512*a^2*b^20 + 1792*a^4*b^18 - 3584*a^6*b^16 + 4480*a^8*b^14 - 3584*a^10*b^12 + 1792*a^12*b^10 - 512*a^14*b^8 + 64*a^16*b^6) - 128*a*b^21 + 832*a^3*b^19 - 2304*a^5*b^17 + 3520*a^7*b^15 - 3200*a^9*b^13 + 1728*a^11*b^11 - 512*a^13*b^9 + 64*a^15*b^7 + (b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(64*a^22*b - 64*b^23 + 576*a^2*b^21 - 2560*a^4*b^19 + 7360*a^6*b^17 - 14880*a^8*b^15 + 21696*a^10*b^13 - 22880*a^12*b^11 + 17280*a^14*b^9 - 9120*a^16*b^7 + 3200*a^18*b^5 - 672*a^20*b^3) + 32*a*b^22 - 320*a^3*b^20 + 1440*a^5*b^18 - 3840*a^7*b^16 + 6720*a^9*b^14 - 8064*a^11*b^12 + 6720*a^13*b^10 - 3840*a^15*b^8 + 1440*a^17*b^6 - 320*a^19*b^4 + 32*a^21*b^2 + (b^5*((a + b)^5*(a - b)^5)^(1/2)*(32*a^23*b + 96*a^3*b^21 - 864*a^5*b^19 + 3488*a^7*b^17 - 8320*a^9*b^15 + 12992*a^11*b^13 - 13888*a^13*b^11 + 10304*a^15*b^9 - 5248*a^17*b^7 + 1760*a^19*b^5 - 352*a^21*b^3 + tan(x/2)*(64*a^2*b^22 - 512*a^4*b^20 + 1792*a^6*b^18 - 3584*a^8*b^16 + 4480*a^10*b^14 - 3584*a^12*b^12 + 1792*a^14*b^10 - 512*a^16*b^8 + 64*a^18*b^6) + (b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(96*a^24*b - 64*a^2*b^23 + 736*a^4*b^21 - 3840*a^6*b^19 + 12000*a^8*b^17 - 24960*a^10*b^15 + 36288*a^12*b^13 - 37632*a^14*b^11 + 27840*a^16*b^9 - 14400*a^18*b^7 + 4960*a^20*b^5 - 1024*a^22*b^3) + 32*a^3*b^22 - 320*a^5*b^20 + 1440*a^7*b^18 - 3840*a^9*b^16 + 6720*a^11*b^14 - 8064*a^13*b^12 + 6720*a^15*b^10 - 3840*a^17*b^8 + 1440*a^19*b^6 - 320*a^21*b^4 + 32*a^23*b^2))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2) - (b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(64*a^22*b - 64*b^23 + 576*a^2*b^21 - 2560*a^4*b^19 + 7360*a^6*b^17 - 14880*a^8*b^15 + 21696*a^10*b^13 - 22880*a^12*b^11 + 17280*a^14*b^9 - 9120*a^16*b^7 + 3200*a^18*b^5 - 672*a^20*b^3) + 32*a*b^22 - 320*a^3*b^20 + 1440*a^5*b^18 - 3840*a^7*b^16 + 6720*a^9*b^14 - 8064*a^11*b^12 + 6720*a^13*b^10 - 3840*a^15*b^8 + 1440*a^17*b^6 - 320*a^19*b^4 + 32*a^21*b^2 - (b^5*((a + b)^5*(a - b)^5)^(1/2)*(32*a^23*b + 96*a^3*b^21 - 864*a^5*b^19 + 3488*a^7*b^17 - 8320*a^9*b^15 + 12992*a^11*b^13 - 13888*a^13*b^11 + 10304*a^15*b^9 - 5248*a^17*b^7 + 1760*a^19*b^5 - 352*a^21*b^3 + tan(x/2)*(64*a^2*b^22 - 512*a^4*b^20 + 1792*a^6*b^18 - 3584*a^8*b^16 + 4480*a^10*b^14 - 3584*a^12*b^12 + 1792*a^14*b^10 - 512*a^16*b^8 + 64*a^18*b^6) - (b^5*((a + b)^5*(a - b)^5)^(1/2)*(tan(x/2)*(96*a^24*b - 64*a^2*b^23 + 736*a^4*b^21 - 3840*a^6*b^19 + 12000*a^8*b^17 - 24960*a^10*b^15 + 36288*a^12*b^13 - 37632*a^14*b^11 + 27840*a^16*b^9 - 14400*a^18*b^7 + 4960*a^20*b^5 - 1024*a^22*b^3) + 32*a^3*b^22 - 320*a^5*b^20 + 1440*a^7*b^18 - 3840*a^9*b^16 + 6720*a^11*b^14 - 8064*a^13*b^12 + 6720*a^15*b^10 - 3840*a^17*b^8 + 1440*a^19*b^6 - 320*a^21*b^4 + 32*a^23*b^2))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)))/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)))*((a + b)^5*(a - b)^5)^(1/2)*2i)/(a*b^10 - a^11 - 5*a^3*b^8 + 10*a^5*b^6 - 10*a^7*b^4 + 5*a^9*b^2)","B"
20,1,2341,84,2.258155,"\text{Not used}","int(tan(x)^2/(a + b/sin(x)),x)","\frac{\frac{2\,b}{a^2-b^2}-\frac{2\,a\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2-b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2-1}+\frac{2\,\mathrm{atan}\left(\frac{64\,a^{11}\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^{11}\,b+384\,a^9\,b^3-960\,a^7\,b^5+1216\,a^5\,b^7-768\,a^3\,b^9+192\,a\,b^{11}}-\frac{192\,a\,b^{11}\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^{11}\,b+384\,a^9\,b^3-960\,a^7\,b^5+1216\,a^5\,b^7-768\,a^3\,b^9+192\,a\,b^{11}}+\frac{768\,a^3\,b^9\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^{11}\,b+384\,a^9\,b^3-960\,a^7\,b^5+1216\,a^5\,b^7-768\,a^3\,b^9+192\,a\,b^{11}}-\frac{1216\,a^5\,b^7\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^{11}\,b+384\,a^9\,b^3-960\,a^7\,b^5+1216\,a^5\,b^7-768\,a^3\,b^9+192\,a\,b^{11}}+\frac{960\,a^7\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^{11}\,b+384\,a^9\,b^3-960\,a^7\,b^5+1216\,a^5\,b^7-768\,a^3\,b^9+192\,a\,b^{11}}-\frac{384\,a^9\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^{11}\,b+384\,a^9\,b^3-960\,a^7\,b^5+1216\,a^5\,b^7-768\,a^3\,b^9+192\,a\,b^{11}}\right)}{a}+\frac{b^3\,\mathrm{atan}\left(\frac{\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{12}\,b-352\,a^{10}\,b^3+800\,a^8\,b^5-992\,a^6\,b^7+736\,a^4\,b^9-320\,a^2\,b^{11}+64\,b^{13}\right)-32\,a\,b^{12}+160\,a^3\,b^{10}-320\,a^5\,b^8+320\,a^7\,b^6-160\,a^9\,b^4+32\,a^{11}\,b^2+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{10}\,b^4-256\,a^8\,b^6+384\,a^6\,b^8-256\,a^4\,b^{10}+64\,a^2\,b^{12}\right)-32\,a^{13}\,b+64\,a^3\,b^{11}-288\,a^5\,b^9+512\,a^7\,b^7-448\,a^9\,b^5+192\,a^{11}\,b^3+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{14}\,b-544\,a^{12}\,b^3+1280\,a^{10}\,b^5-1600\,a^8\,b^7+1120\,a^6\,b^9-416\,a^4\,b^{11}+64\,a^2\,b^{13}\right)-32\,a^3\,b^{12}+160\,a^5\,b^{10}-320\,a^7\,b^8+320\,a^9\,b^6-160\,a^{11}\,b^4+32\,a^{13}\,b^2\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)\,1{}\mathrm{i}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{12}\,b-352\,a^{10}\,b^3+800\,a^8\,b^5-992\,a^6\,b^7+736\,a^4\,b^9-320\,a^2\,b^{11}+64\,b^{13}\right)-32\,a\,b^{12}+160\,a^3\,b^{10}-320\,a^5\,b^8+320\,a^7\,b^6-160\,a^9\,b^4+32\,a^{11}\,b^2-\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{10}\,b^4-256\,a^8\,b^6+384\,a^6\,b^8-256\,a^4\,b^{10}+64\,a^2\,b^{12}\right)-32\,a^{13}\,b+64\,a^3\,b^{11}-288\,a^5\,b^9+512\,a^7\,b^7-448\,a^9\,b^5+192\,a^{11}\,b^3-\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{14}\,b-544\,a^{12}\,b^3+1280\,a^{10}\,b^5-1600\,a^8\,b^7+1120\,a^6\,b^9-416\,a^4\,b^{11}+64\,a^2\,b^{13}\right)-32\,a^3\,b^{12}+160\,a^5\,b^{10}-320\,a^7\,b^8+320\,a^9\,b^6-160\,a^{11}\,b^4+32\,a^{13}\,b^2\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)\,1{}\mathrm{i}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}}{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^8\,b^4-256\,a^6\,b^6+384\,a^4\,b^8-256\,a^2\,b^{10}+64\,b^{12}\right)-64\,a\,b^{11}+192\,a^3\,b^9-192\,a^5\,b^7+64\,a^7\,b^5+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{12}\,b-352\,a^{10}\,b^3+800\,a^8\,b^5-992\,a^6\,b^7+736\,a^4\,b^9-320\,a^2\,b^{11}+64\,b^{13}\right)-32\,a\,b^{12}+160\,a^3\,b^{10}-320\,a^5\,b^8+320\,a^7\,b^6-160\,a^9\,b^4+32\,a^{11}\,b^2+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{10}\,b^4-256\,a^8\,b^6+384\,a^6\,b^8-256\,a^4\,b^{10}+64\,a^2\,b^{12}\right)-32\,a^{13}\,b+64\,a^3\,b^{11}-288\,a^5\,b^9+512\,a^7\,b^7-448\,a^9\,b^5+192\,a^{11}\,b^3+\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{14}\,b-544\,a^{12}\,b^3+1280\,a^{10}\,b^5-1600\,a^8\,b^7+1120\,a^6\,b^9-416\,a^4\,b^{11}+64\,a^2\,b^{13}\right)-32\,a^3\,b^{12}+160\,a^5\,b^{10}-320\,a^7\,b^8+320\,a^9\,b^6-160\,a^{11}\,b^4+32\,a^{13}\,b^2\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}-\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{12}\,b-352\,a^{10}\,b^3+800\,a^8\,b^5-992\,a^6\,b^7+736\,a^4\,b^9-320\,a^2\,b^{11}+64\,b^{13}\right)-32\,a\,b^{12}+160\,a^3\,b^{10}-320\,a^5\,b^8+320\,a^7\,b^6-160\,a^9\,b^4+32\,a^{11}\,b^2-\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(64\,a^{10}\,b^4-256\,a^8\,b^6+384\,a^6\,b^8-256\,a^4\,b^{10}+64\,a^2\,b^{12}\right)-32\,a^{13}\,b+64\,a^3\,b^{11}-288\,a^5\,b^9+512\,a^7\,b^7-448\,a^9\,b^5+192\,a^{11}\,b^3-\frac{b^3\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,\left(\mathrm{tan}\left(\frac{x}{2}\right)\,\left(96\,a^{14}\,b-544\,a^{12}\,b^3+1280\,a^{10}\,b^5-1600\,a^8\,b^7+1120\,a^6\,b^9-416\,a^4\,b^{11}+64\,a^2\,b^{13}\right)-32\,a^3\,b^{12}+160\,a^5\,b^{10}-320\,a^7\,b^8+320\,a^9\,b^6-160\,a^{11}\,b^4+32\,a^{13}\,b^2\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}\right)}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}}\right)\,\sqrt{{\left(a+b\right)}^3\,{\left(a-b\right)}^3}\,2{}\mathrm{i}}{-a^7+3\,a^5\,b^2-3\,a^3\,b^4+a\,b^6}","Not used",1,"((2*b)/(a^2 - b^2) - (2*a*tan(x/2))/(a^2 - b^2))/(tan(x/2)^2 - 1) + (2*atan((64*a^11*b*tan(x/2))/(192*a*b^11 - 64*a^11*b - 768*a^3*b^9 + 1216*a^5*b^7 - 960*a^7*b^5 + 384*a^9*b^3) - (192*a*b^11*tan(x/2))/(192*a*b^11 - 64*a^11*b - 768*a^3*b^9 + 1216*a^5*b^7 - 960*a^7*b^5 + 384*a^9*b^3) + (768*a^3*b^9*tan(x/2))/(192*a*b^11 - 64*a^11*b - 768*a^3*b^9 + 1216*a^5*b^7 - 960*a^7*b^5 + 384*a^9*b^3) - (1216*a^5*b^7*tan(x/2))/(192*a*b^11 - 64*a^11*b - 768*a^3*b^9 + 1216*a^5*b^7 - 960*a^7*b^5 + 384*a^9*b^3) + (960*a^7*b^5*tan(x/2))/(192*a*b^11 - 64*a^11*b - 768*a^3*b^9 + 1216*a^5*b^7 - 960*a^7*b^5 + 384*a^9*b^3) - (384*a^9*b^3*tan(x/2))/(192*a*b^11 - 64*a^11*b - 768*a^3*b^9 + 1216*a^5*b^7 - 960*a^7*b^5 + 384*a^9*b^3)))/a + (b^3*atan(((b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^12*b + 64*b^13 - 320*a^2*b^11 + 736*a^4*b^9 - 992*a^6*b^7 + 800*a^8*b^5 - 352*a^10*b^3) - 32*a*b^12 + 160*a^3*b^10 - 320*a^5*b^8 + 320*a^7*b^6 - 160*a^9*b^4 + 32*a^11*b^2 + (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^2*b^12 - 256*a^4*b^10 + 384*a^6*b^8 - 256*a^8*b^6 + 64*a^10*b^4) - 32*a^13*b + 64*a^3*b^11 - 288*a^5*b^9 + 512*a^7*b^7 - 448*a^9*b^5 + 192*a^11*b^3 + (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(96*a^14*b + 64*a^2*b^13 - 416*a^4*b^11 + 1120*a^6*b^9 - 1600*a^8*b^7 + 1280*a^10*b^5 - 544*a^12*b^3) - 32*a^3*b^12 + 160*a^5*b^10 - 320*a^7*b^8 + 320*a^9*b^6 - 160*a^11*b^4 + 32*a^13*b^2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))*1i)/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2) + (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^12*b + 64*b^13 - 320*a^2*b^11 + 736*a^4*b^9 - 992*a^6*b^7 + 800*a^8*b^5 - 352*a^10*b^3) - 32*a*b^12 + 160*a^3*b^10 - 320*a^5*b^8 + 320*a^7*b^6 - 160*a^9*b^4 + 32*a^11*b^2 - (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^2*b^12 - 256*a^4*b^10 + 384*a^6*b^8 - 256*a^8*b^6 + 64*a^10*b^4) - 32*a^13*b + 64*a^3*b^11 - 288*a^5*b^9 + 512*a^7*b^7 - 448*a^9*b^5 + 192*a^11*b^3 - (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(96*a^14*b + 64*a^2*b^13 - 416*a^4*b^11 + 1120*a^6*b^9 - 1600*a^8*b^7 + 1280*a^10*b^5 - 544*a^12*b^3) - 32*a^3*b^12 + 160*a^5*b^10 - 320*a^7*b^8 + 320*a^9*b^6 - 160*a^11*b^4 + 32*a^13*b^2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))*1i)/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2))/(2*tan(x/2)*(64*b^12 - 256*a^2*b^10 + 384*a^4*b^8 - 256*a^6*b^6 + 64*a^8*b^4) - 64*a*b^11 + 192*a^3*b^9 - 192*a^5*b^7 + 64*a^7*b^5 + (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^12*b + 64*b^13 - 320*a^2*b^11 + 736*a^4*b^9 - 992*a^6*b^7 + 800*a^8*b^5 - 352*a^10*b^3) - 32*a*b^12 + 160*a^3*b^10 - 320*a^5*b^8 + 320*a^7*b^6 - 160*a^9*b^4 + 32*a^11*b^2 + (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^2*b^12 - 256*a^4*b^10 + 384*a^6*b^8 - 256*a^8*b^6 + 64*a^10*b^4) - 32*a^13*b + 64*a^3*b^11 - 288*a^5*b^9 + 512*a^7*b^7 - 448*a^9*b^5 + 192*a^11*b^3 + (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(96*a^14*b + 64*a^2*b^13 - 416*a^4*b^11 + 1120*a^6*b^9 - 1600*a^8*b^7 + 1280*a^10*b^5 - 544*a^12*b^3) - 32*a^3*b^12 + 160*a^5*b^10 - 320*a^7*b^8 + 320*a^9*b^6 - 160*a^11*b^4 + 32*a^13*b^2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2) - (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^12*b + 64*b^13 - 320*a^2*b^11 + 736*a^4*b^9 - 992*a^6*b^7 + 800*a^8*b^5 - 352*a^10*b^3) - 32*a*b^12 + 160*a^3*b^10 - 320*a^5*b^8 + 320*a^7*b^6 - 160*a^9*b^4 + 32*a^11*b^2 - (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(64*a^2*b^12 - 256*a^4*b^10 + 384*a^6*b^8 - 256*a^8*b^6 + 64*a^10*b^4) - 32*a^13*b + 64*a^3*b^11 - 288*a^5*b^9 + 512*a^7*b^7 - 448*a^9*b^5 + 192*a^11*b^3 - (b^3*((a + b)^3*(a - b)^3)^(1/2)*(tan(x/2)*(96*a^14*b + 64*a^2*b^13 - 416*a^4*b^11 + 1120*a^6*b^9 - 1600*a^8*b^7 + 1280*a^10*b^5 - 544*a^12*b^3) - 32*a^3*b^12 + 160*a^5*b^10 - 320*a^7*b^8 + 320*a^9*b^6 - 160*a^11*b^4 + 32*a^13*b^2))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)))*((a + b)^3*(a - b)^3)^(1/2)*2i)/(a*b^6 - a^7 - 3*a^3*b^4 + 3*a^5*b^2)","B"
21,1,697,61,0.526082,"\text{Not used}","int(cot(x)^2/(a + b/sin(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{64\,b^3}{-64\,a^3-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b+64\,a\,b^2+64\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^3}+\frac{64\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^3-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b+64\,a\,b^2+64\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^3}-\frac{64\,a^2\,b}{-64\,a^3-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b+64\,a\,b^2+64\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^3}-\frac{64\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{-64\,a^3-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b+64\,a\,b^2+64\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^3}\right)}{a}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)}{b}-\frac{2\,\mathrm{atanh}\left(\frac{512\,a^4\,\sqrt{a^2-b^2}}{256\,a\,b^4-64\,b^5\,\mathrm{tan}\left(\frac{x}{2}\right)+512\,a^5-768\,a^3\,b^2+832\,a^2\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{1024\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}-1792\,a^4\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{512\,a^2\,\sqrt{a^2-b^2}}{256\,a\,b^2-64\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)-768\,a^3+\frac{512\,a^5}{b^2}-\frac{1792\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{1024\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{b^3}+832\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}+\frac{64\,b^2\,\sqrt{a^2-b^2}}{256\,a\,b^2-64\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)-768\,a^3+\frac{512\,a^5}{b^2}-\frac{1792\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{1024\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{b^3}+832\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}-\frac{1280\,a^3\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}}{256\,a\,b^3-64\,b^4\,\mathrm{tan}\left(\frac{x}{2}\right)-1792\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)-768\,a^3\,b+\frac{512\,a^5}{b}+832\,a^2\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)+\frac{1024\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{b^2}}+\frac{1024\,a^5\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}}{1024\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^6+512\,a^5\,b-1792\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^4\,b^2-768\,a^3\,b^3+832\,\mathrm{tan}\left(\frac{x}{2}\right)\,a^2\,b^4+256\,a\,b^5-64\,\mathrm{tan}\left(\frac{x}{2}\right)\,b^6}+\frac{320\,a\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{a^2-b^2}}{256\,a\,b^2-64\,b^3\,\mathrm{tan}\left(\frac{x}{2}\right)-768\,a^3+\frac{512\,a^5}{b^2}-\frac{1792\,a^4\,\mathrm{tan}\left(\frac{x}{2}\right)}{b}+\frac{1024\,a^6\,\mathrm{tan}\left(\frac{x}{2}\right)}{b^3}+832\,a^2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}\right)\,\sqrt{a^2-b^2}}{a\,b}","Not used",1,"(2*atan((64*b^3)/(64*b^3*tan(x/2) + 64*a*b^2 - 64*a^3 - 64*a^2*b*tan(x/2)) + (64*a^3*tan(x/2))/(64*b^3*tan(x/2) + 64*a*b^2 - 64*a^3 - 64*a^2*b*tan(x/2)) - (64*a^2*b)/(64*b^3*tan(x/2) + 64*a*b^2 - 64*a^3 - 64*a^2*b*tan(x/2)) - (64*a*b^2*tan(x/2))/(64*b^3*tan(x/2) + 64*a*b^2 - 64*a^3 - 64*a^2*b*tan(x/2))))/a + log(tan(x/2))/b - (2*atanh((512*a^4*(a^2 - b^2)^(1/2))/(256*a*b^4 - 64*b^5*tan(x/2) + 512*a^5 - 768*a^3*b^2 + 832*a^2*b^3*tan(x/2) + (1024*a^6*tan(x/2))/b - 1792*a^4*b*tan(x/2)) - (512*a^2*(a^2 - b^2)^(1/2))/(256*a*b^2 - 64*b^3*tan(x/2) - 768*a^3 + (512*a^5)/b^2 - (1792*a^4*tan(x/2))/b + (1024*a^6*tan(x/2))/b^3 + 832*a^2*b*tan(x/2)) + (64*b^2*(a^2 - b^2)^(1/2))/(256*a*b^2 - 64*b^3*tan(x/2) - 768*a^3 + (512*a^5)/b^2 - (1792*a^4*tan(x/2))/b + (1024*a^6*tan(x/2))/b^3 + 832*a^2*b*tan(x/2)) - (1280*a^3*tan(x/2)*(a^2 - b^2)^(1/2))/(256*a*b^3 - 64*b^4*tan(x/2) - 1792*a^4*tan(x/2) - 768*a^3*b + (512*a^5)/b + 832*a^2*b^2*tan(x/2) + (1024*a^6*tan(x/2))/b^2) + (1024*a^5*tan(x/2)*(a^2 - b^2)^(1/2))/(1024*a^6*tan(x/2) - 64*b^6*tan(x/2) + 256*a*b^5 + 512*a^5*b - 768*a^3*b^3 + 832*a^2*b^4*tan(x/2) - 1792*a^4*b^2*tan(x/2)) + (320*a*b*tan(x/2)*(a^2 - b^2)^(1/2))/(256*a*b^2 - 64*b^3*tan(x/2) - 768*a^3 + (512*a^5)/b^2 - (1792*a^4*tan(x/2))/b + (1024*a^6*tan(x/2))/b^3 + 832*a^2*b*tan(x/2)))*(a^2 - b^2)^(1/2))/(a*b)","B"
22,1,2163,91,1.190317,"\text{Not used}","int(cot(x)^4/(a + b/sin(x)),x)","\frac{a^3\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}-\frac{2\,b^3\,\mathrm{atan}\left(\frac{2\,\sin\left(\frac{x}{2}\right)\,a^3-3\,\sin\left(\frac{x}{2}\right)\,a\,b^2+2\,\cos\left(\frac{x}{2}\right)\,b^3}{-2\,\cos\left(\frac{x}{2}\right)\,a^3+3\,\cos\left(\frac{x}{2}\right)\,a\,b^2+2\,\sin\left(\frac{x}{2}\right)\,b^3}\right)}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}-\frac{a^3\,\cos\left(2\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}-\frac{3\,a\,b^2\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{2\,\left(a\,b^3-a\,b^3\,\cos\left(2\,x\right)\right)}+\frac{2\,b^3\,\cos\left(2\,x\right)\,\mathrm{atan}\left(\frac{2\,\sin\left(\frac{x}{2}\right)\,a^3-3\,\sin\left(\frac{x}{2}\right)\,a\,b^2+2\,\cos\left(\frac{x}{2}\right)\,b^3}{-2\,\cos\left(\frac{x}{2}\right)\,a^3+3\,\cos\left(\frac{x}{2}\right)\,a\,b^2+2\,\sin\left(\frac{x}{2}\right)\,b^3}\right)}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}-\frac{a\,b^2\,\cos\left(x\right)}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}+\frac{a^2\,b\,\sin\left(2\,x\right)}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}+\frac{3\,a\,b^2\,\cos\left(2\,x\right)\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{2\,\left(a\,b^3-a\,b^3\,\cos\left(2\,x\right)\right)}-\frac{\mathrm{atan}\left(\frac{32\,a^6\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-14\,b^6\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-14\,b^{12}\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+19\,a\,b^5\,\cos\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+16\,a^5\,b\,\cos\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+13\,a\,b^{11}\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-36\,a^3\,b^3\,\cos\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-24\,a^3\,b^9\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+8\,a^5\,b^7\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+2\,a^7\,b^5\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+63\,a^2\,b^4\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-82\,a^4\,b^2\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+72\,a^2\,b^{10}\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-106\,a^4\,b^8\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+56\,a^6\,b^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-11\,a^8\,b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+2\,a^{10}\,b^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{32{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^{15}+16{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^{14}\,b-224{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^{13}\,b^2-108{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^{12}\,b^3+670{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^{11}\,b^4+309{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^{10}\,b^5-1080{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^9\,b^6-469{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^8\,b^7+982{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^7\,b^8+390{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^6\,b^9-482{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^5\,b^{10}-165{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^4\,b^{11}+108{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^3\,b^{12}+27{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^2\,b^{13}-6{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a\,b^{14}}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}\,2{}\mathrm{i}}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}+\frac{\mathrm{atan}\left(\frac{32\,a^6\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-14\,b^6\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-14\,b^{12}\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+19\,a\,b^5\,\cos\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+16\,a^5\,b\,\cos\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+13\,a\,b^{11}\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-36\,a^3\,b^3\,\cos\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-24\,a^3\,b^9\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+8\,a^5\,b^7\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+2\,a^7\,b^5\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+63\,a^2\,b^4\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}-82\,a^4\,b^2\,\sin\left(\frac{x}{2}\right)\,{\left(a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6\right)}^{3/2}+72\,a^2\,b^{10}\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-106\,a^4\,b^8\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+56\,a^6\,b^6\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}-11\,a^8\,b^4\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}+2\,a^{10}\,b^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}}{32{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^{15}+16{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^{14}\,b-224{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^{13}\,b^2-108{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^{12}\,b^3+670{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^{11}\,b^4+309{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^{10}\,b^5-1080{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^9\,b^6-469{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^8\,b^7+982{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^7\,b^8+390{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^6\,b^9-482{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^5\,b^{10}-165{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^4\,b^{11}+108{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a^3\,b^{12}+27{}\mathrm{i}\,\cos\left(\frac{x}{2}\right)\,a^2\,b^{13}-6{}\mathrm{i}\,\sin\left(\frac{x}{2}\right)\,a\,b^{14}}\right)\,\cos\left(2\,x\right)\,\sqrt{a^6-3\,a^4\,b^2+3\,a^2\,b^4-b^6}\,2{}\mathrm{i}}{a\,b^3-a\,b^3\,\cos\left(2\,x\right)}","Not used",1,"(a^3*log(sin(x/2)/cos(x/2)))/(a*b^3 - a*b^3*cos(2*x)) - (2*b^3*atan((2*b^3*cos(x/2) + 2*a^3*sin(x/2) - 3*a*b^2*sin(x/2))/(2*b^3*sin(x/2) - 2*a^3*cos(x/2) + 3*a*b^2*cos(x/2))))/(a*b^3 - a*b^3*cos(2*x)) - (atan((32*a^6*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 14*b^6*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 14*b^12*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 19*a*b^5*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 16*a^5*b*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 13*a*b^11*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 36*a^3*b^3*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 24*a^3*b^9*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 8*a^5*b^7*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 2*a^7*b^5*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 63*a^2*b^4*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 82*a^4*b^2*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 72*a^2*b^10*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 106*a^4*b^8*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 56*a^6*b^6*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 11*a^8*b^4*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 2*a^10*b^2*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(a^15*sin(x/2)*32i + a^2*b^13*cos(x/2)*27i - a^4*b^11*cos(x/2)*165i + a^6*b^9*cos(x/2)*390i - a^8*b^7*cos(x/2)*469i + a^10*b^5*cos(x/2)*309i - a^12*b^3*cos(x/2)*108i + a^3*b^12*sin(x/2)*108i - a^5*b^10*sin(x/2)*482i + a^7*b^8*sin(x/2)*982i - a^9*b^6*sin(x/2)*1080i + a^11*b^4*sin(x/2)*670i - a^13*b^2*sin(x/2)*224i + a^14*b*cos(x/2)*16i - a*b^14*sin(x/2)*6i))*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2)*2i)/(a*b^3 - a*b^3*cos(2*x)) - (a^3*cos(2*x)*log(sin(x/2)/cos(x/2)))/(a*b^3 - a*b^3*cos(2*x)) + (atan((32*a^6*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 14*b^6*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 14*b^12*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 19*a*b^5*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 16*a^5*b*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 13*a*b^11*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 36*a^3*b^3*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 24*a^3*b^9*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 8*a^5*b^7*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 2*a^7*b^5*cos(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 63*a^2*b^4*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) - 82*a^4*b^2*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(3/2) + 72*a^2*b^10*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 106*a^4*b^8*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 56*a^6*b^6*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) - 11*a^8*b^4*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2) + 2*a^10*b^2*sin(x/2)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2))/(a^15*sin(x/2)*32i + a^2*b^13*cos(x/2)*27i - a^4*b^11*cos(x/2)*165i + a^6*b^9*cos(x/2)*390i - a^8*b^7*cos(x/2)*469i + a^10*b^5*cos(x/2)*309i - a^12*b^3*cos(x/2)*108i + a^3*b^12*sin(x/2)*108i - a^5*b^10*sin(x/2)*482i + a^7*b^8*sin(x/2)*982i - a^9*b^6*sin(x/2)*1080i + a^11*b^4*sin(x/2)*670i - a^13*b^2*sin(x/2)*224i + a^14*b*cos(x/2)*16i - a*b^14*sin(x/2)*6i))*cos(2*x)*(a^6 - b^6 + 3*a^2*b^4 - 3*a^4*b^2)^(1/2)*2i)/(a*b^3 - a*b^3*cos(2*x)) - (3*a*b^2*log(sin(x/2)/cos(x/2)))/(2*(a*b^3 - a*b^3*cos(2*x))) + (2*b^3*cos(2*x)*atan((2*b^3*cos(x/2) + 2*a^3*sin(x/2) - 3*a*b^2*sin(x/2))/(2*b^3*sin(x/2) - 2*a^3*cos(x/2) + 3*a*b^2*cos(x/2))))/(a*b^3 - a*b^3*cos(2*x)) - (a*b^2*cos(x))/(a*b^3 - a*b^3*cos(2*x)) + (a^2*b*sin(2*x))/(a*b^3 - a*b^3*cos(2*x)) + (3*a*b^2*cos(2*x)*log(sin(x/2)/cos(x/2)))/(2*(a*b^3 - a*b^3*cos(2*x)))","B"
23,1,4075,186,1.585631,"\text{Not used}","int(cot(x)^6/(a + b/sin(x)),x)","\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{a}{8\,b^2}+\frac{2\,a\,\left(\frac{1}{2\,b}-\frac{a^2}{4\,b^3}\right)}{b}\right)-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(\frac{1}{4\,b}-\frac{a^2}{8\,b^3}\right)+\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4}{64\,b}-\frac{2\,\mathrm{atan}\left(\frac{\frac{\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}-\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\left(\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}-\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}}{a}-\frac{\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}}{a}}{\frac{8\,\left(8\,a^{15}-68\,a^{13}\,b^2+223\,a^{11}\,b^4-366\,a^9\,b^6+305\,a^7\,b^8-97\,a^5\,b^{10}-20\,a^3\,b^{12}+15\,a\,b^{14}\right)}{b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^8\,b^7-20\,a^6\,b^9+12\,a^4\,b^{11}+4\,a^2\,b^{13}-4\,b^{15}\right)}{b^{12}}+\frac{\left(\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}-\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\left(\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}-\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}+\frac{\left(\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}\right)\,1{}\mathrm{i}}{a}}\right)}{a}-\frac{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24\,b^2}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\left(18\,a\,b^2-8\,a^3\right)+{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(2\,a^2\,b-4\,b^3\right)+\frac{b^3}{4}-\frac{2\,a\,b^2\,\mathrm{tan}\left(\frac{x}{2}\right)}{3}}{16\,b^4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4}+\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,\left(a^4-\frac{5\,a^2\,b^2}{2}+\frac{15\,b^4}{8}\right)}{b^5}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}-\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}-\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)\,1{}\mathrm{i}}{a\,b^5}-\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)\,1{}\mathrm{i}}{a\,b^5}}{\frac{8\,\left(8\,a^{15}-68\,a^{13}\,b^2+223\,a^{11}\,b^4-366\,a^9\,b^6+305\,a^7\,b^8-97\,a^5\,b^{10}-20\,a^3\,b^{12}+15\,a\,b^{14}\right)}{b^{12}}-\frac{8\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^8\,b^7-20\,a^6\,b^9+12\,a^4\,b^{11}+4\,a^2\,b^{13}-4\,b^{15}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}-\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}-\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(8\,a^{11}\,b^5-48\,a^9\,b^7+56\,a^7\,b^9+48\,a^5\,b^{11}-120\,a^3\,b^{13}+53\,a\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{16}-68\,a^{14}\,b^2+255\,a^{12}\,b^4-550\,a^{10}\,b^6+873\,a^8\,b^8-1096\,a^6\,b^{10}+929\,a^4\,b^{12}-410\,a^2\,b^{14}+62\,b^{16}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-32\,a^{13}\,b^4+184\,a^{11}\,b^6-440\,a^9\,b^8+543\,a^7\,b^{10}-345\,a^5\,b^{12}+58\,a^3\,b^{14}+24\,a\,b^{16}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^{12}\,b^5-40\,a^{10}\,b^7+100\,a^8\,b^9-148\,a^6\,b^{11}+252\,a^4\,b^{13}-180\,a^2\,b^{15}+16\,b^{17}\right)}{b^{12}}+\frac{\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,\left(\frac{4\,\left(-64\,a^9\,b^9+208\,a^7\,b^{11}-240\,a^5\,b^{13}+93\,a^3\,b^{15}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^{10}\,b^8-456\,a^8\,b^{10}+604\,a^6\,b^{12}-335\,a^4\,b^{14}+62\,a^2\,b^{16}\right)}{b^{12}}+\frac{\left(\frac{4\,\left(24\,a^3\,b^{16}-32\,a^5\,b^{14}\right)}{b^{12}}-\frac{4\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(128\,a^6\,b^{13}-136\,a^4\,b^{15}+16\,a^2\,b^{17}\right)}{b^{12}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}\right)}{a\,b^5}}\right)\,\sqrt{{\left(a+b\right)}^5\,{\left(a-b\right)}^5}\,2{}\mathrm{i}}{a\,b^5}","Not used",1,"tan(x/2)*(a/(8*b^2) + (2*a*(1/(2*b) - a^2/(4*b^3)))/b) - tan(x/2)^2*(1/(4*b) - a^2/(8*b^3)) + tan(x/2)^4/(64*b) - (2*atan((((((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 + (((((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*1i)/a - (4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 + (4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12)*1i)/a - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12)*1i)/a - (4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 + (4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12)/a - ((4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 + (((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 + (((4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 + (((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*1i)/a - (4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12)*1i)/a - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12)*1i)/a - (4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12)/a)/((((((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 + (((((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*1i)/a - (4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 + (4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12)*1i)/a - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12)*1i)/a - (4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 + (4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12)*1i)/a + (((4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 + (((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 + (((4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 + (((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*1i)/a - (4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12)*1i)/a - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12)*1i)/a - (4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12)*1i)/a + (8*(15*a*b^14 + 8*a^15 - 20*a^3*b^12 - 97*a^5*b^10 + 305*a^7*b^8 - 366*a^9*b^6 + 223*a^11*b^4 - 68*a^13*b^2))/b^12 - (8*tan(x/2)*(4*a^2*b^13 - 4*b^15 + 12*a^4*b^11 - 20*a^6*b^9 + 8*a^8*b^7))/b^12)))/a - (a*tan(x/2)^3)/(24*b^2) - (tan(x/2)^3*(18*a*b^2 - 8*a^3) + tan(x/2)^2*(2*a^2*b - 4*b^3) + b^3/4 - (2*a*b^2*tan(x/2))/3)/(16*b^4*tan(x/2)^4) + (log(tan(x/2))*(a^4 + (15*b^4)/8 - (5*a^2*b^2)/2))/b^5 - (atan(((((a + b)^5*(a - b)^5)^(1/2)*((4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12 - (4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12 - (4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 + (((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5))*1i)/(a*b^5) - (((a + b)^5*(a - b)^5)^(1/2)*((4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 - (4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 - (4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12 + (((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5))*1i)/(a*b^5))/((8*(15*a*b^14 + 8*a^15 - 20*a^3*b^12 - 97*a^5*b^10 + 305*a^7*b^8 - 366*a^9*b^6 + 223*a^11*b^4 - 68*a^13*b^2))/b^12 - (8*tan(x/2)*(4*a^2*b^13 - 4*b^15 + 12*a^4*b^11 - 20*a^6*b^9 + 8*a^8*b^7))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12 - (4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12 - (4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 + (((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5)))/(a*b^5) + (((a + b)^5*(a - b)^5)^(1/2)*((4*(53*a*b^15 - 120*a^3*b^13 + 48*a^5*b^11 + 56*a^7*b^9 - 48*a^9*b^7 + 8*a^11*b^5))/b^12 - (4*tan(x/2)*(8*a^16 + 62*b^16 - 410*a^2*b^14 + 929*a^4*b^12 - 1096*a^6*b^10 + 873*a^8*b^8 - 550*a^10*b^6 + 255*a^12*b^4 - 68*a^14*b^2))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*(24*a*b^16 + 58*a^3*b^14 - 345*a^5*b^12 + 543*a^7*b^10 - 440*a^9*b^8 + 184*a^11*b^6 - 32*a^13*b^4))/b^12 - (4*tan(x/2)*(16*b^17 - 180*a^2*b^15 + 252*a^4*b^13 - 148*a^6*b^11 + 100*a^8*b^9 - 40*a^10*b^7 + 8*a^12*b^5))/b^12 + (((a + b)^5*(a - b)^5)^(1/2)*((4*(93*a^3*b^15 - 240*a^5*b^13 + 208*a^7*b^11 - 64*a^9*b^9))/b^12 - (4*tan(x/2)*(62*a^2*b^16 - 335*a^4*b^14 + 604*a^6*b^12 - 456*a^8*b^10 + 128*a^10*b^8))/b^12 + (((4*(24*a^3*b^16 - 32*a^5*b^14))/b^12 - (4*tan(x/2)*(16*a^2*b^17 - 136*a^4*b^15 + 128*a^6*b^13))/b^12)*((a + b)^5*(a - b)^5)^(1/2))/(a*b^5)))/(a*b^5)))/(a*b^5)))/(a*b^5)))*((a + b)^5*(a - b)^5)^(1/2)*2i)/(a*b^5)","B"