1,1,48,78,0.344651,"\text{Not used}","int(sin(x)^4/(cot(x) + 1i),x)","-\frac{x\,5{}\mathrm{i}}{16}+\frac{\frac{11\,{\mathrm{tan}\left(x\right)}^4}{16}-\frac{{\mathrm{tan}\left(x\right)}^3\,3{}\mathrm{i}}{16}+\frac{31\,{\mathrm{tan}\left(x\right)}^2}{48}-\frac{\mathrm{tan}\left(x\right)\,7{}\mathrm{i}}{48}+\frac{1}{6}}{{\left(\mathrm{tan}\left(x\right)+1{}\mathrm{i}\right)}^2\,{\left(1+\mathrm{tan}\left(x\right)\,1{}\mathrm{i}\right)}^3}","Not used",1,"((31*tan(x)^2)/48 - (tan(x)*7i)/48 - (tan(x)^3*3i)/16 + (11*tan(x)^4)/16 + 1/6)/((tan(x) + 1i)^2*(tan(x)*1i + 1)^3) - (x*5i)/16","B"
2,1,49,37,0.445503,"\text{Not used}","int(sin(x)^3/(cot(x) + 1i),x)","\frac{\left(6\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3-{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,2{}\mathrm{i}+2\,\mathrm{tan}\left(\frac{x}{2}\right)-\mathrm{i}\right)\,16{}\mathrm{i}}{15\,{\left(1+\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)}^5\,{\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}^3}","Not used",1,"((2*tan(x/2) - tan(x/2)^2*2i + 6*tan(x/2)^3 - 1i)*16i)/(15*(tan(x/2)*1i + 1)^5*(tan(x/2) + 1i)^3)","B"
3,1,37,50,0.251808,"\text{Not used}","int(sin(x)^2/(cot(x) + 1i),x)","-\frac{x\,3{}\mathrm{i}}{8}-\frac{\frac{{\mathrm{tan}\left(x\right)}^2\,5{}\mathrm{i}}{8}+\frac{\mathrm{tan}\left(x\right)}{8}+\frac{1}{4}{}\mathrm{i}}{\left(\mathrm{tan}\left(x\right)+1{}\mathrm{i}\right)\,{\left(1+\mathrm{tan}\left(x\right)\,1{}\mathrm{i}\right)}^2}","Not used",1,"- (x*3i)/8 - (tan(x)/8 + (tan(x)^2*5i)/8 + 1i/4)/((tan(x) + 1i)*(tan(x)*1i + 1)^2)","B"
4,1,31,25,0.303569,"\text{Not used}","int(sin(x)/(cot(x) + 1i),x)","-\frac{\frac{4}{3}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,8{}\mathrm{i}}{3}}{{\left(1+\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}\right)}^3\,\left(\mathrm{tan}\left(\frac{x}{2}\right)+1{}\mathrm{i}\right)}","Not used",1,"-((tan(x/2)*8i)/3 + 4/3)/((tan(x/2)*1i + 1)^3*(tan(x/2) + 1i))","B"
5,1,14,14,0.201010,"\text{Not used}","int(1/(sin(x)*(cot(x) + 1i)),x)","\frac{2{}\mathrm{i}}{1+\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}}","Not used",1,"2i/(tan(x/2)*1i + 1)","B"
6,1,11,9,0.247295,"\text{Not used}","int(1/(sin(x)^2*(cot(x) + 1i)),x)","-\mathrm{atan}\left(2\,\mathrm{tan}\left(x\right)-\mathrm{i}\right)\,2{}\mathrm{i}","Not used",1,"-atan(2*tan(x) - 1i)*2i","B"
7,1,23,12,0.228436,"\text{Not used}","int(1/(sin(x)^3*(cot(x) + 1i)),x)","-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{2}-\frac{1}{2\,\mathrm{tan}\left(\frac{x}{2}\right)}-\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,1{}\mathrm{i}","Not used",1,"- tan(x/2)/2 - log(tan(x/2))*1i - 1/(2*tan(x/2))","B"
8,1,9,15,0.163862,"\text{Not used}","int(1/(sin(x)^4*(cot(x) + 1i)),x)","-\frac{\mathrm{cot}\left(x\right)\,\left(\mathrm{cot}\left(x\right)-2{}\mathrm{i}\right)}{2}","Not used",1,"-(cot(x)*(cot(x) - 2i))/2","B"
9,1,55,28,0.232062,"\text{Not used}","int(1/(sin(x)^5*(cot(x) + 1i)),x)","-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{8}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,1{}\mathrm{i}}{2}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}}{8}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{24}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2-\mathrm{tan}\left(\frac{x}{2}\right)\,1{}\mathrm{i}+\frac{1}{3}}{8\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3}","Not used",1,"- tan(x/2)/8 - (log(tan(x/2))*1i)/2 - (tan(x/2)^2*1i)/8 - tan(x/2)^3/24 - (tan(x/2)^2 - tan(x/2)*1i + 1/3)/(8*tan(x/2)^3)","B"
10,1,25,33,0.180473,"\text{Not used}","int(1/(sin(x)^6*(cot(x) + 1i)),x)","-\frac{{\mathrm{cot}\left(x\right)}^4}{4}+\frac{{\mathrm{cot}\left(x\right)}^3\,1{}\mathrm{i}}{3}-\frac{{\mathrm{cot}\left(x\right)}^2}{2}+\mathrm{cot}\left(x\right)\,1{}\mathrm{i}","Not used",1,"cot(x)*1i - cot(x)^2/2 + (cot(x)^3*1i)/3 - cot(x)^4/4","B"
11,1,89,40,0.300209,"\text{Not used}","int(1/(sin(x)^7*(cot(x) + 1i)),x)","-\frac{\mathrm{cot}\left(\frac{x}{2}\right)}{16}-\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{16}-\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^3}{32}-\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^5}{160}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^3}{32}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{160}-\frac{\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)\,3{}\mathrm{i}}{8}+\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}}{8}+\frac{{\mathrm{cot}\left(\frac{x}{2}\right)}^4\,1{}\mathrm{i}}{64}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,1{}\mathrm{i}}{8}-\frac{{\mathrm{tan}\left(\frac{x}{2}\right)}^4\,1{}\mathrm{i}}{64}","Not used",1,"(cot(x/2)^2*1i)/8 - tan(x/2)/16 - (log(tan(x/2))*3i)/8 - cot(x/2)/16 - cot(x/2)^3/32 + (cot(x/2)^4*1i)/64 - cot(x/2)^5/160 - (tan(x/2)^2*1i)/8 - tan(x/2)^3/32 - (tan(x/2)^4*1i)/64 - tan(x/2)^5/160","B"
12,1,110,81,0.375450,"\text{Not used}","int(1/(sin(x)^6*(a + b*cot(x))),x)","-\frac{\frac{1}{4\,b}-\frac{a\,\mathrm{tan}\left(x\right)}{3\,b^2}+\frac{{\mathrm{tan}\left(x\right)}^2\,\left(a^2+2\,b^2\right)}{2\,b^3}-\frac{a\,{\mathrm{tan}\left(x\right)}^3\,\left(a^2+2\,b^2\right)}{b^4}}{{\mathrm{tan}\left(x\right)}^4}-\frac{2\,\mathrm{atanh}\left(\frac{\left(b+2\,a\,\mathrm{tan}\left(x\right)\right)\,{\left(a^2+b^2\right)}^2}{b\,\left(a^4+2\,a^2\,b^2+b^4\right)}\right)\,{\left(a^2+b^2\right)}^2}{b^5}","Not used",1,"- (1/(4*b) - (a*tan(x))/(3*b^2) + (tan(x)^2*(a^2 + 2*b^2))/(2*b^3) - (a*tan(x)^3*(a^2 + 2*b^2))/b^4)/tan(x)^4 - (2*atanh(((b + 2*a*tan(x))*(a^2 + b^2)^2)/(b*(a^4 + b^4 + 2*a^2*b^2)))*(a^2 + b^2)^2)/b^5","B"
13,1,44,38,0.265980,"\text{Not used}","int(1/(sin(x)^4*(a + b*cot(x))),x)","-\frac{\frac{1}{2\,b}-\frac{a\,\mathrm{tan}\left(x\right)}{b^2}}{{\mathrm{tan}\left(x\right)}^2}-\frac{2\,\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(x\right)}{b}+1\right)\,\left(a^2+b^2\right)}{b^3}","Not used",1,"- (1/(2*b) - (a*tan(x))/b^2)/tan(x)^2 - (2*atanh((2*a*tan(x))/b + 1)*(a^2 + b^2))/b^3","B"
14,1,16,12,0.183036,"\text{Not used}","int(1/(sin(x)^2*(a + b*cot(x))),x)","-\frac{2\,\mathrm{atanh}\left(\frac{2\,a\,\mathrm{tan}\left(x\right)}{b}+1\right)}{b}","Not used",1,"-(2*atanh((2*a*tan(x))/b + 1))/b","B"
15,1,126,72,0.353727,"\text{Not used}","int(sin(x)^2/(a + b*cot(x)),x)","{\cos\left(x\right)}^2\,\left(\frac{b}{2\,\left(a^2+b^2\right)}-\frac{a\,\mathrm{tan}\left(x\right)}{2\,\left(a^2+b^2\right)}\right)-\frac{b^3\,\ln\left(b+a\,\mathrm{tan}\left(x\right)\right)}{{\left(a^2+b^2\right)}^2}+\frac{\ln\left(\mathrm{tan}\left(x\right)-\mathrm{i}\right)\,\left(2\,b+a\,1{}\mathrm{i}\right)}{4\,\left(-a^2+a\,b\,2{}\mathrm{i}+b^2\right)}+\frac{\ln\left(\mathrm{tan}\left(x\right)+1{}\mathrm{i}\right)\,\left(a+b\,2{}\mathrm{i}\right)}{4\,\left(-a^2\,1{}\mathrm{i}+2\,a\,b+b^2\,1{}\mathrm{i}\right)}","Not used",1,"cos(x)^2*(b/(2*(a^2 + b^2)) - (a*tan(x))/(2*(a^2 + b^2))) - (b^3*log(b + a*tan(x)))/(a^2 + b^2)^2 + (log(tan(x) - 1i)*(a*1i + 2*b))/(4*(a*b*2i - a^2 + b^2)) + (log(tan(x) + 1i)*(a + b*2i))/(4*(2*a*b - a^2*1i + b^2*1i))","B"
16,1,263,120,0.501302,"\text{Not used}","int(sin(x)^4/(a + b*cot(x)),x)","\frac{\frac{a^2\,b+3\,b^3}{4\,{\left(a^2+b^2\right)}^2}-\frac{{\mathrm{tan}\left(x\right)}^3\,\left(5\,a^3+9\,a\,b^2\right)}{8\,\left(a^4+2\,a^2\,b^2+b^4\right)}+\frac{{\mathrm{tan}\left(x\right)}^2\,\left(a^2\,b+2\,b^3\right)}{2\,{\left(a^2+b^2\right)}^2}-\frac{a\,\mathrm{tan}\left(x\right)\,\left(3\,a^2+7\,b^2\right)}{8\,\left(a^4+2\,a^2\,b^2+b^4\right)}}{{\mathrm{tan}\left(x\right)}^4+2\,{\mathrm{tan}\left(x\right)}^2+1}-\frac{b^5\,\ln\left(b+a\,\mathrm{tan}\left(x\right)\right)}{{\left(a^2+b^2\right)}^3}+\frac{\ln\left(\mathrm{tan}\left(x\right)-\mathrm{i}\right)\,\left(-3\,a^2+a\,b\,9{}\mathrm{i}+8\,b^2\right)}{16\,\left(-a^3\,1{}\mathrm{i}-3\,a^2\,b+a\,b^2\,3{}\mathrm{i}+b^3\right)}+\frac{\ln\left(\mathrm{tan}\left(x\right)+1{}\mathrm{i}\right)\,\left(-a^2\,3{}\mathrm{i}+9\,a\,b+b^2\,8{}\mathrm{i}\right)}{16\,\left(-a^3-a^2\,b\,3{}\mathrm{i}+3\,a\,b^2+b^3\,1{}\mathrm{i}\right)}","Not used",1,"((a^2*b + 3*b^3)/(4*(a^2 + b^2)^2) - (tan(x)^3*(9*a*b^2 + 5*a^3))/(8*(a^4 + b^4 + 2*a^2*b^2)) + (tan(x)^2*(a^2*b + 2*b^3))/(2*(a^2 + b^2)^2) - (a*tan(x)*(3*a^2 + 7*b^2))/(8*(a^4 + b^4 + 2*a^2*b^2)))/(2*tan(x)^2 + tan(x)^4 + 1) - (b^5*log(b + a*tan(x)))/(a^2 + b^2)^3 + (log(tan(x) - 1i)*(a*b*9i - 3*a^2 + 8*b^2))/(16*(a*b^2*3i - 3*a^2*b - a^3*1i + b^3)) + (log(tan(x) + 1i)*(9*a*b - a^2*3i + b^2*8i))/(16*(3*a*b^2 - a^2*b*3i - a^3 + b^3*1i))","B"
17,1,674,101,0.620258,"\text{Not used}","int(1/(sin(x)^5*(a + b*cot(x))),x)","-\mathrm{tan}\left(\frac{x}{2}\right)\,\left(\frac{5}{8\,b}+\frac{a^2}{2\,b^3}\right)-\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+5\,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(a^3+\frac{3\,a\,b^2}{2}\right)}{b^4}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(\frac{4\,a^4\,b^4+7\,a^2\,b^6+2\,b^8}{b^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^5\,b^2+16\,a^3\,b^4+7\,a\,b^6\right)}{b^5}+\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^2\,b^6+6\,b^8\right)}{b^5}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}+\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(\frac{4\,a^4\,b^4+7\,a^2\,b^6+2\,b^8}{b^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^5\,b^2+16\,a^3\,b^4+7\,a\,b^6\right)}{b^5}-\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^2\,b^6+6\,b^8\right)}{b^5}\right)}{b^4}\right)\,1{}\mathrm{i}}{b^4}}{\frac{2\,\left(2\,a^7+7\,a^5\,b^2+8\,a^3\,b^4+3\,a\,b^6\right)}{b^6}+\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(\frac{4\,a^4\,b^4+7\,a^2\,b^6+2\,b^8}{b^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^5\,b^2+16\,a^3\,b^4+7\,a\,b^6\right)}{b^5}+\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^2\,b^6+6\,b^8\right)}{b^5}\right)}{b^4}\right)}{b^4}-\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(\frac{4\,a^4\,b^4+7\,a^2\,b^6+2\,b^8}{b^6}+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^5\,b^2+16\,a^3\,b^4+7\,a\,b^6\right)}{b^5}-\frac{\sqrt{{\left(a^2+b^2\right)}^3}\,\left(2\,a\,b^2+\frac{\mathrm{tan}\left(\frac{x}{2}\right)\,\left(8\,a^2\,b^6+6\,b^8\right)}{b^5}\right)}{b^4}\right)}{b^4}-\frac{2\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(2\,a^6+8\,a^4\,b^2+10\,a^2\,b^4+4\,b^6\right)}{b^5}}\right)\,\sqrt{{\left(a^2+b^2\right)}^3}\,2{}\mathrm{i}}{b^4}","Not used",1,"- tan(x/2)*(5/(8*b) + a^2/(2*b^3)) - tan(x/2)^3/(24*b) - (a*tan(x/2)^2)/(8*b^2) - (tan(x/2)^2*(4*a^2 + 5*b^2) + b^2/3 - a*b*tan(x/2))/(8*b^3*tan(x/2)^3) - (atan(((((a^2 + b^2)^3)^(1/2)*((2*b^8 + 7*a^2*b^6 + 4*a^4*b^4)/b^6 + (tan(x/2)*(7*a*b^6 + 16*a^3*b^4 + 8*a^5*b^2))/b^5 + (((a^2 + b^2)^3)^(1/2)*(2*a*b^2 + (tan(x/2)*(6*b^8 + 8*a^2*b^6))/b^5))/b^4)*1i)/b^4 + (((a^2 + b^2)^3)^(1/2)*((2*b^8 + 7*a^2*b^6 + 4*a^4*b^4)/b^6 + (tan(x/2)*(7*a*b^6 + 16*a^3*b^4 + 8*a^5*b^2))/b^5 - (((a^2 + b^2)^3)^(1/2)*(2*a*b^2 + (tan(x/2)*(6*b^8 + 8*a^2*b^6))/b^5))/b^4)*1i)/b^4)/((2*(3*a*b^6 + 2*a^7 + 8*a^3*b^4 + 7*a^5*b^2))/b^6 + (((a^2 + b^2)^3)^(1/2)*((2*b^8 + 7*a^2*b^6 + 4*a^4*b^4)/b^6 + (tan(x/2)*(7*a*b^6 + 16*a^3*b^4 + 8*a^5*b^2))/b^5 + (((a^2 + b^2)^3)^(1/2)*(2*a*b^2 + (tan(x/2)*(6*b^8 + 8*a^2*b^6))/b^5))/b^4))/b^4 - (((a^2 + b^2)^3)^(1/2)*((2*b^8 + 7*a^2*b^6 + 4*a^4*b^4)/b^6 + (tan(x/2)*(7*a*b^6 + 16*a^3*b^4 + 8*a^5*b^2))/b^5 - (((a^2 + b^2)^3)^(1/2)*(2*a*b^2 + (tan(x/2)*(6*b^8 + 8*a^2*b^6))/b^5))/b^4))/b^4 - (2*tan(x/2)*(2*a^6 + 4*b^6 + 10*a^2*b^4 + 8*a^4*b^2))/b^5))*((a^2 + b^2)^3)^(1/2)*2i)/b^4 - (log(tan(x/2))*((3*a*b^2)/2 + a^3))/b^4","B"
18,1,170,53,0.491897,"\text{Not used}","int(1/(sin(x)^3*(a + b*cot(x))),x)","\frac{2\,\mathrm{atanh}\left(\frac{b^3\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}+4\,a^3\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}+3\,a\,b^2\,\sin\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}+2\,a^2\,b\,\cos\left(\frac{x}{2}\right)\,\sqrt{a^2+b^2}}{4\,\sin\left(\frac{x}{2}\right)\,a^4+2\,\cos\left(\frac{x}{2}\right)\,a^3\,b+5\,\sin\left(\frac{x}{2}\right)\,a^2\,b^2+2\,\cos\left(\frac{x}{2}\right)\,a\,b^3+\sin\left(\frac{x}{2}\right)\,b^4}\right)\,\sqrt{a^2+b^2}}{b^2}-\frac{1}{b\,\sin\left(x\right)}-\frac{a\,\ln\left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)}{b^2}","Not used",1,"(2*atanh((b^3*cos(x/2)*(a^2 + b^2)^(1/2) + 4*a^3*sin(x/2)*(a^2 + b^2)^(1/2) + 3*a*b^2*sin(x/2)*(a^2 + b^2)^(1/2) + 2*a^2*b*cos(x/2)*(a^2 + b^2)^(1/2))/(4*a^4*sin(x/2) + b^4*sin(x/2) + 5*a^2*b^2*sin(x/2) + 2*a*b^3*cos(x/2) + 2*a^3*b*cos(x/2)))*(a^2 + b^2)^(1/2))/b^2 - 1/(b*sin(x)) - (a*log(sin(x/2)/cos(x/2)))/b^2","B"
19,1,31,36,0.284347,"\text{Not used}","int(1/(sin(x)*(a + b*cot(x))),x)","-\frac{2\,\mathrm{atanh}\left(\frac{a-b\,\mathrm{tan}\left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}","Not used",1,"-(2*atanh((a - b*tan(x/2))/(a^2 + b^2)^(1/2)))/(a^2 + b^2)^(1/2)","B"
20,1,94,66,0.389617,"\text{Not used}","int(sin(x)/(a + b*cot(x)),x)","-\frac{\frac{2\,a}{a^2+b^2}+\frac{2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)}{a^2+b^2}}{{\mathrm{tan}\left(\frac{x}{2}\right)}^2+1}-\frac{2\,b^2\,\mathrm{atanh}\left(\frac{2\,a\,b^2+2\,a^3-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^2+b^2\right)}{2\,{\left(a^2+b^2\right)}^{3/2}}\right)}{{\left(a^2+b^2\right)}^{3/2}}","Not used",1,"- ((2*a)/(a^2 + b^2) + (2*b*tan(x/2))/(a^2 + b^2))/(tan(x/2)^2 + 1) - (2*b^2*atanh((2*a*b^2 + 2*a^3 - 2*b*tan(x/2)*(a^2 + b^2))/(2*(a^2 + b^2)^(3/2))))/(a^2 + b^2)^(3/2)","B"
21,1,280,121,0.651302,"\text{Not used}","int(sin(x)^3/(a + b*cot(x)),x)","-\frac{\frac{4\,{\mathrm{tan}\left(\frac{x}{2}\right)}^3\,\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)}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,\left(2\,a^2+5\,b^2\right)}{3\,{\left(a^2+b^2\right)}^2}+\frac{2\,b^3\,{\mathrm{tan}\left(\frac{x}{2}\right)}^5}{a^4+2\,a^2\,b^2+b^4}+\frac{2\,a\,b^2\,{\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)}^2\,\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\,b^4\,\mathrm{atanh}\left(\frac{2\,a\,b^4+2\,a^5+4\,a^3\,b^2-2\,b\,\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a^4+2\,a^2\,b^2+b^4\right)}{2\,{\left(a^2+b^2\right)}^{5/2}}\right)}{{\left(a^2+b^2\right)}^{5/2}}","Not used",1,"- ((4*tan(x/2)^3*(2*a^2*b + 5*b^3))/(3*(a^4 + b^4 + 2*a^2*b^2)) + (2*b^3*tan(x/2))/(a^4 + b^4 + 2*a^2*b^2) + (2*a*(2*a^2 + 5*b^2))/(3*(a^2 + b^2)^2) + (2*b^3*tan(x/2)^5)/(a^4 + b^4 + 2*a^2*b^2) + (2*a*b^2*tan(x/2)^4)/(a^4 + b^4 + 2*a^2*b^2) + (4*a*tan(x/2)^2*(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*b^4*atanh((2*a*b^4 + 2*a^5 + 4*a^3*b^2 - 2*b*tan(x/2)*(a^4 + b^4 + 2*a^2*b^2))/(2*(a^2 + b^2)^(5/2))))/(a^2 + b^2)^(5/2)","B"
22,1,14,12,0.191553,"\text{Not used}","int(1/(sin(x)^2*(a + b*cot(x))^2),x)","-\frac{1}{\mathrm{tan}\left(x\right)\,a^2+b\,a}","Not used",1,"-1/(a^2*tan(x) + a*b)","B"
23,1,43,20,0.479283,"\text{Not used}","int((a + b*cot(x))^n/sin(x)^2,x)","\left\{\begin{array}{cl} -\frac{\ln\left(a+\frac{b}{\mathrm{tan}\left(x\right)}\right)}{b} & \text{\ if\ \ }n=-1\\ -\frac{{\left(a+\frac{b}{\mathrm{tan}\left(x\right)}\right)}^{n+1}}{b\,\left(n+1\right)} & \text{\ if\ \ }n\neq -1 \end{array}\right.","Not used",1,"piecewise(n == -1, -log(a + b/tan(x))/b, n ~= -1, -(a + b/tan(x))^(n + 1)/(b*(n + 1)))","B"