1,1,39,0,0.554002," ","integrate(sin(x)^4/(I+cot(x)),x, algorithm=""fricas"")","\frac{1}{384} \, {\left(-120 i \, x e^{\left(6 i \, x\right)} - 3 \, e^{\left(10 i \, x\right)} + 30 \, e^{\left(8 i \, x\right)} - 60 \, e^{\left(4 i \, x\right)} + 15 \, e^{\left(2 i \, x\right)} - 2\right)} e^{\left(-6 i \, x\right)}"," ",0,"1/384*(-120*I*x*e^(6*I*x) - 3*e^(10*I*x) + 30*e^(8*I*x) - 60*e^(4*I*x) + 15*e^(2*I*x) - 2)*e^(-6*I*x)","A",0
2,1,32,0,0.469282," ","integrate(sin(x)^3/(I+cot(x)),x, algorithm=""fricas"")","\frac{1}{240} \, {\left(-5 i \, e^{\left(8 i \, x\right)} + 60 i \, e^{\left(6 i \, x\right)} + 90 i \, e^{\left(4 i \, x\right)} - 20 i \, e^{\left(2 i \, x\right)} + 3 i\right)} e^{\left(-5 i \, x\right)}"," ",0,"1/240*(-5*I*e^(8*I*x) + 60*I*e^(6*I*x) + 90*I*e^(4*I*x) - 20*I*e^(2*I*x) + 3*I)*e^(-5*I*x)","A",0
3,1,27,0,0.467639," ","integrate(sin(x)^2/(I+cot(x)),x, algorithm=""fricas"")","\frac{1}{32} \, {\left(-12 i \, x e^{\left(4 i \, x\right)} + 2 \, e^{\left(6 i \, x\right)} - 6 \, e^{\left(2 i \, x\right)} + 1\right)} e^{\left(-4 i \, x\right)}"," ",0,"1/32*(-12*I*x*e^(4*I*x) + 2*e^(6*I*x) - 6*e^(2*I*x) + 1)*e^(-4*I*x)","A",0
4,1,20,0,0.517596," ","integrate(sin(x)/(I+cot(x)),x, algorithm=""fricas"")","\frac{1}{12} \, {\left(3 i \, e^{\left(4 i \, x\right)} + 6 i \, e^{\left(2 i \, x\right)} - i\right)} e^{\left(-3 i \, x\right)}"," ",0,"1/12*(3*I*e^(4*I*x) + 6*I*e^(2*I*x) - I)*e^(-3*I*x)","A",0
5,1,6,0,0.450781," ","integrate(csc(x)/(I+cot(x)),x, algorithm=""fricas"")","i \, e^{\left(-i \, x\right)}"," ",0,"I*e^(-I*x)","A",0
6,1,11,0,0.432168," ","integrate(csc(x)^2/(I+cot(x)),x, algorithm=""fricas"")","-2 i \, x + \log\left(e^{\left(2 i \, x\right)} - 1\right)"," ",0,"-2*I*x + log(e^(2*I*x) - 1)","A",0
7,1,48,0,0.696809," ","integrate(csc(x)^3/(I+cot(x)),x, algorithm=""fricas"")","\frac{{\left(i \, e^{\left(2 i \, x\right)} - i\right)} \log\left(e^{\left(i \, x\right)} + 1\right) + {\left(-i \, e^{\left(2 i \, x\right)} + i\right)} \log\left(e^{\left(i \, x\right)} - 1\right) - 2 i \, e^{\left(i \, x\right)}}{e^{\left(2 i \, x\right)} - 1}"," ",0,"((I*e^(2*I*x) - I)*log(e^(I*x) + 1) + (-I*e^(2*I*x) + I)*log(e^(I*x) - 1) - 2*I*e^(I*x))/(e^(2*I*x) - 1)","B",0
8,1,16,0,0.518854," ","integrate(csc(x)^4/(I+cot(x)),x, algorithm=""fricas"")","\frac{2}{e^{\left(4 i \, x\right)} - 2 \, e^{\left(2 i \, x\right)} + 1}"," ",0,"2/(e^(4*I*x) - 2*e^(2*I*x) + 1)","A",0
9,1,97,0,0.463372," ","integrate(csc(x)^5/(I+cot(x)),x, algorithm=""fricas"")","\frac{{\left(3 i \, e^{\left(6 i \, x\right)} - 9 i \, e^{\left(4 i \, x\right)} + 9 i \, e^{\left(2 i \, x\right)} - 3 i\right)} \log\left(e^{\left(i \, x\right)} + 1\right) + {\left(-3 i \, e^{\left(6 i \, x\right)} + 9 i \, e^{\left(4 i \, x\right)} - 9 i \, e^{\left(2 i \, x\right)} + 3 i\right)} \log\left(e^{\left(i \, x\right)} - 1\right) - 6 i \, e^{\left(5 i \, x\right)} + 16 i \, e^{\left(3 i \, x\right)} + 6 i \, e^{\left(i \, x\right)}}{6 \, {\left(e^{\left(6 i \, x\right)} - 3 \, e^{\left(4 i \, x\right)} + 3 \, e^{\left(2 i \, x\right)} - 1\right)}}"," ",0,"1/6*((3*I*e^(6*I*x) - 9*I*e^(4*I*x) + 9*I*e^(2*I*x) - 3*I)*log(e^(I*x) + 1) + (-3*I*e^(6*I*x) + 9*I*e^(4*I*x) - 9*I*e^(2*I*x) + 3*I)*log(e^(I*x) - 1) - 6*I*e^(5*I*x) + 16*I*e^(3*I*x) + 6*I*e^(I*x))/(e^(6*I*x) - 3*e^(4*I*x) + 3*e^(2*I*x) - 1)","B",0
10,1,36,0,0.589974," ","integrate(csc(x)^6/(I+cot(x)),x, algorithm=""fricas"")","-\frac{4 \, {\left(4 \, e^{\left(2 i \, x\right)} - 1\right)}}{3 \, {\left(e^{\left(8 i \, x\right)} - 4 \, e^{\left(6 i \, x\right)} + 6 \, e^{\left(4 i \, x\right)} - 4 \, e^{\left(2 i \, x\right)} + 1\right)}}"," ",0,"-4/3*(4*e^(2*I*x) - 1)/(e^(8*I*x) - 4*e^(6*I*x) + 6*e^(4*I*x) - 4*e^(2*I*x) + 1)","A",0
11,1,145,0,0.762202," ","integrate(csc(x)^7/(I+cot(x)),x, algorithm=""fricas"")","\frac{{\left(15 i \, e^{\left(10 i \, x\right)} - 75 i \, e^{\left(8 i \, x\right)} + 150 i \, e^{\left(6 i \, x\right)} - 150 i \, e^{\left(4 i \, x\right)} + 75 i \, e^{\left(2 i \, x\right)} - 15 i\right)} \log\left(e^{\left(i \, x\right)} + 1\right) + {\left(-15 i \, e^{\left(10 i \, x\right)} + 75 i \, e^{\left(8 i \, x\right)} - 150 i \, e^{\left(6 i \, x\right)} + 150 i \, e^{\left(4 i \, x\right)} - 75 i \, e^{\left(2 i \, x\right)} + 15 i\right)} \log\left(e^{\left(i \, x\right)} - 1\right) - 30 i \, e^{\left(9 i \, x\right)} + 140 i \, e^{\left(7 i \, x\right)} - 256 i \, e^{\left(5 i \, x\right)} - 140 i \, e^{\left(3 i \, x\right)} + 30 i \, e^{\left(i \, x\right)}}{40 \, {\left(e^{\left(10 i \, x\right)} - 5 \, e^{\left(8 i \, x\right)} + 10 \, e^{\left(6 i \, x\right)} - 10 \, e^{\left(4 i \, x\right)} + 5 \, e^{\left(2 i \, x\right)} - 1\right)}}"," ",0,"1/40*((15*I*e^(10*I*x) - 75*I*e^(8*I*x) + 150*I*e^(6*I*x) - 150*I*e^(4*I*x) + 75*I*e^(2*I*x) - 15*I)*log(e^(I*x) + 1) + (-15*I*e^(10*I*x) + 75*I*e^(8*I*x) - 150*I*e^(6*I*x) + 150*I*e^(4*I*x) - 75*I*e^(2*I*x) + 15*I)*log(e^(I*x) - 1) - 30*I*e^(9*I*x) + 140*I*e^(7*I*x) - 256*I*e^(5*I*x) - 140*I*e^(3*I*x) + 30*I*e^(I*x))/(e^(10*I*x) - 5*e^(8*I*x) + 10*e^(6*I*x) - 10*e^(4*I*x) + 5*e^(2*I*x) - 1)","B",0
12,1,248,0,0.704979," ","integrate(csc(x)^6/(a+b*cot(x)),x, algorithm=""fricas"")","-\frac{6 \, a^{2} b^{2} + 9 \, b^{4} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{2} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{2}\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}\right) - 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right) + 4 \, {\left({\left(3 \, a^{3} b + 5 \, a b^{3}\right)} \cos\left(x\right)^{3} - 3 \, {\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{12 \, {\left(b^{5} \cos\left(x\right)^{4} - 2 \, b^{5} \cos\left(x\right)^{2} + b^{5}\right)}}"," ",0,"-1/12*(6*a^2*b^2 + 9*b^4 - 6*(a^2*b^2 + b^4)*cos(x)^2 + 6*((a^4 + 2*a^2*b^2 + b^4)*cos(x)^4 + a^4 + 2*a^2*b^2 + b^4 - 2*(a^4 + 2*a^2*b^2 + b^4)*cos(x)^2)*log(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2) - 6*((a^4 + 2*a^2*b^2 + b^4)*cos(x)^4 + a^4 + 2*a^2*b^2 + b^4 - 2*(a^4 + 2*a^2*b^2 + b^4)*cos(x)^2)*log(-1/4*cos(x)^2 + 1/4) + 4*((3*a^3*b + 5*a*b^3)*cos(x)^3 - 3*(a^3*b + 2*a*b^3)*cos(x))*sin(x))/(b^5*cos(x)^4 - 2*b^5*cos(x)^2 + b^5)","B",0
13,1,118,0,0.477758," ","integrate(csc(x)^4/(a+b*cot(x)),x, algorithm=""fricas"")","-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - b^{2} + {\left({\left(a^{2} + b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - b^{2}\right)} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}\right) - {\left({\left(a^{2} + b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - b^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{2 \, {\left(b^{3} \cos\left(x\right)^{2} - b^{3}\right)}}"," ",0,"-1/2*(2*a*b*cos(x)*sin(x) - b^2 + ((a^2 + b^2)*cos(x)^2 - a^2 - b^2)*log(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2) - ((a^2 + b^2)*cos(x)^2 - a^2 - b^2)*log(-1/4*cos(x)^2 + 1/4))/(b^3*cos(x)^2 - b^3)","B",0
14,1,45,0,0.502125," ","integrate(csc(x)^2/(a+b*cot(x)),x, algorithm=""fricas"")","-\frac{\log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}\right) - \log\left(-\frac{1}{4} \, \cos\left(x\right)^{2} + \frac{1}{4}\right)}{2 \, b}"," ",0,"-1/2*(log(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2) - log(-1/4*cos(x)^2 + 1/4))/b","B",0
15,1,94,0,0.504159," ","integrate(sin(x)^2/(a+b*cot(x)),x, algorithm=""fricas"")","-\frac{b^{3} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}\right) - {\left(a^{2} b + b^{3}\right)} \cos\left(x\right)^{2} + {\left(a^{3} + a b^{2}\right)} \cos\left(x\right) \sin\left(x\right) - {\left(a^{3} + 3 \, a b^{2}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"-1/2*(b^3*log(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2) - (a^2*b + b^3)*cos(x)^2 + (a^3 + a*b^2)*cos(x)*sin(x) - (a^3 + 3*a*b^2)*x)/(a^4 + 2*a^2*b^2 + b^4)","A",0
16,1,184,0,0.911047," ","integrate(sin(x)^4/(a+b*cot(x)),x, algorithm=""fricas"")","-\frac{4 \, b^{5} \log\left(2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}\right) + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{4} - 4 \, {\left(a^{4} b + 3 \, a^{2} b^{3} + 2 \, b^{5}\right)} \cos\left(x\right)^{2} - {\left(3 \, a^{5} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} x - {\left(2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - {\left(5 \, a^{5} + 14 \, a^{3} b^{2} + 9 \, a b^{4}\right)} \cos\left(x\right)\right)} \sin\left(x\right)}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}"," ",0,"-1/8*(4*b^5*log(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2) + 2*(a^4*b + 2*a^2*b^3 + b^5)*cos(x)^4 - 4*(a^4*b + 3*a^2*b^3 + 2*b^5)*cos(x)^2 - (3*a^5 + 10*a^3*b^2 + 15*a*b^4)*x - (2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^3 - (5*a^5 + 14*a^3*b^2 + 9*a*b^4)*cos(x))*sin(x))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)","A",0
17,1,264,0,0.613271," ","integrate(csc(x)^5/(a+b*cot(x)),x, algorithm=""fricas"")","-\frac{6 \, a b^{2} \cos\left(x\right) \sin\left(x\right) - 6 \, {\left({\left(a^{2} + b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - b^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}}\right) \sin\left(x\right) - 12 \, a^{2} b - 16 \, b^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} \cos\left(x\right)^{2} + 3 \, {\left(2 \, a^{3} + 3 \, a b^{2} - {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(x\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2} - {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(x\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right)}{12 \, {\left(b^{4} \cos\left(x\right)^{2} - b^{4}\right)} \sin\left(x\right)}"," ",0,"-1/12*(6*a*b^2*cos(x)*sin(x) - 6*((a^2 + b^2)*cos(x)^2 - a^2 - b^2)*sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 - a^2 - 2*b^2 + 2*sqrt(a^2 + b^2)*(a*cos(x) - b*sin(x)))/(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2))*sin(x) - 12*a^2*b - 16*b^3 + 12*(a^2*b + b^3)*cos(x)^2 + 3*(2*a^3 + 3*a*b^2 - (2*a^3 + 3*a*b^2)*cos(x)^2)*log(1/2*cos(x) + 1/2)*sin(x) - 3*(2*a^3 + 3*a*b^2 - (2*a^3 + 3*a*b^2)*cos(x)^2)*log(-1/2*cos(x) + 1/2)*sin(x))/((b^4*cos(x)^2 - b^4)*sin(x))","B",0
18,1,135,0,0.699778," ","integrate(csc(x)^3/(a+b*cot(x)),x, algorithm=""fricas"")","\frac{a \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) - a \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) \sin\left(x\right) + \sqrt{a^{2} + b^{2}} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}}\right) \sin\left(x\right) - 2 \, b}{2 \, b^{2} \sin\left(x\right)}"," ",0,"1/2*(a*log(1/2*cos(x) + 1/2)*sin(x) - a*log(-1/2*cos(x) + 1/2)*sin(x) + sqrt(a^2 + b^2)*log(-(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 - a^2 - 2*b^2 + 2*sqrt(a^2 + b^2)*(a*cos(x) - b*sin(x)))/(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2))*sin(x) - 2*b)/(b^2*sin(x))","B",0
19,1,98,0,0.834506," ","integrate(csc(x)/(a+b*cot(x)),x, algorithm=""fricas"")","\frac{\log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}}\right)}{2 \, \sqrt{a^{2} + b^{2}}}"," ",0,"1/2*log(-(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 - a^2 - 2*b^2 + 2*sqrt(a^2 + b^2)*(a*cos(x) - b*sin(x)))/(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2))/sqrt(a^2 + b^2)","B",0
20,1,146,0,0.646098," ","integrate(sin(x)/(a+b*cot(x)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} b^{2} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}}\right) - 2 \, {\left(a^{3} + a b^{2}\right)} \cos\left(x\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \sin\left(x\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}}"," ",0,"1/2*(sqrt(a^2 + b^2)*b^2*log(-(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 - a^2 - 2*b^2 + 2*sqrt(a^2 + b^2)*(a*cos(x) - b*sin(x)))/(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2)) - 2*(a^3 + a*b^2)*cos(x) - 2*(a^2*b + b^3)*sin(x))/(a^4 + 2*a^2*b^2 + b^4)","B",0
21,1,220,0,0.626960," ","integrate(sin(x)^3/(a+b*cot(x)),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a^{2} + b^{2}} b^{4} \log\left(-\frac{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} - 2 \, b^{2} + 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cos\left(x\right) - b \sin\left(x\right)\right)}}{2 \, a b \cos\left(x\right) \sin\left(x\right) - {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + a^{2}}\right) + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - 6 \, {\left(a^{5} + 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(x\right) - 2 \, {\left(a^{4} b + 5 \, a^{2} b^{3} + 4 \, b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{6 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}}"," ",0,"1/6*(3*sqrt(a^2 + b^2)*b^4*log(-(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 - a^2 - 2*b^2 + 2*sqrt(a^2 + b^2)*(a*cos(x) - b*sin(x)))/(2*a*b*cos(x)*sin(x) - (a^2 - b^2)*cos(x)^2 + a^2)) + 2*(a^5 + 2*a^3*b^2 + a*b^4)*cos(x)^3 - 6*(a^5 + 3*a^3*b^2 + 2*a*b^4)*cos(x) - 2*(a^4*b + 5*a^2*b^3 + 4*b^5 - (a^4*b + 2*a^2*b^3 + b^5)*cos(x)^2)*sin(x))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)","A",0
22,1,39,0,0.709658," ","integrate(csc(x)^2/(a+b*cot(x))^2,x, algorithm=""fricas"")","-\frac{a \cos\left(x\right) - b \sin\left(x\right)}{{\left(a^{2} b + b^{3}\right)} \cos\left(x\right) + {\left(a^{3} + a b^{2}\right)} \sin\left(x\right)}"," ",0,"-(a*cos(x) - b*sin(x))/((a^2*b + b^3)*cos(x) + (a^3 + a*b^2)*sin(x))","B",0
23,1,38,0,0.453326," ","integrate((a+b*cot(x))^n*csc(x)^2,x, algorithm=""fricas"")","-\frac{{\left(b \cos\left(x\right) + a \sin\left(x\right)\right)} \left(\frac{b \cos\left(x\right) + a \sin\left(x\right)}{\sin\left(x\right)}\right)^{n}}{{\left(b n + b\right)} \sin\left(x\right)}"," ",0,"-(b*cos(x) + a*sin(x))*((b*cos(x) + a*sin(x))/sin(x))^n/((b*n + b)*sin(x))","A",0
