1,1,80,0,0.615214," ","integrate(tan(x)^4/(a+a*csc(x)),x, algorithm=""giac"")","\frac{x}{a} + \frac{15 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 36 \, \tan\left(\frac{1}{2} \, x\right) + 17}{24 \, a {\left(\tan\left(\frac{1}{2} \, x\right) - 1\right)}^{3}} + \frac{55 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 260 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 450 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 300 \, \tan\left(\frac{1}{2} \, x\right) + 71}{40 \, a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{5}}"," ",0,"x/a + 1/24*(15*tan(1/2*x)^2 - 36*tan(1/2*x) + 17)/(a*(tan(1/2*x) - 1)^3) + 1/40*(55*tan(1/2*x)^4 + 260*tan(1/2*x)^3 + 450*tan(1/2*x)^2 + 300*tan(1/2*x) + 71)/(a*(tan(1/2*x) + 1)^5)","A",0
2,1,52,0,0.468358," ","integrate(tan(x)^3/(a+a*csc(x)),x, algorithm=""giac"")","\frac{11 \, \log\left(\sin\left(x\right) + 1\right)}{16 \, a} + \frac{5 \, \log\left(-\sin\left(x\right) + 1\right)}{16 \, a} + \frac{5 \, \sin\left(x\right)^{2} - 3 \, \sin\left(x\right) - 6}{8 \, a {\left(\sin\left(x\right) + 1\right)}^{2} {\left(\sin\left(x\right) - 1\right)}}"," ",0,"11/16*log(sin(x) + 1)/a + 5/16*log(-sin(x) + 1)/a + 1/8*(5*sin(x)^2 - 3*sin(x) - 6)/(a*(sin(x) + 1)^2*(sin(x) - 1))","A",0
3,1,49,0,0.312102," ","integrate(tan(x)^2/(a+a*csc(x)),x, algorithm=""giac"")","-\frac{x}{a} - \frac{1}{2 \, a {\left(\tan\left(\frac{1}{2} \, x\right) - 1\right)}} - \frac{9 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 24 \, \tan\left(\frac{1}{2} \, x\right) + 11}{6 \, a {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"-x/a - 1/2/(a*(tan(1/2*x) - 1)) - 1/6*(9*tan(1/2*x)^2 + 24*tan(1/2*x) + 11)/(a*(tan(1/2*x) + 1)^3)","A",0
4,1,34,0,0.523654," ","integrate(tan(x)/(a+a*csc(x)),x, algorithm=""giac"")","-\frac{3 \, \log\left(\sin\left(x\right) + 1\right)}{4 \, a} - \frac{\log\left(-\sin\left(x\right) + 1\right)}{4 \, a} - \frac{1}{2 \, a {\left(\sin\left(x\right) + 1\right)}}"," ",0,"-3/4*log(sin(x) + 1)/a - 1/4*log(-sin(x) + 1)/a - 1/2/(a*(sin(x) + 1))","A",0
5,1,9,0,0.343077," ","integrate(cot(x)/(a+a*csc(x)),x, algorithm=""giac"")","\frac{\log\left(\sin\left(x\right) + 1\right)}{a}"," ",0,"log(sin(x) + 1)/a","A",0
6,1,17,0,0.277132," ","integrate(cot(x)^2/(a+a*csc(x)),x, algorithm=""giac"")","-\frac{x}{a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a}"," ",0,"-x/a + log(abs(tan(1/2*x)))/a","A",0
7,1,14,0,0.566911," ","integrate(cot(x)^3/(a+a*csc(x)),x, algorithm=""giac"")","-\frac{\frac{1}{\sin\left(x\right)} + \log\left({\left| \sin\left(x\right) \right|}\right)}{a}"," ",0,"-(1/sin(x) + log(abs(sin(x))))/a","A",0
8,1,65,0,0.676370," ","integrate(cot(x)^4/(a+a*csc(x)),x, algorithm=""giac"")","\frac{x}{a} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, a} + \frac{a \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, x\right)}{8 \, a^{2}} + \frac{6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, x\right) - 1}{8 \, a \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"x/a - 1/2*log(abs(tan(1/2*x)))/a + 1/8*(a*tan(1/2*x)^2 - 4*a*tan(1/2*x))/a^2 + 1/8*(6*tan(1/2*x)^2 + 4*tan(1/2*x) - 1)/(a*tan(1/2*x)^2)","B",0
9,1,29,0,0.354213," ","integrate(cot(x)^5/(a+a*csc(x)),x, algorithm=""giac"")","\frac{\frac{6 \, \sin\left(x\right)^{2} + 3 \, \sin\left(x\right) - 2}{\sin\left(x\right)^{3}} + 6 \, \log\left({\left| \sin\left(x\right) \right|}\right)}{6 \, a}"," ",0,"1/6*((6*sin(x)^2 + 3*sin(x) - 2)/sin(x)^3 + 6*log(abs(sin(x))))/a","A",0
10,1,109,0,0.332681," ","integrate(cot(x)^6/(a+a*csc(x)),x, algorithm=""giac"")","-\frac{x}{a} + \frac{3 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{8 \, a} + \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{4} - 8 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 24 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 120 \, a^{3} \tan\left(\frac{1}{2} \, x\right)}{192 \, a^{4}} - \frac{150 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 120 \, \tan\left(\frac{1}{2} \, x\right)^{3} - 24 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, x\right) + 3}{192 \, a \tan\left(\frac{1}{2} \, x\right)^{4}}"," ",0,"-x/a + 3/8*log(abs(tan(1/2*x)))/a + 1/192*(3*a^3*tan(1/2*x)^4 - 8*a^3*tan(1/2*x)^3 - 24*a^3*tan(1/2*x)^2 + 120*a^3*tan(1/2*x))/a^4 - 1/192*(150*tan(1/2*x)^4 + 120*tan(1/2*x)^3 - 24*tan(1/2*x)^2 - 8*tan(1/2*x) + 3)/(a*tan(1/2*x)^4)","B",0
11,1,41,0,0.535116," ","integrate(cot(x)^7/(a+a*csc(x)),x, algorithm=""giac"")","-\frac{\frac{60 \, \sin\left(x\right)^{4} + 60 \, \sin\left(x\right)^{3} - 40 \, \sin\left(x\right)^{2} - 15 \, \sin\left(x\right) + 12}{\sin\left(x\right)^{5}} + 60 \, \log\left({\left| \sin\left(x\right) \right|}\right)}{60 \, a}"," ",0,"-1/60*((60*sin(x)^4 + 60*sin(x)^3 - 40*sin(x)^2 - 15*sin(x) + 12)/sin(x)^5 + 60*log(abs(sin(x))))/a","A",0
12,1,252,0,0.415446," ","integrate(tan(x)^5/(a+b*csc(x)),x, algorithm=""giac"")","\frac{b^{6} \log\left({\left| a \sin\left(x\right) + b \right|}\right)}{a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}} - \frac{{\left(8 \, a^{2} - 21 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(x\right) + 1\right)}{16 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)}} - \frac{{\left(8 \, a^{2} + 21 \, a b + 15 \, b^{2}\right)} \log\left(-\sin\left(x\right) + 1\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} - \frac{6 \, a^{5} - 16 \, a^{3} b^{2} + 10 \, a b^{4} + {\left(5 \, a^{4} b - 14 \, a^{2} b^{3} + 9 \, b^{5}\right)} \sin\left(x\right)^{3} - 4 \, {\left(2 \, a^{5} - 5 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(x\right)^{2} - {\left(3 \, a^{4} b - 10 \, a^{2} b^{3} + 7 \, b^{5}\right)} \sin\left(x\right)}{8 \, {\left(a + b\right)}^{3} {\left(a - b\right)}^{3} {\left(\sin\left(x\right) + 1\right)}^{2} {\left(\sin\left(x\right) - 1\right)}^{2}}"," ",0,"b^6*log(abs(a*sin(x) + b))/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6) - 1/16*(8*a^2 - 21*a*b + 15*b^2)*log(sin(x) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - 1/16*(8*a^2 + 21*a*b + 15*b^2)*log(-sin(x) + 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 1/8*(6*a^5 - 16*a^3*b^2 + 10*a*b^4 + (5*a^4*b - 14*a^2*b^3 + 9*b^5)*sin(x)^3 - 4*(2*a^5 - 5*a^3*b^2 + 3*a*b^4)*sin(x)^2 - (3*a^4*b - 10*a^2*b^3 + 7*b^5)*sin(x))/((a + b)^3*(a - b)^3*(sin(x) + 1)^2*(sin(x) - 1)^2)","A",0
13,1,139,0,0.225986," ","integrate(tan(x)^3/(a+b*csc(x)),x, algorithm=""giac"")","\frac{b^{4} \log\left({\left| a \sin\left(x\right) + b \right|}\right)}{a^{5} - 2 \, a^{3} b^{2} + a b^{4}} + \frac{{\left(2 \, a - 3 \, b\right)} \log\left(\sin\left(x\right) + 1\right)}{4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)}} + \frac{{\left(2 \, a + 3 \, b\right)} \log\left(-\sin\left(x\right) + 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{a^{3} - a b^{2} - {\left(a^{2} b - b^{3}\right)} \sin\left(x\right)}{2 \, {\left(a + b\right)}^{2} {\left(a - b\right)}^{2} {\left(\sin\left(x\right) + 1\right)} {\left(\sin\left(x\right) - 1\right)}}"," ",0,"b^4*log(abs(a*sin(x) + b))/(a^5 - 2*a^3*b^2 + a*b^4) + 1/4*(2*a - 3*b)*log(sin(x) + 1)/(a^2 - 2*a*b + b^2) + 1/4*(2*a + 3*b)*log(-sin(x) + 1)/(a^2 + 2*a*b + b^2) - 1/2*(a^3 - a*b^2 - (a^2*b - b^3)*sin(x))/((a + b)^2*(a - b)^2*(sin(x) + 1)*(sin(x) - 1))","A",0
14,1,53,0,0.472874," ","integrate(tan(x)/(a+b*csc(x)),x, algorithm=""giac"")","\frac{b^{2} \log\left({\left| a \sin\left(x\right) + b \right|}\right)}{a^{3} - a b^{2}} - \frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, {\left(a - b\right)}} - \frac{\log\left(-\sin\left(x\right) + 1\right)}{2 \, {\left(a + b\right)}}"," ",0,"b^2*log(abs(a*sin(x) + b))/(a^3 - a*b^2) - 1/2*log(sin(x) + 1)/(a - b) - 1/2*log(-sin(x) + 1)/(a + b)","A",0
15,1,12,0,0.420214," ","integrate(cot(x)/(a+b*csc(x)),x, algorithm=""giac"")","\frac{\log\left({\left| a \sin\left(x\right) + b \right|}\right)}{a}"," ",0,"log(abs(a*sin(x) + b))/a","A",0
16,1,44,0,0.652808," ","integrate(cot(x)^3/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{a \log\left({\left| \sin\left(x\right) \right|}\right)}{b^{2}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left({\left| a \sin\left(x\right) + b \right|}\right)}{a b^{2}} - \frac{1}{b \sin\left(x\right)}"," ",0,"-a*log(abs(sin(x)))/b^2 + (a^2 - b^2)*log(abs(a*sin(x) + b))/(a*b^2) - 1/(b*sin(x))","A",0
17,1,90,0,0.387800," ","integrate(cot(x)^5/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{{\left(a^{3} - 2 \, a b^{2}\right)} \log\left({\left| \sin\left(x\right) \right|}\right)}{b^{4}} + \frac{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| a \sin\left(x\right) + b \right|}\right)}{a b^{4}} + \frac{3 \, a b^{2} \sin\left(x\right) - 2 \, b^{3} - 6 \, {\left(a^{2} b - 2 \, b^{3}\right)} \sin\left(x\right)^{2}}{6 \, b^{4} \sin\left(x\right)^{3}}"," ",0,"-(a^3 - 2*a*b^2)*log(abs(sin(x)))/b^4 + (a^4 - 2*a^2*b^2 + b^4)*log(abs(a*sin(x) + b))/(a*b^4) + 1/6*(3*a*b^2*sin(x) - 2*b^3 - 6*(a^2*b - 2*b^3)*sin(x)^2)/(b^4*sin(x)^3)","A",0
18,1,155,0,0.408274," ","integrate(cot(x)^7/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{{\left(a^{5} - 3 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left({\left| \sin\left(x\right) \right|}\right)}{b^{6}} + \frac{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \log\left({\left| a \sin\left(x\right) + b \right|}\right)}{a b^{6}} + \frac{15 \, a b^{4} \sin\left(x\right) - 12 \, b^{5} - 60 \, {\left(a^{4} b - 3 \, a^{2} b^{3} + 3 \, b^{5}\right)} \sin\left(x\right)^{4} + 30 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(x\right)^{3} - 20 \, {\left(a^{2} b^{3} - 3 \, b^{5}\right)} \sin\left(x\right)^{2}}{60 \, b^{6} \sin\left(x\right)^{5}}"," ",0,"-(a^5 - 3*a^3*b^2 + 3*a*b^4)*log(abs(sin(x)))/b^6 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*log(abs(a*sin(x) + b))/(a*b^6) + 1/60*(15*a*b^4*sin(x) - 12*b^5 - 60*(a^4*b - 3*a^2*b^3 + 3*b^5)*sin(x)^4 + 30*(a^3*b^2 - 3*a*b^4)*sin(x)^3 - 20*(a^2*b^3 - 3*b^5)*sin(x)^2)/(b^6*sin(x)^5)","A",0
19,1,216,0,0.586816," ","integrate(tan(x)^4/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)\right)} b^{5}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{x}{a} + \frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{5} - 6 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{5} + 3 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{4} - 10 \, a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 16 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, a^{3} \tan\left(\frac{1}{2} \, x\right) - 6 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, a^{2} b + 5 \, b^{3}\right)}}{3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)}^{3}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(b) + arctan((b*tan(1/2*x) + a)/sqrt(-a^2 + b^2)))*b^5/((a^5 - 2*a^3*b^2 + a*b^4)*sqrt(-a^2 + b^2)) + x/a + 2/3*(3*a^3*tan(1/2*x)^5 - 6*a*b^2*tan(1/2*x)^5 + 3*b^3*tan(1/2*x)^4 - 10*a^3*tan(1/2*x)^3 + 16*a*b^2*tan(1/2*x)^3 + 6*a^2*b*tan(1/2*x)^2 - 12*b^3*tan(1/2*x)^2 + 3*a^3*tan(1/2*x) - 6*a*b^2*tan(1/2*x) - 2*a^2*b + 5*b^3)/((a^4 - 2*a^2*b^2 + b^4)*(tan(1/2*x)^2 - 1)^3)","A",0
20,1,103,0,0.363506," ","integrate(tan(x)^2/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)\right)} b^{3}}{{\left(a^{3} - a b^{2}\right)} \sqrt{-a^{2} + b^{2}}} - \frac{x}{a} - \frac{2 \, {\left(a \tan\left(\frac{1}{2} \, x\right) - b\right)}}{{\left(a^{2} - b^{2}\right)} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(b) + arctan((b*tan(1/2*x) + a)/sqrt(-a^2 + b^2)))*b^3/((a^3 - a*b^2)*sqrt(-a^2 + b^2)) - x/a - 2*(a*tan(1/2*x) - b)/((a^2 - b^2)*(tan(1/2*x)^2 - 1))","A",0
21,1,80,0,0.313885," ","integrate(cot(x)^2/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{x}{a} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{b} - \frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)\right)} {\left(a^{2} - b^{2}\right)}}{\sqrt{-a^{2} + b^{2}} a b}"," ",0,"-x/a + log(abs(tan(1/2*x)))/b - 2*(pi*floor(1/2*x/pi + 1/2)*sgn(b) + arctan((b*tan(1/2*x) + a)/sqrt(-a^2 + b^2)))*(a^2 - b^2)/(sqrt(-a^2 + b^2)*a*b)","A",0
22,1,163,0,0.380002," ","integrate(cot(x)^4/(a+b*csc(x)),x, algorithm=""giac"")","\frac{x}{a} + \frac{b \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, x\right)}{8 \, b^{2}} + \frac{{\left(2 \, a^{2} - 3 \, b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{2 \, b^{3}} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a b^{3}} - \frac{12 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 18 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, a b \tan\left(\frac{1}{2} \, x\right) + b^{2}}{8 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2}}"," ",0,"x/a + 1/8*(b*tan(1/2*x)^2 - 4*a*tan(1/2*x))/b^2 + 1/2*(2*a^2 - 3*b^2)*log(abs(tan(1/2*x)))/b^3 - 2*(a^4 - 2*a^2*b^2 + b^4)*(pi*floor(1/2*x/pi + 1/2)*sgn(b) + arctan((b*tan(1/2*x) + a)/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a*b^3) - 1/8*(12*a^2*tan(1/2*x)^2 - 18*b^2*tan(1/2*x)^2 - 4*a*b*tan(1/2*x) + b^2)/(b^3*tan(1/2*x)^2)","B",0
23,1,299,0,1.014342," ","integrate(cot(x)^6/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{x}{a} + \frac{3 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{4} - 8 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} - 48 \, b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 96 \, a^{3} \tan\left(\frac{1}{2} \, x\right) + 216 \, a b^{2} \tan\left(\frac{1}{2} \, x\right)}{192 \, b^{4}} + \frac{{\left(8 \, a^{4} - 20 \, a^{2} b^{2} + 15 \, b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{8 \, b^{5}} - \frac{2 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)\right)}}{\sqrt{-a^{2} + b^{2}} a b^{5}} - \frac{400 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{4} - 1000 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 750 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{4} - 96 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{3} + 216 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 24 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 48 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, a b^{3} \tan\left(\frac{1}{2} \, x\right) + 3 \, b^{4}}{192 \, b^{5} \tan\left(\frac{1}{2} \, x\right)^{4}}"," ",0,"-x/a + 1/192*(3*b^3*tan(1/2*x)^4 - 8*a*b^2*tan(1/2*x)^3 + 24*a^2*b*tan(1/2*x)^2 - 48*b^3*tan(1/2*x)^2 - 96*a^3*tan(1/2*x) + 216*a*b^2*tan(1/2*x))/b^4 + 1/8*(8*a^4 - 20*a^2*b^2 + 15*b^4)*log(abs(tan(1/2*x)))/b^5 - 2*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(pi*floor(1/2*x/pi + 1/2)*sgn(b) + arctan((b*tan(1/2*x) + a)/sqrt(-a^2 + b^2)))/(sqrt(-a^2 + b^2)*a*b^5) - 1/192*(400*a^4*tan(1/2*x)^4 - 1000*a^2*b^2*tan(1/2*x)^4 + 750*b^4*tan(1/2*x)^4 - 96*a^3*b*tan(1/2*x)^3 + 216*a*b^3*tan(1/2*x)^3 + 24*a^2*b^2*tan(1/2*x)^2 - 48*b^4*tan(1/2*x)^2 - 8*a*b^3*tan(1/2*x) + 3*b^4)/(b^5*tan(1/2*x)^4)","A",0
