1,1,50,0,0.792835," ","integrate(tan(x)^4/(a+a*cos(x)),x, algorithm=""fricas"")","\frac{3 \, \cos\left(x\right)^{3} \log\left(\sin\left(x\right) + 1\right) - 3 \, \cos\left(x\right)^{3} \log\left(-\sin\left(x\right) + 1\right) - 2 \, {\left(2 \, \cos\left(x\right)^{2} + 3 \, \cos\left(x\right) - 2\right)} \sin\left(x\right)}{12 \, a \cos\left(x\right)^{3}}"," ",0,"1/12*(3*cos(x)^3*log(sin(x) + 1) - 3*cos(x)^3*log(-sin(x) + 1) - 2*(2*cos(x)^2 + 3*cos(x) - 2)*sin(x))/(a*cos(x)^3)","A",0
2,1,15,0,0.736279," ","integrate(tan(x)^3/(a+a*cos(x)),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(x\right) - 1}{2 \, a \cos\left(x\right)^{2}}"," ",0,"-1/2*(2*cos(x) - 1)/(a*cos(x)^2)","A",0
3,1,33,0,0.844073," ","integrate(tan(x)^2/(a+a*cos(x)),x, algorithm=""fricas"")","-\frac{\cos\left(x\right) \log\left(\sin\left(x\right) + 1\right) - \cos\left(x\right) \log\left(-\sin\left(x\right) + 1\right) - 2 \, \sin\left(x\right)}{2 \, a \cos\left(x\right)}"," ",0,"-1/2*(cos(x)*log(sin(x) + 1) - cos(x)*log(-sin(x) + 1) - 2*sin(x))/(a*cos(x))","B",0
4,1,20,0,0.571187," ","integrate(tan(x)/(a+a*cos(x)),x, algorithm=""fricas"")","-\frac{\log\left(-\cos\left(x\right)\right) - \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{a}"," ",0,"-(log(-cos(x)) - log(1/2*cos(x) + 1/2))/a","A",0
5,1,37,0,0.597284," ","integrate(cot(x)/(a+a*cos(x)),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(\cos\left(x\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 2}{4 \, {\left(a \cos\left(x\right) + a\right)}}"," ",0,"-1/4*((cos(x) + 1)*log(1/2*cos(x) + 1/2) - (cos(x) + 1)*log(-1/2*cos(x) + 1/2) + 2)/(a*cos(x) + a)","A",0
6,1,24,0,0.785752," ","integrate(cot(x)^2/(a+a*cos(x)),x, algorithm=""fricas"")","\frac{\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 2}{3 \, {\left(a \cos\left(x\right) + a\right)} \sin\left(x\right)}"," ",0,"1/3*(cos(x)^2 - 2*cos(x) - 2)/((a*cos(x) + a)*sin(x))","A",0
7,1,83,0,1.269445," ","integrate(cot(x)^3/(a+a*cos(x)),x, algorithm=""fricas"")","\frac{10 \, \cos\left(x\right)^{2} + 3 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)^{2} - \cos\left(x\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(x\right)^{3} + \cos\left(x\right)^{2} - \cos\left(x\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + 2 \, \cos\left(x\right) - 4}{16 \, {\left(a \cos\left(x\right)^{3} + a \cos\left(x\right)^{2} - a \cos\left(x\right) - a\right)}}"," ",0,"1/16*(10*cos(x)^2 + 3*(cos(x)^3 + cos(x)^2 - cos(x) - 1)*log(1/2*cos(x) + 1/2) - 3*(cos(x)^3 + cos(x)^2 - cos(x) - 1)*log(-1/2*cos(x) + 1/2) + 2*cos(x) - 4)/(a*cos(x)^3 + a*cos(x)^2 - a*cos(x) - a)","B",0
8,1,53,0,2.404605," ","integrate(cot(x)^4/(a+a*cos(x)),x, algorithm=""fricas"")","-\frac{3 \, \cos\left(x\right)^{4} - 12 \, \cos\left(x\right)^{3} - 12 \, \cos\left(x\right)^{2} + 8 \, \cos\left(x\right) + 8}{15 \, {\left(a \cos\left(x\right)^{3} + a \cos\left(x\right)^{2} - a \cos\left(x\right) - a\right)} \sin\left(x\right)}"," ",0,"-1/15*(3*cos(x)^4 - 12*cos(x)^3 - 12*cos(x)^2 + 8*cos(x) + 8)/((a*cos(x)^3 + a*cos(x)^2 - a*cos(x) - a)*sin(x))","A",0
9,1,43,0,1.708098," ","integrate(tan(3*x)/(1+cos(3*x))^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(3 \, x\right) + 1\right)} \log\left(-\cos\left(3 \, x\right)\right) - {\left(\cos\left(3 \, x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(3 \, x\right) + \frac{1}{2}\right) + 1}{3 \, {\left(\cos\left(3 \, x\right) + 1\right)}}"," ",0,"-1/3*((cos(3*x) + 1)*log(-cos(3*x)) - (cos(3*x) + 1)*log(1/2*cos(3*x) + 1/2) + 1)/(cos(3*x) + 1)","A",0
10,1,332,0,1.213534," ","integrate(tan(x)^4/(a+b*cos(x)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}} \cos\left(x\right)^{3} \log\left(\frac{2 \, a b \cos\left(x\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(x\right) + b\right)} \sin\left(x\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + a^{2}}\right) - 3 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(x\right)^{3} \log\left(\sin\left(x\right) + 1\right) + 3 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(x\right)^{3} \log\left(-\sin\left(x\right) + 1\right) + 2 \, {\left(3 \, a^{2} b \cos\left(x\right) - 2 \, a^{3} + 2 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{12 \, a^{4} \cos\left(x\right)^{3}}, \frac{12 \, {\left(a^{2} - b^{2}\right)}^{\frac{3}{2}} \arctan\left(-\frac{a \cos\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(x\right)}\right) \cos\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(x\right)^{3} \log\left(\sin\left(x\right) + 1\right) - 3 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(x\right)^{3} \log\left(-\sin\left(x\right) + 1\right) - 2 \, {\left(3 \, a^{2} b \cos\left(x\right) - 2 \, a^{3} + 2 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}{12 \, a^{4} \cos\left(x\right)^{3}}\right]"," ",0,"[-1/12*(6*(a^2 - b^2)*sqrt(-a^2 + b^2)*cos(x)^3*log((2*a*b*cos(x) + (2*a^2 - b^2)*cos(x)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(x) + b)*sin(x) - a^2 + 2*b^2)/(b^2*cos(x)^2 + 2*a*b*cos(x) + a^2)) - 3*(3*a^2*b - 2*b^3)*cos(x)^3*log(sin(x) + 1) + 3*(3*a^2*b - 2*b^3)*cos(x)^3*log(-sin(x) + 1) + 2*(3*a^2*b*cos(x) - 2*a^3 + 2*(4*a^3 - 3*a*b^2)*cos(x)^2)*sin(x))/(a^4*cos(x)^3), 1/12*(12*(a^2 - b^2)^(3/2)*arctan(-(a*cos(x) + b)/(sqrt(a^2 - b^2)*sin(x)))*cos(x)^3 + 3*(3*a^2*b - 2*b^3)*cos(x)^3*log(sin(x) + 1) - 3*(3*a^2*b - 2*b^3)*cos(x)^3*log(-sin(x) + 1) - 2*(3*a^2*b*cos(x) - 2*a^3 + 2*(4*a^3 - 3*a*b^2)*cos(x)^2)*sin(x))/(a^4*cos(x)^3)]","A",0
11,1,66,0,0.927508," ","integrate(tan(x)^3/(a+b*cos(x)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} \log\left(-b \cos\left(x\right) - a\right) - 2 \, {\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} \log\left(-\cos\left(x\right)\right) + 2 \, a b \cos\left(x\right) - a^{2}}{2 \, a^{3} \cos\left(x\right)^{2}}"," ",0,"-1/2*(2*(a^2 - b^2)*cos(x)^2*log(-b*cos(x) - a) - 2*(a^2 - b^2)*cos(x)^2*log(-cos(x)) + 2*a*b*cos(x) - a^2)/(a^3*cos(x)^2)","A",0
12,1,203,0,0.947551," ","integrate(tan(x)^2/(a+b*cos(x)),x, algorithm=""fricas"")","\left[-\frac{b \cos\left(x\right) \log\left(\sin\left(x\right) + 1\right) - b \cos\left(x\right) \log\left(-\sin\left(x\right) + 1\right) - \sqrt{-a^{2} + b^{2}} \cos\left(x\right) \log\left(\frac{2 \, a b \cos\left(x\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(x\right) + b\right)} \sin\left(x\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + a^{2}}\right) - 2 \, a \sin\left(x\right)}{2 \, a^{2} \cos\left(x\right)}, -\frac{b \cos\left(x\right) \log\left(\sin\left(x\right) + 1\right) - b \cos\left(x\right) \log\left(-\sin\left(x\right) + 1\right) + 2 \, \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(x\right)}\right) \cos\left(x\right) - 2 \, a \sin\left(x\right)}{2 \, a^{2} \cos\left(x\right)}\right]"," ",0,"[-1/2*(b*cos(x)*log(sin(x) + 1) - b*cos(x)*log(-sin(x) + 1) - sqrt(-a^2 + b^2)*cos(x)*log((2*a*b*cos(x) + (2*a^2 - b^2)*cos(x)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(x) + b)*sin(x) - a^2 + 2*b^2)/(b^2*cos(x)^2 + 2*a*b*cos(x) + a^2)) - 2*a*sin(x))/(a^2*cos(x)), -1/2*(b*cos(x)*log(sin(x) + 1) - b*cos(x)*log(-sin(x) + 1) + 2*sqrt(a^2 - b^2)*arctan(-(a*cos(x) + b)/(sqrt(a^2 - b^2)*sin(x)))*cos(x) - 2*a*sin(x))/(a^2*cos(x))]","A",0
13,1,22,0,0.648777," ","integrate(tan(x)/(a+b*cos(x)),x, algorithm=""fricas"")","\frac{\log\left(-b \cos\left(x\right) - a\right) - \log\left(-\cos\left(x\right)\right)}{a}"," ",0,"(log(-b*cos(x) - a) - log(-cos(x)))/a","A",0
14,1,53,0,0.926040," ","integrate(cot(x)/(a+b*cos(x)),x, algorithm=""fricas"")","-\frac{2 \, a \log\left(-b \cos\left(x\right) - a\right) - {\left(a + b\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) - {\left(a - b\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{2 \, {\left(a^{2} - b^{2}\right)}}"," ",0,"-1/2*(2*a*log(-b*cos(x) - a) - (a + b)*log(1/2*cos(x) + 1/2) - (a - b)*log(-1/2*cos(x) + 1/2))/(a^2 - b^2)","A",0
15,1,230,0,0.846917," ","integrate(cot(x)^2/(a+b*cos(x)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} a^{2} \log\left(\frac{2 \, a b \cos\left(x\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(x\right) + b\right)} \sin\left(x\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + a^{2}}\right) \sin\left(x\right) + 2 \, a^{2} b - 2 \, b^{3} - 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(x\right)}{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)}, -\frac{\sqrt{a^{2} - b^{2}} a^{2} \arctan\left(-\frac{a \cos\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(x\right)}\right) \sin\left(x\right) - a^{2} b + b^{3} + {\left(a^{3} - a b^{2}\right)} \cos\left(x\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*a^2*log((2*a*b*cos(x) + (2*a^2 - b^2)*cos(x)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(x) + b)*sin(x) - a^2 + 2*b^2)/(b^2*cos(x)^2 + 2*a*b*cos(x) + a^2))*sin(x) + 2*a^2*b - 2*b^3 - 2*(a^3 - a*b^2)*cos(x))/((a^4 - 2*a^2*b^2 + b^4)*sin(x)), -(sqrt(a^2 - b^2)*a^2*arctan(-(a*cos(x) + b)/(sqrt(a^2 - b^2)*sin(x)))*sin(x) - a^2*b + b^3 + (a^3 - a*b^2)*cos(x))/((a^4 - 2*a^2*b^2 + b^4)*sin(x))]","A",0
16,1,185,0,0.594643," ","integrate(cot(x)^3/(a+b*cos(x)),x, algorithm=""fricas"")","-\frac{2 \, a^{3} - 2 \, a b^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(x\right) + 4 \, {\left(a^{3} \cos\left(x\right)^{2} - a^{3}\right)} \log\left(-b \cos\left(x\right) - a\right) + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3} - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cos\left(x\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right) + {\left(2 \, a^{3} - 3 \, a^{2} b + b^{3} - {\left(2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cos\left(x\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2}\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(x\right)^{2}\right)}}"," ",0,"-1/4*(2*a^3 - 2*a*b^2 - 2*(a^2*b - b^3)*cos(x) + 4*(a^3*cos(x)^2 - a^3)*log(-b*cos(x) - a) + (2*a^3 + 3*a^2*b - b^3 - (2*a^3 + 3*a^2*b - b^3)*cos(x)^2)*log(1/2*cos(x) + 1/2) + (2*a^3 - 3*a^2*b + b^3 - (2*a^3 - 3*a^2*b + b^3)*cos(x)^2)*log(-1/2*cos(x) + 1/2))/(a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^2*b^2 + b^4)*cos(x)^2)","B",0
17,1,456,0,0.910967," ","integrate(cot(x)^4/(a+b*cos(x)),x, algorithm=""fricas"")","\left[-\frac{10 \, a^{4} b - 14 \, a^{2} b^{3} + 4 \, b^{5} + 2 \, {\left(4 \, a^{5} - 5 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} - 3 \, {\left(a^{4} \cos\left(x\right)^{2} - a^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{2 \, a b \cos\left(x\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(x\right)^{2} + 2 \, \sqrt{-a^{2} + b^{2}} {\left(a \cos\left(x\right) + b\right)} \sin\left(x\right) - a^{2} + 2 \, b^{2}}{b^{2} \cos\left(x\right)^{2} + 2 \, a b \cos\left(x\right) + a^{2}}\right) \sin\left(x\right) - 6 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2} - 6 \, {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(x\right)}{6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}, -\frac{5 \, a^{4} b - 7 \, a^{2} b^{3} + 2 \, b^{5} + {\left(4 \, a^{5} - 5 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(x\right)^{3} + 3 \, {\left(a^{4} \cos\left(x\right)^{2} - a^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \cos\left(x\right) + b}{\sqrt{a^{2} - b^{2}} \sin\left(x\right)}\right) \sin\left(x\right) - 3 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} \cos\left(x\right)^{2} - 3 \, {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(x\right)}{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} - {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(x\right)^{2}\right)} \sin\left(x\right)}\right]"," ",0,"[-1/6*(10*a^4*b - 14*a^2*b^3 + 4*b^5 + 2*(4*a^5 - 5*a^3*b^2 + a*b^4)*cos(x)^3 - 3*(a^4*cos(x)^2 - a^4)*sqrt(-a^2 + b^2)*log((2*a*b*cos(x) + (2*a^2 - b^2)*cos(x)^2 + 2*sqrt(-a^2 + b^2)*(a*cos(x) + b)*sin(x) - a^2 + 2*b^2)/(b^2*cos(x)^2 + 2*a*b*cos(x) + a^2))*sin(x) - 6*(2*a^4*b - 3*a^2*b^3 + b^5)*cos(x)^2 - 6*(a^5 - a^3*b^2)*cos(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(x)^2)*sin(x)), -1/3*(5*a^4*b - 7*a^2*b^3 + 2*b^5 + (4*a^5 - 5*a^3*b^2 + a*b^4)*cos(x)^3 + 3*(a^4*cos(x)^2 - a^4)*sqrt(a^2 - b^2)*arctan(-(a*cos(x) + b)/(sqrt(a^2 - b^2)*sin(x)))*sin(x) - 3*(2*a^4*b - 3*a^2*b^3 + b^5)*cos(x)^2 - 3*(a^5 - a^3*b^2)*cos(x))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(x)^2)*sin(x))]","A",0
18,1,77,0,0.864030," ","integrate(cot(x)/(3-cos(x))^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{\cos\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cos\left(x\right) - 5 \, \sqrt{2}\right)} \sqrt{-\cos\left(x\right) + 3} - 18 \, \cos\left(x\right) + 49}{\cos\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1}\right) + \frac{1}{4} \, \log\left(-\frac{4 \, \sqrt{-\cos\left(x\right) + 3} + \cos\left(x\right) - 7}{\cos\left(x\right) + 1}\right)"," ",0,"1/8*sqrt(2)*log((cos(x)^2 + 4*(sqrt(2)*cos(x) - 5*sqrt(2))*sqrt(-cos(x) + 3) - 18*cos(x) + 49)/(cos(x)^2 - 2*cos(x) + 1)) + 1/4*log(-(4*sqrt(-cos(x) + 3) + cos(x) - 7)/(cos(x) + 1))","B",0
19,1,109,0,1.338308," ","integrate((a+b*cos(x))^(1/2)*tan(x),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{a} \log\left(-\frac{b^{2} \cos\left(x\right)^{2} + 8 \, a b \cos\left(x\right) + 4 \, {\left(b \cos\left(x\right) + 2 \, a\right)} \sqrt{b \cos\left(x\right) + a} \sqrt{a} + 8 \, a^{2}}{\cos\left(x\right)^{2}}\right) - 2 \, \sqrt{b \cos\left(x\right) + a}, -\sqrt{-a} \arctan\left(\frac{2 \, \sqrt{b \cos\left(x\right) + a} \sqrt{-a}}{b \cos\left(x\right) + 2 \, a}\right) - 2 \, \sqrt{b \cos\left(x\right) + a}\right]"," ",0,"[1/2*sqrt(a)*log(-(b^2*cos(x)^2 + 8*a*b*cos(x) + 4*(b*cos(x) + 2*a)*sqrt(b*cos(x) + a)*sqrt(a) + 8*a^2)/cos(x)^2) - 2*sqrt(b*cos(x) + a), -sqrt(-a)*arctan(2*sqrt(b*cos(x) + a)*sqrt(-a)/(b*cos(x) + 2*a)) - 2*sqrt(b*cos(x) + a)]","A",0
20,1,98,0,0.705248," ","integrate(tan(x)/(a+b*cos(x))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b^{2} \cos\left(x\right)^{2} + 8 \, a b \cos\left(x\right) + 4 \, {\left(b \cos\left(x\right) + 2 \, a\right)} \sqrt{b \cos\left(x\right) + a} \sqrt{a} + 8 \, a^{2}}{\cos\left(x\right)^{2}}\right)}{2 \, \sqrt{a}}, -\frac{\sqrt{-a} \arctan\left(\frac{{\left(b \cos\left(x\right) + 2 \, a\right)} \sqrt{b \cos\left(x\right) + a} \sqrt{-a}}{2 \, {\left(a b \cos\left(x\right) + a^{2}\right)}}\right)}{a}\right]"," ",0,"[1/2*log((b^2*cos(x)^2 + 8*a*b*cos(x) + 4*(b*cos(x) + 2*a)*sqrt(b*cos(x) + a)*sqrt(a) + 8*a^2)/cos(x)^2)/sqrt(a), -sqrt(-a)*arctan(1/2*(b*cos(x) + 2*a)*sqrt(b*cos(x) + a)*sqrt(-a)/(a*b*cos(x) + a^2))/a]","B",0
21,-1,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,0,0,0,3.214662," ","integrate((a+b*cos(f*x+e))^m*(g*tan(f*x+e))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(f x + e\right) + a\right)}^{m} \left(g \tan\left(f x + e\right)\right)^{p}, x\right)"," ",0,"integral((b*cos(f*x + e) + a)^m*(g*tan(f*x + e))^p, x)","F",0
