1,1,294,0,1.243729," ","integrate(sin(x)**4/(a+a*cos(x)),x)","\frac{3 x \tan^{6}{\left(\frac{x}{2} \right)}}{6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a} + \frac{9 x \tan^{4}{\left(\frac{x}{2} \right)}}{6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a} + \frac{9 x \tan^{2}{\left(\frac{x}{2} \right)}}{6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a} + \frac{3 x}{6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a} + \frac{6 \tan^{5}{\left(\frac{x}{2} \right)}}{6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a} - \frac{16 \tan^{3}{\left(\frac{x}{2} \right)}}{6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a} - \frac{6 \tan{\left(\frac{x}{2} \right)}}{6 a \tan^{6}{\left(\frac{x}{2} \right)} + 18 a \tan^{4}{\left(\frac{x}{2} \right)} + 18 a \tan^{2}{\left(\frac{x}{2} \right)} + 6 a}"," ",0,"3*x*tan(x/2)**6/(6*a*tan(x/2)**6 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**2 + 6*a) + 9*x*tan(x/2)**4/(6*a*tan(x/2)**6 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**2 + 6*a) + 9*x*tan(x/2)**2/(6*a*tan(x/2)**6 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**2 + 6*a) + 3*x/(6*a*tan(x/2)**6 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**2 + 6*a) + 6*tan(x/2)**5/(6*a*tan(x/2)**6 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**2 + 6*a) - 16*tan(x/2)**3/(6*a*tan(x/2)**6 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**2 + 6*a) - 6*tan(x/2)/(6*a*tan(x/2)**6 + 18*a*tan(x/2)**4 + 18*a*tan(x/2)**2 + 6*a)","B",0
2,1,51,0,0.664450," ","integrate(sin(x)**3/(a+a*cos(x)),x)","- \frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{a \tan^{4}{\left(\frac{x}{2} \right)} + 2 a \tan^{2}{\left(\frac{x}{2} \right)} + a} - \frac{2}{a \tan^{4}{\left(\frac{x}{2} \right)} + 2 a \tan^{2}{\left(\frac{x}{2} \right)} + a}"," ",0,"-4*tan(x/2)**2/(a*tan(x/2)**4 + 2*a*tan(x/2)**2 + a) - 2/(a*tan(x/2)**4 + 2*a*tan(x/2)**2 + a)","B",0
3,1,46,0,0.373451," ","integrate(sin(x)**2/(a+a*cos(x)),x)","\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{a \tan^{2}{\left(\frac{x}{2} \right)} + a} + \frac{x}{a \tan^{2}{\left(\frac{x}{2} \right)} + a} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{a \tan^{2}{\left(\frac{x}{2} \right)} + a}"," ",0,"x*tan(x/2)**2/(a*tan(x/2)**2 + a) + x/(a*tan(x/2)**2 + a) - 2*tan(x/2)/(a*tan(x/2)**2 + a)","B",0
4,1,8,0,0.123405," ","integrate(sin(x)/(a+a*cos(x)),x)","- \frac{\log{\left(\cos{\left(x \right)} + 1 \right)}}{a}"," ",0,"-log(cos(x) + 1)/a","A",0
5,1,5,0,0.177068," ","integrate(1/(a+a*cos(x)),x)","\frac{\tan{\left(\frac{x}{2} \right)}}{a}"," ",0,"tan(x/2)/a","A",0
6,0,0,0,0.000000," ","integrate(csc(x)/(a+a*cos(x)),x)","\frac{\int \frac{\csc{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)/(cos(x) + 1), x)/a","F",0
7,0,0,0,0.000000," ","integrate(csc(x)**2/(a+a*cos(x)),x)","\frac{\int \frac{\csc^{2}{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)**2/(cos(x) + 1), x)/a","F",0
8,0,0,0,0.000000," ","integrate(csc(x)**3/(a+a*cos(x)),x)","\frac{\int \frac{\csc^{3}{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)**3/(cos(x) + 1), x)/a","F",0
9,0,0,0,0.000000," ","integrate(csc(x)**4/(a+a*cos(x)),x)","\frac{\int \frac{\csc^{4}{\left(x \right)}}{\cos{\left(x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(x)**4/(cos(x) + 1), x)/a","F",0
10,1,10,0,0.106022," ","integrate(sin(2*x)/(1+cos(2*x)),x)","- \frac{\log{\left(\cos{\left(2 x \right)} + 1 \right)}}{2}"," ",0,"-log(cos(2*x) + 1)/2","A",0
11,1,8,0,0.109932," ","integrate(sin(2*x)/(1-cos(2*x)),x)","\frac{\log{\left(\cos{\left(2 x \right)} - 1 \right)}}{2}"," ",0,"log(cos(2*x) - 1)/2","B",0
12,1,5,0,0.320167," ","integrate(sin(x)/(1+cos(x))**2,x)","\frac{1}{\cos{\left(x \right)} + 1}"," ",0,"1/(cos(x) + 1)","A",0
13,1,5,0,0.323196," ","integrate(sin(x)/(1-cos(x))**2,x)","\frac{1}{\cos{\left(x \right)} - 1}"," ",0,"1/(cos(x) - 1)","A",0
14,1,7,0,0.464394," ","integrate(sin(x)**2/(1+cos(x))**2,x)","- x + 2 \tan{\left(\frac{x}{2} \right)}"," ",0,"-x + 2*tan(x/2)","A",0
15,1,8,0,0.875237," ","integrate(sin(x)**2/(1-cos(x))**2,x)","- x - \frac{2}{\tan{\left(\frac{x}{2} \right)}}"," ",0,"-x - 2/tan(x/2)","A",0
16,1,58,0,0.461366," ","integrate(sin(x)**3/(1+cos(x))**2,x)","- \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{\cos{\left(x \right)} + 1} + \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{2 \cos^{2}{\left(x \right)}}{\cos{\left(x \right)} + 1} - \frac{2}{\cos{\left(x \right)} + 1}"," ",0,"-2*log(cos(x) + 1)*cos(x)/(cos(x) + 1) - 2*log(cos(x) + 1)/(cos(x) + 1) + sin(x)**2/(cos(x) + 1) + 2*cos(x)**2/(cos(x) + 1) - 2/(cos(x) + 1)","B",0
17,1,58,0,0.471487," ","integrate(sin(x)**3/(1-cos(x))**2,x)","\frac{2 \log{\left(\cos{\left(x \right)} - 1 \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} - 1} - \frac{2 \log{\left(\cos{\left(x \right)} - 1 \right)}}{\cos{\left(x \right)} - 1} + \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{2 \cos^{2}{\left(x \right)}}{\cos{\left(x \right)} - 1} - \frac{2}{\cos{\left(x \right)} - 1}"," ",0,"2*log(cos(x) - 1)*cos(x)/(cos(x) - 1) - 2*log(cos(x) - 1)/(cos(x) - 1) + sin(x)**2/(cos(x) - 1) + 2*cos(x)**2/(cos(x) - 1) - 2/(cos(x) - 1)","B",0
18,1,14,0,0.547875," ","integrate(sin(x)/(1+cos(x))**3,x)","\frac{1}{2 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 2}"," ",0,"1/(2*cos(x)**2 + 4*cos(x) + 2)","A",0
19,1,15,0,0.551275," ","integrate(sin(x)/(1-cos(x))**3,x)","- \frac{1}{2 \cos^{2}{\left(x \right)} - 4 \cos{\left(x \right)} + 2}"," ",0,"-1/(2*cos(x)**2 - 4*cos(x) + 2)","A",0
20,1,7,0,0.793813," ","integrate(sin(x)**2/(1+cos(x))**3,x)","\frac{\tan^{3}{\left(\frac{x}{2} \right)}}{3}"," ",0,"tan(x/2)**3/3","A",0
21,1,10,0,1.332058," ","integrate(sin(x)**2/(1-cos(x))**3,x)","- \frac{1}{3 \tan^{3}{\left(\frac{x}{2} \right)}}"," ",0,"-1/(3*tan(x/2)**3)","A",0
22,1,126,0,0.585154," ","integrate(sin(x)**3/(1+cos(x))**3,x)","\frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)} \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 2} + \frac{4 \log{\left(\cos{\left(x \right)} + 1 \right)} \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 2} + \frac{2 \log{\left(\cos{\left(x \right)} + 1 \right)}}{2 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 2} + \frac{\sin^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 2} + \frac{2 \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 2} + \frac{2}{2 \cos^{2}{\left(x \right)} + 4 \cos{\left(x \right)} + 2}"," ",0,"2*log(cos(x) + 1)*cos(x)**2/(2*cos(x)**2 + 4*cos(x) + 2) + 4*log(cos(x) + 1)*cos(x)/(2*cos(x)**2 + 4*cos(x) + 2) + 2*log(cos(x) + 1)/(2*cos(x)**2 + 4*cos(x) + 2) + sin(x)**2/(2*cos(x)**2 + 4*cos(x) + 2) + 2*cos(x)/(2*cos(x)**2 + 4*cos(x) + 2) + 2/(2*cos(x)**2 + 4*cos(x) + 2)","B",0
23,1,126,0,0.584096," ","integrate(sin(x)**3/(1-cos(x))**3,x)","- \frac{2 \log{\left(\cos{\left(x \right)} - 1 \right)} \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 4 \cos{\left(x \right)} + 2} + \frac{4 \log{\left(\cos{\left(x \right)} - 1 \right)} \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 4 \cos{\left(x \right)} + 2} - \frac{2 \log{\left(\cos{\left(x \right)} - 1 \right)}}{2 \cos^{2}{\left(x \right)} - 4 \cos{\left(x \right)} + 2} - \frac{\sin^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 4 \cos{\left(x \right)} + 2} + \frac{2 \cos{\left(x \right)}}{2 \cos^{2}{\left(x \right)} - 4 \cos{\left(x \right)} + 2} - \frac{2}{2 \cos^{2}{\left(x \right)} - 4 \cos{\left(x \right)} + 2}"," ",0,"-2*log(cos(x) - 1)*cos(x)**2/(2*cos(x)**2 - 4*cos(x) + 2) + 4*log(cos(x) - 1)*cos(x)/(2*cos(x)**2 - 4*cos(x) + 2) - 2*log(cos(x) - 1)/(2*cos(x)**2 - 4*cos(x) + 2) - sin(x)**2/(2*cos(x)**2 - 4*cos(x) + 2) + 2*cos(x)/(2*cos(x)**2 - 4*cos(x) + 2) - 2/(2*cos(x)**2 - 4*cos(x) + 2)","B",0
24,-1,0,0,0.000000," ","integrate(sin(x)**4/(a+b*cos(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate(sin(x)**3/(a+b*cos(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,1,991,0,88.657099," ","integrate(sin(x)**2/(a+b*cos(x)),x)","\begin{cases} \tilde{\infty} \left(- \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) & \text{for}\: a = 0 \wedge b = 0 \\- \frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{b \tan^{2}{\left(\frac{x}{2} \right)} + b} - \frac{x}{b \tan^{2}{\left(\frac{x}{2} \right)} + b} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{b \tan^{2}{\left(\frac{x}{2} \right)} + b} & \text{for}\: a = - b \\\frac{\frac{x \sin^{2}{\left(x \right)}}{2} + \frac{x \cos^{2}{\left(x \right)}}{2} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}}{a} & \text{for}\: b = 0 \\\frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{b \tan^{2}{\left(\frac{x}{2} \right)} + b} + \frac{x}{b \tan^{2}{\left(\frac{x}{2} \right)} + b} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{b \tan^{2}{\left(\frac{x}{2} \right)} + b} & \text{for}\: a = b \\\frac{a x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a x \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{2 b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan{\left(\frac{x}{2} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \tan^{2}{\left(\frac{x}{2} \right)} + b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-log(tan(x/2) - 1)*tan(x/2)**2/(tan(x/2)**2 + 1) - log(tan(x/2) - 1)/(tan(x/2)**2 + 1) + log(tan(x/2) + 1)*tan(x/2)**2/(tan(x/2)**2 + 1) + log(tan(x/2) + 1)/(tan(x/2)**2 + 1) - 2*tan(x/2)/(tan(x/2)**2 + 1)), Eq(a, 0) & Eq(b, 0)), (-x*tan(x/2)**2/(b*tan(x/2)**2 + b) - x/(b*tan(x/2)**2 + b) - 2*tan(x/2)/(b*tan(x/2)**2 + b), Eq(a, -b)), ((x*sin(x)**2/2 + x*cos(x)**2/2 - sin(x)*cos(x)/2)/a, Eq(b, 0)), (x*tan(x/2)**2/(b*tan(x/2)**2 + b) + x/(b*tan(x/2)**2 + b) - 2*tan(x/2)/(b*tan(x/2)**2 + b), Eq(a, b)), (a*x*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) + a*x*sqrt(-a/(a - b) - b/(a - b))/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) - a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))*tan(x/2)**2/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) - a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) + a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))*tan(x/2)**2/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) + a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) - 2*b*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) - b*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))*tan(x/2)**2/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) - b*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) + b*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))*tan(x/2)**2/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))) + b*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(b**2*sqrt(-a/(a - b) - b/(a - b))*tan(x/2)**2 + b**2*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
27,1,17,0,0.288530," ","integrate(sin(x)/(a+b*cos(x)),x)","\begin{cases} - \frac{\log{\left(\frac{a}{b} + \cos{\left(x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\- \frac{\cos{\left(x \right)}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(a/b + cos(x))/b, Ne(b, 0)), (-cos(x)/a, True))","A",0
28,1,144,0,3.393876," ","integrate(1/(a+b*cos(x)),x)","\begin{cases} \tilde{\infty} \left(- \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{1}{b \tan{\left(\frac{x}{2} \right)}} & \text{for}\: a = - b \\\frac{\tan{\left(\frac{x}{2} \right)}}{b} & \text{for}\: a = b \\\frac{\log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{\log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-log(tan(x/2) - 1) + log(tan(x/2) + 1)), Eq(a, 0) & Eq(b, 0)), (1/(b*tan(x/2)), Eq(a, -b)), (tan(x/2)/b, Eq(a, b)), (log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*sqrt(-a/(a - b) - b/(a - b)) - b*sqrt(-a/(a - b) - b/(a - b))) - log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*sqrt(-a/(a - b) - b/(a - b)) - b*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
29,0,0,0,0.000000," ","integrate(csc(x)/(a+b*cos(x)),x)","\int \frac{\csc{\left(x \right)}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)/(a + b*cos(x)), x)","F",0
30,0,0,0,0.000000," ","integrate(csc(x)**2/(a+b*cos(x)),x)","\int \frac{\csc^{2}{\left(x \right)}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**2/(a + b*cos(x)), x)","F",0
31,0,0,0,0.000000," ","integrate(csc(x)**3/(a+b*cos(x)),x)","\int \frac{\csc^{3}{\left(x \right)}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**3/(a + b*cos(x)), x)","F",0
32,0,0,0,0.000000," ","integrate(csc(x)**4/(a+b*cos(x)),x)","\int \frac{\csc^{4}{\left(x \right)}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**4/(a + b*cos(x)), x)","F",0
33,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))**(3/2),x)","\int \left(e \sin{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cos{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*sin(c + d*x))**(3/2)*(a + b*cos(c + d*x)), x)","F",0
36,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))*(e*sin(d*x+c))**(1/2),x)","\int \sqrt{e \sin{\left(c + d x \right)}} \left(a + b \cos{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(e*sin(c + d*x))*(a + b*cos(c + d*x)), x)","F",0
37,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))**(1/2),x)","\int \frac{a + b \cos{\left(c + d x \right)}}{\sqrt{e \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))/sqrt(e*sin(c + d*x)), x)","F",0
38,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))**(3/2),x)","\int \frac{a + b \cos{\left(c + d x \right)}}{\left(e \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))/(e*sin(c + d*x))**(3/2), x)","F",0
39,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))**(5/2),x)","\int \frac{a + b \cos{\left(c + d x \right)}}{\left(e \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))/(e*sin(c + d*x))**(5/2), x)","F",0
40,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))/(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(e*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(e*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2*(e*sin(d*x+c))**(1/2),x)","\int \sqrt{e \sin{\left(c + d x \right)}} \left(a + b \cos{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(e*sin(c + d*x))*(a + b*cos(c + d*x))**2, x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}{\sqrt{e \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2/sqrt(e*sin(c + d*x)), x)","F",0
46,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(3/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{2}}{\left(e \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**2/(e*sin(c + d*x))**(3/2), x)","F",0
47,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(e*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(e*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3*(e*sin(d*x+c))**(1/2),x)","\int \sqrt{e \sin{\left(c + d x \right)}} \left(a + b \cos{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral(sqrt(e*sin(c + d*x))*(a + b*cos(c + d*x))**3, x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(1/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}{\sqrt{e \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3/sqrt(e*sin(c + d*x)), x)","F",0
54,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(3/2),x)","\int \frac{\left(a + b \cos{\left(c + d x \right)}\right)^{3}}{\left(e \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cos(c + d*x))**3/(e*sin(c + d*x))**(3/2), x)","F",0
55,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(11/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(9/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(7/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(5/2)/(a+b*cos(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,0,0,0,0.000000," ","integrate((e*sin(d*x+c))**(3/2)/(a+b*cos(d*x+c)),x)","\int \frac{\left(e \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((e*sin(c + d*x))**(3/2)/(a + b*cos(c + d*x)), x)","F",0
63,0,0,0,0.000000," ","integrate((e*sin(d*x+c))**(1/2)/(a+b*cos(d*x+c)),x)","\int \frac{\sqrt{e \sin{\left(c + d x \right)}}}{a + b \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(e*sin(c + d*x))/(a + b*cos(c + d*x)), x)","F",0
64,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{e \sin{\left(c + d x \right)}} \left(a + b \cos{\left(c + d x \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(e*sin(c + d*x))*(a + b*cos(c + d*x))), x)","F",0
65,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(e \sin{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cos{\left(c + d x \right)}\right)}\, dx"," ",0,"Integral(1/((e*sin(c + d*x))**(3/2)*(a + b*cos(c + d*x))), x)","F",0
66,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))**(5/2),x)","\int \frac{1}{\left(e \sin{\left(c + d x \right)}\right)^{\frac{5}{2}} \left(a + b \cos{\left(c + d x \right)}\right)}\, dx"," ",0,"Integral(1/((e*sin(c + d*x))**(5/2)*(a + b*cos(c + d*x))), x)","F",0
67,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(11/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(9/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(7/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(5/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(3/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(1/2)/(a+b*cos(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**2/(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(13/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(11/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(9/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(7/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(5/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(3/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate((e*sin(d*x+c))**(1/2)/(a+b*cos(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c))**3/(e*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
