1,1,688,0,22.860676," ","integrate((A+B*sin(x))/(a+b*cos(x)),x)","\begin{cases} \tilde{\infty} \left(- A \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + A \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - B \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} - B \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} + B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{A \tan{\left(\frac{x}{2} \right)}}{b} + \frac{B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b} & \text{for}\: a = b \\\frac{A}{b \tan{\left(\frac{x}{2} \right)}} + \frac{B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b} - \frac{2 B \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{b} & \text{for}\: a = - b \\\frac{A x - B \cos{\left(x \right)}}{a} & \text{for}\: b = 0 \\\frac{A b \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{A b \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{B a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{B a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{B a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{B b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{B b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{B b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-A*log(tan(x/2) - 1) + A*log(tan(x/2) + 1) - B*log(tan(x/2) - 1) - B*log(tan(x/2) + 1) + B*log(tan(x/2)**2 + 1)), Eq(a, 0) & Eq(b, 0)), (A*tan(x/2)/b + B*log(tan(x/2)**2 + 1)/b, Eq(a, b)), (A/(b*tan(x/2)) + B*log(tan(x/2)**2 + 1)/b - 2*B*log(tan(x/2))/b, Eq(a, -b)), ((A*x - B*cos(x))/a, Eq(b, 0)), (A*b*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - A*b*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - B*a*sqrt(-a/(a - b) - b/(a - b))*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - B*a*sqrt(-a/(a - b) - b/(a - b))*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) + B*a*sqrt(-a/(a - b) - b/(a - b))*log(tan(x/2)**2 + 1)/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) + B*b*sqrt(-a/(a - b) - b/(a - b))*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) + B*b*sqrt(-a/(a - b) - b/(a - b))*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - B*b*sqrt(-a/(a - b) - b/(a - b))*log(tan(x/2)**2 + 1)/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
2,1,17,0,0.294073," ","integrate((A+B*sin(x))/(1+cos(x)),x)","A \tan{\left(\frac{x}{2} \right)} + B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}"," ",0,"A*tan(x/2) + B*log(tan(x/2)**2 + 1)","A",0
3,1,27,0,0.449122," ","integrate((A+B*sin(x))/(1-cos(x)),x)","- \frac{A}{\tan{\left(\frac{x}{2} \right)}} - B \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + 2 B \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}"," ",0,"-A/tan(x/2) - B*log(tan(x/2)**2 + 1) + 2*B*log(tan(x/2))","A",0
4,1,804,0,23.957381," ","integrate((b+c+sin(x))/(a+b*cos(x)),x)","\begin{cases} \tilde{\infty} \left(- c \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + c \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\\tan{\left(\frac{x}{2} \right)} + \frac{c \tan{\left(\frac{x}{2} \right)}}{b} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b} & \text{for}\: a = b \\\frac{1}{\tan{\left(\frac{x}{2} \right)}} + \frac{c}{b \tan{\left(\frac{x}{2} \right)}} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{b} & \text{for}\: a = - b \\\frac{c x - \cos{\left(x \right)}}{a} & \text{for}\: b = 0 \\- \frac{a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b^{2} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b^{2} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b c \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b c \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} + \frac{b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{a b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b^{2} \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-c*log(tan(x/2) - 1) + c*log(tan(x/2) + 1) - log(tan(x/2) - 1) - log(tan(x/2) + 1) + log(tan(x/2)**2 + 1)), Eq(a, 0) & Eq(b, 0)), (tan(x/2) + c*tan(x/2)/b + log(tan(x/2)**2 + 1)/b, Eq(a, b)), (1/tan(x/2) + c/(b*tan(x/2)) + log(tan(x/2)**2 + 1)/b - 2*log(tan(x/2))/b, Eq(a, -b)), ((c*x - cos(x))/a, Eq(b, 0)), (-a*sqrt(-a/(a - b) - b/(a - b))*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - a*sqrt(-a/(a - b) - b/(a - b))*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) + a*sqrt(-a/(a - b) - b/(a - b))*log(tan(x/2)**2 + 1)/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) + b**2*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - b**2*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) + b*c*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - b*c*log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*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*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*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*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))) - b*sqrt(-a/(a - b) - b/(a - b))*log(tan(x/2)**2 + 1)/(a*b*sqrt(-a/(a - b) - b/(a - b)) - b**2*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
5,1,748,0,24.571027," ","integrate((b+c+sin(x))/(a-b*cos(x)),x)","\begin{cases} \tilde{\infty} \left(- c \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + c \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\- \tan{\left(\frac{x}{2} \right)} - \frac{c \tan{\left(\frac{x}{2} \right)}}{b} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b} & \text{for}\: a = - b \\- \frac{1}{\tan{\left(\frac{x}{2} \right)}} - \frac{c}{b \tan{\left(\frac{x}{2} \right)}} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{b} + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}}{b} & \text{for}\: a = b \\\frac{c x - \cos{\left(x \right)}}{a} & \text{for}\: b = 0 \\\frac{a \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} \log{\left(- \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} + \frac{a \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} \log{\left(\sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} - \frac{a \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} + \frac{b^{2} \log{\left(- \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} - \frac{b^{2} \log{\left(\sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} + \frac{b c \log{\left(- \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} - \frac{b c \log{\left(\sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} + \frac{b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} \log{\left(- \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} + \frac{b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} \log{\left(\sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} - \frac{b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{a b \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}} + b^{2} \sqrt{- \frac{a}{a + b} + \frac{b}{a + b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-c*log(tan(x/2) - 1) + c*log(tan(x/2) + 1) - log(tan(x/2) - 1) - log(tan(x/2) + 1) + log(tan(x/2)**2 + 1)), Eq(a, 0) & Eq(b, 0)), (-tan(x/2) - c*tan(x/2)/b - log(tan(x/2)**2 + 1)/b, Eq(a, -b)), (-1/tan(x/2) - c/(b*tan(x/2)) - log(tan(x/2)**2 + 1)/b + 2*log(tan(x/2))/b, Eq(a, b)), ((c*x - cos(x))/a, Eq(b, 0)), (a*sqrt(-a/(a + b) + b/(a + b))*log(-sqrt(-a/(a + b) + b/(a + b)) + tan(x/2))/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))) + a*sqrt(-a/(a + b) + b/(a + b))*log(sqrt(-a/(a + b) + b/(a + b)) + tan(x/2))/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))) - a*sqrt(-a/(a + b) + b/(a + b))*log(tan(x/2)**2 + 1)/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))) + b**2*log(-sqrt(-a/(a + b) + b/(a + b)) + tan(x/2))/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))) - b**2*log(sqrt(-a/(a + b) + b/(a + b)) + tan(x/2))/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))) + b*c*log(-sqrt(-a/(a + b) + b/(a + b)) + tan(x/2))/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))) - b*c*log(sqrt(-a/(a + b) + b/(a + b)) + tan(x/2))/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*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*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*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*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))) - b*sqrt(-a/(a + b) + b/(a + b))*log(tan(x/2)**2 + 1)/(a*b*sqrt(-a/(a + b) + b/(a + b)) + b**2*sqrt(-a/(a + b) + b/(a + b))), True))","A",0
6,0,0,0,0.000000," ","integrate((A+B*tan(x))/(a+b*cos(x)),x)","\int \frac{A + B \tan{\left(x \right)}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral((A + B*tan(x))/(a + b*cos(x)), x)","F",0
7,0,0,0,0.000000," ","integrate((A+B*cot(x))/(a+b*cos(x)),x)","\int \frac{A + B \cot{\left(x \right)}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral((A + B*cot(x))/(a + b*cos(x)), x)","F",0
8,0,0,0,0.000000," ","integrate((A+B*csc(x))/(a+b*cos(x)),x)","\int \frac{A + B \csc{\left(x \right)}}{a + b \cos{\left(x \right)}}\, dx"," ",0,"Integral((A + B*csc(x))/(a + b*cos(x)), x)","F",0
9,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))**4/(a+b*cos(f*x+e)),x)","\int \frac{\left(c + d \sec{\left(e + f x \right)}\right)^{4}}{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*sec(e + f*x))**4/(a + b*cos(e + f*x)), x)","F",0
10,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))**3/(a+b*cos(f*x+e)),x)","\int \frac{\left(c + d \sec{\left(e + f x \right)}\right)^{3}}{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*sec(e + f*x))**3/(a + b*cos(e + f*x)), x)","F",0
11,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))**2/(a+b*cos(f*x+e)),x)","\int \frac{\left(c + d \sec{\left(e + f x \right)}\right)^{2}}{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*sec(e + f*x))**2/(a + b*cos(e + f*x)), x)","F",0
12,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+b*cos(f*x+e)),x)","\int \frac{c + d \sec{\left(e + f x \right)}}{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*sec(e + f*x))/(a + b*cos(e + f*x)), x)","F",0
13,0,0,0,0.000000," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e)),x)","\int \frac{1}{\left(a + b \cos{\left(e + f x \right)}\right) \left(c + d \sec{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(1/((a + b*cos(e + f*x))*(c + d*sec(e + f*x))), x)","F",0
14,0,0,0,0.000000," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))**2,x)","\int \frac{1}{\left(a + b \cos{\left(e + f x \right)}\right) \left(c + d \sec{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*cos(e + f*x))*(c + d*sec(e + f*x))**2), x)","F",0
15,0,0,0,0.000000," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))**3,x)","\int \frac{1}{\left(a + b \cos{\left(e + f x \right)}\right) \left(c + d \sec{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/((a + b*cos(e + f*x))*(c + d*sec(e + f*x))**3), x)","F",0
16,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))**(1/2)/(a+b*cos(f*x+e)),x)","\int \frac{\sqrt{c + d \sec{\left(e + f x \right)}}}{a + b \cos{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(c + d*sec(e + f*x))/(a + b*cos(e + f*x)), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))**(1/2),x)","\int \frac{1}{\left(a + b \cos{\left(e + f x \right)}\right) \sqrt{c + d \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/((a + b*cos(e + f*x))*sqrt(c + d*sec(e + f*x))), x)","F",0
18,1,672,0,26.560771," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \cos{\left(d \right)} + C \sin{\left(d \right)}\right)}{\cos{\left(d \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \\\frac{A \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{b e} + \frac{B x}{b} - \frac{B \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}}{b e} + \frac{C \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{b e} & \text{for}\: a = b \\\frac{A}{b e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}} + \frac{B x}{b} + \frac{B}{b e \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)}} + \frac{C \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{b e} - \frac{2 C \log{\left(\tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{b e} & \text{for}\: a = - b \\\frac{A x + \frac{B \sin{\left(d + e x \right)}}{e} - \frac{C \cos{\left(d + e x \right)}}{e}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + B \cos{\left(d \right)} + C \sin{\left(d \right)}\right)}{a + b \cos{\left(d \right)}} & \text{for}\: e = 0 \\- \frac{A b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} + \frac{A b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} + \frac{B a e x}{a b e + b^{2} e} + \frac{B a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} - \frac{B a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} + \frac{B b e x}{a b e + b^{2} e} - \frac{C a \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} - \frac{C a \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} + \frac{C a \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{a b e + b^{2} e} - \frac{C b \log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} - \frac{C b \log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{d}{2} + \frac{e x}{2} \right)} \right)}}{a b e + b^{2} e} + \frac{C b \log{\left(\tan^{2}{\left(\frac{d}{2} + \frac{e x}{2} \right)} + 1 \right)}}{a b e + b^{2} e} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*cos(d) + C*sin(d))/cos(d), Eq(a, 0) & Eq(b, 0) & Eq(e, 0)), (A*tan(d/2 + e*x/2)/(b*e) + B*x/b - B*tan(d/2 + e*x/2)/(b*e) + C*log(tan(d/2 + e*x/2)**2 + 1)/(b*e), Eq(a, b)), (A/(b*e*tan(d/2 + e*x/2)) + B*x/b + B/(b*e*tan(d/2 + e*x/2)) + C*log(tan(d/2 + e*x/2)**2 + 1)/(b*e) - 2*C*log(tan(d/2 + e*x/2))/(b*e), Eq(a, -b)), ((A*x + B*sin(d + e*x)/e - C*cos(d + e*x)/e)/a, Eq(b, 0)), (x*(A + B*cos(d) + C*sin(d))/(a + b*cos(d)), Eq(e, 0)), (-A*b*sqrt(-a/(a - b) - b/(a - b))*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) + A*b*sqrt(-a/(a - b) - b/(a - b))*log(sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) + B*a*e*x/(a*b*e + b**2*e) + B*a*sqrt(-a/(a - b) - b/(a - b))*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) - B*a*sqrt(-a/(a - b) - b/(a - b))*log(sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) + B*b*e*x/(a*b*e + b**2*e) - C*a*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) - C*a*log(sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) + C*a*log(tan(d/2 + e*x/2)**2 + 1)/(a*b*e + b**2*e) - C*b*log(-sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) - C*b*log(sqrt(-a/(a - b) - b/(a - b)) + tan(d/2 + e*x/2))/(a*b*e + b**2*e) + C*b*log(tan(d/2 + e*x/2)**2 + 1)/(a*b*e + b**2*e), True))","A",0
19,-1,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,-1,0,0,0.000000," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
