1,1,79,48,0.174000," ","int((A+B*cos(x))/(a+b*sin(x)),x)","-\frac{B \ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}{b}+\frac{B \ln \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)}{b}+\frac{2 A \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}"," ",0,"-B/b*ln(tan(1/2*x)^2+1)+1/b*B*ln(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)+2*A/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
2,1,35,19,0.147000," ","int((A+B*cos(x))/(1+sin(x)),x)","-B \ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)-\frac{2 A}{\tan \left(\frac{x}{2}\right)+1}+2 B \ln \left(\tan \left(\frac{x}{2}\right)+1\right)"," ",0,"-B*ln(tan(1/2*x)^2+1)-2*A/(tan(1/2*x)+1)+2*B*ln(tan(1/2*x)+1)","A"
3,1,34,23,0.228000," ","int((A+B*cos(x))/(1-sin(x)),x)","-\frac{2 A}{\tan \left(\frac{x}{2}\right)-1}-2 B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)+B \ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)"," ",0,"-2*A/(tan(1/2*x)-1)-2*B*ln(tan(1/2*x)-1)+B*ln(tan(1/2*x)^2+1)","A"
4,1,116,49,0.184000," ","int((b+c+cos(x))/(a+b*sin(x)),x)","-\frac{\ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}{b}+\frac{\ln \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)}{b}+\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) c}{\sqrt{a^{2}-b^{2}}}"," ",0,"-1/b*ln(tan(1/2*x)^2+1)+1/b*ln(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)+2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*c","B"
5,1,116,52,0.176000," ","int((b+c+cos(x))/(a-b*sin(x)),x)","\frac{\ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}{b}-\frac{\ln \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a -2 \tan \left(\frac{x}{2}\right) b +a \right)}{b}+\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}-b^{2}}}\right) c}{\sqrt{a^{2}-b^{2}}}"," ",0,"1/b*ln(tan(1/2*x)^2+1)-1/b*ln(tan(1/2*x)^2*a-2*tan(1/2*x)*b+a)+2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)-2*b)/(a^2-b^2)^(1/2))+2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)-2*b)/(a^2-b^2)^(1/2))*c","B"
6,1,181,87,0.270000," ","int((A+B*tan(x))/(a+b*sin(x)),x)","-\frac{2 B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{2 a +2 b}-\frac{2 B \ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{2 a -2 b}+\frac{a B \ln \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)}{\left(a -b \right) \left(a +b \right)}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2} A}{\left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) A \,b^{2}}{\left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-2*B/(2*a+2*b)*ln(tan(1/2*x)-1)-2*B/(2*a-2*b)*ln(tan(1/2*x)+1)+1/(a-b)/(a+b)*a*B*ln(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)+2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*a^2*A-2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*A*b^2","B"
7,1,75,57,0.264000," ","int((A+B*cot(x))/(a+b*sin(x)),x)","\frac{B \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}-\frac{B \ln \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)}{a}+\frac{2 A \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}"," ",0,"B/a*ln(tan(1/2*x))-1/a*B*ln(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)+2*A/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
8,1,182,88,0.259000," ","int((A+B*sec(x))/(a+b*sin(x)),x)","-\frac{2 B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{2 a +2 b}+\frac{2 B \ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{2 a -2 b}-\frac{B b \ln \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)}{\left(a -b \right) \left(a +b \right)}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2} A}{\left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) A \,b^{2}}{\left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-2*B/(2*a+2*b)*ln(tan(1/2*x)-1)+2*B/(2*a-2*b)*ln(tan(1/2*x)+1)-1/(a-b)/(a+b)*B*b*ln(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)+2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*a^2*A-2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*A*b^2","B"
9,1,94,55,0.237000," ","int((A+B*csc(x))/(a+b*sin(x)),x)","\frac{B \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}+\frac{2 A \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) B b}{a \sqrt{a^{2}-b^{2}}}"," ",0,"B/a*ln(tan(1/2*x))+2*A/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-2/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*B*b","A"