1,1,10,16,0.020000," ","int(3/(5-4*cos(x)),x)","2 \arctan \left(3 \tan \left(\frac{x}{2}\right)\right)"," ",0,"2*arctan(3*tan(1/2*x))","A"
2,1,13,19,0.184000," ","int((1+cos(x)+2*sin(x))/(3+cos(x)^2+2*sin(x)-2*cos(x)*sin(x)),x)","\arctan \left(\tan^{2}\left(\frac{x}{2}\right)+\tan \left(\frac{x}{2}\right)\right)"," ",0,"arctan(tan(1/2*x)^2+tan(1/2*x))","A"
3,1,35,19,0.132000," ","int((2+cos(x)+5*sin(x))/(4*cos(x)-2*sin(x)+cos(x)*sin(x)-2*sin(x)^2),x)","-\ln \left(\tan \left(\frac{x}{2}\right)+1\right)-\ln \left(2 \tan \left(\frac{x}{2}\right)-1\right)+\ln \left(\tan^{2}\left(\frac{x}{2}\right)+\tan \left(\frac{x}{2}\right)+2\right)"," ",0,"-ln(tan(1/2*x)+1)+ln(tan(1/2*x)^2+tan(1/2*x)+2)-ln(2*tan(1/2*x)-1)","A"
4,1,26,19,0.169000," ","int((3+7*cos(x)+2*sin(x))/(1+4*cos(x)+3*cos(x)^2-5*sin(x)-cos(x)*sin(x)),x)","-\ln \left(2 \tan \left(\frac{x}{2}\right)-1\right)+\ln \left(\tan^{2}\left(\frac{x}{2}\right)+\tan \left(\frac{x}{2}\right)+2\right)"," ",0,"ln(tan(1/2*x)^2+tan(1/2*x)+2)-ln(2*tan(1/2*x)-1)","A"
5,1,17,43,0.099000," ","int((-1+4*cos(x)+5*cos(x)^2)/(-1-4*cos(x)-3*cos(x)^2+4*cos(x)^3),x)","2 \arctan \left(\tan^{3}\left(\frac{x}{2}\right)-2 \tan \left(\frac{x}{2}\right)\right)"," ",0,"2*arctan(tan(1/2*x)^3-2*tan(1/2*x))","A"
6,1,19,25,0.117000," ","int((-5+2*cos(x)+7*cos(x)^2)/(-1+2*cos(x)-9*cos(x)^2+4*cos(x)^3),x)","2 \arctan \left(2 \left(\tan^{3}\left(\frac{x}{2}\right)\right)-\tan \left(\frac{x}{2}\right)\right)"," ",0,"2*arctan(2*tan(1/2*x)^3-tan(1/2*x))","A"
7,1,12,14,0.026000," ","int(3/(5+4*sin(x)),x)","2 \arctan \left(\frac{5 \tan \left(\frac{x}{2}\right)}{3}+\frac{4}{3}\right)"," ",0,"2*arctan(5/3*tan(1/2*x)+4/3)","A"
8,1,13,28,0.028000," ","int(2/(cos(x)^2+1),x)","\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \tan \left(x \right)}{2}\right)"," ",0,"2^(1/2)*arctan(1/2*2^(1/2)*tan(x))","A"
9,1,53,48,0.084000," ","int(1/(p+q*cos(x)+r*sin(x)),x)","\frac{2 \arctan \left(\frac{2 r +2 \left(p -q \right) \tan \left(\frac{x}{2}\right)}{2 \sqrt{p^{2}-q^{2}-r^{2}}}\right)}{\sqrt{p^{2}-q^{2}-r^{2}}}"," ",0,"2/(p^2-q^2-r^2)^(1/2)*arctan(1/2*(2*(p-q)*tan(1/2*x)+2*r)/(p^2-q^2-r^2)^(1/2))","A"