1,1,16,0,0.013289,"\int \frac{3}{5-4 \cos (x)} \, dx","Int[3/(5 - 4*Cos[x]),x]","x+2 \tan ^{-1}\left(\frac{\sin (x)}{2-\cos (x)}\right)","x+2 \tan ^{-1}\left(\frac{\sin (x)}{2-\cos (x)}\right)",1,"x + 2*ArcTan[Sin[x]/(2 - Cos[x])]","A",2,2,10,0.2000,1,"{12, 2657}"
2,1,38,0,3.0862199,"\int \frac{1+\cos (x)+2 \sin (x)}{3+\cos ^2(x)+2 \sin (x)-2 \cos (x) \sin (x)} \, dx","Int[(1 + Cos[x] + 2*Sin[x])/(3 + Cos[x]^2 + 2*Sin[x] - 2*Cos[x]*Sin[x]),x]","\cot \left(\frac{x}{2}\right)-\frac{\sin (x)}{1-\cos (x)}-\tan ^{-1}\left(\frac{2 \cos (x)-\sin (x)}{\sin (x)+2}\right)","-\tan ^{-1}\left(\frac{2 \cos (x)-\sin (x)}{\sin (x)+2}\right)",1,"-ArcTan[(2*Cos[x] - Sin[x])/(2 + Sin[x])] + Cot[x/2] - Sin[x]/(1 - Cos[x])","A",43,12,27,0.4444,1,"{4401, 2648, 12, 6742, 1680, 1673, 1094, 634, 618, 204, 628, 1107}"
3,1,42,0,0.6299628,"\int \frac{2+\cos (x)+5 \sin (x)}{4 \cos (x)-2 \sin (x)+\cos (x) \sin (x)-2 \sin ^2(x)} \, dx","Int[(2 + Cos[x] + 5*Sin[x])/(4*Cos[x] - 2*Sin[x] + Cos[x]*Sin[x] - 2*Sin[x]^2),x]","\log \left(\tan ^2\left(\frac{x}{2}\right)+\tan \left(\frac{x}{2}\right)+2\right)-\log \left(1-2 \tan \left(\frac{x}{2}\right)\right)-\log \left(\tan \left(\frac{x}{2}\right)+1\right)","\log (\sin (x)+\cos (x)+3)-\log (\sin (x)-3 \cos (x)+1)",1,"-Log[1 - 2*Tan[x/2]] - Log[1 + Tan[x/2]] + Log[2 + Tan[x/2] + Tan[x/2]^2]","B",25,7,31,0.2258,1,"{4401, 12, 2074, 634, 618, 204, 628}"
4,1,31,0,2.0619246,"\int \frac{3+7 \cos (x)+2 \sin (x)}{1+4 \cos (x)+3 \cos ^2(x)-5 \sin (x)-\cos (x) \sin (x)} \, dx","Int[(3 + 7*Cos[x] + 2*Sin[x])/(1 + 4*Cos[x] + 3*Cos[x]^2 - 5*Sin[x] - Cos[x]*Sin[x]),x]","\log \left(\tan ^2\left(\frac{x}{2}\right)+\tan \left(\frac{x}{2}\right)+2\right)-\log \left(1-2 \tan \left(\frac{x}{2}\right)\right)","\log (\sin (x)+\cos (x)+3)-\log (-2 \sin (x)+\cos (x)+1)",1,"-Log[1 - 2*Tan[x/2]] + Log[2 + Tan[x/2] + Tan[x/2]^2]","A",32,9,35,0.2571,1,"{4401, 2657, 12, 6725, 634, 618, 204, 628, 203}"
5,0,0,0,0.8040751,"\int \frac{-1+4 \cos (x)+5 \cos ^2(x)}{-1-4 \cos (x)-3 \cos ^2(x)+4 \cos ^3(x)} \, dx","Int[(-1 + 4*Cos[x] + 5*Cos[x]^2)/(-1 - 4*Cos[x] - 3*Cos[x]^2 + 4*Cos[x]^3),x]","\int \frac{-1+4 \cos (x)+5 \cos ^2(x)}{-1-4 \cos (x)-3 \cos ^2(x)+4 \cos ^3(x)} \, dx","x-2 \tan ^{-1}\left(\frac{3 \sin (x)+7 \sin (x) \cos (x)}{5 \cos ^2(x)+2 \cos (x)+1}\right)-2 \tan ^{-1}\left(\frac{\sin (x)}{\cos (x)+3}\right)",1,"Defer[Int][(1 + 4*Cos[x] + 3*Cos[x]^2 - 4*Cos[x]^3)^(-1), x] + 4*Defer[Int][Cos[x]/(-1 - 4*Cos[x] - 3*Cos[x]^2 + 4*Cos[x]^3), x] + 5*Defer[Int][Cos[x]^2/(-1 - 4*Cos[x] - 3*Cos[x]^2 + 4*Cos[x]^3), x]","F",0,0,0,0,-1,"{}"
6,0,0,0,0.7853381,"\int \frac{-5+2 \cos (x)+7 \cos ^2(x)}{-1+2 \cos (x)-9 \cos ^2(x)+4 \cos ^3(x)} \, dx","Int[(-5 + 2*Cos[x] + 7*Cos[x]^2)/(-1 + 2*Cos[x] - 9*Cos[x]^2 + 4*Cos[x]^3),x]","\int \frac{-5+2 \cos (x)+7 \cos ^2(x)}{-1+2 \cos (x)-9 \cos ^2(x)+4 \cos ^3(x)} \, dx","x-2 \tan ^{-1}\left(\frac{2 \sin (x) \cos (x)}{2 \cos ^2(x)-\cos (x)+1}\right)",1,"-5*Defer[Int][(-1 + 2*Cos[x] - 9*Cos[x]^2 + 4*Cos[x]^3)^(-1), x] + 2*Defer[Int][Cos[x]/(-1 + 2*Cos[x] - 9*Cos[x]^2 + 4*Cos[x]^3), x] + 7*Defer[Int][Cos[x]^2/(-1 + 2*Cos[x] - 9*Cos[x]^2 + 4*Cos[x]^3), x]","F",0,0,0,0,-1,"{}"
7,1,14,0,0.0107162,"\int \frac{3}{5+4 \sin (x)} \, dx","Int[3/(5 + 4*Sin[x]),x]","x+2 \tan ^{-1}\left(\frac{\cos (x)}{\sin (x)+2}\right)","x+2 \tan ^{-1}\left(\frac{\cos (x)}{\sin (x)+2}\right)",1,"x + 2*ArcTan[Cos[x]/(2 + Sin[x])]","A",2,2,10,0.2000,1,"{12, 2657}"
8,1,34,0,0.0149801,"\int \frac{2}{1+\cos ^2(x)} \, dx","Int[2/(1 + Cos[x]^2),x]","\sqrt{2} x-\sqrt{2} \tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)","\sqrt{2} x-\sqrt{2} \tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)",1,"Sqrt[2]*x - Sqrt[2]*ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Cos[x]^2)]","A",3,3,10,0.3000,1,"{12, 3181, 203}"
9,1,54,0,0.0681303,"\int \frac{1}{p+q \cos (x)+r \sin (x)} \, dx","Int[(p + q*Cos[x] + r*Sin[x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{(p-q) \tan \left(\frac{x}{2}\right)+r}{\sqrt{p^2-q^2-r^2}}\right)}{\sqrt{p^2-q^2-r^2}}","\frac{2 \tan ^{-1}\left(\frac{(p-q) \tan \left(\frac{x}{2}\right)+r}{\sqrt{p^2-q^2-r^2}}\right)}{\sqrt{p^2-q^2-r^2}}",1,"(2*ArcTan[(r + (p - q)*Tan[x/2])/Sqrt[p^2 - q^2 - r^2]])/Sqrt[p^2 - q^2 - r^2]","A",3,3,12,0.2500,1,"{3124, 618, 204}"