1,0,0,16,0.0000418,"\int \frac{3}{5-4 \cos (x)} \, dx","IntegrateAlgebraic[3/(5 - 4*Cos[x]),x]","\int \frac{3}{5-4 \cos (x)} \, dx","x+2 \tan ^{-1}\left(\frac{\sin (x)}{2-\cos (x)}\right)",1,"Could not integrate","F",-1
2,0,0,19,0.0000479,"\int \frac{1+\cos (x)+2 \sin (x)}{3+\cos ^2(x)+2 \sin (x)-2 \cos (x) \sin (x)} \, dx","IntegrateAlgebraic[(1 + Cos[x] + 2*Sin[x])/(3 + Cos[x]^2 + 2*Sin[x] - 2*Cos[x]*Sin[x]),x]","\int \frac{1+\cos (x)+2 \sin (x)}{3+\cos ^2(x)+2 \sin (x)-2 \cos (x) \sin (x)} \, dx","-\tan ^{-1}\left(\frac{2 \cos (x)-\sin (x)}{\sin (x)+2}\right)",1,"Could not integrate","F",-1
3,0,0,19,0.0000705,"\int \frac{2+\cos (x)+5 \sin (x)}{4 \cos (x)-2 \sin (x)+\cos (x) \sin (x)-2 \sin ^2(x)} \, dx","IntegrateAlgebraic[(2 + Cos[x] + 5*Sin[x])/(4*Cos[x] - 2*Sin[x] + Cos[x]*Sin[x] - 2*Sin[x]^2),x]","\int \frac{2+\cos (x)+5 \sin (x)}{4 \cos (x)-2 \sin (x)+\cos (x) \sin (x)-2 \sin ^2(x)} \, dx","\log (\sin (x)+\cos (x)+3)-\log (\sin (x)-3 \cos (x)+1)",1,"Could not integrate","F",-1
4,0,0,19,0.000049,"\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","IntegrateAlgebraic[(3 + 7*Cos[x] + 2*Sin[x])/(1 + 4*Cos[x] + 3*Cos[x]^2 - 5*Sin[x] - Cos[x]*Sin[x]),x]","\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","\log (\sin (x)+\cos (x)+3)-\log (-2 \sin (x)+\cos (x)+1)",1,"Could not integrate","F",-1
5,0,0,43,0.0000493,"\int \frac{-1+4 \cos (x)+5 \cos ^2(x)}{-1-4 \cos (x)-3 \cos ^2(x)+4 \cos ^3(x)} \, dx","IntegrateAlgebraic[(-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,"Could not integrate","F",-1
6,0,0,25,0.0000477,"\int \frac{-5+2 \cos (x)+7 \cos ^2(x)}{-1+2 \cos (x)-9 \cos ^2(x)+4 \cos ^3(x)} \, dx","IntegrateAlgebraic[(-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,"Could not integrate","F",-1
7,0,0,14,0.0000353,"\int \frac{3}{5+4 \sin (x)} \, dx","IntegrateAlgebraic[3/(5 + 4*Sin[x]),x]","\int \frac{3}{5+4 \sin (x)} \, dx","x+2 \tan ^{-1}\left(\frac{\cos (x)}{\sin (x)+2}\right)",1,"Could not integrate","F",-1
8,0,0,34,0.0000311,"\int \frac{2}{1+\cos ^2(x)} \, dx","IntegrateAlgebraic[2/(1 + Cos[x]^2),x]","\int \frac{2}{1+\cos ^2(x)} \, dx","\sqrt{2} x-\sqrt{2} \tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)",1,"Could not integrate","F",-1
9,0,0,54,0.0000353,"\int \frac{1}{p+q \cos (x)+r \sin (x)} \, dx","IntegrateAlgebraic[(p + q*Cos[x] + r*Sin[x])^(-1),x]","\int \frac{1}{p+q \cos (x)+r \sin (x)} \, dx","\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,"Could not integrate","F",-1