1,1,136,0,0.2317902,"\int \frac{\sin ^5(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sin[x]^5/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{\cos (x) \left(b^2-c (a+2 c)\right)}{c^3}+\frac{b \left(b^2-2 c (a+c)\right) \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 c^4}+\frac{\left(-2 b^2 c (2 a+c)+2 c^2 (a+c)^2+b^4\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{b \cos ^2(x)}{2 c^2}-\frac{\cos ^3(x)}{3 c}","-\frac{\cos (x) \left(b^2-c (a+2 c)\right)}{c^3}+\frac{b \left(b^2-2 c (a+c)\right) \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 c^4}+\frac{\left(-2 b^2 c (2 a+c)+2 c^2 (a+c)^2+b^4\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{b \cos ^2(x)}{2 c^2}-\frac{\cos ^3(x)}{3 c}",1,"((b^4 + 2*c^2*(a + c)^2 - 2*b^2*c*(2*a + c))*ArcTanh[(b + 2*c*Cos[x])/Sqrt[b^2 - 4*a*c]])/(c^4*Sqrt[b^2 - 4*a*c]) - ((b^2 - c*(a + 2*c))*Cos[x])/c^3 + (b*Cos[x]^2)/(2*c^2) - Cos[x]^3/(3*c) + (b*(b^2 - 2*c*(a + c))*Log[a + b*Cos[x] + c*Cos[x]^2])/(2*c^4)","A",7,6,19,0.3158,1,"{3259, 1657, 634, 618, 206, 628}"
2,1,76,0,0.1297781,"\int \frac{\sin ^3(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sin[x]^3/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{\left(b^2-2 c (a+c)\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 c^2}+\frac{\cos (x)}{c}","-\frac{\left(b^2-2 c (a+c)\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}-\frac{b \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 c^2}+\frac{\cos (x)}{c}",1,"-(((b^2 - 2*c*(a + c))*ArcTanh[(b + 2*c*Cos[x])/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c])) + Cos[x]/c - (b*Log[a + b*Cos[x] + c*Cos[x]^2])/(2*c^2)","A",7,6,19,0.3158,1,"{3259, 1657, 634, 618, 206, 628}"
3,1,35,0,0.0456803,"\int \frac{\sin (x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sin[x]/(a + b*Cos[x] + c*Cos[x]^2),x]","\frac{2 \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}","\frac{2 \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}",1,"(2*ArcTanh[(b + 2*c*Cos[x])/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",3,3,17,0.1765,1,"{3259, 618, 206}"
4,1,129,0,0.1718335,"\int \frac{\csc (x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Csc[x]/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{\left(-2 a c+b^2-2 c^2\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{(a-b+c) (a+b+c) \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 (a-b+c) (a+b+c)}+\frac{\log (1-\cos (x))}{2 (a+b+c)}-\frac{\log (\cos (x)+1)}{2 (a-b+c)}","-\frac{\left(-2 a c+b^2-2 c^2\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{(a-b+c) (a+b+c) \sqrt{b^2-4 a c}}+\frac{b \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 (a-b+c) (a+b+c)}+\frac{\log (1-\cos (x))}{2 (a+b+c)}-\frac{\log (\cos (x)+1)}{2 (a-b+c)}",1,"-(((b^2 - 2*a*c - 2*c^2)*ArcTanh[(b + 2*c*Cos[x])/Sqrt[b^2 - 4*a*c]])/((a - b + c)*(a + b + c)*Sqrt[b^2 - 4*a*c])) + Log[1 - Cos[x]]/(2*(a + b + c)) - Log[1 + Cos[x]]/(2*(a - b + c)) + (b*Log[a + b*Cos[x] + c*Cos[x]^2])/(2*(a - b + c)*(a + b + c))","A",9,8,17,0.4706,1,"{3259, 981, 634, 618, 206, 628, 633, 31}"
5,1,205,0,0.464729,"\int \frac{\csc ^3(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Csc[x]^3/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{b \left(b^2-2 c (a+c)\right) \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 \left(a^2+2 a c-b^2+c^2\right)^2}+\frac{\left(-2 b^2 c (2 a+c)+2 c^2 (a+c)^2+b^4\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a^2+2 a c-b^2+c^2\right)^2}+\frac{(a+2 b+3 c) \log (1-\cos (x))}{4 (a+b+c)^2}-\frac{(a-2 b+3 c) \log (\cos (x)+1)}{4 (a-b+c)^2}+\frac{\csc ^2(x) (b-(a+c) \cos (x))}{2 (a-b+c) (a+b+c)}","-\frac{b \left(b^2-2 c (a+c)\right) \log \left(a+b \cos (x)+c \cos ^2(x)\right)}{2 \left(a^2+2 a c-b^2+c^2\right)^2}+\frac{\left(-2 b^2 c (2 a+c)+2 c^2 (a+c)^2+b^4\right) \tanh ^{-1}\left(\frac{b+2 c \cos (x)}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a^2+2 a c-b^2+c^2\right)^2}+\frac{(a+2 b+3 c) \log (1-\cos (x))}{4 (a+b+c)^2}-\frac{(a-2 b+3 c) \log (\cos (x)+1)}{4 (a-b+c)^2}+\frac{\csc ^2(x) (b-(a+c) \cos (x))}{2 (a-b+c) (a+b+c)}",1,"((b^4 + 2*c^2*(a + c)^2 - 2*b^2*c*(2*a + c))*ArcTanh[(b + 2*c*Cos[x])/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(a^2 - b^2 + 2*a*c + c^2)^2) + ((b - (a + c)*Cos[x])*Csc[x]^2)/(2*(a - b + c)*(a + b + c)) + ((a + 2*b + 3*c)*Log[1 - Cos[x]])/(4*(a + b + c)^2) - ((a - 2*b + 3*c)*Log[1 + Cos[x]])/(4*(a - b + c)^2) - (b*(b^2 - 2*c*(a + c))*Log[a + b*Cos[x] + c*Cos[x]^2])/(2*(a^2 - b^2 + 2*a*c + c^2)^2)","A",10,9,19,0.4737,1,"{3259, 976, 1074, 634, 618, 206, 628, 633, 31}"
6,1,386,0,11.0126993,"\int \frac{\sin ^4(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sin[x]^4/(a + b*Cos[x] + c*Cos[x]^2),x]","\frac{x \left(b^2-c (a+2 c)\right)}{c^3}+\frac{2 \left(-2 b^2 c (a+c)-b \sqrt{b^2-4 a c} \left(b^2-2 c (a+c)\right)-2 c \left(a b^2-c (a+c)^2\right)+b^4\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 \left(b^3 \sqrt{b^2-4 a c}-2 b^2 c (2 a+c)-2 b c (a+c) \sqrt{b^2-4 a c}+2 c^2 (a+c)^2+b^4\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b \sin (x)}{c^2}+\frac{x}{2 c}+\frac{\sin (x) \cos (x)}{2 c}","\frac{x \left(b^2-c (a+2 c)\right)}{c^3}+\frac{2 \left(b^2 \left(b^2-2 c (a+c)\right)-b \sqrt{b^2-4 a c} \left(b^2-2 c (a+c)\right)-2 c \left(a b^2-c (a+c)^2\right)\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 \left(b^3 \sqrt{b^2-4 a c}-2 b^2 c (2 a+c)-2 b c (a+c) \sqrt{b^2-4 a c}+2 c^2 (a+c)^2+b^4\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b \sin (x)}{c^2}+\frac{x}{2 c}+\frac{\sin (x) \cos (x)}{2 c}",1,"x/(2*c) + ((b^2 - c*(a + 2*c))*x)/c^3 + (2*(b^4 - 2*b^2*c*(a + c) - b*Sqrt[b^2 - 4*a*c]*(b^2 - 2*c*(a + c)) - 2*c*(a*b^2 - c*(a + c)^2))*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(c^3*Sqrt[b^2 - 4*a*c]*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (2*(b^4 + 2*c^2*(a + c)^2 - 2*b^2*c*(2*a + c) + b^3*Sqrt[b^2 - 4*a*c] - 2*b*c*(a + c)*Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(c^3*Sqrt[b^2 - 4*a*c]*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]) - (b*Sin[x])/c^2 + (Cos[x]*Sin[x])/(2*c)","A",10,7,19,0.3684,1,"{3267, 2637, 2635, 8, 3293, 2659, 205}"
7,1,260,0,1.2841216,"\int \frac{\sin ^2(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sin[x]^2/(a + b*Cos[x] + c*Cos[x]^2),x]","\frac{2 \left(b-\frac{b^2-2 c (a+c)}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(\frac{b^2-2 c (a+c)}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{x}{c}","\frac{2 \left(b-\frac{b^2-2 c (a+c)}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(\frac{b^2-2 c (a+c)}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{x}{c}",1,"-(x/c) + (2*(b - (b^2 - 2*c*(a + c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(c*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) + (2*(b + (b^2 - 2*c*(a + c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(c*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",7,4,19,0.2105,1,"{3267, 3293, 2659, 205}"
8,1,326,0,3.3395076,"\int \frac{\csc ^2(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Csc[x]^2/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{2 b c \left(\frac{b^2-2 c (a+c)}{b \sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{(a-b+c) (a+b+c) \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 b c \left(1-\frac{b^2-2 c (a+c)}{b \sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{(a-b+c) (a+b+c) \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sin (x)}{2 (1-\cos (x)) (a+b+c)}+\frac{\sin (x)}{2 (\cos (x)+1) (a-b+c)}","-\frac{2 b c \left(\frac{b^2-2 c (a+c)}{b \sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{(a-b+c) (a+b+c) \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 b c \left(1-\frac{b^2-2 c (a+c)}{b \sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{(a-b+c) (a+b+c) \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{\sin (x)}{2 (1-\cos (x)) (a+b+c)}+\frac{\sin (x)}{2 (\cos (x)+1) (a-b+c)}",1,"(-2*b*c*(1 + (b^2 - 2*c*(a + c))/(b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/((a - b + c)*(a + b + c)*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (2*b*c*(1 - (b^2 - 2*c*(a + c))/(b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/((a - b + c)*(a + b + c)*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]) - Sin[x]/(2*(a + b + c)*(1 - Cos[x])) + Sin[x]/(2*(a - b + c)*(1 + Cos[x]))","A",9,5,19,0.2632,1,"{3267, 2648, 3293, 2659, 205}"
9,1,21,0,0.0244769,"\int \frac{\sin (x)}{-2+\cos (x)+\cos ^2(x)} \, dx","Int[Sin[x]/(-2 + Cos[x] + Cos[x]^2),x]","\frac{1}{3} \log (\cos (x)+2)-\frac{1}{3} \log (1-\cos (x))","\frac{1}{3} \log (\cos (x)+2)-\frac{1}{3} \log (1-\cos (x))",1,"-Log[1 - Cos[x]]/3 + Log[2 + Cos[x]]/3","A",4,3,13,0.2308,1,"{3259, 616, 31}"
10,1,23,0,0.0275162,"\int \frac{\sin (x)}{4-5 \cos (x)+\cos ^2(x)} \, dx","Int[Sin[x]/(4 - 5*Cos[x] + Cos[x]^2),x]","\frac{1}{3} \log (1-\cos (x))-\frac{1}{3} \log (4-\cos (x))","\frac{1}{3} \log (1-\cos (x))-\frac{1}{3} \log (4-\cos (x))",1,"Log[1 - Cos[x]]/3 - Log[4 - Cos[x]]/3","A",4,3,15,0.2000,1,"{3259, 616, 31}"
11,1,19,0,0.0363224,"\int \frac{\sin (x)}{3-2 \cos (x)+\cos ^2(x)} \, dx","Int[Sin[x]/(3 - 2*Cos[x] + Cos[x]^2),x]","\frac{\tan ^{-1}\left(\frac{1-\cos (x)}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\frac{1-\cos (x)}{\sqrt{2}}\right)}{\sqrt{2}}",1,"ArcTan[(1 - Cos[x])/Sqrt[2]]/Sqrt[2]","A",3,3,15,0.2000,1,"{3259, 618, 204}"
12,1,36,0,0.033036,"\int \frac{\sin (x)}{\left(13-4 \cos (x)+\cos ^2(x)\right)^2} \, dx","Int[Sin[x]/(13 - 4*Cos[x] + Cos[x]^2)^2,x]","\frac{2-\cos (x)}{18 \left(\cos ^2(x)-4 \cos (x)+13\right)}-\frac{1}{54} \tan ^{-1}\left(\frac{1}{3} (\cos (x)-2)\right)","\frac{2-\cos (x)}{18 \left(\cos ^2(x)-4 \cos (x)+13\right)}-\frac{1}{54} \tan ^{-1}\left(\frac{1}{3} (\cos (x)-2)\right)",1,"-ArcTan[(-2 + Cos[x])/3]/54 + (2 - Cos[x])/(18*(13 - 4*Cos[x] + Cos[x]^2))","A",4,4,15,0.2667,1,"{3259, 614, 618, 204}"
13,1,326,0,4.0621164,"\int \frac{\cos ^4(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Cos[x]^4/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{2 \left(-\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 \left(\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{x \left(b^2-a c\right)}{c^3}-\frac{b \sin (x)}{c^2}+\frac{x}{2 c}+\frac{\sin (x) \cos (x)}{2 c}","-\frac{2 \left(-\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 \left(\frac{2 a^2 c^2-4 a b^2 c+b^4}{\sqrt{b^2-4 a c}}-2 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^3 \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{x \left(b^2-a c\right)}{c^3}-\frac{b \sin (x)}{c^2}+\frac{x}{2 c}+\frac{\sin (x) \cos (x)}{2 c}",1,"x/(2*c) + ((b^2 - a*c)*x)/c^3 - (2*(b^3 - 2*a*b*c - (b^4 - 4*a*b^2*c + 2*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(c^3*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (2*(b^3 - 2*a*b*c + (b^4 - 4*a*b^2*c + 2*a^2*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(c^3*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]) - (b*Sin[x])/c^2 + (Cos[x]*Sin[x])/(2*c)","A",10,7,19,0.3684,1,"{3257, 2637, 2635, 8, 3293, 2659, 205}"
14,1,299,0,6.7579037,"\int \frac{\cos ^3(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Cos[x]^3/(a + b*Cos[x] + c*Cos[x]^2),x]","\frac{2 \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{3 a b c}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^2 \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(\frac{b^3}{\sqrt{b^2-4 a c}}-\frac{3 a b c}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b x}{c^2}+\frac{\sin (x)}{c}","\frac{2 \left(-\frac{b^3}{\sqrt{b^2-4 a c}}+\frac{3 a b c}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^2 \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(\frac{b^3}{\sqrt{b^2-4 a c}}-\frac{3 a b c}{\sqrt{b^2-4 a c}}-a c+b^2\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c^2 \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b x}{c^2}+\frac{\sin (x)}{c}",1,"-((b*x)/c^2) + (2*(b^2 - a*c - b^3/Sqrt[b^2 - 4*a*c] + (3*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(c^2*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) + (2*(b^2 - a*c + b^3/Sqrt[b^2 - 4*a*c] - (3*a*b*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(c^2*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]) + Sin[x]/c","A",8,5,19,0.2632,1,"{3257, 2637, 3293, 2659, 205}"
15,1,255,0,1.262321,"\int \frac{\cos ^2(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Cos[x]^2/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{2 \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{x}{c}","-\frac{2 \left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 \left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{c \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{x}{c}",1,"x/c - (2*(b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(c*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (2*(b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(c*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",7,4,19,0.2105,1,"{3257, 3293, 2659, 205}"
16,1,230,0,0.5461582,"\int \frac{\cos (x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Cos[x]/(a + b*Cos[x] + c*Cos[x]^2),x]","\frac{2 \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}","\frac{2 \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}",1,"(2*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) + (2*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",6,3,17,0.1765,1,"{3257, 2659, 205}"
17,1,223,0,0.3502995,"\int \frac{1}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[(a + b*Cos[x] + c*Cos[x]^2)^(-1),x]","\frac{4 c \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{4 c \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}","\frac{4 c \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{4 c \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{\sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}",1,"(4*c*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (4*c*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(Sqrt[b^2 - 4*a*c]*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]])","A",5,3,14,0.2143,1,"{3249, 2659, 205}"
18,1,245,0,0.7724112,"\int \frac{\sec (x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sec[x]/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{2 c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{a \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{\tanh ^{-1}(\sin (x))}{a}","-\frac{2 c \left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{a \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}-\frac{2 c \left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{\tanh ^{-1}(\sin (x))}{a}",1,"(-2*c*(1 + b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(a*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) - (2*c*(1 - b/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(a*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]) + ArcTanh[Sin[x]]/a","A",8,5,17,0.2941,1,"{3257, 3293, 2659, 205, 3770}"
19,1,275,0,1.1889919,"\int \frac{\sec ^2(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sec[x]^2/(a + b*Cos[x] + c*Cos[x]^2),x]","\frac{2 b c \left(\frac{b^2-2 a c}{b \sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^2 \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 b c \left(1-\frac{b^2-2 a c}{b \sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b \tanh ^{-1}(\sin (x))}{a^2}+\frac{\tan (x)}{a}","\frac{2 b c \left(\frac{b^2-2 a c}{b \sqrt{b^2-4 a c}}+1\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^2 \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 b c \left(1-\frac{b^2-2 a c}{b \sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^2 \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}-\frac{b \tanh ^{-1}(\sin (x))}{a^2}+\frac{\tan (x)}{a}",1,"(2*b*c*(1 + (b^2 - 2*a*c)/(b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(a^2*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) + (2*b*c*(1 - (b^2 - 2*a*c)/(b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(a^2*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]) - (b*ArcTanh[Sin[x]])/a^2 + Tan[x]/a","A",10,7,19,0.3684,1,"{3257, 3293, 2659, 205, 3770, 3767, 8}"
20,1,334,0,4.6738451,"\int \frac{\sec ^3(x)}{a+b \cos (x)+c \cos ^2(x)} \, dx","Int[Sec[x]^3/(a + b*Cos[x] + c*Cos[x]^2),x]","-\frac{2 c \left(\sqrt{b^2-4 a c} \left(b^2-a c\right)-3 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 c \left(-\sqrt{b^2-4 a c} \left(b^2-a c\right)-3 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{\left(b^2-a c\right) \tanh ^{-1}(\sin (x))}{a^3}-\frac{b \tan (x)}{a^2}+\frac{\tanh ^{-1}(\sin (x))}{2 a}+\frac{\tan (x) \sec (x)}{2 a}","-\frac{2 c \left(\sqrt{b^2-4 a c} \left(b^2-a c\right)-3 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{-\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{-\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{-\sqrt{b^2-4 a c}+b-2 c} \sqrt{-\sqrt{b^2-4 a c}+b+2 c}}+\frac{2 c \left(-\sqrt{b^2-4 a c} \left(b^2-a c\right)-3 a b c+b^3\right) \tan ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right) \sqrt{\sqrt{b^2-4 a c}+b-2 c}}{\sqrt{\sqrt{b^2-4 a c}+b+2 c}}\right)}{a^3 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b-2 c} \sqrt{\sqrt{b^2-4 a c}+b+2 c}}+\frac{\left(b^2-a c\right) \tanh ^{-1}(\sin (x))}{a^3}-\frac{b \tan (x)}{a^2}+\frac{\tanh ^{-1}(\sin (x))}{2 a}+\frac{\tan (x) \sec (x)}{2 a}",1,"(-2*c*(b^3 - 3*a*b*c + Sqrt[b^2 - 4*a*c]*(b^2 - a*c))*ArcTan[(Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[b - 2*c - Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c - Sqrt[b^2 - 4*a*c]]) + (2*c*(b^3 - 3*a*b*c - Sqrt[b^2 - 4*a*c]*(b^2 - a*c))*ArcTan[(Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Tan[x/2])/Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]])/(a^3*Sqrt[b^2 - 4*a*c]*Sqrt[b - 2*c + Sqrt[b^2 - 4*a*c]]*Sqrt[b + 2*c + Sqrt[b^2 - 4*a*c]]) + ArcTanh[Sin[x]]/(2*a) + ((b^2 - a*c)*ArcTanh[Sin[x]])/a^3 - (b*Tan[x])/a^2 + (Sec[x]*Tan[x])/(2*a)","A",12,8,19,0.4211,1,"{3257, 3293, 2659, 205, 3770, 3767, 8, 3768}"