1,1,33,0,0.0524986,"\int \frac{\sin ^6(x)}{a-a \cos ^2(x)} \, dx","Int[Sin[x]^6/(a - a*Cos[x]^2),x]","\frac{3 x}{8 a}-\frac{\sin ^3(x) \cos (x)}{4 a}-\frac{3 \sin (x) \cos (x)}{8 a}","\frac{3 x}{8 a}-\frac{\sin ^3(x) \cos (x)}{4 a}-\frac{3 \sin (x) \cos (x)}{8 a}",1,"(3*x)/(8*a) - (3*Cos[x]*Sin[x])/(8*a) - (Cos[x]*Sin[x]^3)/(4*a)","A",4,3,16,0.1875,1,"{3175, 2635, 8}"
2,1,19,0,0.0451872,"\int \frac{\sin ^5(x)}{a-a \cos ^2(x)} \, dx","Int[Sin[x]^5/(a - a*Cos[x]^2),x]","\frac{\cos ^3(x)}{3 a}-\frac{\cos (x)}{a}","\frac{\cos ^3(x)}{3 a}-\frac{\cos (x)}{a}",1,"-(Cos[x]/a) + Cos[x]^3/(3*a)","A",3,2,16,0.1250,1,"{3175, 2633}"
3,1,20,0,0.0452092,"\int \frac{\sin ^4(x)}{a-a \cos ^2(x)} \, dx","Int[Sin[x]^4/(a - a*Cos[x]^2),x]","\frac{x}{2 a}-\frac{\sin (x) \cos (x)}{2 a}","\frac{x}{2 a}-\frac{\sin (x) \cos (x)}{2 a}",1,"x/(2*a) - (Cos[x]*Sin[x])/(2*a)","A",3,3,16,0.1875,1,"{3175, 2635, 8}"
4,1,7,0,0.0413498,"\int \frac{\sin ^3(x)}{a-a \cos ^2(x)} \, dx","Int[Sin[x]^3/(a - a*Cos[x]^2),x]","-\frac{\cos (x)}{a}","-\frac{\cos (x)}{a}",1,"-(Cos[x]/a)","A",2,2,16,0.1250,1,"{3175, 2638}"
5,1,5,0,0.0402654,"\int \frac{\sin ^2(x)}{a-a \cos ^2(x)} \, dx","Int[Sin[x]^2/(a - a*Cos[x]^2),x]","\frac{x}{a}","\frac{x}{a}",1,"x/a","A",2,2,16,0.1250,1,"{3175, 8}"
6,1,8,0,0.0249527,"\int \frac{\sin (x)}{a-a \cos ^2(x)} \, dx","Int[Sin[x]/(a - a*Cos[x]^2),x]","-\frac{\tanh ^{-1}(\cos (x))}{a}","-\frac{\tanh ^{-1}(\cos (x))}{a}",1,"-(ArcTanh[Cos[x]]/a)","A",2,2,14,0.1429,1,"{3175, 3770}"
7,1,22,0,0.0439701,"\int \frac{\csc (x)}{a-a \cos ^2(x)} \, dx","Int[Csc[x]/(a - a*Cos[x]^2),x]","-\frac{\tanh ^{-1}(\cos (x))}{2 a}-\frac{\cot (x) \csc (x)}{2 a}","-\frac{\tanh ^{-1}(\cos (x))}{2 a}-\frac{\cot (x) \csc (x)}{2 a}",1,"-ArcTanh[Cos[x]]/(2*a) - (Cot[x]*Csc[x])/(2*a)","A",3,3,14,0.2143,1,"{3175, 3768, 3770}"
8,1,19,0,0.0477914,"\int \frac{\csc ^2(x)}{a-a \cos ^2(x)} \, dx","Int[Csc[x]^2/(a - a*Cos[x]^2),x]","-\frac{\cot ^3(x)}{3 a}-\frac{\cot (x)}{a}","-\frac{\cot ^3(x)}{3 a}-\frac{\cot (x)}{a}",1,"-(Cot[x]/a) - Cot[x]^3/(3*a)","A",3,2,16,0.1250,1,"{3175, 3767}"
9,1,35,0,0.0551938,"\int \frac{\csc ^3(x)}{a-a \cos ^2(x)} \, dx","Int[Csc[x]^3/(a - a*Cos[x]^2),x]","-\frac{3 \tanh ^{-1}(\cos (x))}{8 a}-\frac{\cot (x) \csc ^3(x)}{4 a}-\frac{3 \cot (x) \csc (x)}{8 a}","-\frac{3 \tanh ^{-1}(\cos (x))}{8 a}-\frac{\cot (x) \csc ^3(x)}{4 a}-\frac{3 \cot (x) \csc (x)}{8 a}",1,"(-3*ArcTanh[Cos[x]])/(8*a) - (3*Cot[x]*Csc[x])/(8*a) - (Cot[x]*Csc[x]^3)/(4*a)","A",4,3,16,0.1875,1,"{3175, 3768, 3770}"
10,1,78,0,0.0903888,"\int \frac{\sin ^7(x)}{a+b \cos ^2(x)} \, dx","Int[Sin[x]^7/(a + b*Cos[x]^2),x]","\frac{\left(a^2+3 a b+3 b^2\right) \cos (x)}{b^3}-\frac{(a+3 b) \cos ^3(x)}{3 b^2}-\frac{(a+b)^3 \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}+\frac{\cos ^5(x)}{5 b}","\frac{\left(a^2+3 a b+3 b^2\right) \cos (x)}{b^3}-\frac{(a+3 b) \cos ^3(x)}{3 b^2}-\frac{(a+b)^3 \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}+\frac{\cos ^5(x)}{5 b}",1,"-(((a + b)^3*ArcTan[(Sqrt[b]*Cos[x])/Sqrt[a]])/(Sqrt[a]*b^(7/2))) + ((a^2 + 3*a*b + 3*b^2)*Cos[x])/b^3 - ((a + 3*b)*Cos[x]^3)/(3*b^2) + Cos[x]^5/(5*b)","A",4,3,15,0.2000,1,"{3190, 390, 205}"
11,1,54,0,0.0726949,"\int \frac{\sin ^5(x)}{a+b \cos ^2(x)} \, dx","Int[Sin[x]^5/(a + b*Cos[x]^2),x]","\frac{(a+2 b) \cos (x)}{b^2}-\frac{(a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}-\frac{\cos ^3(x)}{3 b}","\frac{(a+2 b) \cos (x)}{b^2}-\frac{(a+b)^2 \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}-\frac{\cos ^3(x)}{3 b}",1,"-(((a + b)^2*ArcTan[(Sqrt[b]*Cos[x])/Sqrt[a]])/(Sqrt[a]*b^(5/2))) + ((a + 2*b)*Cos[x])/b^2 - Cos[x]^3/(3*b)","A",4,3,15,0.2000,1,"{3190, 390, 205}"
12,1,36,0,0.0531164,"\int \frac{\sin ^3(x)}{a+b \cos ^2(x)} \, dx","Int[Sin[x]^3/(a + b*Cos[x]^2),x]","\frac{\cos (x)}{b}-\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}","\frac{\cos (x)}{b}-\frac{(a+b) \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}",1,"-(((a + b)*ArcTan[(Sqrt[b]*Cos[x])/Sqrt[a]])/(Sqrt[a]*b^(3/2))) + Cos[x]/b","A",3,3,15,0.2000,1,"{3190, 388, 205}"
13,1,26,0,0.0272752,"\int \frac{\sin (x)}{a+b \cos ^2(x)} \, dx","Int[Sin[x]/(a + b*Cos[x]^2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"-(ArcTan[(Sqrt[b]*Cos[x])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]))","A",2,2,13,0.1538,1,"{3190, 205}"
14,1,42,0,0.0491304,"\int \frac{\csc (x)}{a+b \cos ^2(x)} \, dx","Int[Csc[x]/(a + b*Cos[x]^2),x]","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)}-\frac{\tanh ^{-1}(\cos (x))}{a+b}","-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)}-\frac{\tanh ^{-1}(\cos (x))}{a+b}",1,"-((Sqrt[b]*ArcTan[(Sqrt[b]*Cos[x])/Sqrt[a]])/(Sqrt[a]*(a + b))) - ArcTanh[Cos[x]]/(a + b)","A",4,4,13,0.3077,1,"{3190, 391, 206, 205}"
15,1,62,0,0.085531,"\int \frac{\csc ^3(x)}{a+b \cos ^2(x)} \, dx","Int[Csc[x]^3/(a + b*Cos[x]^2),x]","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^2}-\frac{(a+3 b) \tanh ^{-1}(\cos (x))}{2 (a+b)^2}-\frac{\cot (x) \csc (x)}{2 (a+b)}","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^2}-\frac{(a+3 b) \tanh ^{-1}(\cos (x))}{2 (a+b)^2}-\frac{\cot (x) \csc (x)}{2 (a+b)}",1,"-((b^(3/2)*ArcTan[(Sqrt[b]*Cos[x])/Sqrt[a]])/(Sqrt[a]*(a + b)^2)) - ((a + 3*b)*ArcTanh[Cos[x]])/(2*(a + b)^2) - (Cot[x]*Csc[x])/(2*(a + b))","A",5,5,15,0.3333,1,"{3190, 414, 522, 206, 205}"
16,1,94,0,0.1378883,"\int \frac{\csc ^5(x)}{a+b \cos ^2(x)} \, dx","Int[Csc[x]^5/(a + b*Cos[x]^2),x]","-\frac{\left(3 a^2+10 a b+15 b^2\right) \tanh ^{-1}(\cos (x))}{8 (a+b)^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^3}-\frac{\cot (x) \csc ^3(x)}{4 (a+b)}-\frac{(3 a+7 b) \cot (x) \csc (x)}{8 (a+b)^2}","-\frac{\left(3 a^2+10 a b+15 b^2\right) \tanh ^{-1}(\cos (x))}{8 (a+b)^3}-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} \cos (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^3}-\frac{\cot (x) \csc ^3(x)}{4 (a+b)}-\frac{(3 a+7 b) \cot (x) \csc (x)}{8 (a+b)^2}",1,"-((b^(5/2)*ArcTan[(Sqrt[b]*Cos[x])/Sqrt[a]])/(Sqrt[a]*(a + b)^3)) - ((3*a^2 + 10*a*b + 15*b^2)*ArcTanh[Cos[x]])/(8*(a + b)^3) - ((3*a + 7*b)*Cot[x]*Csc[x])/(8*(a + b)^2) - (Cot[x]*Csc[x]^3)/(4*(a + b))","A",6,6,15,0.4000,1,"{3190, 414, 527, 522, 206, 205}"
17,1,88,0,0.1812152,"\int \frac{\sin ^6(x)}{a+b \cos ^2(x)} \, dx","Int[Sin[x]^6/(a + b*Cos[x]^2),x]","-\frac{x \left(8 a^2+20 a b+15 b^2\right)}{8 b^3}+\frac{(4 a+7 b) \sin (x) \cos (x)}{8 b^2}-\frac{(a+b)^{5/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} b^3}+\frac{\sin ^3(x) \cos (x)}{4 b}","-\frac{x \left(8 a^2+20 a b+15 b^2\right)}{8 b^3}+\frac{(4 a+7 b) \sin (x) \cos (x)}{8 b^2}-\frac{(a+b)^{5/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} b^3}+\frac{\sin ^3(x) \cos (x)}{4 b}",1,"-((8*a^2 + 20*a*b + 15*b^2)*x)/(8*b^3) - ((a + b)^(5/2)*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(Sqrt[a]*b^3) + ((4*a + 7*b)*Cos[x]*Sin[x])/(8*b^2) + (Cos[x]*Sin[x]^3)/(4*b)","A",6,6,15,0.4000,1,"{3191, 414, 527, 522, 203, 205}"
18,1,60,0,0.1051332,"\int \frac{\sin ^4(x)}{a+b \cos ^2(x)} \, dx","Int[Sin[x]^4/(a + b*Cos[x]^2),x]","-\frac{x (2 a+3 b)}{2 b^2}-\frac{(a+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} b^2}+\frac{\sin (x) \cos (x)}{2 b}","-\frac{x (2 a+3 b)}{2 b^2}-\frac{(a+b)^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} b^2}+\frac{\sin (x) \cos (x)}{2 b}",1,"-((2*a + 3*b)*x)/(2*b^2) - ((a + b)^(3/2)*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(Sqrt[a]*b^2) + (Cos[x]*Sin[x])/(2*b)","A",5,5,15,0.3333,1,"{3191, 414, 522, 203, 205}"
19,1,40,0,0.0589508,"\int \frac{\sin ^2(x)}{a+b \cos ^2(x)} \, dx","Int[Sin[x]^2/(a + b*Cos[x]^2),x]","-\frac{\sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} b}-\frac{x}{b}","-\frac{\sqrt{a+b} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} b}-\frac{x}{b}",1,"-(x/b) - (Sqrt[a + b]*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(Sqrt[a]*b)","A",4,4,15,0.2667,1,"{3191, 391, 203, 205}"
20,1,30,0,0.0185856,"\int \frac{1}{a+b \cos ^2(x)} \, dx","Int[(a + b*Cos[x]^2)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{a+b}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{a+b}}",1,"-(ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]]/(Sqrt[a]*Sqrt[a + b]))","A",2,2,10,0.2000,1,"{3181, 205}"
21,1,41,0,0.0560492,"\int \frac{\csc ^2(x)}{a+b \cos ^2(x)} \, dx","Int[Csc[x]^2/(a + b*Cos[x]^2),x]","-\frac{\cot (x)}{a+b}-\frac{b \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^{3/2}}","-\frac{\cot (x)}{a+b}-\frac{b \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^{3/2}}",1,"-((b*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(Sqrt[a]*(a + b)^(3/2))) - Cot[x]/(a + b)","A",3,3,15,0.2000,1,"{3191, 388, 205}"
22,1,61,0,0.0802187,"\int \frac{\csc ^4(x)}{a+b \cos ^2(x)} \, dx","Int[Csc[x]^4/(a + b*Cos[x]^2),x]","-\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^{5/2}}-\frac{\cot ^3(x)}{3 (a+b)}-\frac{(a+2 b) \cot (x)}{(a+b)^2}","-\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^{5/2}}-\frac{\cot ^3(x)}{3 (a+b)}-\frac{(a+2 b) \cot (x)}{(a+b)^2}",1,"-((b^2*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(Sqrt[a]*(a + b)^(5/2))) - ((a + 2*b)*Cot[x])/(a + b)^2 - Cot[x]^3/(3*(a + b))","A",4,3,15,0.2000,1,"{3191, 390, 205}"
23,1,89,0,0.1016013,"\int \frac{\csc ^6(x)}{a+b \cos ^2(x)} \, dx","Int[Csc[x]^6/(a + b*Cos[x]^2),x]","-\frac{\left(a^2+3 a b+3 b^2\right) \cot (x)}{(a+b)^3}-\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^{7/2}}-\frac{\cot ^5(x)}{5 (a+b)}-\frac{(2 a+3 b) \cot ^3(x)}{3 (a+b)^2}","-\frac{\left(a^2+3 a b+3 b^2\right) \cot (x)}{(a+b)^3}-\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} (a+b)^{7/2}}-\frac{\cot ^5(x)}{5 (a+b)}-\frac{(2 a+3 b) \cot ^3(x)}{3 (a+b)^2}",1,"-((b^3*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(Sqrt[a]*(a + b)^(7/2))) - ((a^2 + 3*a*b + 3*b^2)*Cot[x])/(a + b)^3 - ((2*a + 3*b)*Cot[x]^3)/(3*(a + b)^2) - Cot[x]^5/(5*(a + b))","A",4,3,15,0.2000,1,"{3191, 390, 205}"
24,1,98,0,0.0903281,"\int \frac{\sin (x)}{4-3 \cos ^3(x)} \, dx","Int[Sin[x]/(4 - 3*Cos[x]^3),x]","-\frac{\log \left(3^{2/3} \cos ^2(x)+2^{2/3} \sqrt[3]{3} \cos (x)+2 \sqrt[3]{2}\right)}{12 \sqrt[3]{6}}+\frac{\log \left(2^{2/3}-\sqrt[3]{3} \cos (x)\right)}{6 \sqrt[3]{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{6} \cos (x)+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} 3^{5/6}}","-\frac{\log \left(3^{2/3} \cos ^2(x)+2^{2/3} \sqrt[3]{3} \cos (x)+2 \sqrt[3]{2}\right)}{12 \sqrt[3]{6}}+\frac{\log \left(2^{2/3}-\sqrt[3]{3} \cos (x)\right)}{6 \sqrt[3]{6}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{6} \cos (x)+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} 3^{5/6}}",1,"-ArcTan[(1 + 6^(1/3)*Cos[x])/Sqrt[3]]/(2*2^(1/3)*3^(5/6)) + Log[2^(2/3) - 3^(1/3)*Cos[x]]/(6*6^(1/3)) - Log[2*2^(1/3) + 2^(2/3)*3^(1/3)*Cos[x] + 3^(2/3)*Cos[x]^2]/(12*6^(1/3))","A",7,7,13,0.5385,1,"{3223, 200, 31, 634, 617, 204, 628}"
25,1,4,0,0.0135559,"\int \frac{1}{1-\cos ^2(x)} \, dx","Int[(1 - Cos[x]^2)^(-1),x]","-\cot (x)","-\cot (x)",1,"-Cot[x]","A",3,3,10,0.3000,1,"{3175, 3767, 8}"
26,1,13,0,0.0148672,"\int \frac{1}{\left(1-\cos ^2(x)\right)^2} \, dx","Int[(1 - Cos[x]^2)^(-2),x]","-\frac{1}{3} \cot ^3(x)-\cot (x)","-\frac{1}{3} \cot ^3(x)-\cot (x)",1,"-Cot[x] - Cot[x]^3/3","A",3,2,10,0.2000,1,"{3175, 3767}"
27,1,21,0,0.0171482,"\int \frac{1}{\left(1-\cos ^2(x)\right)^3} \, dx","Int[(1 - Cos[x]^2)^(-3),x]","-\frac{1}{5} \cot ^5(x)-\frac{2 \cot ^3(x)}{3}-\cot (x)","-\frac{1}{5} \cot ^5(x)-\frac{2 \cot ^3(x)}{3}-\cot (x)",1,"-Cot[x] - (2*Cot[x]^3)/3 - Cot[x]^5/5","A",3,2,10,0.2000,1,"{3175, 3767}"
28,1,78,0,0.0840385,"\int \frac{\cos ^7(x)}{a+b \cos ^2(x)} \, dx","Int[Cos[x]^7/(a + b*Cos[x]^2),x]","\frac{\left(a^2-a b+b^2\right) \sin (x)}{b^3}-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{b^{7/2} \sqrt{a+b}}+\frac{(a-2 b) \sin ^3(x)}{3 b^2}+\frac{\sin ^5(x)}{5 b}","\frac{\left(a^2-a b+b^2\right) \sin (x)}{b^3}-\frac{a^3 \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{b^{7/2} \sqrt{a+b}}+\frac{(a-2 b) \sin ^3(x)}{3 b^2}+\frac{\sin ^5(x)}{5 b}",1,"-((a^3*ArcTanh[(Sqrt[b]*Sin[x])/Sqrt[a + b]])/(b^(7/2)*Sqrt[a + b])) + ((a^2 - a*b + b^2)*Sin[x])/b^3 + ((a - 2*b)*Sin[x]^3)/(3*b^2) + Sin[x]^5/(5*b)","A",4,3,15,0.2000,1,"{3186, 390, 208}"
29,1,56,0,0.071169,"\int \frac{\cos ^5(x)}{a+b \cos ^2(x)} \, dx","Int[Cos[x]^5/(a + b*Cos[x]^2),x]","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{b^{5/2} \sqrt{a+b}}-\frac{(a-b) \sin (x)}{b^2}-\frac{\sin ^3(x)}{3 b}","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{b^{5/2} \sqrt{a+b}}-\frac{(a-b) \sin (x)}{b^2}-\frac{\sin ^3(x)}{3 b}",1,"(a^2*ArcTanh[(Sqrt[b]*Sin[x])/Sqrt[a + b]])/(b^(5/2)*Sqrt[a + b]) - ((a - b)*Sin[x])/b^2 - Sin[x]^3/(3*b)","A",4,3,15,0.2000,1,"{3186, 390, 208}"
30,1,38,0,0.0550803,"\int \frac{\cos ^3(x)}{a+b \cos ^2(x)} \, dx","Int[Cos[x]^3/(a + b*Cos[x]^2),x]","\frac{\sin (x)}{b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{b^{3/2} \sqrt{a+b}}","\frac{\sin (x)}{b}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{b^{3/2} \sqrt{a+b}}",1,"-((a*ArcTanh[(Sqrt[b]*Sin[x])/Sqrt[a + b]])/(b^(3/2)*Sqrt[a + b])) + Sin[x]/b","A",3,3,15,0.2000,1,"{3186, 388, 208}"
31,1,29,0,0.030828,"\int \frac{\cos (x)}{a+b \cos ^2(x)} \, dx","Int[Cos[x]/(a + b*Cos[x]^2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{\sqrt{b} \sqrt{a+b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{\sqrt{b} \sqrt{a+b}}",1,"ArcTanh[(Sqrt[b]*Sin[x])/Sqrt[a + b]]/(Sqrt[b]*Sqrt[a + b])","A",2,2,13,0.1538,1,"{3186, 208}"
32,1,41,0,0.0524032,"\int \frac{\sec (x)}{a+b \cos ^2(x)} \, dx","Int[Sec[x]/(a + b*Cos[x]^2),x]","\frac{\tanh ^{-1}(\sin (x))}{a}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{a \sqrt{a+b}}","\frac{\tanh ^{-1}(\sin (x))}{a}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{a \sqrt{a+b}}",1,"ArcTanh[Sin[x]]/a - (Sqrt[b]*ArcTanh[(Sqrt[b]*Sin[x])/Sqrt[a + b]])/(a*Sqrt[a + b])","A",4,4,13,0.3077,1,"{3186, 391, 206, 208}"
33,1,59,0,0.0981543,"\int \frac{\sec ^3(x)}{a+b \cos ^2(x)} \, dx","Int[Sec[x]^3/(a + b*Cos[x]^2),x]","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{a^2 \sqrt{a+b}}+\frac{(a-2 b) \tanh ^{-1}(\sin (x))}{2 a^2}+\frac{\tan (x) \sec (x)}{2 a}","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{a^2 \sqrt{a+b}}+\frac{(a-2 b) \tanh ^{-1}(\sin (x))}{2 a^2}+\frac{\tan (x) \sec (x)}{2 a}",1,"((a - 2*b)*ArcTanh[Sin[x]])/(2*a^2) + (b^(3/2)*ArcTanh[(Sqrt[b]*Sin[x])/Sqrt[a + b]])/(a^2*Sqrt[a + b]) + (Sec[x]*Tan[x])/(2*a)","A",5,5,15,0.3333,1,"{3186, 414, 522, 206, 208}"
34,1,90,0,0.165703,"\int \frac{\sec ^5(x)}{a+b \cos ^2(x)} \, dx","Int[Sec[x]^5/(a + b*Cos[x]^2),x]","\frac{\left(3 a^2-4 a b+8 b^2\right) \tanh ^{-1}(\sin (x))}{8 a^3}-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{a^3 \sqrt{a+b}}+\frac{(3 a-4 b) \tan (x) \sec (x)}{8 a^2}+\frac{\tan (x) \sec ^3(x)}{4 a}","\frac{\left(3 a^2-4 a b+8 b^2\right) \tanh ^{-1}(\sin (x))}{8 a^3}-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sin (x)}{\sqrt{a+b}}\right)}{a^3 \sqrt{a+b}}+\frac{(3 a-4 b) \tan (x) \sec (x)}{8 a^2}+\frac{\tan (x) \sec ^3(x)}{4 a}",1,"((3*a^2 - 4*a*b + 8*b^2)*ArcTanh[Sin[x]])/(8*a^3) - (b^(5/2)*ArcTanh[(Sqrt[b]*Sin[x])/Sqrt[a + b]])/(a^3*Sqrt[a + b]) + ((3*a - 4*b)*Sec[x]*Tan[x])/(8*a^2) + (Sec[x]^3*Tan[x])/(4*a)","A",6,6,15,0.4000,1,"{3186, 414, 527, 522, 206, 208}"
35,1,87,0,0.196291,"\int \frac{\cos ^6(x)}{a+b \cos ^2(x)} \, dx","Int[Cos[x]^6/(a + b*Cos[x]^2),x]","\frac{x \left(8 a^2-4 a b+3 b^2\right)}{8 b^3}+\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{b^3 \sqrt{a+b}}-\frac{(4 a-3 b) \sin (x) \cos (x)}{8 b^2}+\frac{\sin (x) \cos ^3(x)}{4 b}","\frac{x \left(8 a^2-4 a b+3 b^2\right)}{8 b^3}+\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{b^3 \sqrt{a+b}}-\frac{(4 a-3 b) \sin (x) \cos (x)}{8 b^2}+\frac{\sin (x) \cos ^3(x)}{4 b}",1,"((8*a^2 - 4*a*b + 3*b^2)*x)/(8*b^3) + (a^(5/2)*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(b^3*Sqrt[a + b]) - ((4*a - 3*b)*Cos[x]*Sin[x])/(8*b^2) + (Cos[x]^3*Sin[x])/(4*b)","A",6,6,15,0.4000,1,"{3187, 470, 578, 522, 203, 205}"
36,1,60,0,0.0980954,"\int \frac{\cos ^4(x)}{a+b \cos ^2(x)} \, dx","Int[Cos[x]^4/(a + b*Cos[x]^2),x]","-\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{b^2 \sqrt{a+b}}-\frac{x (2 a-b)}{2 b^2}+\frac{\sin (x) \cos (x)}{2 b}","-\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{b^2 \sqrt{a+b}}-\frac{x (2 a-b)}{2 b^2}+\frac{\sin (x) \cos (x)}{2 b}",1,"-((2*a - b)*x)/(2*b^2) - (a^(3/2)*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(b^2*Sqrt[a + b]) + (Cos[x]*Sin[x])/(2*b)","A",5,5,15,0.3333,1,"{3187, 470, 522, 203, 205}"
37,1,38,0,0.0596243,"\int \frac{\cos ^2(x)}{a+b \cos ^2(x)} \, dx","Int[Cos[x]^2/(a + b*Cos[x]^2),x]","\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{b \sqrt{a+b}}+\frac{x}{b}","\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{b \sqrt{a+b}}+\frac{x}{b}",1,"x/b + (Sqrt[a]*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(b*Sqrt[a + b])","A",3,3,15,0.2000,1,"{3171, 3181, 205}"
38,1,30,0,0.0187539,"\int \frac{1}{a+b \cos ^2(x)} \, dx","Int[(a + b*Cos[x]^2)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{a+b}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{a+b}}",1,"-(ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]]/(Sqrt[a]*Sqrt[a + b]))","A",2,2,10,0.2000,1,"{3181, 205}"
39,1,37,0,0.0605322,"\int \frac{\sec ^2(x)}{a+b \cos ^2(x)} \, dx","Int[Sec[x]^2/(a + b*Cos[x]^2),x]","\frac{b \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{a^{3/2} \sqrt{a+b}}+\frac{\tan (x)}{a}","\frac{b \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{a^{3/2} \sqrt{a+b}}+\frac{\tan (x)}{a}",1,"(b*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(a^(3/2)*Sqrt[a + b]) + Tan[x]/a","A",3,3,15,0.2000,1,"{3187, 453, 205}"
40,1,56,0,0.0860343,"\int \frac{\sec ^4(x)}{a+b \cos ^2(x)} \, dx","Int[Sec[x]^4/(a + b*Cos[x]^2),x]","-\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{a^{5/2} \sqrt{a+b}}+\frac{(a-b) \tan (x)}{a^2}+\frac{\tan ^3(x)}{3 a}","-\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{a^{5/2} \sqrt{a+b}}+\frac{(a-b) \tan (x)}{a^2}+\frac{\tan ^3(x)}{3 a}",1,"-((b^2*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(a^(5/2)*Sqrt[a + b])) + ((a - b)*Tan[x])/a^2 + Tan[x]^3/(3*a)","A",4,3,15,0.2000,1,"{3187, 461, 205}"
41,1,79,0,0.1012289,"\int \frac{\sec ^6(x)}{a+b \cos ^2(x)} \, dx","Int[Sec[x]^6/(a + b*Cos[x]^2),x]","\frac{\left(a^2-a b+b^2\right) \tan (x)}{a^3}+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{a^{7/2} \sqrt{a+b}}+\frac{(2 a-b) \tan ^3(x)}{3 a^2}+\frac{\tan ^5(x)}{5 a}","\frac{\left(a^2-a b+b^2\right) \tan (x)}{a^3}+\frac{b^3 \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{a^{7/2} \sqrt{a+b}}+\frac{(2 a-b) \tan ^3(x)}{3 a^2}+\frac{\tan ^5(x)}{5 a}",1,"(b^3*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(a^(7/2)*Sqrt[a + b]) + ((a^2 - a*b + b^2)*Tan[x])/a^3 + ((2*a - b)*Tan[x]^3)/(3*a^2) + Tan[x]^5/(5*a)","A",4,3,15,0.2000,1,"{3187, 461, 205}"
42,1,65,0,0.0493253,"\int \frac{1}{\left(a+b \cos ^2(x)\right)^2} \, dx","Int[(a + b*Cos[x]^2)^(-2),x]","-\frac{(2 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{2 a^{3/2} (a+b)^{3/2}}-\frac{b \sin (x) \cos (x)}{2 a (a+b) \left(a+b \cos ^2(x)\right)}","-\frac{(2 a+b) \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{2 a^{3/2} (a+b)^{3/2}}-\frac{b \sin (x) \cos (x)}{2 a (a+b) \left(a+b \cos ^2(x)\right)}",1,"-((2*a + b)*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(2*a^(3/2)*(a + b)^(3/2)) - (b*Cos[x]*Sin[x])/(2*a*(a + b)*(a + b*Cos[x]^2))","A",4,4,10,0.4000,1,"{3184, 12, 3181, 205}"
43,1,107,0,0.1171565,"\int \frac{1}{\left(a+b \cos ^2(x)\right)^3} \, dx","Int[(a + b*Cos[x]^2)^(-3),x]","-\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{8 a^{5/2} (a+b)^{5/2}}-\frac{3 b (2 a+b) \sin (x) \cos (x)}{8 a^2 (a+b)^2 \left(a+b \cos ^2(x)\right)}-\frac{b \sin (x) \cos (x)}{4 a (a+b) \left(a+b \cos ^2(x)\right)^2}","-\frac{\left(8 a^2+8 a b+3 b^2\right) \tan ^{-1}\left(\frac{\sqrt{a+b} \cot (x)}{\sqrt{a}}\right)}{8 a^{5/2} (a+b)^{5/2}}-\frac{3 b (2 a+b) \sin (x) \cos (x)}{8 a^2 (a+b)^2 \left(a+b \cos ^2(x)\right)}-\frac{b \sin (x) \cos (x)}{4 a (a+b) \left(a+b \cos ^2(x)\right)^2}",1,"-((8*a^2 + 8*a*b + 3*b^2)*ArcTan[(Sqrt[a + b]*Cot[x])/Sqrt[a]])/(8*a^(5/2)*(a + b)^(5/2)) - (b*Cos[x]*Sin[x])/(4*a*(a + b)*(a + b*Cos[x]^2)^2) - (3*b*(2*a + b)*Cos[x]*Sin[x])/(8*a^2*(a + b)^2*(a + b*Cos[x]^2))","A",5,5,10,0.5000,1,"{3184, 3173, 12, 3181, 205}"
44,1,34,0,0.0129128,"\int \frac{1}{1+\cos ^2(x)} \, dx","Int[(1 + Cos[x]^2)^(-1),x]","\frac{x}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{\sqrt{2}}","\frac{x}{\sqrt{2}}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{\sqrt{2}}",1,"x/Sqrt[2] - ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Cos[x]^2)]/Sqrt[2]","A",2,2,8,0.2500,1,"{3181, 203}"
45,1,55,0,0.0257585,"\int \frac{1}{\left(1+\cos ^2(x)\right)^2} \, dx","Int[(1 + Cos[x]^2)^(-2),x]","\frac{3 x}{4 \sqrt{2}}-\frac{\sin (x) \cos (x)}{4 \left(\cos ^2(x)+1\right)}-\frac{3 \tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{4 \sqrt{2}}","\frac{3 x}{4 \sqrt{2}}-\frac{\sin (x) \cos (x)}{4 \left(\cos ^2(x)+1\right)}-\frac{3 \tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{4 \sqrt{2}}",1,"(3*x)/(4*Sqrt[2]) - (3*ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Cos[x]^2)])/(4*Sqrt[2]) - (Cos[x]*Sin[x])/(4*(1 + Cos[x]^2))","A",4,4,8,0.5000,1,"{3184, 12, 3181, 203}"
46,1,71,0,0.0523739,"\int \frac{1}{\left(1+\cos ^2(x)\right)^3} \, dx","Int[(1 + Cos[x]^2)^(-3),x]","\frac{19 x}{32 \sqrt{2}}-\frac{9 \sin (x) \cos (x)}{32 \left(\cos ^2(x)+1\right)}-\frac{\sin (x) \cos (x)}{8 \left(\cos ^2(x)+1\right)^2}-\frac{19 \tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{32 \sqrt{2}}","\frac{19 x}{32 \sqrt{2}}-\frac{9 \sin (x) \cos (x)}{32 \left(\cos ^2(x)+1\right)}-\frac{\sin (x) \cos (x)}{8 \left(\cos ^2(x)+1\right)^2}-\frac{19 \tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{32 \sqrt{2}}",1,"(19*x)/(32*Sqrt[2]) - (19*ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Cos[x]^2)])/(32*Sqrt[2]) - (Cos[x]*Sin[x])/(8*(1 + Cos[x]^2)^2) - (9*Cos[x]*Sin[x])/(32*(1 + Cos[x]^2))","A",5,5,8,0.6250,1,"{3184, 3173, 12, 3181, 203}"
47,1,12,0,0.0158364,"\int \sqrt{1-\cos ^2(x)} \, dx","Int[Sqrt[1 - Cos[x]^2],x]","\sqrt{\sin ^2(x)} (-\cot (x))","\sqrt{\sin ^2(x)} (-\cot (x))",1,"-(Cot[x]*Sqrt[Sin[x]^2])","A",3,3,12,0.2500,1,"{3176, 3207, 2638}"
48,1,14,0,0.0158867,"\int \sqrt{-1+\cos ^2(x)} \, dx","Int[Sqrt[-1 + Cos[x]^2],x]","\sqrt{-\sin ^2(x)} (-\cot (x))","\sqrt{-\sin ^2(x)} (-\cot (x))",1,"-(Cot[x]*Sqrt[-Sin[x]^2])","A",3,3,10,0.3000,1,"{3176, 3207, 2638}"
49,1,29,0,0.022335,"\int \left(1-\cos ^2(x)\right)^{3/2} \, dx","Int[(1 - Cos[x]^2)^(3/2),x]","-\frac{1}{3} \sin ^2(x)^{3/2} \cot (x)-\frac{2}{3} \sqrt{\sin ^2(x)} \cot (x)","-\frac{1}{3} \sin ^2(x)^{3/2} \cot (x)-\frac{2}{3} \sqrt{\sin ^2(x)} \cot (x)",1,"(-2*Cot[x]*Sqrt[Sin[x]^2])/3 - (Cot[x]*(Sin[x]^2)^(3/2))/3","A",4,4,12,0.3333,1,"{3176, 3203, 3207, 2638}"
50,1,33,0,0.0246809,"\int \left(-1+\cos ^2(x)\right)^{3/2} \, dx","Int[(-1 + Cos[x]^2)^(3/2),x]","\frac{2}{3} \sqrt{-\sin ^2(x)} \cot (x)-\frac{1}{3} \left(-\sin ^2(x)\right)^{3/2} \cot (x)","\frac{2}{3} \sqrt{-\sin ^2(x)} \cot (x)-\frac{1}{3} \left(-\sin ^2(x)\right)^{3/2} \cot (x)",1,"(2*Cot[x]*Sqrt[-Sin[x]^2])/3 - (Cot[x]*(-Sin[x]^2)^(3/2))/3","A",4,4,10,0.4000,1,"{3176, 3203, 3207, 2638}"
51,1,15,0,0.0198256,"\int \frac{1}{\sqrt{1-\cos ^2(x)}} \, dx","Int[1/Sqrt[1 - Cos[x]^2],x]","-\frac{\sin (x) \tanh ^{-1}(\cos (x))}{\sqrt{\sin ^2(x)}}","-\frac{\sin (x) \tanh ^{-1}(\cos (x))}{\sqrt{\sin ^2(x)}}",1,"-((ArcTanh[Cos[x]]*Sin[x])/Sqrt[Sin[x]^2])","A",3,3,12,0.2500,1,"{3176, 3207, 3770}"
52,1,17,0,0.0184225,"\int \frac{1}{\sqrt{-1+\cos ^2(x)}} \, dx","Int[1/Sqrt[-1 + Cos[x]^2],x]","-\frac{\sin (x) \tanh ^{-1}(\cos (x))}{\sqrt{-\sin ^2(x)}}","-\frac{\sin (x) \tanh ^{-1}(\cos (x))}{\sqrt{-\sin ^2(x)}}",1,"-((ArcTanh[Cos[x]]*Sin[x])/Sqrt[-Sin[x]^2])","A",3,3,10,0.3000,1,"{3176, 3207, 3770}"
53,1,32,0,0.0269628,"\int \frac{1}{\left(1-\cos ^2(x)\right)^{3/2}} \, dx","Int[(1 - Cos[x]^2)^(-3/2),x]","-\frac{\cot (x)}{2 \sqrt{\sin ^2(x)}}-\frac{\sin (x) \tanh ^{-1}(\cos (x))}{2 \sqrt{\sin ^2(x)}}","-\frac{\cot (x)}{2 \sqrt{\sin ^2(x)}}-\frac{\sin (x) \tanh ^{-1}(\cos (x))}{2 \sqrt{\sin ^2(x)}}",1,"-Cot[x]/(2*Sqrt[Sin[x]^2]) - (ArcTanh[Cos[x]]*Sin[x])/(2*Sqrt[Sin[x]^2])","A",4,4,12,0.3333,1,"{3176, 3204, 3207, 3770}"
54,1,36,0,0.025746,"\int \frac{1}{\left(-1+\cos ^2(x)\right)^{3/2}} \, dx","Int[(-1 + Cos[x]^2)^(-3/2),x]","\frac{\cot (x)}{2 \sqrt{-\sin ^2(x)}}+\frac{\sin (x) \tanh ^{-1}(\cos (x))}{2 \sqrt{-\sin ^2(x)}}","\frac{\cot (x)}{2 \sqrt{-\sin ^2(x)}}+\frac{\sin (x) \tanh ^{-1}(\cos (x))}{2 \sqrt{-\sin ^2(x)}}",1,"Cot[x]/(2*Sqrt[-Sin[x]^2]) + (ArcTanh[Cos[x]]*Sin[x])/(2*Sqrt[-Sin[x]^2])","A",4,4,10,0.4000,1,"{3176, 3204, 3207, 3770}"
55,1,9,0,0.0080177,"\int \sqrt{1+\cos ^2(x)} \, dx","Int[Sqrt[1 + Cos[x]^2],x]","E\left(\left.x+\frac{\pi }{2}\right|-1\right)","E\left(\left.x+\frac{\pi }{2}\right|-1\right)",1,"EllipticE[Pi/2 + x, -1]","A",1,1,10,0.1000,1,"{3177}"
56,1,32,0,0.0222627,"\int \sqrt{-1-\cos ^2(x)} \, dx","Int[Sqrt[-1 - Cos[x]^2],x]","\frac{\sqrt{-\cos ^2(x)-1} E\left(\left.x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cos ^2(x)+1}}","\frac{\sqrt{-\cos ^2(x)-1} E\left(\left.x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cos ^2(x)+1}}",1,"(Sqrt[-1 - Cos[x]^2]*EllipticE[Pi/2 + x, -1])/Sqrt[1 + Cos[x]^2]","A",2,2,12,0.1667,1,"{3178, 3177}"
57,1,42,0,0.0350783,"\int \sqrt{a+b \cos ^2(x)} \, dx","Int[Sqrt[a + b*Cos[x]^2],x]","\frac{\sqrt{a+b \cos ^2(x)} E\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{\frac{b \cos ^2(x)}{a}+1}}","\frac{\sqrt{a+b \cos ^2(x)} E\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{\frac{b \cos ^2(x)}{a}+1}}",1,"(Sqrt[a + b*Cos[x]^2]*EllipticE[Pi/2 + x, -(b/a)])/Sqrt[1 + (b*Cos[x]^2)/a]","A",2,2,12,0.1667,1,"{3178, 3177}"
58,1,43,0,0.054289,"\int \left(1+\cos ^2(x)\right)^{3/2} \, dx","Int[(1 + Cos[x]^2)^(3/2),x]","-\frac{2}{3} F\left(\left.x+\frac{\pi }{2}\right|-1\right)+2 E\left(\left.x+\frac{\pi }{2}\right|-1\right)+\frac{1}{3} \sin (x) \cos (x) \sqrt{\cos ^2(x)+1}","-\frac{2}{3} F\left(\left.x+\frac{\pi }{2}\right|-1\right)+2 E\left(\left.x+\frac{\pi }{2}\right|-1\right)+\frac{1}{3} \sin (x) \cos (x) \sqrt{\cos ^2(x)+1}",1,"2*EllipticE[Pi/2 + x, -1] - (2*EllipticF[Pi/2 + x, -1])/3 + (Cos[x]*Sqrt[1 + Cos[x]^2]*Sin[x])/3","A",4,4,10,0.4000,1,"{3180, 3172, 3177, 3182}"
59,1,89,0,0.0941136,"\int \left(-1-\cos ^2(x)\right)^{3/2} \, dx","Int[(-1 - Cos[x]^2)^(3/2),x]","-\frac{1}{3} \sin (x) \cos (x) \sqrt{-\cos ^2(x)-1}-\frac{2 \sqrt{\cos ^2(x)+1} F\left(\left.x+\frac{\pi }{2}\right|-1\right)}{3 \sqrt{-\cos ^2(x)-1}}-\frac{2 \sqrt{-\cos ^2(x)-1} E\left(\left.x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cos ^2(x)+1}}","-\frac{1}{3} \sin (x) \cos (x) \sqrt{-\cos ^2(x)-1}-\frac{2 \sqrt{\cos ^2(x)+1} F\left(\left.x+\frac{\pi }{2}\right|-1\right)}{3 \sqrt{-\cos ^2(x)-1}}-\frac{2 \sqrt{-\cos ^2(x)-1} E\left(\left.x+\frac{\pi }{2}\right|-1\right)}{\sqrt{\cos ^2(x)+1}}",1,"(-2*Sqrt[-1 - Cos[x]^2]*EllipticE[Pi/2 + x, -1])/Sqrt[1 + Cos[x]^2] - (2*Sqrt[1 + Cos[x]^2]*EllipticF[Pi/2 + x, -1])/(3*Sqrt[-1 - Cos[x]^2]) - (Cos[x]*Sqrt[-1 - Cos[x]^2]*Sin[x])/3","A",6,6,12,0.5000,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
60,1,121,0,0.1617385,"\int \left(a+b \cos ^2(x)\right)^{3/2} \, dx","Int[(a + b*Cos[x]^2)^(3/2),x]","\frac{1}{3} b \sin (x) \cos (x) \sqrt{a+b \cos ^2(x)}-\frac{a (a+b) \sqrt{\frac{b \cos ^2(x)}{a}+1} F\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{a+b \cos ^2(x)}}+\frac{2 (2 a+b) \sqrt{a+b \cos ^2(x)} E\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{\frac{b \cos ^2(x)}{a}+1}}","\frac{1}{3} b \sin (x) \cos (x) \sqrt{a+b \cos ^2(x)}-\frac{a (a+b) \sqrt{\frac{b \cos ^2(x)}{a}+1} F\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{a+b \cos ^2(x)}}+\frac{2 (2 a+b) \sqrt{a+b \cos ^2(x)} E\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{3 \sqrt{\frac{b \cos ^2(x)}{a}+1}}",1,"(2*(2*a + b)*Sqrt[a + b*Cos[x]^2]*EllipticE[Pi/2 + x, -(b/a)])/(3*Sqrt[1 + (b*Cos[x]^2)/a]) - (a*(a + b)*Sqrt[1 + (b*Cos[x]^2)/a]*EllipticF[Pi/2 + x, -(b/a)])/(3*Sqrt[a + b*Cos[x]^2]) + (b*Cos[x]*Sqrt[a + b*Cos[x]^2]*Sin[x])/3","A",6,6,12,0.5000,1,"{3180, 3172, 3178, 3177, 3183, 3182}"
61,1,9,0,0.0077743,"\int \frac{1}{\sqrt{1+\cos ^2(x)}} \, dx","Int[1/Sqrt[1 + Cos[x]^2],x]","F\left(\left.x+\frac{\pi }{2}\right|-1\right)","F\left(\left.x+\frac{\pi }{2}\right|-1\right)",1,"EllipticF[Pi/2 + x, -1]","A",1,1,10,0.1000,1,"{3182}"
62,1,32,0,0.0183404,"\int \frac{1}{\sqrt{-1-\cos ^2(x)}} \, dx","Int[1/Sqrt[-1 - Cos[x]^2],x]","\frac{\sqrt{\cos ^2(x)+1} F\left(\left.x+\frac{\pi }{2}\right|-1\right)}{\sqrt{-\cos ^2(x)-1}}","\frac{\sqrt{\cos ^2(x)+1} F\left(\left.x+\frac{\pi }{2}\right|-1\right)}{\sqrt{-\cos ^2(x)-1}}",1,"(Sqrt[1 + Cos[x]^2]*EllipticF[Pi/2 + x, -1])/Sqrt[-1 - Cos[x]^2]","A",2,2,12,0.1667,1,"{3183, 3182}"
63,1,42,0,0.0289905,"\int \frac{1}{\sqrt{a+b \cos ^2(x)}} \, dx","Int[1/Sqrt[a + b*Cos[x]^2],x]","\frac{\sqrt{\frac{b \cos ^2(x)}{a}+1} F\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{a+b \cos ^2(x)}}","\frac{\sqrt{\frac{b \cos ^2(x)}{a}+1} F\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{\sqrt{a+b \cos ^2(x)}}",1,"(Sqrt[1 + (b*Cos[x]^2)/a]*EllipticF[Pi/2 + x, -(b/a)])/Sqrt[a + b*Cos[x]^2]","A",2,2,12,0.1667,1,"{3183, 3182}"
64,1,32,0,0.0182579,"\int \frac{1}{\left(1+\cos ^2(x)\right)^{3/2}} \, dx","Int[(1 + Cos[x]^2)^(-3/2),x]","\frac{1}{2} E\left(\left.x+\frac{\pi }{2}\right|-1\right)-\frac{\sin (x) \cos (x)}{2 \sqrt{\cos ^2(x)+1}}","\frac{1}{2} E\left(\left.x+\frac{\pi }{2}\right|-1\right)-\frac{\sin (x) \cos (x)}{2 \sqrt{\cos ^2(x)+1}}",1,"EllipticE[Pi/2 + x, -1]/2 - (Cos[x]*Sin[x])/(2*Sqrt[1 + Cos[x]^2])","A",3,3,10,0.3000,1,"{3184, 21, 3177}"
65,1,56,0,0.03296,"\int \frac{1}{\left(-1-\cos ^2(x)\right)^{3/2}} \, dx","Int[(-1 - Cos[x]^2)^(-3/2),x]","\frac{\sin (x) \cos (x)}{2 \sqrt{-\cos ^2(x)-1}}+\frac{\sqrt{-\cos ^2(x)-1} E\left(\left.x+\frac{\pi }{2}\right|-1\right)}{2 \sqrt{\cos ^2(x)+1}}","\frac{\sin (x) \cos (x)}{2 \sqrt{-\cos ^2(x)-1}}+\frac{\sqrt{-\cos ^2(x)-1} E\left(\left.x+\frac{\pi }{2}\right|-1\right)}{2 \sqrt{\cos ^2(x)+1}}",1,"(Sqrt[-1 - Cos[x]^2]*EllipticE[Pi/2 + x, -1])/(2*Sqrt[1 + Cos[x]^2]) + (Cos[x]*Sin[x])/(2*Sqrt[-1 - Cos[x]^2])","A",4,4,12,0.3333,1,"{3184, 21, 3178, 3177}"
66,1,78,0,0.0474696,"\int \frac{1}{\left(a+b \cos ^2(x)\right)^{3/2}} \, dx","Int[(a + b*Cos[x]^2)^(-3/2),x]","\frac{\sqrt{a+b \cos ^2(x)} E\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{a (a+b) \sqrt{\frac{b \cos ^2(x)}{a}+1}}-\frac{b \sin (x) \cos (x)}{a (a+b) \sqrt{a+b \cos ^2(x)}}","\frac{\sqrt{a+b \cos ^2(x)} E\left(x+\frac{\pi }{2}|-\frac{b}{a}\right)}{a (a+b) \sqrt{\frac{b \cos ^2(x)}{a}+1}}-\frac{b \sin (x) \cos (x)}{a (a+b) \sqrt{a+b \cos ^2(x)}}",1,"(Sqrt[a + b*Cos[x]^2]*EllipticE[Pi/2 + x, -(b/a)])/(a*(a + b)*Sqrt[1 + (b*Cos[x]^2)/a]) - (b*Cos[x]*Sin[x])/(a*(a + b)*Sqrt[a + b*Cos[x]^2])","A",4,4,12,0.3333,1,"{3184, 21, 3178, 3177}"
67,1,9,0,0.0211736,"\int \frac{\cos (x)}{\sqrt{1+\cos ^2(x)}} \, dx","Int[Cos[x]/Sqrt[1 + Cos[x]^2],x]","\sin ^{-1}\left(\frac{\sin (x)}{\sqrt{2}}\right)","\sin ^{-1}\left(\frac{\sin (x)}{\sqrt{2}}\right)",1,"ArcSin[Sin[x]/Sqrt[2]]","A",2,2,13,0.1538,1,"{3186, 216}"
68,1,15,0,0.0272563,"\int \frac{\cos (5+3 x)}{\sqrt{3+\cos ^2(5+3 x)}} \, dx","Int[Cos[5 + 3*x]/Sqrt[3 + Cos[5 + 3*x]^2],x]","\frac{1}{3} \sin ^{-1}\left(\frac{1}{2} \sin (3 x+5)\right)","\frac{1}{3} \sin ^{-1}\left(\frac{1}{2} \sin (3 x+5)\right)",1,"ArcSin[Sin[5 + 3*x]/2]/3","A",2,2,21,0.09524,1,"{3186, 216}"
69,1,9,0,0.0257469,"\int \frac{\cos (x)}{\sqrt{4-\cos ^2(x)}} \, dx","Int[Cos[x]/Sqrt[4 - Cos[x]^2],x]","\sinh ^{-1}\left(\frac{\sin (x)}{\sqrt{3}}\right)","\sinh ^{-1}\left(\frac{\sin (x)}{\sqrt{3}}\right)",1,"ArcSinh[Sin[x]/Sqrt[3]]","A",2,2,15,0.1333,1,"{3186, 215}"
70,1,487,0,1.1008694,"\int \frac{1}{a+b \cos ^4(x)} \, dx","Int[(a + b*Cos[x]^4)^(-1),x]","-\frac{\left(\sqrt{a}-\sqrt{a+b}\right) \log \left((a+b)^{3/4} \cot ^2(x)-\sqrt{2} \sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b} \cot (x)+\sqrt{a} \sqrt[4]{a+b}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}+\frac{\left(\sqrt{a}-\sqrt{a+b}\right) \log \left((a+b)^{3/4} \cot ^2(x)+\sqrt{2} \sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b} \cot (x)+\sqrt{a} \sqrt[4]{a+b}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}+\frac{\left(\sqrt{a+b}+\sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}-\sqrt{2} (a+b)^{3/4} \cot (x)}{\sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}-\frac{\left(\sqrt{a+b}+\sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{2} (a+b)^{3/4} \cot (x)+\sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}{\sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}","-\frac{\left(\sqrt{a}-\sqrt{a+b}\right) \log \left((a+b)^{3/4} \cot ^2(x)-\sqrt{2} \sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b} \cot (x)+\sqrt{a} \sqrt[4]{a+b}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}+\frac{\left(\sqrt{a}-\sqrt{a+b}\right) \log \left((a+b)^{3/4} \cot ^2(x)+\sqrt{2} \sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b} \cot (x)+\sqrt{a} \sqrt[4]{a+b}\right)}{4 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}+\frac{\left(\sqrt{a+b}+\sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}-\sqrt{2} (a+b)^{3/4} \cot (x)}{\sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}-\frac{\left(\sqrt{a+b}+\sqrt{a}\right) \tan ^{-1}\left(\frac{\sqrt{2} (a+b)^{3/4} \cot (x)+\sqrt[4]{a} \sqrt{-\sqrt{a} \sqrt{a+b}+a+b}}{\sqrt[4]{a} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}\right)}{2 \sqrt{2} a^{3/4} \sqrt[4]{a+b} \sqrt{\sqrt{a} \sqrt{a+b}+a+b}}",1,"((Sqrt[a] + Sqrt[a + b])*ArcTan[(a^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]] - Sqrt[2]*(a + b)^(3/4)*Cot[x])/(a^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]])])/(2*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]]) - ((Sqrt[a] + Sqrt[a + b])*ArcTan[(a^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]] + Sqrt[2]*(a + b)^(3/4)*Cot[x])/(a^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]])])/(2*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b + Sqrt[a]*Sqrt[a + b]]) - ((Sqrt[a] - Sqrt[a + b])*Log[Sqrt[a]*(a + b)^(1/4) - Sqrt[2]*a^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]]*Cot[x] + (a + b)^(3/4)*Cot[x]^2])/(4*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]]) + ((Sqrt[a] - Sqrt[a + b])*Log[Sqrt[a]*(a + b)^(1/4) + Sqrt[2]*a^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]]*Cot[x] + (a + b)^(3/4)*Cot[x]^2])/(4*Sqrt[2]*a^(3/4)*(a + b)^(1/4)*Sqrt[a + b - Sqrt[a]*Sqrt[a + b]])","A",10,6,10,0.6000,1,"{3209, 1169, 634, 618, 204, 628}"
71,1,101,0,0.1159084,"\int \frac{1}{a-b \cos ^4(x)} \, dx","Int[(a - b*Cos[x]^4)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \cot (x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \cot (x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}+\sqrt{b}}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a}-\sqrt{b}} \cot (x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}-\sqrt{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{a}+\sqrt{b}} \cot (x)}{\sqrt[4]{a}}\right)}{2 a^{3/4} \sqrt{\sqrt{a}+\sqrt{b}}}",1,"-ArcTan[(Sqrt[Sqrt[a] - Sqrt[b]]*Cot[x])/a^(1/4)]/(2*a^(3/4)*Sqrt[Sqrt[a] - Sqrt[b]]) - ArcTan[(Sqrt[Sqrt[a] + Sqrt[b]]*Cot[x])/a^(1/4)]/(2*a^(3/4)*Sqrt[Sqrt[a] + Sqrt[b]])","A",4,3,11,0.2727,1,"{3209, 1166, 205}"
72,1,292,0,0.19086,"\int \frac{1}{1+\cos ^4(x)} \, dx","Int[(1 + Cos[x]^4)^(-1),x]","\frac{x}{2 \sqrt{\sqrt{2}-1}}+\frac{1}{8} \sqrt{\sqrt{2}-1} \log \left(2 \cot ^2(x)-2 \sqrt{\sqrt{2}-1} \cot (x)+\sqrt{2}\right)-\frac{1}{8} \sqrt{\sqrt{2}-1} \log \left(\sqrt{2} \cot ^2(x)+\sqrt{2 \left(\sqrt{2}-1\right)} \cot (x)+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{2}-1} \left(1-2 \sin ^2(x)\right)+\left(\sqrt{2}-2\right) \sin (x) \cos (x)}{\left(\sqrt{2}-2\right) \sin ^2(x)+2 \sqrt{\sqrt{2}-1} \sin (x) \cos (x)+\sqrt{1+\sqrt{2}}+2}\right)}{4 \sqrt{\sqrt{2}-1}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{2}-1} \left(2 \sin ^2(x)-1\right)+\left(\sqrt{2}-2\right) \sin (x) \cos (x)}{\left(\sqrt{2}-2\right) \sin ^2(x)-2 \sqrt{\sqrt{2}-1} \sin (x) \cos (x)+\sqrt{1+\sqrt{2}}+2}\right)}{4 \sqrt{\sqrt{2}-1}}","\frac{x}{2 \sqrt{\sqrt{2}-1}}+\frac{1}{8} \sqrt{\sqrt{2}-1} \log \left(2 \cot ^2(x)-2 \sqrt{\sqrt{2}-1} \cot (x)+\sqrt{2}\right)-\frac{1}{8} \sqrt{\sqrt{2}-1} \log \left(\sqrt{2} \cot ^2(x)+\sqrt{2 \left(\sqrt{2}-1\right)} \cot (x)+1\right)+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{2}-1} \left(1-2 \sin ^2(x)\right)+\left(\sqrt{2}-2\right) \sin (x) \cos (x)}{\left(\sqrt{2}-2\right) \sin ^2(x)+2 \sqrt{\sqrt{2}-1} \sin (x) \cos (x)+\sqrt{1+\sqrt{2}}+2}\right)}{4 \sqrt{\sqrt{2}-1}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt{2}-1} \left(2 \sin ^2(x)-1\right)+\left(\sqrt{2}-2\right) \sin (x) \cos (x)}{\left(\sqrt{2}-2\right) \sin ^2(x)-2 \sqrt{\sqrt{2}-1} \sin (x) \cos (x)+\sqrt{1+\sqrt{2}}+2}\right)}{4 \sqrt{\sqrt{2}-1}}",1,"x/(2*Sqrt[-1 + Sqrt[2]]) + ArcTan[((-2 + Sqrt[2])*Cos[x]*Sin[x] + Sqrt[-1 + Sqrt[2]]*(1 - 2*Sin[x]^2))/(2 + Sqrt[1 + Sqrt[2]] + 2*Sqrt[-1 + Sqrt[2]]*Cos[x]*Sin[x] + (-2 + Sqrt[2])*Sin[x]^2)]/(4*Sqrt[-1 + Sqrt[2]]) + ArcTan[((-2 + Sqrt[2])*Cos[x]*Sin[x] + Sqrt[-1 + Sqrt[2]]*(-1 + 2*Sin[x]^2))/(2 + Sqrt[1 + Sqrt[2]] - 2*Sqrt[-1 + Sqrt[2]]*Cos[x]*Sin[x] + (-2 + Sqrt[2])*Sin[x]^2)]/(4*Sqrt[-1 + Sqrt[2]]) + (Sqrt[-1 + Sqrt[2]]*Log[Sqrt[2] - 2*Sqrt[-1 + Sqrt[2]]*Cot[x] + 2*Cot[x]^2])/8 - (Sqrt[-1 + Sqrt[2]]*Log[1 + Sqrt[2*(-1 + Sqrt[2])]*Cot[x] + Sqrt[2]*Cot[x]^2])/8","A",10,6,8,0.7500,1,"{3209, 1169, 634, 618, 204, 628}"
73,1,45,0,0.0183842,"\int \frac{1}{1-\cos ^4(x)} \, dx","Int[(1 - Cos[x]^4)^(-1),x]","\frac{x}{2 \sqrt{2}}-\frac{\cot (x)}{2}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{2 \sqrt{2}}","\frac{x}{2 \sqrt{2}}-\frac{\cot (x)}{2}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{2 \sqrt{2}}",1,"x/(2*Sqrt[2]) - ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Cos[x]^2)]/(2*Sqrt[2]) - Cot[x]/2","A",3,3,10,0.3000,1,"{3209, 388, 203}"
74,1,494,0,0.9185,"\int \frac{1}{a+b \cos ^5(x)} \, dx","Int[(a + b*Cos[x]^5)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}",1,"(2*ArcTan[(Sqrt[a^(1/5) - b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) + b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - b^(1/5)]*Sqrt[a^(1/5) + b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)])","A",12,3,10,0.3000,1,"{3213, 2659, 205}"
75,1,171,0,0.2382463,"\int \frac{1}{a+b \cos ^6(x)} \, dx","Int[(a + b*Cos[x]^6)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b}}}",1,"-ArcTan[(Sqrt[a^(1/3) + b^(1/3)]*Cot[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) + b^(1/3)]) - ArcTan[(Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]*Cot[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) - (-1)^(1/3)*b^(1/3)]) - ArcTan[(Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)]*Cot[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) + (-1)^(2/3)*b^(1/3)])","A",7,3,10,0.3000,1,"{3211, 3181, 203}"
76,1,245,0,0.486312,"\int \frac{1}{a+b \cos ^8(x)} \, dx","Int[(a + b*Cos[x]^8)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}} \cot (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{a \sqrt[4]{b}+(-a)^{5/4}} \cot (x)}{(-a)^{5/8}}\right)}{4 (-a)^{3/8} \sqrt{a \sqrt[4]{b}+(-a)^{5/4}}}","\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}-\sqrt[4]{b}} \cot (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-\sqrt[4]{b}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}-i \sqrt[4]{b}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+i \sqrt[4]{b}}}+\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{-a}+\sqrt[4]{b}} \cot (x)}{\sqrt[8]{-a}}\right)}{4 (-a)^{7/8} \sqrt{\sqrt[4]{-a}+\sqrt[4]{b}}}",1,"ArcTan[(Sqrt[(-a)^(1/4) - I*b^(1/4)]*Cot[x])/(-a)^(1/8)]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) - I*b^(1/4)]) + ArcTan[(Sqrt[(-a)^(1/4) + I*b^(1/4)]*Cot[x])/(-a)^(1/8)]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) + I*b^(1/4)]) + ArcTan[(Sqrt[(-a)^(1/4) + b^(1/4)]*Cot[x])/(-a)^(1/8)]/(4*(-a)^(7/8)*Sqrt[(-a)^(1/4) + b^(1/4)]) + ArcTan[(Sqrt[(-a)^(5/4) + a*b^(1/4)]*Cot[x])/(-a)^(5/8)]/(4*(-a)^(3/8)*Sqrt[(-a)^(5/4) + a*b^(1/4)])","A",9,3,10,0.3000,1,"{3211, 3181, 203}"
77,1,494,0,0.5890419,"\int \frac{1}{a-b \cos ^5(x)} \, dx","Int[(a - b*Cos[x]^5)^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+\sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-\sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-\sqrt[5]{-1} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+\sqrt[5]{-1} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{2/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{2/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{3/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{3/5} \sqrt[5]{b}}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}} \tan \left(\frac{x}{2}\right)}{\sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}}}\right)}{5 a^{4/5} \sqrt{\sqrt[5]{a}-(-1)^{4/5} \sqrt[5]{b}} \sqrt{\sqrt[5]{a}+(-1)^{4/5} \sqrt[5]{b}}}",1,"(2*ArcTan[(Sqrt[a^(1/5) + b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) - b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - b^(1/5)]*Sqrt[a^(1/5) + b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(1/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(1/5)*b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(2/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(2/5)*b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(3/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(3/5)*b^(1/5)]) + (2*ArcTan[(Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)]*Tan[x/2])/Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]])/(5*a^(4/5)*Sqrt[a^(1/5) - (-1)^(4/5)*b^(1/5)]*Sqrt[a^(1/5) + (-1)^(4/5)*b^(1/5)])","A",12,3,11,0.2727,1,"{3213, 2659, 205}"
78,1,175,0,0.2492012,"\int \frac{1}{a-b \cos ^6(x)} \, dx","Int[(a - b*Cos[x]^6)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-\sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-\sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}+\sqrt[3]{-1} \sqrt[3]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}} \cot (x)}{\sqrt[6]{a}}\right)}{3 a^{5/6} \sqrt{\sqrt[3]{a}-(-1)^{2/3} \sqrt[3]{b}}}",1,"-ArcTan[(Sqrt[a^(1/3) - b^(1/3)]*Cot[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) - b^(1/3)]) - ArcTan[(Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]*Cot[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) + (-1)^(1/3)*b^(1/3)]) - ArcTan[(Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)]*Cot[x])/a^(1/6)]/(3*a^(5/6)*Sqrt[a^(1/3) - (-1)^(2/3)*b^(1/3)])","A",7,3,11,0.2727,1,"{3211, 3181, 203}"
79,1,213,0,0.2156147,"\int \frac{1}{a-b \cos ^8(x)} \, dx","Int[(a - b*Cos[x]^8)^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}-\sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}-i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}+i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}+\sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}-\sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-\sqrt[4]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}-i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}-i \sqrt[4]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}+i \sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+i \sqrt[4]{b}}}-\frac{\tan ^{-1}\left(\frac{\sqrt{\sqrt[4]{a}+\sqrt[4]{b}} \cot (x)}{\sqrt[8]{a}}\right)}{4 a^{7/8} \sqrt{\sqrt[4]{a}+\sqrt[4]{b}}}",1,"-ArcTan[(Sqrt[a^(1/4) - b^(1/4)]*Cot[x])/a^(1/8)]/(4*a^(7/8)*Sqrt[a^(1/4) - b^(1/4)]) - ArcTan[(Sqrt[a^(1/4) - I*b^(1/4)]*Cot[x])/a^(1/8)]/(4*a^(7/8)*Sqrt[a^(1/4) - I*b^(1/4)]) - ArcTan[(Sqrt[a^(1/4) + I*b^(1/4)]*Cot[x])/a^(1/8)]/(4*a^(7/8)*Sqrt[a^(1/4) + I*b^(1/4)]) - ArcTan[(Sqrt[a^(1/4) + b^(1/4)]*Cot[x])/a^(1/8)]/(4*a^(7/8)*Sqrt[a^(1/4) + b^(1/4)])","A",9,3,11,0.2727,1,"{3211, 3181, 203}"
80,1,223,0,0.5623008,"\int \frac{1}{1+\cos ^5(x)} \, dx","Int[(1 + Cos[x]^5)^(-1),x]","\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{4/5}}}+\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-(-1)^{4/5}}{1+(-1)^{4/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+(-1)^{3/5}}}+\frac{\sin (x)}{5 (\cos (x)+1)}-\frac{2 \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}}}\right)}{5 \sqrt{(-1)^{2/5}-1}}-\frac{2 \sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tanh ^{-1}\left(\sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \left(1+(-1)^{3/5}\right)}","\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{4/5}}}+\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-(-1)^{4/5}}{1+(-1)^{4/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+(-1)^{3/5}}}+\frac{\sin (x)}{5 (\cos (x)+1)}-\frac{2 \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}}}\right)}{5 \sqrt{(-1)^{2/5}-1}}-\frac{2 \sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tanh ^{-1}\left(\sqrt{-\frac{1+(-1)^{3/5}}{1-(-1)^{3/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \left(1+(-1)^{3/5}\right)}",1,"(2*ArcTan[Sqrt[(1 - (-1)^(2/5))/(1 + (-1)^(2/5))]*Tan[x/2]])/(5*Sqrt[1 - (-1)^(4/5)]) + (2*ArcTan[Sqrt[(1 - (-1)^(4/5))/(1 + (-1)^(4/5))]*Tan[x/2]])/(5*Sqrt[1 + (-1)^(3/5)]) - (2*ArcTanh[Tan[x/2]/Sqrt[-((1 - (-1)^(1/5))/(1 + (-1)^(1/5)))]])/(5*Sqrt[-1 + (-1)^(2/5)]) - (2*Sqrt[-((1 + (-1)^(3/5))/(1 - (-1)^(3/5)))]*ArcTanh[Sqrt[-((1 + (-1)^(3/5))/(1 - (-1)^(3/5)))]*Tan[x/2]])/(5*(1 + (-1)^(3/5))) + Sin[x]/(5*(1 + Cos[x]))","A",11,5,8,0.6250,1,"{3213, 2648, 2659, 208, 205}"
81,1,103,0,0.1040556,"\int \frac{1}{1+\cos ^6(x)} \, dx","Int[(1 + Cos[x]^6)^(-1),x]","\frac{x}{3 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{1-\sqrt[3]{-1}} \cot (x)\right)}{3 \sqrt{1-\sqrt[3]{-1}}}-\frac{\tan ^{-1}\left(\sqrt{1+(-1)^{2/3}} \cot (x)\right)}{3 \sqrt{1+(-1)^{2/3}}}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{3 \sqrt{2}}","\frac{\tan ^{-1}\left(\frac{\tan (x)}{\sqrt{2}}\right)}{3 \sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\tan (x)}{\sqrt{1-\sqrt[3]{-1}}}\right)}{3 \sqrt{1-\sqrt[3]{-1}}}+\frac{\tan ^{-1}\left(\frac{\tan (x)}{\sqrt{1+(-1)^{2/3}}}\right)}{3 \sqrt{1+(-1)^{2/3}}}",1,"x/(3*Sqrt[2]) - ArcTan[Sqrt[1 - (-1)^(1/3)]*Cot[x]]/(3*Sqrt[1 - (-1)^(1/3)]) - ArcTan[Sqrt[1 + (-1)^(2/3)]*Cot[x]]/(3*Sqrt[1 + (-1)^(2/3)]) - ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Cos[x]^2)]/(3*Sqrt[2])","A",7,3,8,0.3750,1,"{3211, 3181, 203}"
82,1,129,0,0.1797865,"\int \frac{1}{1+\cos ^8(x)} \, dx","Int[(1 + Cos[x]^8)^(-1),x]","-\frac{\tan ^{-1}\left(\sqrt{1-\sqrt[4]{-1}} \cot (x)\right)}{4 \sqrt{1-\sqrt[4]{-1}}}-\frac{\tan ^{-1}\left(\sqrt{1+\sqrt[4]{-1}} \cot (x)\right)}{4 \sqrt{1+\sqrt[4]{-1}}}-\frac{\tan ^{-1}\left(\sqrt{1-(-1)^{3/4}} \cot (x)\right)}{4 \sqrt{1-(-1)^{3/4}}}-\frac{\tan ^{-1}\left(\sqrt{1+(-1)^{3/4}} \cot (x)\right)}{4 \sqrt{1+(-1)^{3/4}}}","-\frac{\tan ^{-1}\left(\sqrt{1-\sqrt[4]{-1}} \cot (x)\right)}{4 \sqrt{1-\sqrt[4]{-1}}}-\frac{\tan ^{-1}\left(\sqrt{1+\sqrt[4]{-1}} \cot (x)\right)}{4 \sqrt{1+\sqrt[4]{-1}}}-\frac{\tan ^{-1}\left(\sqrt{1-(-1)^{3/4}} \cot (x)\right)}{4 \sqrt{1-(-1)^{3/4}}}-\frac{\tan ^{-1}\left(\sqrt{1+(-1)^{3/4}} \cot (x)\right)}{4 \sqrt{1+(-1)^{3/4}}}",1,"-ArcTan[Sqrt[1 - (-1)^(1/4)]*Cot[x]]/(4*Sqrt[1 - (-1)^(1/4)]) - ArcTan[Sqrt[1 + (-1)^(1/4)]*Cot[x]]/(4*Sqrt[1 + (-1)^(1/4)]) - ArcTan[Sqrt[1 - (-1)^(3/4)]*Cot[x]]/(4*Sqrt[1 - (-1)^(3/4)]) - ArcTan[Sqrt[1 + (-1)^(3/4)]*Cot[x]]/(4*Sqrt[1 + (-1)^(3/4)])","A",9,3,8,0.3750,1,"{3211, 3181, 203}"
83,1,205,0,0.4734753,"\int \frac{1}{1-\cos ^5(x)} \, dx","Int[(1 - Cos[x]^5)^(-1),x]","\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{2/5}}}+\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-(-1)^{3/5}}{1+(-1)^{3/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+\sqrt[5]{-1}}}-\frac{\sin (x)}{5 (1-\cos (x))}-\frac{2 \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}}}\right)}{5 \sqrt{(-1)^{4/5}-1}}+\frac{2 \tanh ^{-1}\left(\sqrt{-\frac{1+(-1)^{4/5}}{1-(-1)^{4/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{-1-(-1)^{3/5}}}","\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-\sqrt[5]{-1}}{1+\sqrt[5]{-1}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1-(-1)^{2/5}}}+\frac{2 \tan ^{-1}\left(\sqrt{\frac{1-(-1)^{3/5}}{1+(-1)^{3/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{1+\sqrt[5]{-1}}}-\frac{\sin (x)}{5 (1-\cos (x))}-\frac{2 \tanh ^{-1}\left(\frac{\tan \left(\frac{x}{2}\right)}{\sqrt{-\frac{1-(-1)^{2/5}}{1+(-1)^{2/5}}}}\right)}{5 \sqrt{(-1)^{4/5}-1}}+\frac{2 \tanh ^{-1}\left(\sqrt{-\frac{1+(-1)^{4/5}}{1-(-1)^{4/5}}} \tan \left(\frac{x}{2}\right)\right)}{5 \sqrt{-1-(-1)^{3/5}}}",1,"(2*ArcTan[Sqrt[(1 - (-1)^(1/5))/(1 + (-1)^(1/5))]*Tan[x/2]])/(5*Sqrt[1 - (-1)^(2/5)]) + (2*ArcTan[Sqrt[(1 - (-1)^(3/5))/(1 + (-1)^(3/5))]*Tan[x/2]])/(5*Sqrt[1 + (-1)^(1/5)]) - (2*ArcTanh[Tan[x/2]/Sqrt[-((1 - (-1)^(2/5))/(1 + (-1)^(2/5)))]])/(5*Sqrt[-1 + (-1)^(4/5)]) + (2*ArcTanh[Sqrt[-((1 + (-1)^(4/5))/(1 - (-1)^(4/5)))]*Tan[x/2]])/(5*Sqrt[-1 - (-1)^(3/5)]) - Sin[x]/(5*(1 - Cos[x]))","A",11,5,10,0.5000,1,"{3213, 2648, 2659, 205, 208}"
84,1,71,0,0.1186223,"\int \frac{1}{1-\cos ^6(x)} \, dx","Int[(1 - Cos[x]^6)^(-1),x]","-\frac{\cot (x)}{3}-\frac{\tan ^{-1}\left(\sqrt{1+\sqrt[3]{-1}} \cot (x)\right)}{3 \sqrt{1+\sqrt[3]{-1}}}-\frac{\tan ^{-1}\left(\sqrt{1-(-1)^{2/3}} \cot (x)\right)}{3 \sqrt{1-(-1)^{2/3}}}","-\frac{\cot (x)}{3}-\frac{\tan ^{-1}\left(\sqrt{1+\sqrt[3]{-1}} \cot (x)\right)}{3 \sqrt{1+\sqrt[3]{-1}}}-\frac{\tan ^{-1}\left(\sqrt{1-(-1)^{2/3}} \cot (x)\right)}{3 \sqrt{1-(-1)^{2/3}}}",1,"-ArcTan[Sqrt[1 + (-1)^(1/3)]*Cot[x]]/(3*Sqrt[1 + (-1)^(1/3)]) - ArcTan[Sqrt[1 - (-1)^(2/3)]*Cot[x]]/(3*Sqrt[1 - (-1)^(2/3)]) - Cot[x]/3","A",8,6,10,0.6000,1,"{3211, 3181, 203, 3175, 3767, 8}"
85,1,89,0,0.0773313,"\int \frac{1}{1-\cos ^8(x)} \, dx","Int[(1 - Cos[x]^8)^(-1),x]","\frac{x}{4 \sqrt{2}}-\frac{\cot (x)}{4}-\frac{\tan ^{-1}\left(\sqrt{1-i} \cot (x)\right)}{4 \sqrt{1-i}}-\frac{\tan ^{-1}\left(\sqrt{1+i} \cot (x)\right)}{4 \sqrt{1+i}}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{4 \sqrt{2}}","\frac{x}{4 \sqrt{2}}-\frac{\cot (x)}{4}-\frac{\tan ^{-1}\left(\sqrt{1-i} \cot (x)\right)}{4 \sqrt{1-i}}-\frac{\tan ^{-1}\left(\sqrt{1+i} \cot (x)\right)}{4 \sqrt{1+i}}-\frac{\tan ^{-1}\left(\frac{\sin (x) \cos (x)}{\cos ^2(x)+\sqrt{2}+1}\right)}{4 \sqrt{2}}",1,"x/(4*Sqrt[2]) - ArcTan[Sqrt[1 - I]*Cot[x]]/(4*Sqrt[1 - I]) - ArcTan[Sqrt[1 + I]*Cot[x]]/(4*Sqrt[1 + I]) - ArcTan[(Cos[x]*Sin[x])/(1 + Sqrt[2] + Cos[x]^2)]/(4*Sqrt[2]) - Cot[x]/4","A",10,6,10,0.6000,1,"{3211, 3181, 203, 3175, 3767, 8}"
86,1,17,0,0.0290009,"\int \frac{\tan (x)}{1+\cos ^2(x)} \, dx","Int[Tan[x]/(1 + Cos[x]^2),x]","\frac{1}{2} \log \left(\cos ^2(x)+1\right)-\log (\cos (x))","\frac{1}{2} \log \left(\cos ^2(x)+1\right)-\log (\cos (x))",1,"-Log[Cos[x]] + Log[1 + Cos[x]^2]/2","A",4,4,11,0.3636,1,"{3194, 36, 29, 31}"
87,1,40,0,0.0627249,"\int \sqrt{a+b \cos ^2(x)} \tan (x) \, dx","Int[Sqrt[a + b*Cos[x]^2]*Tan[x],x]","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^2(x)}}{\sqrt{a}}\right)-\sqrt{a+b \cos ^2(x)}","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^2(x)}}{\sqrt{a}}\right)-\sqrt{a+b \cos ^2(x)}",1,"Sqrt[a]*ArcTanh[Sqrt[a + b*Cos[x]^2]/Sqrt[a]] - Sqrt[a + b*Cos[x]^2]","A",4,4,15,0.2667,1,"{3194, 50, 63, 208}"
88,1,20,0,0.0505617,"\int \sqrt{1-\cos ^2(x)} \tan (x) \, dx","Int[Sqrt[1 - Cos[x]^2]*Tan[x],x]","\tanh ^{-1}\left(\sqrt{\sin ^2(x)}\right)-\sqrt{\sin ^2(x)}","\tanh ^{-1}\left(\sqrt{\sin ^2(x)}\right)-\sqrt{\sin ^2(x)}",1,"ArcTanh[Sqrt[Sin[x]^2]] - Sqrt[Sin[x]^2]","A",5,5,15,0.3333,1,"{3176, 3205, 50, 63, 206}"
89,1,25,0,0.0599249,"\int \frac{\tan (x)}{\sqrt{a+b \cos ^2(x)}} \, dx","Int[Tan[x]/Sqrt[a + b*Cos[x]^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^2(x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"ArcTanh[Sqrt[a + b*Cos[x]^2]/Sqrt[a]]/Sqrt[a]","A",3,3,15,0.2000,1,"{3194, 63, 208}"
90,1,11,0,0.0352519,"\int \frac{\tan (x)}{\sqrt{1+\cos ^2(x)}} \, dx","Int[Tan[x]/Sqrt[1 + Cos[x]^2],x]","\tanh ^{-1}\left(\sqrt{\cos ^2(x)+1}\right)","\tanh ^{-1}\left(\sqrt{\cos ^2(x)+1}\right)",1,"ArcTanh[Sqrt[1 + Cos[x]^2]]","A",3,3,13,0.2308,1,"{3194, 63, 207}"
91,1,9,0,0.0529505,"\int \frac{\tan (x)}{\sqrt{1-\cos ^2(x)}} \, dx","Int[Tan[x]/Sqrt[1 - Cos[x]^2],x]","\tanh ^{-1}\left(\sqrt{\sin ^2(x)}\right)","\tanh ^{-1}\left(\sqrt{\sin ^2(x)}\right)",1,"ArcTanh[Sqrt[Sin[x]^2]]","A",4,4,15,0.2667,1,"{3176, 3205, 63, 206}"
92,1,153,0,0.196729,"\int \frac{\tan ^3(x)}{a+b \cos ^3(x)} \, dx","Int[Tan[x]^3/(a + b*Cos[x]^3),x]","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \cos (x)+b^{2/3} \cos ^2(x)\right)}{6 a^{5/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \cos (x)\right)}{3 a^{5/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \cos (x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\log \left(a+b \cos ^3(x)\right)}{3 a}+\frac{\sec ^2(x)}{2 a}+\frac{\log (\cos (x))}{a}","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} \cos (x)+b^{2/3} \cos ^2(x)\right)}{6 a^{5/3}}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} \cos (x)\right)}{3 a^{5/3}}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} \cos (x)}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3}}-\frac{\log \left(a+b \cos ^3(x)\right)}{3 a}+\frac{\sec ^2(x)}{2 a}+\frac{\log (\cos (x))}{a}",1,"-((b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*Cos[x])/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3))) + Log[Cos[x]]/a + (b^(2/3)*Log[a^(1/3) + b^(1/3)*Cos[x]])/(3*a^(5/3)) - (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*Cos[x] + b^(2/3)*Cos[x]^2])/(6*a^(5/3)) - Log[a + b*Cos[x]^3]/(3*a) + Sec[x]^2/(2*a)","A",11,10,15,0.6667,1,"{3230, 1834, 1871, 200, 31, 634, 617, 204, 628, 260}"
93,1,45,0,0.0729281,"\int \sqrt{a+b \cos ^3(x)} \tan (x) \, dx","Int[Sqrt[a + b*Cos[x]^3]*Tan[x],x]","\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^3(x)}}{\sqrt{a}}\right)-\frac{2}{3} \sqrt{a+b \cos ^3(x)}","\frac{2}{3} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^3(x)}}{\sqrt{a}}\right)-\frac{2}{3} \sqrt{a+b \cos ^3(x)}",1,"(2*Sqrt[a]*ArcTanh[Sqrt[a + b*Cos[x]^3]/Sqrt[a]])/3 - (2*Sqrt[a + b*Cos[x]^3])/3","A",5,5,15,0.3333,1,"{3230, 266, 50, 63, 208}"
94,1,28,0,0.0673431,"\int \frac{\tan (x)}{\sqrt{a+b \cos ^3(x)}} \, dx","Int[Tan[x]/Sqrt[a + b*Cos[x]^3],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^3(x)}}{\sqrt{a}}\right)}{3 \sqrt{a}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^3(x)}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(2*ArcTanh[Sqrt[a + b*Cos[x]^3]/Sqrt[a]])/(3*Sqrt[a])","A",4,4,15,0.2667,1,"{3230, 266, 63, 208}"
95,1,45,0,0.0765254,"\int \sqrt{a+b \cos ^4(x)} \tan (x) \, dx","Int[Sqrt[a + b*Cos[x]^4]*Tan[x],x]","\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^4(x)}}{\sqrt{a}}\right)-\frac{1}{2} \sqrt{a+b \cos ^4(x)}","\frac{1}{2} \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^4(x)}}{\sqrt{a}}\right)-\frac{1}{2} \sqrt{a+b \cos ^4(x)}",1,"(Sqrt[a]*ArcTanh[Sqrt[a + b*Cos[x]^4]/Sqrt[a]])/2 - Sqrt[a + b*Cos[x]^4]/2","A",5,5,15,0.3333,1,"{3229, 266, 50, 63, 208}"
96,1,28,0,0.0709482,"\int \frac{\tan (x)}{\sqrt{a+b \cos ^4(x)}} \, dx","Int[Tan[x]/Sqrt[a + b*Cos[x]^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^4(x)}}{\sqrt{a}}\right)}{2 \sqrt{a}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^4(x)}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"ArcTanh[Sqrt[a + b*Cos[x]^4]/Sqrt[a]]/(2*Sqrt[a])","A",4,4,15,0.2667,1,"{3229, 266, 63, 208}"
97,1,47,0,0.0788629,"\int \sqrt{a+b \cos ^n(x)} \tan (x) \, dx","Int[Sqrt[a + b*Cos[x]^n]*Tan[x],x]","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^n(x)}}{\sqrt{a}}\right)}{n}-\frac{2 \sqrt{a+b \cos ^n(x)}}{n}","\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^n(x)}}{\sqrt{a}}\right)}{n}-\frac{2 \sqrt{a+b \cos ^n(x)}}{n}",1,"(2*Sqrt[a]*ArcTanh[Sqrt[a + b*Cos[x]^n]/Sqrt[a]])/n - (2*Sqrt[a + b*Cos[x]^n])/n","A",5,5,15,0.3333,1,"{3230, 266, 50, 63, 208}"
98,1,29,0,0.0769956,"\int \frac{\tan (x)}{\sqrt{a+b \cos ^n(x)}} \, dx","Int[Tan[x]/Sqrt[a + b*Cos[x]^n],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^n(x)}}{\sqrt{a}}\right)}{\sqrt{a} n}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \cos ^n(x)}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"(2*ArcTanh[Sqrt[a + b*Cos[x]^n]/Sqrt[a]])/(Sqrt[a]*n)","A",4,4,15,0.2667,1,"{3230, 266, 63, 208}"