1,1,119,0,0.0696602,"\int (a+a \cos (c+d x))^{7/2} \, dx","Int[(a + a*Cos[c + d*x])^(7/2),x]","\frac{256 a^4 \sin (c+d x)}{35 d \sqrt{a \cos (c+d x)+a}}+\frac{64 a^3 \sin (c+d x) \sqrt{a \cos (c+d x)+a}}{35 d}+\frac{24 a^2 \sin (c+d x) (a \cos (c+d x)+a)^{3/2}}{35 d}+\frac{2 a \sin (c+d x) (a \cos (c+d x)+a)^{5/2}}{7 d}","\frac{256 a^4 \sin (c+d x)}{35 d \sqrt{a \cos (c+d x)+a}}+\frac{64 a^3 \sin (c+d x) \sqrt{a \cos (c+d x)+a}}{35 d}+\frac{24 a^2 \sin (c+d x) (a \cos (c+d x)+a)^{3/2}}{35 d}+\frac{2 a \sin (c+d x) (a \cos (c+d x)+a)^{5/2}}{7 d}",1,"(256*a^4*Sin[c + d*x])/(35*d*Sqrt[a + a*Cos[c + d*x]]) + (64*a^3*Sqrt[a + a*Cos[c + d*x]]*Sin[c + d*x])/(35*d) + (24*a^2*(a + a*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(35*d) + (2*a*(a + a*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*d)","A",4,2,14,0.1429,1,"{2647, 2646}"
2,1,89,0,0.0491412,"\int (a+a \cos (c+d x))^{5/2} \, dx","Int[(a + a*Cos[c + d*x])^(5/2),x]","\frac{64 a^3 \sin (c+d x)}{15 d \sqrt{a \cos (c+d x)+a}}+\frac{16 a^2 \sin (c+d x) \sqrt{a \cos (c+d x)+a}}{15 d}+\frac{2 a \sin (c+d x) (a \cos (c+d x)+a)^{3/2}}{5 d}","\frac{64 a^3 \sin (c+d x)}{15 d \sqrt{a \cos (c+d x)+a}}+\frac{16 a^2 \sin (c+d x) \sqrt{a \cos (c+d x)+a}}{15 d}+\frac{2 a \sin (c+d x) (a \cos (c+d x)+a)^{3/2}}{5 d}",1,"(64*a^3*Sin[c + d*x])/(15*d*Sqrt[a + a*Cos[c + d*x]]) + (16*a^2*Sqrt[a + a*Cos[c + d*x]]*Sin[c + d*x])/(15*d) + (2*a*(a + a*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",3,2,14,0.1429,1,"{2647, 2646}"
3,1,59,0,0.0282855,"\int (a+a \cos (c+d x))^{3/2} \, dx","Int[(a + a*Cos[c + d*x])^(3/2),x]","\frac{8 a^2 \sin (c+d x)}{3 d \sqrt{a \cos (c+d x)+a}}+\frac{2 a \sin (c+d x) \sqrt{a \cos (c+d x)+a}}{3 d}","\frac{8 a^2 \sin (c+d x)}{3 d \sqrt{a \cos (c+d x)+a}}+\frac{2 a \sin (c+d x) \sqrt{a \cos (c+d x)+a}}{3 d}",1,"(8*a^2*Sin[c + d*x])/(3*d*Sqrt[a + a*Cos[c + d*x]]) + (2*a*Sqrt[a + a*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",2,2,14,0.1429,1,"{2647, 2646}"
4,1,26,0,0.0127332,"\int \sqrt{a+a \cos (c+d x)} \, dx","Int[Sqrt[a + a*Cos[c + d*x]],x]","\frac{2 a \sin (c+d x)}{d \sqrt{a \cos (c+d x)+a}}","\frac{2 a \sin (c+d x)}{d \sqrt{a \cos (c+d x)+a}}",1,"(2*a*Sin[c + d*x])/(d*Sqrt[a + a*Cos[c + d*x]])","A",1,1,14,0.07143,1,"{2646}"
5,1,46,0,0.0213317,"\int \frac{1}{\sqrt{a+a \cos (c+d x)}} \, dx","Int[1/Sqrt[a + a*Cos[c + d*x]],x]","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{\sqrt{a} d}","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{\sqrt{a} d}",1,"(Sqrt[2]*ArcTanh[(Sqrt[a]*Sin[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cos[c + d*x]])])/(Sqrt[a]*d)","A",2,2,14,0.1429,1,"{2649, 206}"
6,1,77,0,0.0414197,"\int \frac{1}{(a+a \cos (c+d x))^{3/2}} \, dx","Int[(a + a*Cos[c + d*x])^(-3/2),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{\sin (c+d x)}{2 d (a \cos (c+d x)+a)^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{\sin (c+d x)}{2 d (a \cos (c+d x)+a)^{3/2}}",1,"ArcTanh[(Sqrt[a]*Sin[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cos[c + d*x]])]/(2*Sqrt[2]*a^(3/2)*d) + Sin[c + d*x]/(2*d*(a + a*Cos[c + d*x])^(3/2))","A",3,3,14,0.2143,1,"{2650, 2649, 206}"
7,1,107,0,0.0631678,"\int \frac{1}{(a+a \cos (c+d x))^{5/2}} \, dx","Int[(a + a*Cos[c + d*x])^(-5/2),x]","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{16 \sqrt{2} a^{5/2} d}+\frac{3 \sin (c+d x)}{16 a d (a \cos (c+d x)+a)^{3/2}}+\frac{\sin (c+d x)}{4 d (a \cos (c+d x)+a)^{5/2}}","\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{16 \sqrt{2} a^{5/2} d}+\frac{3 \sin (c+d x)}{16 a d (a \cos (c+d x)+a)^{3/2}}+\frac{\sin (c+d x)}{4 d (a \cos (c+d x)+a)^{5/2}}",1,"(3*ArcTanh[(Sqrt[a]*Sin[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cos[c + d*x]])])/(16*Sqrt[2]*a^(5/2)*d) + Sin[c + d*x]/(4*d*(a + a*Cos[c + d*x])^(5/2)) + (3*Sin[c + d*x])/(16*a*d*(a + a*Cos[c + d*x])^(3/2))","A",4,3,14,0.2143,1,"{2650, 2649, 206}"
8,1,67,0,0.0359337,"\int (a+a \cos (c+d x))^{4/3} \, dx","Int[(a + a*Cos[c + d*x])^(4/3),x]","\frac{2\ 2^{5/6} a \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d (\cos (c+d x)+1)^{5/6}}","\frac{2\ 2^{5/6} a \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d (\cos (c+d x)+1)^{5/6}}",1,"(2*2^(5/6)*a*(a + a*Cos[c + d*x])^(1/3)*Hypergeometric2F1[-5/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(d*(1 + Cos[c + d*x])^(5/6))","A",2,2,14,0.1429,1,"{2652, 2651}"
9,1,66,0,0.0344978,"\int (a+a \cos (c+d x))^{2/3} \, dx","Int[(a + a*Cos[c + d*x])^(2/3),x]","\frac{2 \sqrt[6]{2} \sin (c+d x) (a \cos (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d (\cos (c+d x)+1)^{7/6}}","\frac{2 \sqrt[6]{2} \sin (c+d x) (a \cos (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d (\cos (c+d x)+1)^{7/6}}",1,"(2*2^(1/6)*(a + a*Cos[c + d*x])^(2/3)*Hypergeometric2F1[-1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(d*(1 + Cos[c + d*x])^(7/6))","A",2,2,14,0.1429,1,"{2652, 2651}"
10,1,65,0,0.0301443,"\int \sqrt[3]{a+a \cos (c+d x)} \, dx","Int[(a + a*Cos[c + d*x])^(1/3),x]","\frac{2^{5/6} \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d (\cos (c+d x)+1)^{5/6}}","\frac{2^{5/6} \sin (c+d x) \sqrt[3]{a \cos (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d (\cos (c+d x)+1)^{5/6}}",1,"(2^(5/6)*(a + a*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(d*(1 + Cos[c + d*x])^(5/6))","A",2,2,14,0.1429,1,"{2652, 2651}"
11,1,65,0,0.0316252,"\int \frac{1}{\sqrt[3]{a+a \cos (c+d x)}} \, dx","Int[(a + a*Cos[c + d*x])^(-1/3),x]","\frac{\sqrt[6]{2} \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}","\frac{\sqrt[6]{2} \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}",1,"(2^(1/6)*Hypergeometric2F1[1/2, 5/6, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(d*(1 + Cos[c + d*x])^(1/6)*(a + a*Cos[c + d*x])^(1/3))","A",2,2,14,0.1429,1,"{2652, 2651}"
12,1,65,0,0.0312535,"\int \frac{1}{(a+a \cos (c+d x))^{2/3}} \, dx","Int[(a + a*Cos[c + d*x])^(-2/3),x]","\frac{\sin (c+d x) \sqrt[6]{\cos (c+d x)+1} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{\sqrt[6]{2} d (a \cos (c+d x)+a)^{2/3}}","\frac{\sin (c+d x) \sqrt[6]{\cos (c+d x)+1} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{\sqrt[6]{2} d (a \cos (c+d x)+a)^{2/3}}",1,"((1 + Cos[c + d*x])^(1/6)*Hypergeometric2F1[1/2, 7/6, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(2^(1/6)*d*(a + a*Cos[c + d*x])^(2/3))","A",2,2,14,0.1429,1,"{2652, 2651}"
13,1,68,0,0.0321445,"\int \frac{1}{(a+a \cos (c+d x))^{4/3}} \, dx","Int[(a + a*Cos[c + d*x])^(-4/3),x]","\frac{\sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{2^{5/6} a d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}","\frac{\sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{2^{5/6} a d \sqrt[6]{\cos (c+d x)+1} \sqrt[3]{a \cos (c+d x)+a}}",1,"(Hypergeometric2F1[1/2, 11/6, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(2^(5/6)*a*d*(1 + Cos[c + d*x])^(1/6)*(a + a*Cos[c + d*x])^(1/3))","A",2,2,14,0.1429,1,"{2652, 2651}"
14,1,73,0,0.0345538,"\int (a+a \cos (c+d x))^n \, dx","Int[(a + a*Cos[c + d*x])^n,x]","\frac{2^{n+\frac{1}{2}} \sin (c+d x) (\cos (c+d x)+1)^{-n-\frac{1}{2}} (a \cos (c+d x)+a)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d}","\frac{2^{n+\frac{1}{2}} \sin (c+d x) (\cos (c+d x)+1)^{-n-\frac{1}{2}} (a \cos (c+d x)+a)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d}",1,"(2^(1/2 + n)*(1 + Cos[c + d*x])^(-1/2 - n)*(a + a*Cos[c + d*x])^n*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/d","A",2,2,12,0.1667,1,"{2652, 2651}"
15,1,75,0,0.0334317,"\int (a-a \cos (c+d x))^n \, dx","Int[(a - a*Cos[c + d*x])^n,x]","-\frac{2^{n+\frac{1}{2}} \sin (c+d x) (1-\cos (c+d x))^{-n-\frac{1}{2}} (a-a \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\cos (c+d x)+1)\right)}{d}","-\frac{2^{n+\frac{1}{2}} \sin (c+d x) (1-\cos (c+d x))^{-n-\frac{1}{2}} (a-a \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\cos (c+d x)+1)\right)}{d}",1,"-((2^(1/2 + n)*(1 - Cos[c + d*x])^(-1/2 - n)*(a - a*Cos[c + d*x])^n*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 + Cos[c + d*x])/2]*Sin[c + d*x])/d)","A",2,2,13,0.1538,1,"{2652, 2651}"
16,1,59,0,0.0184571,"\int (2+2 \cos (c+d x))^n \, dx","Int[(2 + 2*Cos[c + d*x])^n,x]","\frac{2^{2 n+\frac{1}{2}} \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d \sqrt{\cos (c+d x)+1}}","\frac{2^{2 n+\frac{1}{2}} \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\cos (c+d x))\right)}{d \sqrt{\cos (c+d x)+1}}",1,"(2^(1/2 + 2*n)*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 - Cos[c + d*x])/2]*Sin[c + d*x])/(d*Sqrt[1 + Cos[c + d*x]])","A",1,1,12,0.08333,1,"{2651}"
17,1,60,0,0.0163111,"\int (2-2 \cos (c+d x))^n \, dx","Int[(2 - 2*Cos[c + d*x])^n,x]","-\frac{2^{2 n+\frac{1}{2}} \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\cos (c+d x)+1)\right)}{d \sqrt{1-\cos (c+d x)}}","-\frac{2^{2 n+\frac{1}{2}} \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\cos (c+d x)+1)\right)}{d \sqrt{1-\cos (c+d x)}}",1,"-((2^(1/2 + 2*n)*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 + Cos[c + d*x])/2]*Sin[c + d*x])/(d*Sqrt[1 - Cos[c + d*x]]))","A",1,1,12,0.08333,1,"{2651}"
18,1,31,0,0.0122529,"\int \frac{1}{5+3 \cos (c+d x)} \, dx","Int[(5 + 3*Cos[c + d*x])^(-1),x]","\frac{x}{4}-\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{2 d}","\frac{x}{4}-\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{2 d}",1,"x/4 - ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2657}"
19,1,56,0,0.0350288,"\int \frac{1}{(5+3 \cos (c+d x))^2} \, dx","Int[(5 + 3*Cos[c + d*x])^(-2),x]","-\frac{3 \sin (c+d x)}{16 d (3 \cos (c+d x)+5)}-\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}","-\frac{3 \sin (c+d x)}{16 d (3 \cos (c+d x)+5)}-\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 - (5*ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])])/(32*d) - (3*Sin[c + d*x])/(16*d*(5 + 3*Cos[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2657}"
20,1,81,0,0.0616755,"\int \frac{1}{(5+3 \cos (c+d x))^3} \, dx","Int[(5 + 3*Cos[c + d*x])^(-3),x]","-\frac{45 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)}-\frac{3 \sin (c+d x)}{32 d (3 \cos (c+d x)+5)^2}-\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{1024 d}+\frac{59 x}{2048}","-\frac{45 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)}-\frac{3 \sin (c+d x)}{32 d (3 \cos (c+d x)+5)^2}-\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{1024 d}+\frac{59 x}{2048}",1,"(59*x)/2048 - (59*ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])])/(1024*d) - (3*Sin[c + d*x])/(32*d*(5 + 3*Cos[c + d*x])^2) - (45*Sin[c + d*x])/(512*d*(5 + 3*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
21,1,106,0,0.0933855,"\int \frac{1}{(5+3 \cos (c+d x))^4} \, dx","Int[(5 + 3*Cos[c + d*x])^(-4),x]","-\frac{311 \sin (c+d x)}{8192 d (3 \cos (c+d x)+5)}-\frac{25 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)^2}-\frac{\sin (c+d x)}{16 d (3 \cos (c+d x)+5)^3}-\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}","-\frac{311 \sin (c+d x)}{8192 d (3 \cos (c+d x)+5)}-\frac{25 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)^2}-\frac{\sin (c+d x)}{16 d (3 \cos (c+d x)+5)^3}-\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 - (385*ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])])/(16384*d) - Sin[c + d*x]/(16*d*(5 + 3*Cos[c + d*x])^3) - (25*Sin[c + d*x])/(512*d*(5 + 3*Cos[c + d*x])^2) - (311*Sin[c + d*x])/(8192*d*(5 + 3*Cos[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
22,1,33,0,0.0126643,"\int \frac{1}{5-3 \cos (c+d x)} \, dx","Int[(5 - 3*Cos[c + d*x])^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{2 d}+\frac{x}{4}","\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{2 d}+\frac{x}{4}",1,"x/4 + ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2657}"
23,1,58,0,0.0358829,"\int \frac{1}{(5-3 \cos (c+d x))^2} \, dx","Int[(5 - 3*Cos[c + d*x])^(-2),x]","\frac{3 \sin (c+d x)}{16 d (5-3 \cos (c+d x))}+\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{32 d}+\frac{5 x}{64}","\frac{3 \sin (c+d x)}{16 d (5-3 \cos (c+d x))}+\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 + (5*ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])])/(32*d) + (3*Sin[c + d*x])/(16*d*(5 - 3*Cos[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2657}"
24,1,83,0,0.0626456,"\int \frac{1}{(5-3 \cos (c+d x))^3} \, dx","Int[(5 - 3*Cos[c + d*x])^(-3),x]","\frac{45 \sin (c+d x)}{512 d (5-3 \cos (c+d x))}+\frac{3 \sin (c+d x)}{32 d (5-3 \cos (c+d x))^2}+\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{1024 d}+\frac{59 x}{2048}","\frac{45 \sin (c+d x)}{512 d (5-3 \cos (c+d x))}+\frac{3 \sin (c+d x)}{32 d (5-3 \cos (c+d x))^2}+\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{1024 d}+\frac{59 x}{2048}",1,"(59*x)/2048 + (59*ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])])/(1024*d) + (3*Sin[c + d*x])/(32*d*(5 - 3*Cos[c + d*x])^2) + (45*Sin[c + d*x])/(512*d*(5 - 3*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
25,1,108,0,0.0962501,"\int \frac{1}{(5-3 \cos (c+d x))^4} \, dx","Int[(5 - 3*Cos[c + d*x])^(-4),x]","\frac{311 \sin (c+d x)}{8192 d (5-3 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (5-3 \cos (c+d x))^2}+\frac{\sin (c+d x)}{16 d (5-3 \cos (c+d x))^3}+\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}","\frac{311 \sin (c+d x)}{8192 d (5-3 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (5-3 \cos (c+d x))^2}+\frac{\sin (c+d x)}{16 d (5-3 \cos (c+d x))^3}+\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 + (385*ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])])/(16384*d) + Sin[c + d*x]/(16*d*(5 - 3*Cos[c + d*x])^3) + (25*Sin[c + d*x])/(512*d*(5 - 3*Cos[c + d*x])^2) + (311*Sin[c + d*x])/(8192*d*(5 - 3*Cos[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
26,1,33,0,0.0127241,"\int \frac{1}{-5+3 \cos (c+d x)} \, dx","Int[(-5 + 3*Cos[c + d*x])^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{2 d}-\frac{x}{4}","-\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{2 d}-\frac{x}{4}",1,"-x/4 - ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2658}"
27,1,58,0,0.0327876,"\int \frac{1}{(-5+3 \cos (c+d x))^2} \, dx","Int[(-5 + 3*Cos[c + d*x])^(-2),x]","\frac{3 \sin (c+d x)}{16 d (5-3 \cos (c+d x))}+\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{32 d}+\frac{5 x}{64}","\frac{3 \sin (c+d x)}{16 d (5-3 \cos (c+d x))}+\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 + (5*ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])])/(32*d) + (3*Sin[c + d*x])/(16*d*(5 - 3*Cos[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2658}"
28,1,83,0,0.0635439,"\int \frac{1}{(-5+3 \cos (c+d x))^3} \, dx","Int[(-5 + 3*Cos[c + d*x])^(-3),x]","-\frac{45 \sin (c+d x)}{512 d (5-3 \cos (c+d x))}-\frac{3 \sin (c+d x)}{32 d (5-3 \cos (c+d x))^2}-\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{1024 d}-\frac{59 x}{2048}","-\frac{45 \sin (c+d x)}{512 d (5-3 \cos (c+d x))}-\frac{3 \sin (c+d x)}{32 d (5-3 \cos (c+d x))^2}-\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{1024 d}-\frac{59 x}{2048}",1,"(-59*x)/2048 - (59*ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])])/(1024*d) - (3*Sin[c + d*x])/(32*d*(5 - 3*Cos[c + d*x])^2) - (45*Sin[c + d*x])/(512*d*(5 - 3*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
29,1,108,0,0.0949558,"\int \frac{1}{(-5+3 \cos (c+d x))^4} \, dx","Int[(-5 + 3*Cos[c + d*x])^(-4),x]","\frac{311 \sin (c+d x)}{8192 d (5-3 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (5-3 \cos (c+d x))^2}+\frac{\sin (c+d x)}{16 d (5-3 \cos (c+d x))^3}+\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}","\frac{311 \sin (c+d x)}{8192 d (5-3 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (5-3 \cos (c+d x))^2}+\frac{\sin (c+d x)}{16 d (5-3 \cos (c+d x))^3}+\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{3-\cos (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 + (385*ArcTan[Sin[c + d*x]/(3 - Cos[c + d*x])])/(16384*d) + Sin[c + d*x]/(16*d*(5 - 3*Cos[c + d*x])^3) + (25*Sin[c + d*x])/(512*d*(5 - 3*Cos[c + d*x])^2) + (311*Sin[c + d*x])/(8192*d*(5 - 3*Cos[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
30,1,31,0,0.0127493,"\int \frac{1}{-5-3 \cos (c+d x)} \, dx","Int[(-5 - 3*Cos[c + d*x])^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{2 d}-\frac{x}{4}","\frac{\tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{2 d}-\frac{x}{4}",1,"-x/4 + ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2658}"
31,1,56,0,0.0294425,"\int \frac{1}{(-5-3 \cos (c+d x))^2} \, dx","Int[(-5 - 3*Cos[c + d*x])^(-2),x]","-\frac{3 \sin (c+d x)}{16 d (3 \cos (c+d x)+5)}-\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}","-\frac{3 \sin (c+d x)}{16 d (3 \cos (c+d x)+5)}-\frac{5 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 - (5*ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])])/(32*d) - (3*Sin[c + d*x])/(16*d*(5 + 3*Cos[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2658}"
32,1,81,0,0.0611682,"\int \frac{1}{(-5-3 \cos (c+d x))^3} \, dx","Int[(-5 - 3*Cos[c + d*x])^(-3),x]","\frac{45 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)}+\frac{3 \sin (c+d x)}{32 d (3 \cos (c+d x)+5)^2}+\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{1024 d}-\frac{59 x}{2048}","\frac{45 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)}+\frac{3 \sin (c+d x)}{32 d (3 \cos (c+d x)+5)^2}+\frac{59 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{1024 d}-\frac{59 x}{2048}",1,"(-59*x)/2048 + (59*ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])])/(1024*d) + (3*Sin[c + d*x])/(32*d*(5 + 3*Cos[c + d*x])^2) + (45*Sin[c + d*x])/(512*d*(5 + 3*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
33,1,106,0,0.0960106,"\int \frac{1}{(-5-3 \cos (c+d x))^4} \, dx","Int[(-5 - 3*Cos[c + d*x])^(-4),x]","-\frac{311 \sin (c+d x)}{8192 d (3 \cos (c+d x)+5)}-\frac{25 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)^2}-\frac{\sin (c+d x)}{16 d (3 \cos (c+d x)+5)^3}-\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}","-\frac{311 \sin (c+d x)}{8192 d (3 \cos (c+d x)+5)}-\frac{25 \sin (c+d x)}{512 d (3 \cos (c+d x)+5)^2}-\frac{\sin (c+d x)}{16 d (3 \cos (c+d x)+5)^3}-\frac{385 \tan ^{-1}\left(\frac{\sin (c+d x)}{\cos (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 - (385*ArcTan[Sin[c + d*x]/(3 + Cos[c + d*x])])/(16384*d) - Sin[c + d*x]/(16*d*(5 + 3*Cos[c + d*x])^3) - (25*Sin[c + d*x])/(512*d*(5 + 3*Cos[c + d*x])^2) - (311*Sin[c + d*x])/(8192*d*(5 + 3*Cos[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
34,1,65,0,0.0193186,"\int \frac{1}{3+5 \cos (c+d x)} \, dx","Int[(3 + 5*Cos[c + d*x])^(-1),x]","\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"-Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]]/(4*d) + Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]]/(4*d)","A",2,2,12,0.1667,1,"{2659, 206}"
35,1,90,0,0.0412816,"\int \frac{1}{(3+5 \cos (c+d x))^2} \, dx","Int[(3 + 5*Cos[c + d*x])^(-2),x]","\frac{5 \sin (c+d x)}{16 d (5 \cos (c+d x)+3)}+\frac{3 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","\frac{5 \sin (c+d x)}{16 d (5 \cos (c+d x)+3)}+\frac{3 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(3*Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(64*d) - (3*Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(64*d) + (5*Sin[c + d*x])/(16*d*(3 + 5*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 12, 2659, 206}"
36,1,115,0,0.0750301,"\int \frac{1}{(3+5 \cos (c+d x))^3} \, dx","Int[(3 + 5*Cos[c + d*x])^(-3),x]","-\frac{45 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)}+\frac{5 \sin (c+d x)}{32 d (5 \cos (c+d x)+3)^2}-\frac{43 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","-\frac{45 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)}+\frac{5 \sin (c+d x)}{32 d (5 \cos (c+d x)+3)^2}-\frac{43 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(-43*Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(2048*d) + (43*Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(2048*d) + (5*Sin[c + d*x])/(32*d*(3 + 5*Cos[c + d*x])^2) - (45*Sin[c + d*x])/(512*d*(3 + 5*Cos[c + d*x]))","A",5,5,12,0.4167,1,"{2664, 2754, 12, 2659, 206}"
37,1,140,0,0.1134427,"\int \frac{1}{(3+5 \cos (c+d x))^4} \, dx","Int[(3 + 5*Cos[c + d*x])^(-4),x]","\frac{995 \sin (c+d x)}{24576 d (5 \cos (c+d x)+3)}-\frac{25 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)^2}+\frac{5 \sin (c+d x)}{48 d (5 \cos (c+d x)+3)^3}+\frac{279 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","\frac{995 \sin (c+d x)}{24576 d (5 \cos (c+d x)+3)}-\frac{25 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)^2}+\frac{5 \sin (c+d x)}{48 d (5 \cos (c+d x)+3)^3}+\frac{279 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(279*Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(32768*d) - (279*Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(32768*d) + (5*Sin[c + d*x])/(48*d*(3 + 5*Cos[c + d*x])^3) - (25*Sin[c + d*x])/(512*d*(3 + 5*Cos[c + d*x])^2) + (995*Sin[c + d*x])/(24576*d*(3 + 5*Cos[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 2754, 12, 2659, 206}"
38,1,63,0,0.0178129,"\int \frac{1}{3-5 \cos (c+d x)} \, dx","Int[(3 - 5*Cos[c + d*x])^(-1),x]","\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]]/(4*d) - Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]]/(4*d)","A",2,2,12,0.1667,1,"{2659, 207}"
39,1,88,0,0.0419783,"\int \frac{1}{(3-5 \cos (c+d x))^2} \, dx","Int[(3 - 5*Cos[c + d*x])^(-2),x]","-\frac{5 \sin (c+d x)}{16 d (3-5 \cos (c+d x))}-\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}+\frac{3 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","-\frac{5 \sin (c+d x)}{16 d (3-5 \cos (c+d x))}-\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}+\frac{3 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(-3*Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]])/(64*d) + (3*Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]])/(64*d) - (5*Sin[c + d*x])/(16*d*(3 - 5*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 12, 2659, 207}"
40,1,113,0,0.0724024,"\int \frac{1}{(3-5 \cos (c+d x))^3} \, dx","Int[(3 - 5*Cos[c + d*x])^(-3),x]","\frac{45 \sin (c+d x)}{512 d (3-5 \cos (c+d x))}-\frac{5 \sin (c+d x)}{32 d (3-5 \cos (c+d x))^2}+\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","\frac{45 \sin (c+d x)}{512 d (3-5 \cos (c+d x))}-\frac{5 \sin (c+d x)}{32 d (3-5 \cos (c+d x))^2}+\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(43*Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]])/(2048*d) - (43*Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]])/(2048*d) - (5*Sin[c + d*x])/(32*d*(3 - 5*Cos[c + d*x])^2) + (45*Sin[c + d*x])/(512*d*(3 - 5*Cos[c + d*x]))","A",5,5,12,0.4167,1,"{2664, 2754, 12, 2659, 207}"
41,1,138,0,0.113442,"\int \frac{1}{(3-5 \cos (c+d x))^4} \, dx","Int[(3 - 5*Cos[c + d*x])^(-4),x]","-\frac{995 \sin (c+d x)}{24576 d (3-5 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (3-5 \cos (c+d x))^2}-\frac{5 \sin (c+d x)}{48 d (3-5 \cos (c+d x))^3}-\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}+\frac{279 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","-\frac{995 \sin (c+d x)}{24576 d (3-5 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (3-5 \cos (c+d x))^2}-\frac{5 \sin (c+d x)}{48 d (3-5 \cos (c+d x))^3}-\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}+\frac{279 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(-279*Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]])/(32768*d) + (279*Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]])/(32768*d) - (5*Sin[c + d*x])/(48*d*(3 - 5*Cos[c + d*x])^3) + (25*Sin[c + d*x])/(512*d*(3 - 5*Cos[c + d*x])^2) - (995*Sin[c + d*x])/(24576*d*(3 - 5*Cos[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 2754, 12, 2659, 207}"
42,1,63,0,0.0170166,"\int \frac{1}{-3+5 \cos (c+d x)} \, dx","Int[(-3 + 5*Cos[c + d*x])^(-1),x]","\frac{\log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"-Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]]/(4*d) + Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]]/(4*d)","A",2,2,12,0.1667,1,"{2659, 206}"
43,1,88,0,0.039762,"\int \frac{1}{(-3+5 \cos (c+d x))^2} \, dx","Int[(-3 + 5*Cos[c + d*x])^(-2),x]","-\frac{5 \sin (c+d x)}{16 d (3-5 \cos (c+d x))}-\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}+\frac{3 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","-\frac{5 \sin (c+d x)}{16 d (3-5 \cos (c+d x))}-\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}+\frac{3 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(-3*Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]])/(64*d) + (3*Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]])/(64*d) - (5*Sin[c + d*x])/(16*d*(3 - 5*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 12, 2659, 206}"
44,1,113,0,0.0719102,"\int \frac{1}{(-3+5 \cos (c+d x))^3} \, dx","Int[(-3 + 5*Cos[c + d*x])^(-3),x]","-\frac{45 \sin (c+d x)}{512 d (3-5 \cos (c+d x))}+\frac{5 \sin (c+d x)}{32 d (3-5 \cos (c+d x))^2}-\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","-\frac{45 \sin (c+d x)}{512 d (3-5 \cos (c+d x))}+\frac{5 \sin (c+d x)}{32 d (3-5 \cos (c+d x))^2}-\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(-43*Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]])/(2048*d) + (43*Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]])/(2048*d) + (5*Sin[c + d*x])/(32*d*(3 - 5*Cos[c + d*x])^2) - (45*Sin[c + d*x])/(512*d*(3 - 5*Cos[c + d*x]))","A",5,5,12,0.4167,1,"{2664, 2754, 12, 2659, 206}"
45,1,138,0,0.1079863,"\int \frac{1}{(-3+5 \cos (c+d x))^4} \, dx","Int[(-3 + 5*Cos[c + d*x])^(-4),x]","-\frac{995 \sin (c+d x)}{24576 d (3-5 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (3-5 \cos (c+d x))^2}-\frac{5 \sin (c+d x)}{48 d (3-5 \cos (c+d x))^3}-\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}+\frac{279 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","-\frac{995 \sin (c+d x)}{24576 d (3-5 \cos (c+d x))}+\frac{25 \sin (c+d x)}{512 d (3-5 \cos (c+d x))^2}-\frac{5 \sin (c+d x)}{48 d (3-5 \cos (c+d x))^3}-\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-2 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}+\frac{279 \log \left(2 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(-279*Log[Cos[(c + d*x)/2] - 2*Sin[(c + d*x)/2]])/(32768*d) + (279*Log[Cos[(c + d*x)/2] + 2*Sin[(c + d*x)/2]])/(32768*d) - (5*Sin[c + d*x])/(48*d*(3 - 5*Cos[c + d*x])^3) + (25*Sin[c + d*x])/(512*d*(3 - 5*Cos[c + d*x])^2) - (995*Sin[c + d*x])/(24576*d*(3 - 5*Cos[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 2754, 12, 2659, 206}"
46,1,65,0,0.0177694,"\int \frac{1}{-3-5 \cos (c+d x)} \, dx","Int[(-3 - 5*Cos[c + d*x])^(-1),x]","\frac{\log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]]/(4*d) - Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]]/(4*d)","A",2,2,12,0.1667,1,"{2659, 207}"
47,1,90,0,0.0414251,"\int \frac{1}{(-3-5 \cos (c+d x))^2} \, dx","Int[(-3 - 5*Cos[c + d*x])^(-2),x]","\frac{5 \sin (c+d x)}{16 d (5 \cos (c+d x)+3)}+\frac{3 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","\frac{5 \sin (c+d x)}{16 d (5 \cos (c+d x)+3)}+\frac{3 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(3*Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(64*d) - (3*Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(64*d) + (5*Sin[c + d*x])/(16*d*(3 + 5*Cos[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 12, 2659, 207}"
48,1,115,0,0.0723293,"\int \frac{1}{(-3-5 \cos (c+d x))^3} \, dx","Int[(-3 - 5*Cos[c + d*x])^(-3),x]","\frac{45 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)}-\frac{5 \sin (c+d x)}{32 d (5 \cos (c+d x)+3)^2}+\frac{43 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","\frac{45 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)}-\frac{5 \sin (c+d x)}{32 d (5 \cos (c+d x)+3)^2}+\frac{43 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(43*Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(2048*d) - (43*Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(2048*d) - (5*Sin[c + d*x])/(32*d*(3 + 5*Cos[c + d*x])^2) + (45*Sin[c + d*x])/(512*d*(3 + 5*Cos[c + d*x]))","A",5,5,12,0.4167,1,"{2664, 2754, 12, 2659, 207}"
49,1,140,0,0.1200534,"\int \frac{1}{(-3-5 \cos (c+d x))^4} \, dx","Int[(-3 - 5*Cos[c + d*x])^(-4),x]","\frac{995 \sin (c+d x)}{24576 d (5 \cos (c+d x)+3)}-\frac{25 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)^2}+\frac{5 \sin (c+d x)}{48 d (5 \cos (c+d x)+3)^3}+\frac{279 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","\frac{995 \sin (c+d x)}{24576 d (5 \cos (c+d x)+3)}-\frac{25 \sin (c+d x)}{512 d (5 \cos (c+d x)+3)^2}+\frac{5 \sin (c+d x)}{48 d (5 \cos (c+d x)+3)^3}+\frac{279 \log \left(2 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+2 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(279*Log[2*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(32768*d) - (279*Log[2*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(32768*d) + (5*Sin[c + d*x])/(48*d*(3 + 5*Cos[c + d*x])^3) - (25*Sin[c + d*x])/(512*d*(3 + 5*Cos[c + d*x])^2) + (995*Sin[c + d*x])/(24576*d*(3 + 5*Cos[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 2754, 12, 2659, 207}"
50,1,197,0,0.281776,"\int (a+b \cos (c+d x))^{5/2} \, dx","Int[(a + b*Cos[c + d*x])^(5/2),x]","-\frac{16 a \left(a^2-b^2\right) \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{15 d \sqrt{a+b \cos (c+d x)}}+\frac{2 \left(23 a^2+9 b^2\right) \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{15 d \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{2 b \sin (c+d x) (a+b \cos (c+d x))^{3/2}}{5 d}+\frac{16 a b \sin (c+d x) \sqrt{a+b \cos (c+d x)}}{15 d}","-\frac{16 a \left(a^2-b^2\right) \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{15 d \sqrt{a+b \cos (c+d x)}}+\frac{2 \left(23 a^2+9 b^2\right) \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{15 d \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}+\frac{2 b \sin (c+d x) (a+b \cos (c+d x))^{3/2}}{5 d}+\frac{16 a b \sin (c+d x) \sqrt{a+b \cos (c+d x)}}{15 d}",1,"(2*(23*a^2 + 9*b^2)*Sqrt[a + b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, (2*b)/(a + b)])/(15*d*Sqrt[(a + b*Cos[c + d*x])/(a + b)]) - (16*a*(a^2 - b^2)*Sqrt[(a + b*Cos[c + d*x])/(a + b)]*EllipticF[(c + d*x)/2, (2*b)/(a + b)])/(15*d*Sqrt[a + b*Cos[c + d*x]]) + (16*a*b*Sqrt[a + b*Cos[c + d*x]]*Sin[c + d*x])/(15*d) + (2*b*(a + b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",7,7,14,0.5000,1,"{2656, 2753, 2752, 2663, 2661, 2655, 2653}"
51,1,157,0,0.1708709,"\int (a+b \cos (c+d x))^{3/2} \, dx","Int[(a + b*Cos[c + d*x])^(3/2),x]","-\frac{2 \left(a^2-b^2\right) \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \sqrt{a+b \cos (c+d x)}}+\frac{2 b \sin (c+d x) \sqrt{a+b \cos (c+d x)}}{3 d}+\frac{8 a \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}","-\frac{2 \left(a^2-b^2\right) \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \sqrt{a+b \cos (c+d x)}}+\frac{2 b \sin (c+d x) \sqrt{a+b \cos (c+d x)}}{3 d}+\frac{8 a \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}",1,"(8*a*Sqrt[a + b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, (2*b)/(a + b)])/(3*d*Sqrt[(a + b*Cos[c + d*x])/(a + b)]) - (2*(a^2 - b^2)*Sqrt[(a + b*Cos[c + d*x])/(a + b)]*EllipticF[(c + d*x)/2, (2*b)/(a + b)])/(3*d*Sqrt[a + b*Cos[c + d*x]]) + (2*b*Sqrt[a + b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",6,6,14,0.4286,1,"{2656, 2752, 2663, 2661, 2655, 2653}"
52,1,57,0,0.0368909,"\int \sqrt{a+b \cos (c+d x)} \, dx","Int[Sqrt[a + b*Cos[c + d*x]],x]","\frac{2 \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{d \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}","\frac{2 \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{d \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}",1,"(2*Sqrt[a + b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, (2*b)/(a + b)])/(d*Sqrt[(a + b*Cos[c + d*x])/(a + b)])","A",2,2,14,0.1429,1,"{2655, 2653}"
53,1,57,0,0.0394945,"\int \frac{1}{\sqrt{a+b \cos (c+d x)}} \, dx","Int[1/Sqrt[a + b*Cos[c + d*x]],x]","\frac{2 \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{d \sqrt{a+b \cos (c+d x)}}","\frac{2 \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{d \sqrt{a+b \cos (c+d x)}}",1,"(2*Sqrt[(a + b*Cos[c + d*x])/(a + b)]*EllipticF[(c + d*x)/2, (2*b)/(a + b)])/(d*Sqrt[a + b*Cos[c + d*x]])","A",2,2,14,0.1429,1,"{2663, 2661}"
54,1,106,0,0.0679506,"\int \frac{1}{(a+b \cos (c+d x))^{3/2}} \, dx","Int[(a + b*Cos[c + d*x])^(-3/2),x]","\frac{2 \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{d \left(a^2-b^2\right) \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}-\frac{2 b \sin (c+d x)}{d \left(a^2-b^2\right) \sqrt{a+b \cos (c+d x)}}","\frac{2 \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{d \left(a^2-b^2\right) \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}-\frac{2 b \sin (c+d x)}{d \left(a^2-b^2\right) \sqrt{a+b \cos (c+d x)}}",1,"(2*Sqrt[a + b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, (2*b)/(a + b)])/((a^2 - b^2)*d*Sqrt[(a + b*Cos[c + d*x])/(a + b)]) - (2*b*Sin[c + d*x])/((a^2 - b^2)*d*Sqrt[a + b*Cos[c + d*x]])","A",4,4,14,0.2857,1,"{2664, 21, 2655, 2653}"
55,1,221,0,0.2334401,"\int \frac{1}{(a+b \cos (c+d x))^{5/2}} \, dx","Int[(a + b*Cos[c + d*x])^(-5/2),x]","-\frac{8 a b \sin (c+d x)}{3 d \left(a^2-b^2\right)^2 \sqrt{a+b \cos (c+d x)}}-\frac{2 b \sin (c+d x)}{3 d \left(a^2-b^2\right) (a+b \cos (c+d x))^{3/2}}-\frac{2 \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right) \sqrt{a+b \cos (c+d x)}}+\frac{8 a \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}","-\frac{8 a b \sin (c+d x)}{3 d \left(a^2-b^2\right)^2 \sqrt{a+b \cos (c+d x)}}-\frac{2 b \sin (c+d x)}{3 d \left(a^2-b^2\right) (a+b \cos (c+d x))^{3/2}}-\frac{2 \sqrt{\frac{a+b \cos (c+d x)}{a+b}} F\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right) \sqrt{a+b \cos (c+d x)}}+\frac{8 a \sqrt{a+b \cos (c+d x)} E\left(\frac{1}{2} (c+d x)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \cos (c+d x)}{a+b}}}",1,"(8*a*Sqrt[a + b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, (2*b)/(a + b)])/(3*(a^2 - b^2)^2*d*Sqrt[(a + b*Cos[c + d*x])/(a + b)]) - (2*Sqrt[(a + b*Cos[c + d*x])/(a + b)]*EllipticF[(c + d*x)/2, (2*b)/(a + b)])/(3*(a^2 - b^2)*d*Sqrt[a + b*Cos[c + d*x]]) - (2*b*Sin[c + d*x])/(3*(a^2 - b^2)*d*(a + b*Cos[c + d*x])^(3/2)) - (8*a*b*Sin[c + d*x])/(3*(a^2 - b^2)^2*d*Sqrt[a + b*Cos[c + d*x]])","A",7,7,14,0.5000,1,"{2664, 2754, 2752, 2663, 2661, 2655, 2653}"
56,1,108,0,0.0774197,"\int (a+b \cos (c+d x))^{4/3} \, dx","Int[(a + b*Cos[c + d*x])^(4/3),x]","\frac{\sqrt{2} (a+b) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}","\frac{\sqrt{2} (a+b) \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}",1,"(Sqrt[2]*(a + b)*AppellF1[1/2, 1/2, -4/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
57,1,105,0,0.0667001,"\int (a+b \cos (c+d x))^{2/3} \, dx","Int[(a + b*Cos[c + d*x])^(2/3),x]","\frac{\sqrt{2} \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}","\frac{\sqrt{2} \sin (c+d x) (a+b \cos (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3}}",1,"(Sqrt[2]*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(2/3)*Sin[c + d*x])/(d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(2/3))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
58,1,105,0,0.0631823,"\int \sqrt[3]{a+b \cos (c+d x)} \, dx","Int[(a + b*Cos[c + d*x])^(1/3),x]","\frac{\sqrt{2} \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}","\frac{\sqrt{2} \sin (c+d x) \sqrt[3]{a+b \cos (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}}}",1,"(Sqrt[2]*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^(1/3)*Sin[c + d*x])/(d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^(1/3))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
59,1,105,0,0.0660175,"\int \frac{1}{\sqrt[3]{a+b \cos (c+d x)}} \, dx","Int[(a + b*Cos[c + d*x])^(-1/3),x]","\frac{\sqrt{2} \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}","\frac{\sqrt{2} \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}",1,"(Sqrt[2]*AppellF1[1/2, 1/2, 1/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(1/3)*Sin[c + d*x])/(d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(1/3))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
60,1,105,0,0.0642733,"\int \frac{1}{(a+b \cos (c+d x))^{2/3}} \, dx","Int[(a + b*Cos[c + d*x])^(-2/3),x]","\frac{\sqrt{2} \sin (c+d x) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}","\frac{\sqrt{2} \sin (c+d x) \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1} (a+b \cos (c+d x))^{2/3}}",1,"(Sqrt[2]*AppellF1[1/2, 1/2, 2/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(2/3)*Sin[c + d*x])/(d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(2/3))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
61,1,110,0,0.0692391,"\int \frac{1}{(a+b \cos (c+d x))^{4/3}} \, dx","Int[(a + b*Cos[c + d*x])^(-4/3),x]","\frac{\sqrt{2} \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d (a+b) \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}","\frac{\sqrt{2} \sin (c+d x) \sqrt[3]{\frac{a+b \cos (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d (a+b) \sqrt{\cos (c+d x)+1} \sqrt[3]{a+b \cos (c+d x)}}",1,"(Sqrt[2]*AppellF1[1/2, 1/2, 4/3, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*((a + b*Cos[c + d*x])/(a + b))^(1/3)*Sin[c + d*x])/((a + b)*d*Sqrt[1 + Cos[c + d*x]]*(a + b*Cos[c + d*x])^(1/3))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
62,1,103,0,0.0665137,"\int (a+b \cos (c+d x))^n \, dx","Int[(a + b*Cos[c + d*x])^n,x]","\frac{\sqrt{2} \sin (c+d x) (a+b \cos (c+d x))^n \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{-n} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1}}","\frac{\sqrt{2} \sin (c+d x) (a+b \cos (c+d x))^n \left(\frac{a+b \cos (c+d x)}{a+b}\right)^{-n} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\cos (c+d x)),\frac{b (1-\cos (c+d x))}{a+b}\right)}{d \sqrt{\cos (c+d x)+1}}",1,"(Sqrt[2]*AppellF1[1/2, 1/2, -n, 3/2, (1 - Cos[c + d*x])/2, (b*(1 - Cos[c + d*x]))/(a + b)]*(a + b*Cos[c + d*x])^n*Sin[c + d*x])/(d*Sqrt[1 + Cos[c + d*x]]*((a + b*Cos[c + d*x])/(a + b))^n)","A",3,3,12,0.2500,1,"{2665, 139, 138}"