1,1,119,0,0.0706675,"\int (a+a \sin (c+d x))^{7/2} \, dx","Int[(a + a*Sin[c + d*x])^(7/2),x]","-\frac{256 a^4 \cos (c+d x)}{35 d \sqrt{a \sin (c+d x)+a}}-\frac{64 a^3 \cos (c+d x) \sqrt{a \sin (c+d x)+a}}{35 d}-\frac{24 a^2 \cos (c+d x) (a \sin (c+d x)+a)^{3/2}}{35 d}-\frac{2 a \cos (c+d x) (a \sin (c+d x)+a)^{5/2}}{7 d}","-\frac{256 a^4 \cos (c+d x)}{35 d \sqrt{a \sin (c+d x)+a}}-\frac{64 a^3 \cos (c+d x) \sqrt{a \sin (c+d x)+a}}{35 d}-\frac{24 a^2 \cos (c+d x) (a \sin (c+d x)+a)^{3/2}}{35 d}-\frac{2 a \cos (c+d x) (a \sin (c+d x)+a)^{5/2}}{7 d}",1,"(-256*a^4*Cos[c + d*x])/(35*d*Sqrt[a + a*Sin[c + d*x]]) - (64*a^3*Cos[c + d*x]*Sqrt[a + a*Sin[c + d*x]])/(35*d) - (24*a^2*Cos[c + d*x]*(a + a*Sin[c + d*x])^(3/2))/(35*d) - (2*a*Cos[c + d*x]*(a + a*Sin[c + d*x])^(5/2))/(7*d)","A",4,2,14,0.1429,1,"{2647, 2646}"
2,1,89,0,0.0470163,"\int (a+a \sin (c+d x))^{5/2} \, dx","Int[(a + a*Sin[c + d*x])^(5/2),x]","-\frac{64 a^3 \cos (c+d x)}{15 d \sqrt{a \sin (c+d x)+a}}-\frac{16 a^2 \cos (c+d x) \sqrt{a \sin (c+d x)+a}}{15 d}-\frac{2 a \cos (c+d x) (a \sin (c+d x)+a)^{3/2}}{5 d}","-\frac{64 a^3 \cos (c+d x)}{15 d \sqrt{a \sin (c+d x)+a}}-\frac{16 a^2 \cos (c+d x) \sqrt{a \sin (c+d x)+a}}{15 d}-\frac{2 a \cos (c+d x) (a \sin (c+d x)+a)^{3/2}}{5 d}",1,"(-64*a^3*Cos[c + d*x])/(15*d*Sqrt[a + a*Sin[c + d*x]]) - (16*a^2*Cos[c + d*x]*Sqrt[a + a*Sin[c + d*x]])/(15*d) - (2*a*Cos[c + d*x]*(a + a*Sin[c + d*x])^(3/2))/(5*d)","A",3,2,14,0.1429,1,"{2647, 2646}"
3,1,59,0,0.0292287,"\int (a+a \sin (c+d x))^{3/2} \, dx","Int[(a + a*Sin[c + d*x])^(3/2),x]","-\frac{8 a^2 \cos (c+d x)}{3 d \sqrt{a \sin (c+d x)+a}}-\frac{2 a \cos (c+d x) \sqrt{a \sin (c+d x)+a}}{3 d}","-\frac{8 a^2 \cos (c+d x)}{3 d \sqrt{a \sin (c+d x)+a}}-\frac{2 a \cos (c+d x) \sqrt{a \sin (c+d x)+a}}{3 d}",1,"(-8*a^2*Cos[c + d*x])/(3*d*Sqrt[a + a*Sin[c + d*x]]) - (2*a*Cos[c + d*x]*Sqrt[a + a*Sin[c + d*x]])/(3*d)","A",2,2,14,0.1429,1,"{2647, 2646}"
4,1,26,0,0.0133678,"\int \sqrt{a+a \sin (c+d x)} \, dx","Int[Sqrt[a + a*Sin[c + d*x]],x]","-\frac{2 a \cos (c+d x)}{d \sqrt{a \sin (c+d x)+a}}","-\frac{2 a \cos (c+d x)}{d \sqrt{a \sin (c+d x)+a}}",1,"(-2*a*Cos[c + d*x])/(d*Sqrt[a + a*Sin[c + d*x]])","A",1,1,14,0.07143,1,"{2646}"
5,1,47,0,0.0248641,"\int \frac{1}{\sqrt{a+a \sin (c+d x)}} \, dx","Int[1/Sqrt[a + a*Sin[c + d*x]],x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \cos (c+d x)}{\sqrt{2} \sqrt{a \sin (c+d x)+a}}\right)}{\sqrt{a} d}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \cos (c+d x)}{\sqrt{2} \sqrt{a \sin (c+d x)+a}}\right)}{\sqrt{a} d}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[a]*Cos[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sin[c + d*x]])])/(Sqrt[a]*d))","A",2,2,14,0.1429,1,"{2649, 206}"
6,1,77,0,0.0419245,"\int \frac{1}{(a+a \sin (c+d x))^{3/2}} \, dx","Int[(a + a*Sin[c + d*x])^(-3/2),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cos (c+d x)}{\sqrt{2} \sqrt{a \sin (c+d x)+a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{\cos (c+d x)}{2 d (a \sin (c+d x)+a)^{3/2}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{a} \cos (c+d x)}{\sqrt{2} \sqrt{a \sin (c+d x)+a}}\right)}{2 \sqrt{2} a^{3/2} d}-\frac{\cos (c+d x)}{2 d (a \sin (c+d x)+a)^{3/2}}",1,"-ArcTanh[(Sqrt[a]*Cos[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sin[c + d*x]])]/(2*Sqrt[2]*a^(3/2)*d) - Cos[c + d*x]/(2*d*(a + a*Sin[c + d*x])^(3/2))","A",3,3,14,0.2143,1,"{2650, 2649, 206}"
7,1,107,0,0.0630014,"\int \frac{1}{(a+a \sin (c+d x))^{5/2}} \, dx","Int[(a + a*Sin[c + d*x])^(-5/2),x]","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a} \cos (c+d x)}{\sqrt{2} \sqrt{a \sin (c+d x)+a}}\right)}{16 \sqrt{2} a^{5/2} d}-\frac{3 \cos (c+d x)}{16 a d (a \sin (c+d x)+a)^{3/2}}-\frac{\cos (c+d x)}{4 d (a \sin (c+d x)+a)^{5/2}}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{a} \cos (c+d x)}{\sqrt{2} \sqrt{a \sin (c+d x)+a}}\right)}{16 \sqrt{2} a^{5/2} d}-\frac{3 \cos (c+d x)}{16 a d (a \sin (c+d x)+a)^{3/2}}-\frac{\cos (c+d x)}{4 d (a \sin (c+d x)+a)^{5/2}}",1,"(-3*ArcTanh[(Sqrt[a]*Cos[c + d*x])/(Sqrt[2]*Sqrt[a + a*Sin[c + d*x]])])/(16*Sqrt[2]*a^(5/2)*d) - Cos[c + d*x]/(4*d*(a + a*Sin[c + d*x])^(5/2)) - (3*Cos[c + d*x])/(16*a*d*(a + a*Sin[c + d*x])^(3/2))","A",4,3,14,0.2143,1,"{2650, 2649, 206}"
8,1,67,0,0.0362315,"\int (a+a \sin (c+d x))^{4/3} \, dx","Int[(a + a*Sin[c + d*x])^(4/3),x]","-\frac{2\ 2^{5/6} a \cos (c+d x) \sqrt[3]{a \sin (c+d x)+a} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d (\sin (c+d x)+1)^{5/6}}","-\frac{2\ 2^{5/6} a \cos (c+d x) \sqrt[3]{a \sin (c+d x)+a} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d (\sin (c+d x)+1)^{5/6}}",1,"(-2*2^(5/6)*a*Cos[c + d*x]*Hypergeometric2F1[-5/6, 1/2, 3/2, (1 - Sin[c + d*x])/2]*(a + a*Sin[c + d*x])^(1/3))/(d*(1 + Sin[c + d*x])^(5/6))","A",2,2,14,0.1429,1,"{2652, 2651}"
9,1,66,0,0.03377,"\int (a+a \sin (c+d x))^{2/3} \, dx","Int[(a + a*Sin[c + d*x])^(2/3),x]","-\frac{2 \sqrt[6]{2} \cos (c+d x) (a \sin (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d (\sin (c+d x)+1)^{7/6}}","-\frac{2 \sqrt[6]{2} \cos (c+d x) (a \sin (c+d x)+a)^{2/3} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d (\sin (c+d x)+1)^{7/6}}",1,"(-2*2^(1/6)*Cos[c + d*x]*Hypergeometric2F1[-1/6, 1/2, 3/2, (1 - Sin[c + d*x])/2]*(a + a*Sin[c + d*x])^(2/3))/(d*(1 + Sin[c + d*x])^(7/6))","A",2,2,14,0.1429,1,"{2652, 2651}"
10,1,66,0,0.0314145,"\int \sqrt[3]{a+a \sin (c+d x)} \, dx","Int[(a + a*Sin[c + d*x])^(1/3),x]","-\frac{2^{5/6} \cos (c+d x) \sqrt[3]{a \sin (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d (\sin (c+d x)+1)^{5/6}}","-\frac{2^{5/6} \cos (c+d x) \sqrt[3]{a \sin (c+d x)+a} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d (\sin (c+d x)+1)^{5/6}}",1,"-((2^(5/6)*Cos[c + d*x]*Hypergeometric2F1[1/6, 1/2, 3/2, (1 - Sin[c + d*x])/2]*(a + a*Sin[c + d*x])^(1/3))/(d*(1 + Sin[c + d*x])^(5/6)))","A",2,2,14,0.1429,1,"{2652, 2651}"
11,1,66,0,0.0302201,"\int \frac{1}{\sqrt[3]{a+a \sin (c+d x)}} \, dx","Int[(a + a*Sin[c + d*x])^(-1/3),x]","-\frac{\sqrt[6]{2} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d \sqrt[6]{\sin (c+d x)+1} \sqrt[3]{a \sin (c+d x)+a}}","-\frac{\sqrt[6]{2} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d \sqrt[6]{\sin (c+d x)+1} \sqrt[3]{a \sin (c+d x)+a}}",1,"-((2^(1/6)*Cos[c + d*x]*Hypergeometric2F1[1/2, 5/6, 3/2, (1 - Sin[c + d*x])/2])/(d*(1 + Sin[c + d*x])^(1/6)*(a + a*Sin[c + d*x])^(1/3)))","A",2,2,14,0.1429,1,"{2652, 2651}"
12,1,66,0,0.0332749,"\int \frac{1}{(a+a \sin (c+d x))^{2/3}} \, dx","Int[(a + a*Sin[c + d*x])^(-2/3),x]","-\frac{\sqrt[6]{\sin (c+d x)+1} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{\sqrt[6]{2} d (a \sin (c+d x)+a)^{2/3}}","-\frac{\sqrt[6]{\sin (c+d x)+1} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{\sqrt[6]{2} d (a \sin (c+d x)+a)^{2/3}}",1,"-((Cos[c + d*x]*Hypergeometric2F1[1/2, 7/6, 3/2, (1 - Sin[c + d*x])/2]*(1 + Sin[c + d*x])^(1/6))/(2^(1/6)*d*(a + a*Sin[c + d*x])^(2/3)))","A",2,2,14,0.1429,1,"{2652, 2651}"
13,1,69,0,0.0336768,"\int \frac{1}{(a+a \sin (c+d x))^{4/3}} \, dx","Int[(a + a*Sin[c + d*x])^(-4/3),x]","-\frac{\cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{2^{5/6} a d \sqrt[6]{\sin (c+d x)+1} \sqrt[3]{a \sin (c+d x)+a}}","-\frac{\cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{2^{5/6} a d \sqrt[6]{\sin (c+d x)+1} \sqrt[3]{a \sin (c+d x)+a}}",1,"-((Cos[c + d*x]*Hypergeometric2F1[1/2, 11/6, 3/2, (1 - Sin[c + d*x])/2])/(2^(5/6)*a*d*(1 + Sin[c + d*x])^(1/6)*(a + a*Sin[c + d*x])^(1/3)))","A",2,2,14,0.1429,1,"{2652, 2651}"
14,1,74,0,0.0382396,"\int (a+a \sin (c+d x))^n \, dx","Int[(a + a*Sin[c + d*x])^n,x]","-\frac{2^{n+\frac{1}{2}} \cos (c+d x) (\sin (c+d x)+1)^{-n-\frac{1}{2}} (a \sin (c+d x)+a)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d}","-\frac{2^{n+\frac{1}{2}} \cos (c+d x) (\sin (c+d x)+1)^{-n-\frac{1}{2}} (a \sin (c+d x)+a)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d}",1,"-((2^(1/2 + n)*Cos[c + d*x]*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 - Sin[c + d*x])/2]*(1 + Sin[c + d*x])^(-1/2 - n)*(a + a*Sin[c + d*x])^n)/d)","A",2,2,12,0.1667,1,"{2652, 2651}"
15,1,74,0,0.033747,"\int (a-a \sin (c+d x))^n \, dx","Int[(a - a*Sin[c + d*x])^n,x]","\frac{2^{n+\frac{1}{2}} \cos (c+d x) (1-\sin (c+d x))^{-n-\frac{1}{2}} (a-a \sin (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\sin (c+d x)+1)\right)}{d}","\frac{2^{n+\frac{1}{2}} \cos (c+d x) (1-\sin (c+d x))^{-n-\frac{1}{2}} (a-a \sin (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\sin (c+d x)+1)\right)}{d}",1,"(2^(1/2 + n)*Cos[c + d*x]*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 + Sin[c + d*x])/2]*(1 - Sin[c + d*x])^(-1/2 - n)*(a - a*Sin[c + d*x])^n)/d","A",2,2,13,0.1538,1,"{2652, 2651}"
16,1,60,0,0.0178978,"\int (2+2 \sin (c+d x))^n \, dx","Int[(2 + 2*Sin[c + d*x])^n,x]","-\frac{2^{2 n+\frac{1}{2}} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d \sqrt{\sin (c+d x)+1}}","-\frac{2^{2 n+\frac{1}{2}} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x))\right)}{d \sqrt{\sin (c+d x)+1}}",1,"-((2^(1/2 + 2*n)*Cos[c + d*x]*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 - Sin[c + d*x])/2])/(d*Sqrt[1 + Sin[c + d*x]]))","A",1,1,12,0.08333,1,"{2651}"
17,1,59,0,0.0156874,"\int (2-2 \sin (c+d x))^n \, dx","Int[(2 - 2*Sin[c + d*x])^n,x]","\frac{2^{2 n+\frac{1}{2}} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}","\frac{2^{2 n+\frac{1}{2}} \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-n;\frac{3}{2};\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}",1,"(2^(1/2 + 2*n)*Cos[c + d*x]*Hypergeometric2F1[1/2, 1/2 - n, 3/2, (1 + Sin[c + d*x])/2])/(d*Sqrt[1 - Sin[c + d*x]])","A",1,1,12,0.08333,1,"{2651}"
18,1,31,0,0.0129195,"\int \frac{1}{5+3 \sin (c+d x)} \, dx","Int[(5 + 3*Sin[c + d*x])^(-1),x]","\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{2 d}+\frac{x}{4}","\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{2 d}+\frac{x}{4}",1,"x/4 + ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2657}"
19,1,56,0,0.03421,"\int \frac{1}{(5+3 \sin (c+d x))^2} \, dx","Int[(5 + 3*Sin[c + d*x])^(-2),x]","\frac{3 \cos (c+d x)}{16 d (3 \sin (c+d x)+5)}+\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}","\frac{3 \cos (c+d x)}{16 d (3 \sin (c+d x)+5)}+\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 + (5*ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])])/(32*d) + (3*Cos[c + d*x])/(16*d*(5 + 3*Sin[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2657}"
20,1,81,0,0.0612872,"\int \frac{1}{(5+3 \sin (c+d x))^3} \, dx","Int[(5 + 3*Sin[c + d*x])^(-3),x]","\frac{45 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)}+\frac{3 \cos (c+d x)}{32 d (3 \sin (c+d x)+5)^2}+\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{1024 d}+\frac{59 x}{2048}","\frac{45 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)}+\frac{3 \cos (c+d x)}{32 d (3 \sin (c+d x)+5)^2}+\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{1024 d}+\frac{59 x}{2048}",1,"(59*x)/2048 + (59*ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])])/(1024*d) + (3*Cos[c + d*x])/(32*d*(5 + 3*Sin[c + d*x])^2) + (45*Cos[c + d*x])/(512*d*(5 + 3*Sin[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
21,1,106,0,0.0975227,"\int \frac{1}{(5+3 \sin (c+d x))^4} \, dx","Int[(5 + 3*Sin[c + d*x])^(-4),x]","\frac{311 \cos (c+d x)}{8192 d (3 \sin (c+d x)+5)}+\frac{25 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)^2}+\frac{\cos (c+d x)}{16 d (3 \sin (c+d x)+5)^3}+\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}","\frac{311 \cos (c+d x)}{8192 d (3 \sin (c+d x)+5)}+\frac{25 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)^2}+\frac{\cos (c+d x)}{16 d (3 \sin (c+d x)+5)^3}+\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 + (385*ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])])/(16384*d) + Cos[c + d*x]/(16*d*(5 + 3*Sin[c + d*x])^3) + (25*Cos[c + d*x])/(512*d*(5 + 3*Sin[c + d*x])^2) + (311*Cos[c + d*x])/(8192*d*(5 + 3*Sin[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
22,1,33,0,0.0125714,"\int \frac{1}{5-3 \sin (c+d x)} \, dx","Int[(5 - 3*Sin[c + d*x])^(-1),x]","\frac{x}{4}-\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{2 d}","\frac{x}{4}-\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{2 d}",1,"x/4 - ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2657}"
23,1,58,0,0.0313792,"\int \frac{1}{(5-3 \sin (c+d x))^2} \, dx","Int[(5 - 3*Sin[c + d*x])^(-2),x]","-\frac{3 \cos (c+d x)}{16 d (5-3 \sin (c+d x))}-\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{32 d}+\frac{5 x}{64}","-\frac{3 \cos (c+d x)}{16 d (5-3 \sin (c+d x))}-\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 - (5*ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])])/(32*d) - (3*Cos[c + d*x])/(16*d*(5 - 3*Sin[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2657}"
24,1,83,0,0.0633842,"\int \frac{1}{(5-3 \sin (c+d x))^3} \, dx","Int[(5 - 3*Sin[c + d*x])^(-3),x]","-\frac{45 \cos (c+d x)}{512 d (5-3 \sin (c+d x))}-\frac{3 \cos (c+d x)}{32 d (5-3 \sin (c+d x))^2}-\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{1024 d}+\frac{59 x}{2048}","-\frac{45 \cos (c+d x)}{512 d (5-3 \sin (c+d x))}-\frac{3 \cos (c+d x)}{32 d (5-3 \sin (c+d x))^2}-\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{1024 d}+\frac{59 x}{2048}",1,"(59*x)/2048 - (59*ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])])/(1024*d) - (3*Cos[c + d*x])/(32*d*(5 - 3*Sin[c + d*x])^2) - (45*Cos[c + d*x])/(512*d*(5 - 3*Sin[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
25,1,108,0,0.0960948,"\int \frac{1}{(5-3 \sin (c+d x))^4} \, dx","Int[(5 - 3*Sin[c + d*x])^(-4),x]","-\frac{311 \cos (c+d x)}{8192 d (5-3 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (5-3 \sin (c+d x))^2}-\frac{\cos (c+d x)}{16 d (5-3 \sin (c+d x))^3}-\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}","-\frac{311 \cos (c+d x)}{8192 d (5-3 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (5-3 \sin (c+d x))^2}-\frac{\cos (c+d x)}{16 d (5-3 \sin (c+d x))^3}-\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 - (385*ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])])/(16384*d) - Cos[c + d*x]/(16*d*(5 - 3*Sin[c + d*x])^3) - (25*Cos[c + d*x])/(512*d*(5 - 3*Sin[c + d*x])^2) - (311*Cos[c + d*x])/(8192*d*(5 - 3*Sin[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2657}"
26,1,33,0,0.0121246,"\int \frac{1}{-5+3 \sin (c+d x)} \, dx","Int[(-5 + 3*Sin[c + d*x])^(-1),x]","\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{2 d}-\frac{x}{4}","\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{2 d}-\frac{x}{4}",1,"-x/4 + ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2658}"
27,1,58,0,0.0315041,"\int \frac{1}{(-5+3 \sin (c+d x))^2} \, dx","Int[(-5 + 3*Sin[c + d*x])^(-2),x]","-\frac{3 \cos (c+d x)}{16 d (5-3 \sin (c+d x))}-\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{32 d}+\frac{5 x}{64}","-\frac{3 \cos (c+d x)}{16 d (5-3 \sin (c+d x))}-\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 - (5*ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])])/(32*d) - (3*Cos[c + d*x])/(16*d*(5 - 3*Sin[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2658}"
28,1,83,0,0.0631747,"\int \frac{1}{(-5+3 \sin (c+d x))^3} \, dx","Int[(-5 + 3*Sin[c + d*x])^(-3),x]","\frac{45 \cos (c+d x)}{512 d (5-3 \sin (c+d x))}+\frac{3 \cos (c+d x)}{32 d (5-3 \sin (c+d x))^2}+\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{1024 d}-\frac{59 x}{2048}","\frac{45 \cos (c+d x)}{512 d (5-3 \sin (c+d x))}+\frac{3 \cos (c+d x)}{32 d (5-3 \sin (c+d x))^2}+\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{1024 d}-\frac{59 x}{2048}",1,"(-59*x)/2048 + (59*ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])])/(1024*d) + (3*Cos[c + d*x])/(32*d*(5 - 3*Sin[c + d*x])^2) + (45*Cos[c + d*x])/(512*d*(5 - 3*Sin[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
29,1,108,0,0.0945206,"\int \frac{1}{(-5+3 \sin (c+d x))^4} \, dx","Int[(-5 + 3*Sin[c + d*x])^(-4),x]","-\frac{311 \cos (c+d x)}{8192 d (5-3 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (5-3 \sin (c+d x))^2}-\frac{\cos (c+d x)}{16 d (5-3 \sin (c+d x))^3}-\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}","-\frac{311 \cos (c+d x)}{8192 d (5-3 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (5-3 \sin (c+d x))^2}-\frac{\cos (c+d x)}{16 d (5-3 \sin (c+d x))^3}-\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{3-\sin (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 - (385*ArcTan[Cos[c + d*x]/(3 - Sin[c + d*x])])/(16384*d) - Cos[c + d*x]/(16*d*(5 - 3*Sin[c + d*x])^3) - (25*Cos[c + d*x])/(512*d*(5 - 3*Sin[c + d*x])^2) - (311*Cos[c + d*x])/(8192*d*(5 - 3*Sin[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
30,1,31,0,0.0117896,"\int \frac{1}{-5-3 \sin (c+d x)} \, dx","Int[(-5 - 3*Sin[c + d*x])^(-1),x]","-\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{2 d}-\frac{x}{4}","-\frac{\tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{2 d}-\frac{x}{4}",1,"-x/4 - ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])]/(2*d)","A",1,1,12,0.08333,1,"{2658}"
31,1,56,0,0.0307029,"\int \frac{1}{(-5-3 \sin (c+d x))^2} \, dx","Int[(-5 - 3*Sin[c + d*x])^(-2),x]","\frac{3 \cos (c+d x)}{16 d (3 \sin (c+d x)+5)}+\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}","\frac{3 \cos (c+d x)}{16 d (3 \sin (c+d x)+5)}+\frac{5 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{32 d}+\frac{5 x}{64}",1,"(5*x)/64 + (5*ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])])/(32*d) + (3*Cos[c + d*x])/(16*d*(5 + 3*Sin[c + d*x]))","A",3,3,12,0.2500,1,"{2664, 12, 2658}"
32,1,81,0,0.0613149,"\int \frac{1}{(-5-3 \sin (c+d x))^3} \, dx","Int[(-5 - 3*Sin[c + d*x])^(-3),x]","-\frac{45 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)}-\frac{3 \cos (c+d x)}{32 d (3 \sin (c+d x)+5)^2}-\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{1024 d}-\frac{59 x}{2048}","-\frac{45 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)}-\frac{3 \cos (c+d x)}{32 d (3 \sin (c+d x)+5)^2}-\frac{59 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{1024 d}-\frac{59 x}{2048}",1,"(-59*x)/2048 - (59*ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])])/(1024*d) - (3*Cos[c + d*x])/(32*d*(5 + 3*Sin[c + d*x])^2) - (45*Cos[c + d*x])/(512*d*(5 + 3*Sin[c + d*x]))","A",4,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
33,1,106,0,0.0897962,"\int \frac{1}{(-5-3 \sin (c+d x))^4} \, dx","Int[(-5 - 3*Sin[c + d*x])^(-4),x]","\frac{311 \cos (c+d x)}{8192 d (3 \sin (c+d x)+5)}+\frac{25 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)^2}+\frac{\cos (c+d x)}{16 d (3 \sin (c+d x)+5)^3}+\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}","\frac{311 \cos (c+d x)}{8192 d (3 \sin (c+d x)+5)}+\frac{25 \cos (c+d x)}{512 d (3 \sin (c+d x)+5)^2}+\frac{\cos (c+d x)}{16 d (3 \sin (c+d x)+5)^3}+\frac{385 \tan ^{-1}\left(\frac{\cos (c+d x)}{\sin (c+d x)+3}\right)}{16384 d}+\frac{385 x}{32768}",1,"(385*x)/32768 + (385*ArcTan[Cos[c + d*x]/(3 + Sin[c + d*x])])/(16384*d) + Cos[c + d*x]/(16*d*(5 + 3*Sin[c + d*x])^3) + (25*Cos[c + d*x])/(512*d*(5 + 3*Sin[c + d*x])^2) + (311*Cos[c + d*x])/(8192*d*(5 + 3*Sin[c + d*x]))","A",5,4,12,0.3333,1,"{2664, 2754, 12, 2658}"
34,1,63,0,0.0232539,"\int \frac{1}{3+5 \sin (c+d x)} \, dx","Int[(3 + 5*Sin[c + d*x])^(-1),x]","\frac{\log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"-Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]]/(4*d) + Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]]/(4*d)","A",4,3,12,0.2500,1,"{2660, 616, 31}"
35,1,88,0,0.0482032,"\int \frac{1}{(3+5 \sin (c+d x))^2} \, dx","Int[(3 + 5*Sin[c + d*x])^(-2),x]","-\frac{5 \cos (c+d x)}{16 d (5 \sin (c+d x)+3)}+\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","-\frac{5 \cos (c+d x)}{16 d (5 \sin (c+d x)+3)}+\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(3*Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(64*d) - (3*Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]])/(64*d) - (5*Cos[c + d*x])/(16*d*(3 + 5*Sin[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 12, 2660, 616, 31}"
36,1,113,0,0.0778509,"\int \frac{1}{(3+5 \sin (c+d x))^3} \, dx","Int[(3 + 5*Sin[c + d*x])^(-3),x]","\frac{45 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)}-\frac{5 \cos (c+d x)}{32 d (5 \sin (c+d x)+3)^2}-\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","\frac{45 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)}-\frac{5 \cos (c+d x)}{32 d (5 \sin (c+d x)+3)^2}-\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(-43*Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(2048*d) + (43*Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]])/(2048*d) - (5*Cos[c + d*x])/(32*d*(3 + 5*Sin[c + d*x])^2) + (45*Cos[c + d*x])/(512*d*(3 + 5*Sin[c + d*x]))","A",7,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
37,1,138,0,0.1114004,"\int \frac{1}{(3+5 \sin (c+d x))^4} \, dx","Int[(3 + 5*Sin[c + d*x])^(-4),x]","-\frac{995 \cos (c+d x)}{24576 d (5 \sin (c+d x)+3)}+\frac{25 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)^2}-\frac{5 \cos (c+d x)}{48 d (5 \sin (c+d x)+3)^3}+\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","-\frac{995 \cos (c+d x)}{24576 d (5 \sin (c+d x)+3)}+\frac{25 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)^2}-\frac{5 \cos (c+d x)}{48 d (5 \sin (c+d x)+3)^3}+\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(279*Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(32768*d) - (279*Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]])/(32768*d) - (5*Cos[c + d*x])/(48*d*(3 + 5*Sin[c + d*x])^3) + (25*Cos[c + d*x])/(512*d*(3 + 5*Sin[c + d*x])^2) - (995*Cos[c + d*x])/(24576*d*(3 + 5*Sin[c + d*x]))","A",8,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
38,1,65,0,0.0229075,"\int \frac{1}{3-5 \sin (c+d x)} \, dx","Int[(3 - 5*Sin[c + d*x])^(-1),x]","\frac{\log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"-Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]]/(4*d) + Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]]/(4*d)","A",4,3,12,0.2500,1,"{2660, 616, 31}"
39,1,90,0,0.0460987,"\int \frac{1}{(3-5 \sin (c+d x))^2} \, dx","Int[(3 - 5*Sin[c + d*x])^(-2),x]","\frac{5 \cos (c+d x)}{16 d (3-5 \sin (c+d x))}+\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","\frac{5 \cos (c+d x)}{16 d (3-5 \sin (c+d x))}+\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(3*Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]])/(64*d) - (3*Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(64*d) + (5*Cos[c + d*x])/(16*d*(3 - 5*Sin[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 12, 2660, 616, 31}"
40,1,115,0,0.077858,"\int \frac{1}{(3-5 \sin (c+d x))^3} \, dx","Int[(3 - 5*Sin[c + d*x])^(-3),x]","-\frac{45 \cos (c+d x)}{512 d (3-5 \sin (c+d x))}+\frac{5 \cos (c+d x)}{32 d (3-5 \sin (c+d x))^2}-\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","-\frac{45 \cos (c+d x)}{512 d (3-5 \sin (c+d x))}+\frac{5 \cos (c+d x)}{32 d (3-5 \sin (c+d x))^2}-\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}+\frac{43 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(-43*Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]])/(2048*d) + (43*Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(2048*d) + (5*Cos[c + d*x])/(32*d*(3 - 5*Sin[c + d*x])^2) - (45*Cos[c + d*x])/(512*d*(3 - 5*Sin[c + d*x]))","A",7,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
41,1,140,0,0.1152863,"\int \frac{1}{(3-5 \sin (c+d x))^4} \, dx","Int[(3 - 5*Sin[c + d*x])^(-4),x]","\frac{995 \cos (c+d x)}{24576 d (3-5 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (3-5 \sin (c+d x))^2}+\frac{5 \cos (c+d x)}{48 d (3-5 \sin (c+d x))^3}+\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","\frac{995 \cos (c+d x)}{24576 d (3-5 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (3-5 \sin (c+d x))^2}+\frac{5 \cos (c+d x)}{48 d (3-5 \sin (c+d x))^3}+\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(279*Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]])/(32768*d) - (279*Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(32768*d) + (5*Cos[c + d*x])/(48*d*(3 - 5*Sin[c + d*x])^3) - (25*Cos[c + d*x])/(512*d*(3 - 5*Sin[c + d*x])^2) + (995*Cos[c + d*x])/(24576*d*(3 - 5*Sin[c + d*x]))","A",8,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
42,1,65,0,0.0217311,"\int \frac{1}{-3+5 \sin (c+d x)} \, dx","Int[(-3 + 5*Sin[c + d*x])^(-1),x]","\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]]/(4*d) - Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]]/(4*d)","A",4,3,12,0.2500,1,"{2660, 616, 31}"
43,1,90,0,0.0476817,"\int \frac{1}{(-3+5 \sin (c+d x))^2} \, dx","Int[(-3 + 5*Sin[c + d*x])^(-2),x]","\frac{5 \cos (c+d x)}{16 d (3-5 \sin (c+d x))}+\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","\frac{5 \cos (c+d x)}{16 d (3-5 \sin (c+d x))}+\frac{3 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(3*Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]])/(64*d) - (3*Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(64*d) + (5*Cos[c + d*x])/(16*d*(3 - 5*Sin[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 12, 2660, 616, 31}"
44,1,115,0,0.0787804,"\int \frac{1}{(-3+5 \sin (c+d x))^3} \, dx","Int[(-3 + 5*Sin[c + d*x])^(-3),x]","\frac{45 \cos (c+d x)}{512 d (3-5 \sin (c+d x))}-\frac{5 \cos (c+d x)}{32 d (3-5 \sin (c+d x))^2}+\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","\frac{45 \cos (c+d x)}{512 d (3-5 \sin (c+d x))}-\frac{5 \cos (c+d x)}{32 d (3-5 \sin (c+d x))^2}+\frac{43 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(43*Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]])/(2048*d) - (43*Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(2048*d) - (5*Cos[c + d*x])/(32*d*(3 - 5*Sin[c + d*x])^2) + (45*Cos[c + d*x])/(512*d*(3 - 5*Sin[c + d*x]))","A",7,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
45,1,140,0,0.1155741,"\int \frac{1}{(-3+5 \sin (c+d x))^4} \, dx","Int[(-3 + 5*Sin[c + d*x])^(-4),x]","\frac{995 \cos (c+d x)}{24576 d (3-5 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (3-5 \sin (c+d x))^2}+\frac{5 \cos (c+d x)}{48 d (3-5 \sin (c+d x))^3}+\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","\frac{995 \cos (c+d x)}{24576 d (3-5 \sin (c+d x))}-\frac{25 \cos (c+d x)}{512 d (3-5 \sin (c+d x))^2}+\frac{5 \cos (c+d x)}{48 d (3-5 \sin (c+d x))^3}+\frac{279 \log \left(\cos \left(\frac{1}{2} (c+d x)\right)-3 \sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \cos \left(\frac{1}{2} (c+d x)\right)-\sin \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(279*Log[Cos[(c + d*x)/2] - 3*Sin[(c + d*x)/2]])/(32768*d) - (279*Log[3*Cos[(c + d*x)/2] - Sin[(c + d*x)/2]])/(32768*d) + (5*Cos[c + d*x])/(48*d*(3 - 5*Sin[c + d*x])^3) - (25*Cos[c + d*x])/(512*d*(3 - 5*Sin[c + d*x])^2) + (995*Cos[c + d*x])/(24576*d*(3 - 5*Sin[c + d*x]))","A",8,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
46,1,63,0,0.021568,"\int \frac{1}{-3-5 \sin (c+d x)} \, dx","Int[(-3 - 5*Sin[c + d*x])^(-1),x]","\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{\log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{\log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]]/(4*d) - Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]]/(4*d)","A",4,3,12,0.2500,1,"{2660, 616, 31}"
47,1,88,0,0.0433838,"\int \frac{1}{(-3-5 \sin (c+d x))^2} \, dx","Int[(-3 - 5*Sin[c + d*x])^(-2),x]","-\frac{5 \cos (c+d x)}{16 d (5 \sin (c+d x)+3)}+\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}","-\frac{5 \cos (c+d x)}{16 d (5 \sin (c+d x)+3)}+\frac{3 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}-\frac{3 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(3*Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(64*d) - (3*Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]])/(64*d) - (5*Cos[c + d*x])/(16*d*(3 + 5*Sin[c + d*x]))","A",6,5,12,0.4167,1,"{2664, 12, 2660, 616, 31}"
48,1,113,0,0.0770199,"\int \frac{1}{(-3-5 \sin (c+d x))^3} \, dx","Int[(-3 - 5*Sin[c + d*x])^(-3),x]","-\frac{45 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)}+\frac{5 \cos (c+d x)}{32 d (5 \sin (c+d x)+3)^2}+\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}","-\frac{45 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)}+\frac{5 \cos (c+d x)}{32 d (5 \sin (c+d x)+3)^2}+\frac{43 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(43*Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(2048*d) - (43*Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]])/(2048*d) + (5*Cos[c + d*x])/(32*d*(3 + 5*Sin[c + d*x])^2) - (45*Cos[c + d*x])/(512*d*(3 + 5*Sin[c + d*x]))","A",7,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
49,1,138,0,0.1128219,"\int \frac{1}{(-3-5 \sin (c+d x))^4} \, dx","Int[(-3 - 5*Sin[c + d*x])^(-4),x]","-\frac{995 \cos (c+d x)}{24576 d (5 \sin (c+d x)+3)}+\frac{25 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)^2}-\frac{5 \cos (c+d x)}{48 d (5 \sin (c+d x)+3)^3}+\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}","-\frac{995 \cos (c+d x)}{24576 d (5 \sin (c+d x)+3)}+\frac{25 \cos (c+d x)}{512 d (5 \sin (c+d x)+3)^2}-\frac{5 \cos (c+d x)}{48 d (5 \sin (c+d x)+3)^3}+\frac{279 \log \left(\sin \left(\frac{1}{2} (c+d x)\right)+3 \cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}-\frac{279 \log \left(3 \sin \left(\frac{1}{2} (c+d x)\right)+\cos \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(279*Log[3*Cos[(c + d*x)/2] + Sin[(c + d*x)/2]])/(32768*d) - (279*Log[Cos[(c + d*x)/2] + 3*Sin[(c + d*x)/2]])/(32768*d) - (5*Cos[c + d*x])/(48*d*(3 + 5*Sin[c + d*x])^3) + (25*Cos[c + d*x])/(512*d*(3 + 5*Sin[c + d*x])^2) - (995*Cos[c + d*x])/(24576*d*(3 + 5*Sin[c + d*x]))","A",8,6,12,0.5000,1,"{2664, 2754, 12, 2660, 616, 31}"
50,1,256,0,0.382149,"\int (a+b \sin (c+d x))^{7/2} \, dx","Int[(a + b*Sin[c + d*x])^(7/2),x]","-\frac{2 b \left(71 a^2+25 b^2\right) \cos (c+d x) \sqrt{a+b \sin (c+d x)}}{105 d}-\frac{2 \left(-46 a^2 b^2+71 a^4-25 b^4\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{105 d \sqrt{a+b \sin (c+d x)}}+\frac{32 a \left(11 a^2+13 b^2\right) \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{105 d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}-\frac{2 b \cos (c+d x) (a+b \sin (c+d x))^{5/2}}{7 d}-\frac{24 a b \cos (c+d x) (a+b \sin (c+d x))^{3/2}}{35 d}","-\frac{2 b \left(71 a^2+25 b^2\right) \cos (c+d x) \sqrt{a+b \sin (c+d x)}}{105 d}-\frac{2 \left(-46 a^2 b^2+71 a^4-25 b^4\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{105 d \sqrt{a+b \sin (c+d x)}}+\frac{32 a \left(11 a^2+13 b^2\right) \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{105 d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}-\frac{2 b \cos (c+d x) (a+b \sin (c+d x))^{5/2}}{7 d}-\frac{24 a b \cos (c+d x) (a+b \sin (c+d x))^{3/2}}{35 d}",1,"(-2*b*(71*a^2 + 25*b^2)*Cos[c + d*x]*Sqrt[a + b*Sin[c + d*x]])/(105*d) - (24*a*b*Cos[c + d*x]*(a + b*Sin[c + d*x])^(3/2))/(35*d) - (2*b*Cos[c + d*x]*(a + b*Sin[c + d*x])^(5/2))/(7*d) + (32*a*(11*a^2 + 13*b^2)*EllipticE[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[a + b*Sin[c + d*x]])/(105*d*Sqrt[(a + b*Sin[c + d*x])/(a + b)]) - (2*(71*a^4 - 46*a^2*b^2 - 25*b^4)*EllipticF[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[(a + b*Sin[c + d*x])/(a + b)])/(105*d*Sqrt[a + b*Sin[c + d*x]])","A",8,7,14,0.5000,1,"{2656, 2753, 2752, 2663, 2661, 2655, 2653}"
51,1,207,0,0.2599806,"\int (a+b \sin (c+d x))^{5/2} \, dx","Int[(a + b*Sin[c + d*x])^(5/2),x]","-\frac{16 a \left(a^2-b^2\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \sqrt{a+b \sin (c+d x)}}+\frac{2 \left(23 a^2+9 b^2\right) \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}-\frac{2 b \cos (c+d x) (a+b \sin (c+d x))^{3/2}}{5 d}-\frac{16 a b \cos (c+d x) \sqrt{a+b \sin (c+d x)}}{15 d}","-\frac{16 a \left(a^2-b^2\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \sqrt{a+b \sin (c+d x)}}+\frac{2 \left(23 a^2+9 b^2\right) \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}-\frac{2 b \cos (c+d x) (a+b \sin (c+d x))^{3/2}}{5 d}-\frac{16 a b \cos (c+d x) \sqrt{a+b \sin (c+d x)}}{15 d}",1,"(-16*a*b*Cos[c + d*x]*Sqrt[a + b*Sin[c + d*x]])/(15*d) - (2*b*Cos[c + d*x]*(a + b*Sin[c + d*x])^(3/2))/(5*d) + (2*(23*a^2 + 9*b^2)*EllipticE[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[a + b*Sin[c + d*x]])/(15*d*Sqrt[(a + b*Sin[c + d*x])/(a + b)]) - (16*a*(a^2 - b^2)*EllipticF[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[(a + b*Sin[c + d*x])/(a + b)])/(15*d*Sqrt[a + b*Sin[c + d*x]])","A",7,7,14,0.5000,1,"{2656, 2753, 2752, 2663, 2661, 2655, 2653}"
52,1,167,0,0.1642474,"\int (a+b \sin (c+d x))^{3/2} \, dx","Int[(a + b*Sin[c + d*x])^(3/2),x]","-\frac{2 \left(a^2-b^2\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \sqrt{a+b \sin (c+d x)}}-\frac{2 b \cos (c+d x) \sqrt{a+b \sin (c+d x)}}{3 d}+\frac{8 a \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}","-\frac{2 \left(a^2-b^2\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \sqrt{a+b \sin (c+d x)}}-\frac{2 b \cos (c+d x) \sqrt{a+b \sin (c+d x)}}{3 d}+\frac{8 a \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}",1,"(-2*b*Cos[c + d*x]*Sqrt[a + b*Sin[c + d*x]])/(3*d) + (8*a*EllipticE[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[a + b*Sin[c + d*x]])/(3*d*Sqrt[(a + b*Sin[c + d*x])/(a + b)]) - (2*(a^2 - b^2)*EllipticF[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[(a + b*Sin[c + d*x])/(a + b)])/(3*d*Sqrt[a + b*Sin[c + d*x]])","A",6,6,14,0.4286,1,"{2656, 2752, 2663, 2661, 2655, 2653}"
53,1,62,0,0.0353472,"\int \sqrt{a+b \sin (c+d x)} \, dx","Int[Sqrt[a + b*Sin[c + d*x]],x]","\frac{2 \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}","\frac{2 \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{d \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}",1,"(2*EllipticE[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[a + b*Sin[c + d*x]])/(d*Sqrt[(a + b*Sin[c + d*x])/(a + b)])","A",2,2,14,0.1429,1,"{2655, 2653}"
54,1,62,0,0.041871,"\int \frac{1}{\sqrt{a+b \sin (c+d x)}} \, dx","Int[1/Sqrt[a + b*Sin[c + d*x]],x]","\frac{2 \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{d \sqrt{a+b \sin (c+d x)}}","\frac{2 \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{d \sqrt{a+b \sin (c+d x)}}",1,"(2*EllipticF[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[(a + b*Sin[c + d*x])/(a + b)])/(d*Sqrt[a + b*Sin[c + d*x]])","A",2,2,14,0.1429,1,"{2663, 2661}"
55,1,111,0,0.0648819,"\int \frac{1}{(a+b \sin (c+d x))^{3/2}} \, dx","Int[(a + b*Sin[c + d*x])^(-3/2),x]","\frac{2 b \cos (c+d x)}{d \left(a^2-b^2\right) \sqrt{a+b \sin (c+d x)}}+\frac{2 \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{d \left(a^2-b^2\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}","\frac{2 b \cos (c+d x)}{d \left(a^2-b^2\right) \sqrt{a+b \sin (c+d x)}}+\frac{2 \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{d \left(a^2-b^2\right) \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}",1,"(2*b*Cos[c + d*x])/((a^2 - b^2)*d*Sqrt[a + b*Sin[c + d*x]]) + (2*EllipticE[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[a + b*Sin[c + d*x]])/((a^2 - b^2)*d*Sqrt[(a + b*Sin[c + d*x])/(a + b)])","A",4,4,14,0.2857,1,"{2664, 21, 2655, 2653}"
56,1,231,0,0.2283732,"\int \frac{1}{(a+b \sin (c+d x))^{5/2}} \, dx","Int[(a + b*Sin[c + d*x])^(-5/2),x]","\frac{8 a b \cos (c+d x)}{3 d \left(a^2-b^2\right)^2 \sqrt{a+b \sin (c+d x)}}+\frac{2 b \cos (c+d x)}{3 d \left(a^2-b^2\right) (a+b \sin (c+d x))^{3/2}}-\frac{2 \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right) \sqrt{a+b \sin (c+d x)}}+\frac{8 a \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}","\frac{8 a b \cos (c+d x)}{3 d \left(a^2-b^2\right)^2 \sqrt{a+b \sin (c+d x)}}+\frac{2 b \cos (c+d x)}{3 d \left(a^2-b^2\right) (a+b \sin (c+d x))^{3/2}}-\frac{2 \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right) \sqrt{a+b \sin (c+d x)}}+\frac{8 a \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{3 d \left(a^2-b^2\right)^2 \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}",1,"(2*b*Cos[c + d*x])/(3*(a^2 - b^2)*d*(a + b*Sin[c + d*x])^(3/2)) + (8*a*b*Cos[c + d*x])/(3*(a^2 - b^2)^2*d*Sqrt[a + b*Sin[c + d*x]]) + (8*a*EllipticE[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[a + b*Sin[c + d*x]])/(3*(a^2 - b^2)^2*d*Sqrt[(a + b*Sin[c + d*x])/(a + b)]) - (2*EllipticF[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[(a + b*Sin[c + d*x])/(a + b)])/(3*(a^2 - b^2)*d*Sqrt[a + b*Sin[c + d*x]])","A",7,7,14,0.5000,1,"{2664, 2754, 2752, 2663, 2661, 2655, 2653}"
57,1,292,0,0.3496819,"\int \frac{1}{(a+b \sin (c+d x))^{7/2}} \, dx","Int[(a + b*Sin[c + d*x])^(-7/2),x]","\frac{2 b \left(23 a^2+9 b^2\right) \cos (c+d x)}{15 d \left(a^2-b^2\right)^3 \sqrt{a+b \sin (c+d x)}}+\frac{16 a b \cos (c+d x)}{15 d \left(a^2-b^2\right)^2 (a+b \sin (c+d x))^{3/2}}+\frac{2 b \cos (c+d x)}{5 d \left(a^2-b^2\right) (a+b \sin (c+d x))^{5/2}}-\frac{16 a \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \left(a^2-b^2\right)^2 \sqrt{a+b \sin (c+d x)}}+\frac{2 \left(23 a^2+9 b^2\right) \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \left(a^2-b^2\right)^3 \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}","\frac{2 b \left(23 a^2+9 b^2\right) \cos (c+d x)}{15 d \left(a^2-b^2\right)^3 \sqrt{a+b \sin (c+d x)}}+\frac{16 a b \cos (c+d x)}{15 d \left(a^2-b^2\right)^2 (a+b \sin (c+d x))^{3/2}}+\frac{2 b \cos (c+d x)}{5 d \left(a^2-b^2\right) (a+b \sin (c+d x))^{5/2}}-\frac{16 a \sqrt{\frac{a+b \sin (c+d x)}{a+b}} F\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \left(a^2-b^2\right)^2 \sqrt{a+b \sin (c+d x)}}+\frac{2 \left(23 a^2+9 b^2\right) \sqrt{a+b \sin (c+d x)} E\left(\frac{1}{2} \left(c+d x-\frac{\pi }{2}\right)|\frac{2 b}{a+b}\right)}{15 d \left(a^2-b^2\right)^3 \sqrt{\frac{a+b \sin (c+d x)}{a+b}}}",1,"(2*b*Cos[c + d*x])/(5*(a^2 - b^2)*d*(a + b*Sin[c + d*x])^(5/2)) + (16*a*b*Cos[c + d*x])/(15*(a^2 - b^2)^2*d*(a + b*Sin[c + d*x])^(3/2)) + (2*b*(23*a^2 + 9*b^2)*Cos[c + d*x])/(15*(a^2 - b^2)^3*d*Sqrt[a + b*Sin[c + d*x]]) + (2*(23*a^2 + 9*b^2)*EllipticE[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[a + b*Sin[c + d*x]])/(15*(a^2 - b^2)^3*d*Sqrt[(a + b*Sin[c + d*x])/(a + b)]) - (16*a*EllipticF[(c - Pi/2 + d*x)/2, (2*b)/(a + b)]*Sqrt[(a + b*Sin[c + d*x])/(a + b)])/(15*(a^2 - b^2)^2*d*Sqrt[a + b*Sin[c + d*x]])","A",8,7,14,0.5000,1,"{2664, 2754, 2752, 2663, 2661, 2655, 2653}"
58,1,109,0,0.0792112,"\int (a+b \sin (c+d x))^{4/3} \, dx","Int[(a + b*Sin[c + d*x])^(4/3),x]","-\frac{\sqrt{2} (a+b) \cos (c+d x) \sqrt[3]{a+b \sin (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}}}","-\frac{\sqrt{2} (a+b) \cos (c+d x) \sqrt[3]{a+b \sin (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}}}",1,"-((Sqrt[2]*(a + b)*AppellF1[1/2, 1/2, -4/3, 3/2, (1 - Sin[c + d*x])/2, (b*(1 - Sin[c + d*x]))/(a + b)]*Cos[c + d*x]*(a + b*Sin[c + d*x])^(1/3))/(d*Sqrt[1 + Sin[c + d*x]]*((a + b*Sin[c + d*x])/(a + b))^(1/3)))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
59,1,106,0,0.0675249,"\int (a+b \sin (c+d x))^{2/3} \, dx","Int[(a + b*Sin[c + d*x])^(2/3),x]","-\frac{\sqrt{2} \cos (c+d x) (a+b \sin (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \left(\frac{a+b \sin (c+d x)}{a+b}\right)^{2/3}}","-\frac{\sqrt{2} \cos (c+d x) (a+b \sin (c+d x))^{2/3} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{2}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \left(\frac{a+b \sin (c+d x)}{a+b}\right)^{2/3}}",1,"-((Sqrt[2]*AppellF1[1/2, 1/2, -2/3, 3/2, (1 - Sin[c + d*x])/2, (b*(1 - Sin[c + d*x]))/(a + b)]*Cos[c + d*x]*(a + b*Sin[c + d*x])^(2/3))/(d*Sqrt[1 + Sin[c + d*x]]*((a + b*Sin[c + d*x])/(a + b))^(2/3)))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
60,1,106,0,0.0655527,"\int \sqrt[3]{a+b \sin (c+d x)} \, dx","Int[(a + b*Sin[c + d*x])^(1/3),x]","-\frac{\sqrt{2} \cos (c+d x) \sqrt[3]{a+b \sin (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}}}","-\frac{\sqrt{2} \cos (c+d x) \sqrt[3]{a+b \sin (c+d x)} F_1\left(\frac{1}{2};\frac{1}{2},-\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}}}",1,"-((Sqrt[2]*AppellF1[1/2, 1/2, -1/3, 3/2, (1 - Sin[c + d*x])/2, (b*(1 - Sin[c + d*x]))/(a + b)]*Cos[c + d*x]*(a + b*Sin[c + d*x])^(1/3))/(d*Sqrt[1 + Sin[c + d*x]]*((a + b*Sin[c + d*x])/(a + b))^(1/3)))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
61,1,106,0,0.0644144,"\int \frac{1}{\sqrt[3]{a+b \sin (c+d x)}} \, dx","Int[(a + b*Sin[c + d*x])^(-1/3),x]","-\frac{\sqrt{2} \cos (c+d x) \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \sqrt[3]{a+b \sin (c+d x)}}","-\frac{\sqrt{2} \cos (c+d x) \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{1}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} \sqrt[3]{a+b \sin (c+d x)}}",1,"-((Sqrt[2]*AppellF1[1/2, 1/2, 1/3, 3/2, (1 - Sin[c + d*x])/2, (b*(1 - Sin[c + d*x]))/(a + b)]*Cos[c + d*x]*((a + b*Sin[c + d*x])/(a + b))^(1/3))/(d*Sqrt[1 + Sin[c + d*x]]*(a + b*Sin[c + d*x])^(1/3)))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
62,1,106,0,0.0670976,"\int \frac{1}{(a+b \sin (c+d x))^{2/3}} \, dx","Int[(a + b*Sin[c + d*x])^(-2/3),x]","-\frac{\sqrt{2} \cos (c+d x) \left(\frac{a+b \sin (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-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} (a+b \sin (c+d x))^{2/3}}","-\frac{\sqrt{2} \cos (c+d x) \left(\frac{a+b \sin (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-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1} (a+b \sin (c+d x))^{2/3}}",1,"-((Sqrt[2]*AppellF1[1/2, 1/2, 2/3, 3/2, (1 - Sin[c + d*x])/2, (b*(1 - Sin[c + d*x]))/(a + b)]*Cos[c + d*x]*((a + b*Sin[c + d*x])/(a + b))^(2/3))/(d*Sqrt[1 + Sin[c + d*x]]*(a + b*Sin[c + d*x])^(2/3)))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
63,1,111,0,0.0724101,"\int \frac{1}{(a+b \sin (c+d x))^{4/3}} \, dx","Int[(a + b*Sin[c + d*x])^(-4/3),x]","-\frac{\sqrt{2} \cos (c+d x) \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d (a+b) \sqrt{\sin (c+d x)+1} \sqrt[3]{a+b \sin (c+d x)}}","-\frac{\sqrt{2} \cos (c+d x) \sqrt[3]{\frac{a+b \sin (c+d x)}{a+b}} F_1\left(\frac{1}{2};\frac{1}{2},\frac{4}{3};\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d (a+b) \sqrt{\sin (c+d x)+1} \sqrt[3]{a+b \sin (c+d x)}}",1,"-((Sqrt[2]*AppellF1[1/2, 1/2, 4/3, 3/2, (1 - Sin[c + d*x])/2, (b*(1 - Sin[c + d*x]))/(a + b)]*Cos[c + d*x]*((a + b*Sin[c + d*x])/(a + b))^(1/3))/((a + b)*d*Sqrt[1 + Sin[c + d*x]]*(a + b*Sin[c + d*x])^(1/3)))","A",3,3,14,0.2143,1,"{2665, 139, 138}"
64,1,104,0,0.0656679,"\int (a+b \sin (c+d x))^n \, dx","Int[(a + b*Sin[c + d*x])^n,x]","-\frac{\sqrt{2} \cos (c+d x) (a+b \sin (c+d x))^n \left(\frac{a+b \sin (c+d x)}{a+b}\right)^{-n} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1}}","-\frac{\sqrt{2} \cos (c+d x) (a+b \sin (c+d x))^n \left(\frac{a+b \sin (c+d x)}{a+b}\right)^{-n} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{b (1-\sin (c+d x))}{a+b}\right)}{d \sqrt{\sin (c+d x)+1}}",1,"-((Sqrt[2]*AppellF1[1/2, 1/2, -n, 3/2, (1 - Sin[c + d*x])/2, (b*(1 - Sin[c + d*x]))/(a + b)]*Cos[c + d*x]*(a + b*Sin[c + d*x])^n)/(d*Sqrt[1 + Sin[c + d*x]]*((a + b*Sin[c + d*x])/(a + b))^n))","A",3,3,12,0.2500,1,"{2665, 139, 138}"
65,1,72,0,0.0407541,"\int (3+4 \sin (c+d x))^n \, dx","Int[(3 + 4*Sin[c + d*x])^n,x]","-\frac{\sqrt{2} 7^n \cos (c+d x) F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{4}{7} (1-\sin (c+d x))\right)}{d \sqrt{\sin (c+d x)+1}}","-\frac{\sqrt{2} 7^n \cos (c+d x) F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),\frac{4}{7} (1-\sin (c+d x))\right)}{d \sqrt{\sin (c+d x)+1}}",1,"-((Sqrt[2]*7^n*AppellF1[1/2, 1/2, -n, 3/2, (1 - Sin[c + d*x])/2, (4*(1 - Sin[c + d*x]))/7]*Cos[c + d*x])/(d*Sqrt[1 + Sin[c + d*x]]))","A",2,2,12,0.1667,1,"{2665, 138}"
66,1,69,0,0.0345415,"\int (3-4 \sin (c+d x))^n \, dx","Int[(3 - 4*Sin[c + d*x])^n,x]","\frac{\sqrt{2} 7^n \cos (c+d x) F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{4}{7} (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}","\frac{\sqrt{2} 7^n \cos (c+d x) F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{4}{7} (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}",1,"(Sqrt[2]*7^n*AppellF1[1/2, -n, 1/2, 3/2, (4*(1 + Sin[c + d*x]))/7, (1 + Sin[c + d*x])/2]*Cos[c + d*x])/(d*Sqrt[1 - Sin[c + d*x]])","A",2,2,12,0.1667,1,"{2665, 138}"
67,1,64,0,0.0346196,"\int (4+3 \sin (c+d x))^n \, dx","Int[(4 + 3*Sin[c + d*x])^n,x]","\frac{\sqrt{2} \cos (c+d x) F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (\sin (c+d x)+1),-3 (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}","\frac{\sqrt{2} \cos (c+d x) F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (\sin (c+d x)+1),-3 (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}",1,"(Sqrt[2]*AppellF1[1/2, 1/2, -n, 3/2, (1 + Sin[c + d*x])/2, -3*(1 + Sin[c + d*x])]*Cos[c + d*x])/(d*Sqrt[1 - Sin[c + d*x]])","A",2,2,12,0.1667,1,"{2665, 138}"
68,1,69,0,0.0339597,"\int (4-3 \sin (c+d x))^n \, dx","Int[(4 - 3*Sin[c + d*x])^n,x]","\frac{\sqrt{2} 7^n \cos (c+d x) F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{3}{7} (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}","\frac{\sqrt{2} 7^n \cos (c+d x) F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{3}{7} (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}",1,"(Sqrt[2]*7^n*AppellF1[1/2, -n, 1/2, 3/2, (3*(1 + Sin[c + d*x]))/7, (1 + Sin[c + d*x])/2]*Cos[c + d*x])/(d*Sqrt[1 - Sin[c + d*x]])","A",2,2,12,0.1667,1,"{2665, 138}"
69,1,67,0,0.0381583,"\int (-3+4 \sin (c+d x))^n \, dx","Int[(-3 + 4*Sin[c + d*x])^n,x]","-\frac{\sqrt{2} \cos (c+d x) F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),4 (1-\sin (c+d x))\right)}{d \sqrt{\sin (c+d x)+1}}","-\frac{\sqrt{2} \cos (c+d x) F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (c+d x)),4 (1-\sin (c+d x))\right)}{d \sqrt{\sin (c+d x)+1}}",1,"-((Sqrt[2]*AppellF1[1/2, 1/2, -n, 3/2, (1 - Sin[c + d*x])/2, 4*(1 - Sin[c + d*x])]*Cos[c + d*x])/(d*Sqrt[1 + Sin[c + d*x]]))","A",2,2,12,0.1667,1,"{2665, 138}"
70,1,64,0,0.0352115,"\int (-3-4 \sin (c+d x))^n \, dx","Int[(-3 - 4*Sin[c + d*x])^n,x]","\frac{\sqrt{2} \cos (c+d x) F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};4 (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}","\frac{\sqrt{2} \cos (c+d x) F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};4 (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}",1,"(Sqrt[2]*AppellF1[1/2, -n, 1/2, 3/2, 4*(1 + Sin[c + d*x]), (1 + Sin[c + d*x])/2]*Cos[c + d*x])/(d*Sqrt[1 - Sin[c + d*x]])","A",2,2,12,0.1667,1,"{2665, 138}"
71,1,95,0,0.0509589,"\int (-4+3 \sin (c+d x))^n \, dx","Int[(-4 + 3*Sin[c + d*x])^n,x]","\frac{\sqrt{2} 7^n \cos (c+d x) (4-3 \sin (c+d x))^{-n} (3 \sin (c+d x)-4)^n F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{3}{7} (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}","\frac{\sqrt{2} 7^n \cos (c+d x) (4-3 \sin (c+d x))^{-n} (3 \sin (c+d x)-4)^n F_1\left(\frac{1}{2};-n,\frac{1}{2};\frac{3}{2};\frac{3}{7} (\sin (c+d x)+1),\frac{1}{2} (\sin (c+d x)+1)\right)}{d \sqrt{1-\sin (c+d x)}}",1,"(Sqrt[2]*7^n*AppellF1[1/2, -n, 1/2, 3/2, (3*(1 + Sin[c + d*x]))/7, (1 + Sin[c + d*x])/2]*Cos[c + d*x]*(-4 + 3*Sin[c + d*x])^n)/(d*(4 - 3*Sin[c + d*x])^n*Sqrt[1 - Sin[c + d*x]])","A",3,3,12,0.2500,1,"{2665, 139, 138}"
72,1,110,0,0.0665753,"\int (-4-3 \sin (c+d x))^n \, dx","Int[(-4 - 3*Sin[c + d*x])^n,x]","-\frac{\sqrt{-\sin (c+d x)-1} \cos (c+d x) (-3 \sin (c+d x)-4)^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;3 \sin (c+d x)+4,\frac{1}{7} (3 \sin (c+d x)+4)\right)}{\sqrt{7} d (n+1) \sqrt{1-\sin (c+d x)} (\sin (c+d x)+1)}","-\frac{\sqrt{-\sin (c+d x)-1} \cos (c+d x) (-3 \sin (c+d x)-4)^{n+1} F_1\left(n+1;\frac{1}{2},\frac{1}{2};n+2;3 \sin (c+d x)+4,\frac{1}{7} (3 \sin (c+d x)+4)\right)}{\sqrt{7} d (n+1) \sqrt{1-\sin (c+d x)} (\sin (c+d x)+1)}",1,"-((AppellF1[1 + n, 1/2, 1/2, 2 + n, 4 + 3*Sin[c + d*x], (4 + 3*Sin[c + d*x])/7]*Cos[c + d*x]*(-4 - 3*Sin[c + d*x])^(1 + n)*Sqrt[-1 - Sin[c + d*x]])/(Sqrt[7]*d*(1 + n)*Sqrt[1 - Sin[c + d*x]]*(1 + Sin[c + d*x])))","A",3,3,12,0.2500,1,"{2665, 139, 138}"