1,1,21,10,0.0813541,"\int \cos (a+b x) \, dx","Integrate[Cos[a + b*x],x]","\frac{\sin (a) \cos (b x)}{b}+\frac{\cos (a) \sin (b x)}{b}","\frac{\sin (a+b x)}{b}",1,"(Cos[b*x]*Sin[a])/b + (Cos[a]*Sin[b*x])/b","B",1
2,1,23,25,0.0233129,"\int \cos ^2(a+b x) \, dx","Integrate[Cos[a + b*x]^2,x]","\frac{2 (a+b x)+\sin (2 (a+b x))}{4 b}","\frac{\sin (a+b x) \cos (a+b x)}{2 b}+\frac{x}{2}",1,"(2*(a + b*x) + Sin[2*(a + b*x)])/(4*b)","A",1
3,1,26,26,0.0077739,"\int \cos ^3(a+b x) \, dx","Integrate[Cos[a + b*x]^3,x]","\frac{\sin (a+b x)}{b}-\frac{\sin ^3(a+b x)}{3 b}","\frac{\sin (a+b x)}{b}-\frac{\sin ^3(a+b x)}{3 b}",1,"Sin[a + b*x]/b - Sin[a + b*x]^3/(3*b)","A",1
4,1,33,46,0.0365826,"\int \cos ^4(a+b x) \, dx","Integrate[Cos[a + b*x]^4,x]","\frac{12 (a+b x)+8 \sin (2 (a+b x))+\sin (4 (a+b x))}{32 b}","\frac{\sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{3 \sin (a+b x) \cos (a+b x)}{8 b}+\frac{3 x}{8}",1,"(12*(a + b*x) + 8*Sin[2*(a + b*x)] + Sin[4*(a + b*x)])/(32*b)","A",1
5,1,41,41,0.0128879,"\int \cos ^5(a+b x) \, dx","Integrate[Cos[a + b*x]^5,x]","\frac{\sin ^5(a+b x)}{5 b}-\frac{2 \sin ^3(a+b x)}{3 b}+\frac{\sin (a+b x)}{b}","\frac{\sin ^5(a+b x)}{5 b}-\frac{2 \sin ^3(a+b x)}{3 b}+\frac{\sin (a+b x)}{b}",1,"Sin[a + b*x]/b - (2*Sin[a + b*x]^3)/(3*b) + Sin[a + b*x]^5/(5*b)","A",1
6,1,43,67,0.0349469,"\int \cos ^6(a+b x) \, dx","Integrate[Cos[a + b*x]^6,x]","\frac{45 \sin (2 (a+b x))+9 \sin (4 (a+b x))+\sin (6 (a+b x))+60 a+60 b x}{192 b}","\frac{\sin (a+b x) \cos ^5(a+b x)}{6 b}+\frac{5 \sin (a+b x) \cos ^3(a+b x)}{24 b}+\frac{5 \sin (a+b x) \cos (a+b x)}{16 b}+\frac{5 x}{16}",1,"(60*a + 60*b*x + 45*Sin[2*(a + b*x)] + 9*Sin[4*(a + b*x)] + Sin[6*(a + b*x)])/(192*b)","A",1
7,1,54,54,0.0116241,"\int \cos ^7(a+b x) \, dx","Integrate[Cos[a + b*x]^7,x]","-\frac{\sin ^7(a+b x)}{7 b}+\frac{3 \sin ^5(a+b x)}{5 b}-\frac{\sin ^3(a+b x)}{b}+\frac{\sin (a+b x)}{b}","-\frac{\sin ^7(a+b x)}{7 b}+\frac{3 \sin ^5(a+b x)}{5 b}-\frac{\sin ^3(a+b x)}{b}+\frac{\sin (a+b x)}{b}",1,"Sin[a + b*x]/b - Sin[a + b*x]^3/b + (3*Sin[a + b*x]^5)/(5*b) - Sin[a + b*x]^7/(7*b)","A",1
8,1,55,88,0.0509753,"\int \cos ^8(a+b x) \, dx","Integrate[Cos[a + b*x]^8,x]","\frac{672 \sin (2 (a+b x))+168 \sin (4 (a+b x))+32 \sin (6 (a+b x))+3 \sin (8 (a+b x))+840 a+840 b x}{3072 b}","\frac{\sin (a+b x) \cos ^7(a+b x)}{8 b}+\frac{7 \sin (a+b x) \cos ^5(a+b x)}{48 b}+\frac{35 \sin (a+b x) \cos ^3(a+b x)}{192 b}+\frac{35 \sin (a+b x) \cos (a+b x)}{128 b}+\frac{35 x}{128}",1,"(840*a + 840*b*x + 672*Sin[2*(a + b*x)] + 168*Sin[4*(a + b*x)] + 32*Sin[6*(a + b*x)] + 3*Sin[8*(a + b*x)])/(3072*b)","A",1
9,1,51,65,0.2650552,"\int \cos ^{\frac{7}{2}}(a+b x) \, dx","Integrate[Cos[a + b*x]^(7/2),x]","\frac{20 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)+(23 \sin (a+b x)+3 \sin (3 (a+b x))) \sqrt{\cos (a+b x)}}{42 b}","\frac{10 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b}+\frac{2 \sin (a+b x) \cos ^{\frac{5}{2}}(a+b x)}{7 b}+\frac{10 \sin (a+b x) \sqrt{\cos (a+b x)}}{21 b}",1,"(20*EllipticF[(a + b*x)/2, 2] + Sqrt[Cos[a + b*x]]*(23*Sin[a + b*x] + 3*Sin[3*(a + b*x)]))/(42*b)","A",1
10,1,40,42,0.0450067,"\int \cos ^{\frac{5}{2}}(a+b x) \, dx","Integrate[Cos[a + b*x]^(5/2),x]","\frac{6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)+\sin (2 (a+b x)) \sqrt{\cos (a+b x)}}{5 b}","\frac{6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}+\frac{2 \sin (a+b x) \cos ^{\frac{3}{2}}(a+b x)}{5 b}",1,"(6*EllipticE[(a + b*x)/2, 2] + Sqrt[Cos[a + b*x]]*Sin[2*(a + b*x)])/(5*b)","A",1
11,1,36,42,0.0391828,"\int \cos ^{\frac{3}{2}}(a+b x) \, dx","Integrate[Cos[a + b*x]^(3/2),x]","\frac{2 \left(F\left(\left.\frac{1}{2} (a+b x)\right|2\right)+\sin (a+b x) \sqrt{\cos (a+b x)}\right)}{3 b}","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}+\frac{2 \sin (a+b x) \sqrt{\cos (a+b x)}}{3 b}",1,"(2*(EllipticF[(a + b*x)/2, 2] + Sqrt[Cos[a + b*x]]*Sin[a + b*x]))/(3*b)","A",1
12,1,16,16,0.0254657,"\int \sqrt{\cos (a+b x)} \, dx","Integrate[Sqrt[Cos[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*EllipticE[(a + b*x)/2, 2])/b","A",1
13,1,16,16,0.0279712,"\int \frac{1}{\sqrt{\cos (a+b x)}} \, dx","Integrate[1/Sqrt[Cos[a + b*x]],x]","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*EllipticF[(a + b*x)/2, 2])/b","A",1
14,1,38,38,0.0597673,"\int \frac{1}{\cos ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[Cos[a + b*x]^(-3/2),x]","\frac{2 \sin (a+b x)}{b \sqrt{\cos (a+b x)}}-\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 \sin (a+b x)}{b \sqrt{\cos (a+b x)}}-\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(-2*EllipticE[(a + b*x)/2, 2])/b + (2*Sin[a + b*x])/(b*Sqrt[Cos[a + b*x]])","A",1
15,1,36,42,0.0576823,"\int \frac{1}{\cos ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Cos[a + b*x]^(-5/2),x]","\frac{2 \left(F\left(\left.\frac{1}{2} (a+b x)\right|2\right)+\frac{\sin (a+b x)}{\cos ^{\frac{3}{2}}(a+b x)}\right)}{3 b}","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}+\frac{2 \sin (a+b x)}{3 b \cos ^{\frac{3}{2}}(a+b x)}",1,"(2*(EllipticF[(a + b*x)/2, 2] + Sin[a + b*x]/Cos[a + b*x]^(3/2)))/(3*b)","A",1
16,1,59,65,0.0929075,"\int \frac{1}{\cos ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[Cos[a + b*x]^(-7/2),x]","\frac{3 \sin (2 (a+b x))+2 \tan (a+b x)-6 \cos ^{\frac{3}{2}}(a+b x) E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b \cos ^{\frac{3}{2}}(a+b x)}","-\frac{6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}+\frac{2 \sin (a+b x)}{5 b \cos ^{\frac{5}{2}}(a+b x)}+\frac{6 \sin (a+b x)}{5 b \sqrt{\cos (a+b x)}}",1,"(-6*Cos[a + b*x]^(3/2)*EllipticE[(a + b*x)/2, 2] + 3*Sin[2*(a + b*x)] + 2*Tan[a + b*x])/(5*b*Cos[a + b*x]^(3/2))","A",1
17,1,76,98,0.0895735,"\int (c \cos (a+b x))^{7/2} \, dx","Integrate[(c*Cos[a + b*x])^(7/2),x]","\frac{c^3 \sqrt{c \cos (a+b x)} \left(20 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)+(23 \sin (a+b x)+3 \sin (3 (a+b x))) \sqrt{\cos (a+b x)}\right)}{42 b \sqrt{\cos (a+b x)}}","\frac{10 c^4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b \sqrt{c \cos (a+b x)}}+\frac{10 c^3 \sin (a+b x) \sqrt{c \cos (a+b x)}}{21 b}+\frac{2 c \sin (a+b x) (c \cos (a+b x))^{5/2}}{7 b}",1,"(c^3*Sqrt[c*Cos[a + b*x]]*(20*EllipticF[(a + b*x)/2, 2] + Sqrt[Cos[a + b*x]]*(23*Sin[a + b*x] + 3*Sin[3*(a + b*x)])))/(42*b*Sqrt[Cos[a + b*x]])","A",1
18,1,62,70,0.0838723,"\int (c \cos (a+b x))^{5/2} \, dx","Integrate[(c*Cos[a + b*x])^(5/2),x]","\frac{(c \cos (a+b x))^{5/2} \left(6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)+\sin (2 (a+b x)) \sqrt{\cos (a+b x)}\right)}{5 b \cos ^{\frac{5}{2}}(a+b x)}","\frac{6 c^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \cos (a+b x)}}{5 b \sqrt{\cos (a+b x)}}+\frac{2 c \sin (a+b x) (c \cos (a+b x))^{3/2}}{5 b}",1,"((c*Cos[a + b*x])^(5/2)*(6*EllipticE[(a + b*x)/2, 2] + Sqrt[Cos[a + b*x]]*Sin[2*(a + b*x)]))/(5*b*Cos[a + b*x]^(5/2))","A",1
19,1,58,70,0.0432649,"\int (c \cos (a+b x))^{3/2} \, dx","Integrate[(c*Cos[a + b*x])^(3/2),x]","\frac{2 (c \cos (a+b x))^{3/2} \left(F\left(\left.\frac{1}{2} (a+b x)\right|2\right)+\sin (a+b x) \sqrt{\cos (a+b x)}\right)}{3 b \cos ^{\frac{3}{2}}(a+b x)}","\frac{2 c^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b \sqrt{c \cos (a+b x)}}+\frac{2 c \sin (a+b x) \sqrt{c \cos (a+b x)}}{3 b}",1,"(2*(c*Cos[a + b*x])^(3/2)*(EllipticF[(a + b*x)/2, 2] + Sqrt[Cos[a + b*x]]*Sin[a + b*x]))/(3*b*Cos[a + b*x]^(3/2))","A",1
20,1,38,38,0.0182606,"\int \sqrt{c \cos (a+b x)} \, dx","Integrate[Sqrt[c*Cos[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \cos (a+b x)}}{b \sqrt{\cos (a+b x)}}","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \cos (a+b x)}}{b \sqrt{\cos (a+b x)}}",1,"(2*Sqrt[c*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(b*Sqrt[Cos[a + b*x]])","A",1
21,1,38,38,0.0249673,"\int \frac{1}{\sqrt{c \cos (a+b x)}} \, dx","Integrate[1/Sqrt[c*Cos[a + b*x]],x]","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{c \cos (a+b x)}}","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{c \cos (a+b x)}}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(b*Sqrt[c*Cos[a + b*x]])","A",1
22,1,50,68,0.0277658,"\int \frac{1}{(c \cos (a+b x))^{3/2}} \, dx","Integrate[(c*Cos[a + b*x])^(-3/2),x]","\frac{2 \left(\sin (a+b x)-\sqrt{\cos (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{b c \sqrt{c \cos (a+b x)}}","\frac{2 \sin (a+b x)}{b c \sqrt{c \cos (a+b x)}}-\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \cos (a+b x)}}{b c^2 \sqrt{\cos (a+b x)}}",1,"(2*(-(Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]) + Sin[a + b*x]))/(b*c*Sqrt[c*Cos[a + b*x]])","A",1
23,1,51,72,0.0586047,"\int \frac{1}{(c \cos (a+b x))^{5/2}} \, dx","Integrate[(c*Cos[a + b*x])^(-5/2),x]","\frac{2 \left(\tan (a+b x)+\sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{3 b c^2 \sqrt{c \cos (a+b x)}}","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b c^2 \sqrt{c \cos (a+b x)}}+\frac{2 \sin (a+b x)}{3 b c (c \cos (a+b x))^{3/2}}",1,"(2*(Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2] + Tan[a + b*x]))/(3*b*c^2*Sqrt[c*Cos[a + b*x]])","A",1
24,1,68,100,0.091411,"\int \frac{1}{(c \cos (a+b x))^{7/2}} \, dx","Integrate[(c*Cos[a + b*x])^(-7/2),x]","\frac{6 \sin (a+b x)-6 \sqrt{\cos (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)+2 \tan (a+b x) \sec (a+b x)}{5 b c^3 \sqrt{c \cos (a+b x)}}","-\frac{6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \cos (a+b x)}}{5 b c^4 \sqrt{\cos (a+b x)}}+\frac{6 \sin (a+b x)}{5 b c^3 \sqrt{c \cos (a+b x)}}+\frac{2 \sin (a+b x)}{5 b c (c \cos (a+b x))^{5/2}}",1,"(-6*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2] + 6*Sin[a + b*x] + 2*Sec[a + b*x]*Tan[a + b*x])/(5*b*c^3*Sqrt[c*Cos[a + b*x]])","A",1
25,1,53,53,0.0610327,"\int \cos ^{\frac{4}{3}}(a+b x) \, dx","Integrate[Cos[a + b*x]^(4/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cos ^{\frac{7}{3}}(a+b x) \csc (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b}","-\frac{3 \sin (a+b x) \cos ^{\frac{7}{3}}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b \sqrt{\sin ^2(a+b x)}}",1,"(-3*Cos[a + b*x]^(7/3)*Csc[a + b*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(7*b)","A",1
26,1,53,53,0.0301589,"\int \cos ^{\frac{2}{3}}(a+b x) \, dx","Integrate[Cos[a + b*x]^(2/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cos ^{\frac{5}{3}}(a+b x) \csc (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b}","-\frac{3 \sin (a+b x) \cos ^{\frac{5}{3}}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b \sqrt{\sin ^2(a+b x)}}",1,"(-3*Cos[a + b*x]^(5/3)*Csc[a + b*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(5*b)","A",1
27,1,53,53,0.0281322,"\int \sqrt[3]{\cos (a+b x)} \, dx","Integrate[Cos[a + b*x]^(1/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cos ^{\frac{4}{3}}(a+b x) \csc (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b}","-\frac{3 \sin (a+b x) \cos ^{\frac{4}{3}}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b \sqrt{\sin ^2(a+b x)}}",1,"(-3*Cos[a + b*x]^(4/3)*Csc[a + b*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(4*b)","A",1
28,1,53,53,0.0249434,"\int \frac{1}{\sqrt[3]{\cos (a+b x)}} \, dx","Integrate[Cos[a + b*x]^(-1/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cos ^{\frac{2}{3}}(a+b x) \csc (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b}","-\frac{3 \sin (a+b x) \cos ^{\frac{2}{3}}(a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b \sqrt{\sin ^2(a+b x)}}",1,"(-3*Cos[a + b*x]^(2/3)*Csc[a + b*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(2*b)","A",1
29,1,51,51,0.024018,"\int \frac{1}{\cos ^{\frac{2}{3}}(a+b x)} \, dx","Integrate[Cos[a + b*x]^(-2/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \sqrt[3]{\cos (a+b x)} \csc (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b}","-\frac{3 \sin (a+b x) \sqrt[3]{\cos (a+b x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)}}",1,"(-3*Cos[a + b*x]^(1/3)*Csc[a + b*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/b","A",1
30,1,51,51,0.0249717,"\int \frac{1}{\cos ^{\frac{4}{3}}(a+b x)} \, dx","Integrate[Cos[a + b*x]^(-4/3),x]","\frac{3 \sqrt{\sin ^2(a+b x)} \csc (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b \sqrt[3]{\cos (a+b x)}}","\frac{3 \sin (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b \sqrt{\sin ^2(a+b x)} \sqrt[3]{\cos (a+b x)}}",1,"(3*Csc[a + b*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*Cos[a + b*x]^(1/3))","A",1
31,1,55,58,0.0482128,"\int (c \cos (a+b x))^{4/3} \, dx","Integrate[(c*Cos[a + b*x])^(4/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cot (a+b x) (c \cos (a+b x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b}","-\frac{3 \sin (a+b x) (c \cos (a+b x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(a+b x)\right)}{7 b c \sqrt{\sin ^2(a+b x)}}",1,"(-3*(c*Cos[a + b*x])^(4/3)*Cot[a + b*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(7*b)","A",1
32,1,55,58,0.0386985,"\int (c \cos (a+b x))^{2/3} \, dx","Integrate[(c*Cos[a + b*x])^(2/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cot (a+b x) (c \cos (a+b x))^{2/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b}","-\frac{3 \sin (a+b x) (c \cos (a+b x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(a+b x)\right)}{5 b c \sqrt{\sin ^2(a+b x)}}",1,"(-3*(c*Cos[a + b*x])^(2/3)*Cot[a + b*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(5*b)","A",1
33,1,55,58,0.0345099,"\int \sqrt[3]{c \cos (a+b x)} \, dx","Integrate[(c*Cos[a + b*x])^(1/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \sqrt[3]{c \cos (a+b x)} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b}","-\frac{3 \sin (a+b x) (c \cos (a+b x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(a+b x)\right)}{4 b c \sqrt{\sin ^2(a+b x)}}",1,"(-3*(c*Cos[a + b*x])^(1/3)*Cot[a + b*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(4*b)","A",1
34,1,55,58,0.039238,"\int \frac{1}{\sqrt[3]{c \cos (a+b x)}} \, dx","Integrate[(c*Cos[a + b*x])^(-1/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b \sqrt[3]{c \cos (a+b x)}}","-\frac{3 \sin (a+b x) (c \cos (a+b x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(a+b x)\right)}{2 b c \sqrt{\sin ^2(a+b x)}}",1,"(-3*Cot[a + b*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(2*b*(c*Cos[a + b*x])^(1/3))","A",1
35,1,53,56,0.0393738,"\int \frac{1}{(c \cos (a+b x))^{2/3}} \, dx","Integrate[(c*Cos[a + b*x])^(-2/3),x]","-\frac{3 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b (c \cos (a+b x))^{2/3}}","-\frac{3 \sin (a+b x) \sqrt[3]{c \cos (a+b x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(a+b x)\right)}{b c \sqrt{\sin ^2(a+b x)}}",1,"(-3*Cot[a + b*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(c*Cos[a + b*x])^(2/3))","A",1
36,1,53,56,0.0394251,"\int \frac{1}{(c \cos (a+b x))^{4/3}} \, dx","Integrate[(c*Cos[a + b*x])^(-4/3),x]","\frac{3 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b (c \cos (a+b x))^{4/3}}","\frac{3 \sin (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(a+b x)\right)}{b c \sqrt{\sin ^2(a+b x)} \sqrt[3]{c \cos (a+b x)}}",1,"(3*Cot[a + b*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(c*Cos[a + b*x])^(4/3))","A",1
37,1,64,64,0.0443014,"\int \cos ^n(a+b x) \, dx","Integrate[Cos[a + b*x]^n,x]","-\frac{\sqrt{\sin ^2(a+b x)} \csc (a+b x) \cos ^{n+1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b (n+1)}","-\frac{\sin (a+b x) \cos ^{n+1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b (n+1) \sqrt{\sin ^2(a+b x)}}",1,"-((Cos[a + b*x]^(1 + n)*Csc[a + b*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(1 + n)))","A",1
38,1,64,69,0.0411343,"\int (c \cos (a+b x))^n \, dx","Integrate[(c*Cos[a + b*x])^n,x]","-\frac{\sqrt{\sin ^2(a+b x)} \cot (a+b x) (c \cos (a+b x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b (n+1)}","-\frac{\sin (a+b x) (c \cos (a+b x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b c (n+1) \sqrt{\sin ^2(a+b x)}}",1,"-(((c*Cos[a + b*x])^n*Cot[a + b*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(1 + n)))","A",1
39,1,36,53,0.0180386,"\int \left(a \cos ^2(x)\right)^{5/2} \, dx","Integrate[(a*Cos[x]^2)^(5/2),x]","\frac{1}{240} a^2 (150 \sin (x)+25 \sin (3 x)+3 \sin (5 x)) \sec (x) \sqrt{a \cos ^2(x)}","\frac{8}{15} a^2 \tan (x) \sqrt{a \cos ^2(x)}+\frac{1}{5} \tan (x) \left(a \cos ^2(x)\right)^{5/2}+\frac{4}{15} a \tan (x) \left(a \cos ^2(x)\right)^{3/2}",1,"(a^2*Sqrt[a*Cos[x]^2]*Sec[x]*(150*Sin[x] + 25*Sin[3*x] + 3*Sin[5*x]))/240","A",1
40,1,26,34,0.0085681,"\int \left(a \cos ^2(x)\right)^{3/2} \, dx","Integrate[(a*Cos[x]^2)^(3/2),x]","\frac{1}{12} a (9 \sin (x)+\sin (3 x)) \sec (x) \sqrt{a \cos ^2(x)}","\frac{1}{3} \tan (x) \left(a \cos ^2(x)\right)^{3/2}+\frac{2}{3} a \tan (x) \sqrt{a \cos ^2(x)}",1,"(a*Sqrt[a*Cos[x]^2]*Sec[x]*(9*Sin[x] + Sin[3*x]))/12","A",1
41,1,13,13,0.0041624,"\int \sqrt{a \cos ^2(x)} \, dx","Integrate[Sqrt[a*Cos[x]^2],x]","\tan (x) \sqrt{a \cos ^2(x)}","\tan (x) \sqrt{a \cos ^2(x)}",1,"Sqrt[a*Cos[x]^2]*Tan[x]","A",1
42,1,46,16,0.0248343,"\int \frac{1}{\sqrt{a \cos ^2(x)}} \, dx","Integrate[1/Sqrt[a*Cos[x]^2],x]","\frac{\cos (x) \left(\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)\right)}{\sqrt{a \cos ^2(x)}}","\frac{\cos (x) \tanh ^{-1}(\sin (x))}{\sqrt{a \cos ^2(x)}}",1,"(Cos[x]*(-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]]))/Sqrt[a*Cos[x]^2]","B",1
43,1,91,42,0.0594704,"\int \frac{1}{\left(a \cos ^2(x)\right)^{3/2}} \, dx","Integrate[(a*Cos[x]^2)^(-3/2),x]","-\frac{\cos (x) \left(-2 \sin (x)+\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+\cos (2 x) \left(\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)-\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)}{4 \left(a \cos ^2(x)\right)^{3/2}}","\frac{\tan (x)}{2 a \sqrt{a \cos ^2(x)}}+\frac{\cos (x) \tanh ^{-1}(\sin (x))}{2 a \sqrt{a \cos ^2(x)}}",1,"-1/4*(Cos[x]*(Log[Cos[x/2] - Sin[x/2]] + Cos[2*x]*(Log[Cos[x/2] - Sin[x/2]] - Log[Cos[x/2] + Sin[x/2]]) - Log[Cos[x/2] + Sin[x/2]] - 2*Sin[x]))/(a*Cos[x]^2)^(3/2)","B",1
44,1,72,61,0.1385715,"\int \frac{1}{\left(a \cos ^2(x)\right)^{5/2}} \, dx","Integrate[(a*Cos[x]^2)^(-5/2),x]","\frac{\cos ^5(x) \left(\frac{1}{2} (11 \sin (x)+3 \sin (3 x)) \sec ^4(x)-6 \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+6 \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)}{16 \left(a \cos ^2(x)\right)^{5/2}}","\frac{3 \tan (x)}{8 a^2 \sqrt{a \cos ^2(x)}}+\frac{3 \cos (x) \tanh ^{-1}(\sin (x))}{8 a^2 \sqrt{a \cos ^2(x)}}+\frac{\tan (x)}{4 a \left(a \cos ^2(x)\right)^{3/2}}",1,"(Cos[x]^5*(-6*Log[Cos[x/2] - Sin[x/2]] + 6*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^4*(11*Sin[x] + 3*Sin[3*x]))/2))/(16*(a*Cos[x]^2)^(5/2))","A",1
45,1,61,117,0.1136123,"\int \left(a \cos ^3(x)\right)^{5/2} \, dx","Integrate[(a*Cos[x]^3)^(5/2),x]","\frac{a \left(a \cos ^3(x)\right)^{3/2} \left(12480 F\left(\left.\frac{x}{2}\right|2\right)+(15465 \sin (x)+3657 \sin (3 x)+749 \sin (5 x)+77 \sin (7 x)) \sqrt{\cos (x)}\right)}{36960 \cos ^{\frac{9}{2}}(x)}","\frac{26}{165} a^2 \sin (x) \cos ^3(x) \sqrt{a \cos ^3(x)}+\frac{78}{385} a^2 \sin (x) \cos (x) \sqrt{a \cos ^3(x)}+\frac{26}{77} a^2 \tan (x) \sqrt{a \cos ^3(x)}+\frac{26 a^2 F\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \cos ^3(x)}}{77 \cos ^{\frac{3}{2}}(x)}+\frac{2}{15} a^2 \sin (x) \cos ^5(x) \sqrt{a \cos ^3(x)}",1,"(a*(a*Cos[x]^3)^(3/2)*(12480*EllipticF[x/2, 2] + Sqrt[Cos[x]]*(15465*Sin[x] + 3657*Sin[3*x] + 749*Sin[5*x] + 77*Sin[7*x])))/(36960*Cos[x]^(9/2))","A",1
46,1,50,67,0.0709283,"\int \left(a \cos ^3(x)\right)^{3/2} \, dx","Integrate[(a*Cos[x]^3)^(3/2),x]","\frac{\left(a \cos ^3(x)\right)^{3/2} \left(168 E\left(\left.\frac{x}{2}\right|2\right)+(38 \sin (2 x)+5 \sin (4 x)) \sqrt{\cos (x)}\right)}{180 \cos ^{\frac{9}{2}}(x)}","\frac{14}{45} a \sin (x) \sqrt{a \cos ^3(x)}+\frac{14 a E\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \cos ^3(x)}}{15 \cos ^{\frac{3}{2}}(x)}+\frac{2}{9} a \sin (x) \cos ^2(x) \sqrt{a \cos ^3(x)}",1,"((a*Cos[x]^3)^(3/2)*(168*EllipticE[x/2, 2] + Sqrt[Cos[x]]*(38*Sin[2*x] + 5*Sin[4*x])))/(180*Cos[x]^(9/2))","A",1
47,1,37,44,0.0239354,"\int \sqrt{a \cos ^3(x)} \, dx","Integrate[Sqrt[a*Cos[x]^3],x]","\frac{2 \sqrt{a \cos ^3(x)} \left(F\left(\left.\frac{x}{2}\right|2\right)+\sin (x) \sqrt{\cos (x)}\right)}{3 \cos ^{\frac{3}{2}}(x)}","\frac{2}{3} \tan (x) \sqrt{a \cos ^3(x)}+\frac{2 F\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \cos ^3(x)}}{3 \cos ^{\frac{3}{2}}(x)}",1,"(2*Sqrt[a*Cos[x]^3]*(EllipticF[x/2, 2] + Sqrt[Cos[x]]*Sin[x]))/(3*Cos[x]^(3/2))","A",1
48,1,31,42,0.0191835,"\int \frac{1}{\sqrt{a \cos ^3(x)}} \, dx","Integrate[1/Sqrt[a*Cos[x]^3],x]","\frac{\sin (2 x)-2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right)}{\sqrt{a \cos ^3(x)}}","\frac{2 \sin (x) \cos (x)}{\sqrt{a \cos ^3(x)}}-\frac{2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right)}{\sqrt{a \cos ^3(x)}}",1,"(-2*Cos[x]^(3/2)*EllipticE[x/2, 2] + Sin[2*x])/Sqrt[a*Cos[x]^3]","A",1
49,1,44,71,0.0567168,"\int \frac{1}{\left(a \cos ^3(x)\right)^{3/2}} \, dx","Integrate[(a*Cos[x]^3)^(-3/2),x]","\frac{2 \cos ^2(x) \left(3 \tan (x)+5 \cos ^{\frac{5}{2}}(x) F\left(\left.\frac{x}{2}\right|2\right)+5 \sin (x) \cos (x)\right)}{21 \left(a \cos ^3(x)\right)^{3/2}}","\frac{10 \sin (x)}{21 a \sqrt{a \cos ^3(x)}}+\frac{10 \cos ^{\frac{3}{2}}(x) F\left(\left.\frac{x}{2}\right|2\right)}{21 a \sqrt{a \cos ^3(x)}}+\frac{2 \tan (x) \sec (x)}{7 a \sqrt{a \cos ^3(x)}}",1,"(2*Cos[x]^2*(5*Cos[x]^(5/2)*EllipticF[x/2, 2] + 5*Cos[x]*Sin[x] + 3*Tan[x]))/(21*(a*Cos[x]^3)^(3/2))","A",1
50,1,57,117,0.0972681,"\int \frac{1}{\left(a \cos ^3(x)\right)^{5/2}} \, dx","Integrate[(a*Cos[x]^3)^(-5/2),x]","\frac{-462 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right)+462 \sin (x) \cos (x)+2 \tan (x) \left(45 \sec ^4(x)+55 \sec ^2(x)+77\right)}{585 a^2 \sqrt{a \cos ^3(x)}}","\frac{154 \sin (x) \cos (x)}{195 a^2 \sqrt{a \cos ^3(x)}}+\frac{154 \tan (x)}{585 a^2 \sqrt{a \cos ^3(x)}}-\frac{154 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right)}{195 a^2 \sqrt{a \cos ^3(x)}}+\frac{2 \tan (x) \sec ^4(x)}{13 a^2 \sqrt{a \cos ^3(x)}}+\frac{22 \tan (x) \sec ^2(x)}{117 a^2 \sqrt{a \cos ^3(x)}}",1,"(-462*Cos[x]^(3/2)*EllipticE[x/2, 2] + 462*Cos[x]*Sin[x] + 2*(77 + 55*Sec[x]^2 + 45*Sec[x]^4)*Tan[x])/(585*a^2*Sqrt[a*Cos[x]^3])","A",1
51,1,53,132,0.1162035,"\int \left(a \cos ^4(x)\right)^{5/2} \, dx","Integrate[(a*Cos[x]^4)^(5/2),x]","\frac{a (2520 x+2100 \sin (2 x)+600 \sin (4 x)+150 \sin (6 x)+25 \sin (8 x)+2 \sin (10 x)) \sec ^6(x) \left(a \cos ^4(x)\right)^{3/2}}{10240}","\frac{21}{128} a^2 \sin (x) \cos (x) \sqrt{a \cos ^4(x)}+\frac{63}{256} a^2 \tan (x) \sqrt{a \cos ^4(x)}+\frac{63}{256} a^2 x \sec ^2(x) \sqrt{a \cos ^4(x)}+\frac{1}{10} a^2 \sin (x) \cos ^7(x) \sqrt{a \cos ^4(x)}+\frac{9}{80} a^2 \sin (x) \cos ^5(x) \sqrt{a \cos ^4(x)}+\frac{21}{160} a^2 \sin (x) \cos ^3(x) \sqrt{a \cos ^4(x)}",1,"(a*(a*Cos[x]^4)^(3/2)*Sec[x]^6*(2520*x + 2100*Sin[2*x] + 600*Sin[4*x] + 150*Sin[6*x] + 25*Sin[8*x] + 2*Sin[10*x]))/10240","A",1
52,1,38,78,0.0675942,"\int \left(a \cos ^4(x)\right)^{3/2} \, dx","Integrate[(a*Cos[x]^4)^(3/2),x]","\frac{1}{192} (60 x+45 \sin (2 x)+9 \sin (4 x)+\sin (6 x)) \sec ^6(x) \left(a \cos ^4(x)\right)^{3/2}","\frac{5}{24} a \sin (x) \cos (x) \sqrt{a \cos ^4(x)}+\frac{5}{16} a \tan (x) \sqrt{a \cos ^4(x)}+\frac{5}{16} a x \sec ^2(x) \sqrt{a \cos ^4(x)}+\frac{1}{6} a \sin (x) \cos ^3(x) \sqrt{a \cos ^4(x)}",1,"((a*Cos[x]^4)^(3/2)*Sec[x]^6*(60*x + 45*Sin[2*x] + 9*Sin[4*x] + Sin[6*x]))/192","A",1
53,1,25,36,0.0138154,"\int \sqrt{a \cos ^4(x)} \, dx","Integrate[Sqrt[a*Cos[x]^4],x]","\frac{1}{2} \sec ^2(x) \sqrt{a \cos ^4(x)} (x+\sin (x) \cos (x))","\frac{1}{2} \tan (x) \sqrt{a \cos ^4(x)}+\frac{1}{2} x \sec ^2(x) \sqrt{a \cos ^4(x)}",1,"(Sqrt[a*Cos[x]^4]*Sec[x]^2*(x + Cos[x]*Sin[x]))/2","A",1
54,1,15,15,0.0045962,"\int \frac{1}{\sqrt{a \cos ^4(x)}} \, dx","Integrate[1/Sqrt[a*Cos[x]^4],x]","\frac{\sin (x) \cos (x)}{\sqrt{a \cos ^4(x)}}","\frac{\sin (x) \cos (x)}{\sqrt{a \cos ^4(x)}}",1,"(Cos[x]*Sin[x])/Sqrt[a*Cos[x]^4]","A",1
55,1,30,67,0.0263717,"\int \frac{1}{\left(a \cos ^4(x)\right)^{3/2}} \, dx","Integrate[(a*Cos[x]^4)^(-3/2),x]","\frac{\sin (x) \cos (x) (6 \cos (2 x)+\cos (4 x)+8)}{15 \left(a \cos ^4(x)\right)^{3/2}}","\frac{\sin (x) \cos (x)}{a \sqrt{a \cos ^4(x)}}+\frac{\sin ^2(x) \tan ^3(x)}{5 a \sqrt{a \cos ^4(x)}}+\frac{2 \sin ^2(x) \tan (x)}{3 a \sqrt{a \cos ^4(x)}}",1,"(Cos[x]*(8 + 6*Cos[2*x] + Cos[4*x])*Sin[x])/(15*(a*Cos[x]^4)^(3/2))","A",1
56,1,47,117,0.045262,"\int \frac{1}{\left(a \cos ^4(x)\right)^{5/2}} \, dx","Integrate[(a*Cos[x]^4)^(-5/2),x]","\frac{(130 \cos (2 x)+46 \cos (4 x)+10 \cos (6 x)+\cos (8 x)+128) \tan (x) \sec ^6(x)}{315 a^2 \sqrt{a \cos ^4(x)}}","\frac{\sin (x) \cos (x)}{a^2 \sqrt{a \cos ^4(x)}}+\frac{\sin ^2(x) \tan ^7(x)}{9 a^2 \sqrt{a \cos ^4(x)}}+\frac{4 \sin ^2(x) \tan ^5(x)}{7 a^2 \sqrt{a \cos ^4(x)}}+\frac{6 \sin ^2(x) \tan ^3(x)}{5 a^2 \sqrt{a \cos ^4(x)}}+\frac{4 \sin ^2(x) \tan (x)}{3 a^2 \sqrt{a \cos ^4(x)}}",1,"((128 + 130*Cos[2*x] + 46*Cos[4*x] + 10*Cos[6*x] + Cos[8*x])*Sec[x]^6*Tan[x])/(315*a^2*Sqrt[a*Cos[x]^4])","A",1
57,1,72,78,0.0635776,"\int \left(b \cos ^m(c+d x)\right)^n \, dx","Integrate[(b*Cos[c + d*x]^m)^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cot (c+d x) \left(b \cos ^m(c+d x)\right)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\cos ^2(c+d x)\right)}{d (m n+1)}","-\frac{\sin (c+d x) \cos (c+d x) \left(b \cos ^m(c+d x)\right)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m n+1);\frac{1}{2} (m n+3);\cos ^2(c+d x)\right)}{d (m n+1) \sqrt{\sin ^2(c+d x)}}",1,"-(((b*Cos[c + d*x]^m)^n*Cot[c + d*x]*Hypergeometric2F1[1/2, (1 + m*n)/2, (3 + m*n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(1 + m*n)))","A",1
58,1,74,89,0.1584595,"\int \left(c \cos ^m(a+b x)\right)^{5/2} \, dx","Integrate[(c*Cos[a + b*x]^m)^(5/2),x]","-\frac{2 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \left(c \cos ^m(a+b x)\right)^{5/2} \, _2F_1\left(\frac{1}{2},\frac{1}{4} (5 m+2);\frac{1}{4} (5 m+6);\cos ^2(a+b x)\right)}{b (5 m+2)}","-\frac{2 c^2 \sin (a+b x) \cos ^{2 m+1}(a+b x) \sqrt{c \cos ^m(a+b x)} \, _2F_1\left(\frac{1}{2},\frac{1}{4} (5 m+2);\frac{1}{4} (5 m+6);\cos ^2(a+b x)\right)}{b (5 m+2) \sqrt{\sin ^2(a+b x)}}",1,"(-2*(c*Cos[a + b*x]^m)^(5/2)*Cot[a + b*x]*Hypergeometric2F1[1/2, (2 + 5*m)/4, (6 + 5*m)/4, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(2 + 5*m))","A",1
59,1,72,83,0.1127046,"\int \left(c \cos ^m(a+b x)\right)^{3/2} \, dx","Integrate[(c*Cos[a + b*x]^m)^(3/2),x]","-\frac{2 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \left(c \cos ^m(a+b x)\right)^{3/2} \, _2F_1\left(\frac{1}{2},\frac{1}{4} (3 m+2);\frac{3 (m+2)}{4};\cos ^2(a+b x)\right)}{b (3 m+2)}","-\frac{2 c \sin (a+b x) \cos ^{m+1}(a+b x) \sqrt{c \cos ^m(a+b x)} \, _2F_1\left(\frac{1}{2},\frac{1}{4} (3 m+2);\frac{3 (m+2)}{4};\cos ^2(a+b x)\right)}{b (3 m+2) \sqrt{\sin ^2(a+b x)}}",1,"(-2*(c*Cos[a + b*x]^m)^(3/2)*Cot[a + b*x]*Hypergeometric2F1[1/2, (2 + 3*m)/4, (3*(2 + m))/4, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(2 + 3*m))","A",1
60,1,68,74,0.0684952,"\int \sqrt{c \cos ^m(a+b x)} \, dx","Integrate[Sqrt[c*Cos[a + b*x]^m],x]","-\frac{2 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \sqrt{c \cos ^m(a+b x)} \, _2F_1\left(\frac{1}{2},\frac{m+2}{4};\frac{m+6}{4};\cos ^2(a+b x)\right)}{b (m+2)}","-\frac{2 \sin (a+b x) \cos (a+b x) \sqrt{c \cos ^m(a+b x)} \, _2F_1\left(\frac{1}{2},\frac{m+2}{4};\frac{m+6}{4};\cos ^2(a+b x)\right)}{b (m+2) \sqrt{\sin ^2(a+b x)}}",1,"(-2*Sqrt[c*Cos[a + b*x]^m]*Cot[a + b*x]*Hypergeometric2F1[1/2, (2 + m)/4, (6 + m)/4, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(2 + m))","A",1
61,1,72,80,0.0729888,"\int \frac{1}{\sqrt{c \cos ^m(a+b x)}} \, dx","Integrate[1/Sqrt[c*Cos[a + b*x]^m],x]","\frac{2 \sqrt{\sin ^2(a+b x)} \cot (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2-m}{4};\frac{6-m}{4};\cos ^2(a+b x)\right)}{b (m-2) \sqrt{c \cos ^m(a+b x)}}","-\frac{2 \sin (a+b x) \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2-m}{4};\frac{6-m}{4};\cos ^2(a+b x)\right)}{b (2-m) \sqrt{\sin ^2(a+b x)} \sqrt{c \cos ^m(a+b x)}}",1,"(2*Cot[a + b*x]*Hypergeometric2F1[1/2, (2 - m)/4, (6 - m)/4, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*(-2 + m)*Sqrt[c*Cos[a + b*x]^m])","A",1
62,1,72,89,0.1033836,"\int \frac{1}{\left(c \cos ^m(a+b x)\right)^{3/2}} \, dx","Integrate[(c*Cos[a + b*x]^m)^(-3/2),x]","-\frac{\sqrt{\sin ^2(a+b x)} \cot (a+b x) \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2-3 m);-\frac{3}{4} (m-2);\cos ^2(a+b x)\right)}{\left(b-\frac{3 b m}{2}\right) \left(c \cos ^m(a+b x)\right)^{3/2}}","-\frac{2 \sin (a+b x) \cos ^{1-m}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2-3 m);\frac{3 (2-m)}{4};\cos ^2(a+b x)\right)}{b c (2-3 m) \sqrt{\sin ^2(a+b x)} \sqrt{c \cos ^m(a+b x)}}",1,"-((Cot[a + b*x]*Hypergeometric2F1[1/2, (2 - 3*m)/4, (-3*(-2 + m))/4, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/((b - (3*b*m)/2)*(c*Cos[a + b*x]^m)^(3/2)))","A",1
63,1,74,89,0.1028023,"\int \frac{1}{\left(c \cos ^m(a+b x)\right)^{5/2}} \, dx","Integrate[(c*Cos[a + b*x]^m)^(-5/2),x]","-\frac{\sqrt{\sin ^2(a+b x)} \cot (a+b x) \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2-5 m);\frac{1}{4} (6-5 m);\cos ^2(a+b x)\right)}{\left(b-\frac{5 b m}{2}\right) \left(c \cos ^m(a+b x)\right)^{5/2}}","-\frac{2 \sin (a+b x) \cos ^{1-2 m}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2-5 m);\frac{1}{4} (6-5 m);\cos ^2(a+b x)\right)}{b c^2 (2-5 m) \sqrt{\sin ^2(a+b x)} \sqrt{c \cos ^m(a+b x)}}",1,"-((Cot[a + b*x]*Hypergeometric2F1[1/2, (2 - 5*m)/4, (6 - 5*m)/4, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/((b - (5*b*m)/2)*(c*Cos[a + b*x]^m)^(5/2)))","A",1
64,1,24,24,0.0257287,"\int \left(c \cos ^m(a+b x)\right)^{\frac{1}{m}} \, dx","Integrate[(c*Cos[a + b*x]^m)^m^(-1),x]","\frac{\tan (a+b x) \left(c \cos ^m(a+b x)\right)^{\frac{1}{m}}}{b}","\frac{\tan (a+b x) \left(c \cos ^m(a+b x)\right)^{\frac{1}{m}}}{b}",1,"((c*Cos[a + b*x]^m)^m^(-1)*Tan[a + b*x])/b","A",1
65,1,74,80,0.0525036,"\int \left(a (b \cos (c+d x))^p\right)^n \, dx","Integrate[(a*(b*Cos[c + d*x])^p)^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);\cos ^2(c+d x)\right) \left(a (b \cos (c+d x))^p\right)^n}{d (n p+1)}","-\frac{\sin (c+d x) \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} (n p+1);\frac{1}{2} (n p+3);\cos ^2(c+d x)\right) \left(a (b \cos (c+d x))^p\right)^n}{d (n p+1) \sqrt{\sin ^2(c+d x)}}",1,"-(((a*(b*Cos[c + d*x])^p)^n*Cot[c + d*x]*Hypergeometric2F1[1/2, (1 + n*p)/2, (3 + n*p)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(1 + n*p)))","A",1
66,1,83,123,0.1957716,"\int \cos ^5(c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^5*Sqrt[b*Cos[c + d*x]],x]","\frac{\sqrt{b \cos (c+d x)} \left(240 F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(290 \sin (c+d x)+57 \sin (3 (c+d x))+7 \sin (5 (c+d x))) \sqrt{\cos (c+d x)}\right)}{616 d \sqrt{\cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^4 d}+\frac{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 b^2 d}+\frac{30 \sin (c+d x) \sqrt{b \cos (c+d x)}}{77 d}+\frac{30 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{77 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(240*EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(290*Sin[c + d*x] + 57*Sin[3*(c + d*x)] + 7*Sin[5*(c + d*x)])))/(616*d*Sqrt[Cos[c + d*x]])","A",1
67,1,75,97,0.1451198,"\int \cos ^4(c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^4*Sqrt[b*Cos[c + d*x]],x]","\frac{\sqrt{b \cos (c+d x)} \left(168 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(38 \sin (2 (c+d x))+5 \sin (4 (c+d x))) \sqrt{\cos (c+d x)}\right)}{180 d \sqrt{\cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^3 d}+\frac{14 \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b d}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(168*EllipticE[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(38*Sin[2*(c + d*x)] + 5*Sin[4*(c + d*x)])))/(180*d*Sqrt[Cos[c + d*x]])","A",1
68,1,73,95,0.1366334,"\int \cos ^3(c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^3*Sqrt[b*Cos[c + d*x]],x]","\frac{\sqrt{b \cos (c+d x)} \left(20 F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(23 \sin (c+d x)+3 \sin (3 (c+d x))) \sqrt{\cos (c+d x)}\right)}{42 d \sqrt{\cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^2 d}+\frac{10 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{10 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(20*EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(23*Sin[c + d*x] + 3*Sin[3*(c + d*x)])))/(42*d*Sqrt[Cos[c + d*x]])","A",1
69,1,62,69,0.0595015,"\int \cos ^2(c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^2*Sqrt[b*Cos[c + d*x]],x]","\frac{\sqrt{b \cos (c+d x)} \left(6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+\sin (2 (c+d x)) \sqrt{\cos (c+d x)}\right)}{5 d \sqrt{\cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b d}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(6*EllipticE[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*Sin[2*(c + d*x)]))/(5*d*Sqrt[Cos[c + d*x]])","A",1
70,1,61,67,0.0576845,"\int \cos (c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]*Sqrt[b*Cos[c + d*x]],x]","\frac{2 (b \cos (c+d x))^{3/2} \left(F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+\sin (c+d x) \sqrt{\cos (c+d x)}\right)}{3 b d \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*(b*Cos[c + d*x])^(3/2)*(EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*Sin[c + d*x]))/(3*b*d*Cos[c + d*x]^(3/2))","A",1
71,1,38,38,0.0217594,"\int \sqrt{b \cos (c+d x)} \, dx","Integrate[Sqrt[b*Cos[c + d*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]])","A",1
72,1,39,39,0.0290988,"\int \sqrt{b \cos (c+d x)} \sec (c+d x) \, dx","Integrate[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x],x]","\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(2*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]])","A",1
73,1,48,63,0.0535893,"\int \sqrt{b \cos (c+d x)} \sec ^2(c+d x) \, dx","Integrate[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^2,x]","\frac{2 b \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 b \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(2*b*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/(d*Sqrt[b*Cos[c + d*x]])","A",1
74,1,49,70,0.0856916,"\int \sqrt{b \cos (c+d x)} \sec ^3(c+d x) \, dx","Integrate[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^3,x]","\frac{2 b \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 b^2 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*b*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*d*Sqrt[b*Cos[c + d*x]])","A",1
75,1,69,95,0.2204693,"\int \sqrt{b \cos (c+d x)} \sec ^4(c+d x) \, dx","Integrate[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^4,x]","\frac{2 \sec ^2(c+d x) \sqrt{b \cos (c+d x)} \left(\frac{3}{2} \sin (2 (c+d x))+\tan (c+d x)-3 \cos ^{\frac{3}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{5 d}","\frac{2 b^3 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"(2*Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^2*(-3*Cos[c + d*x]^(3/2)*EllipticE[(c + d*x)/2, 2] + (3*Sin[2*(c + d*x)])/2 + Tan[c + d*x]))/(5*d)","A",1
76,1,69,98,0.1802229,"\int \sqrt{b \cos (c+d x)} \sec ^5(c+d x) \, dx","Integrate[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^5,x]","\frac{\sec ^3(c+d x) \sqrt{b \cos (c+d x)} \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 d}","\frac{2 b^4 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{10 b^2 \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{10 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^3*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*d)","A",1
77,1,79,123,0.2044087,"\int \sqrt{b \cos (c+d x)} \sec ^6(c+d x) \, dx","Integrate[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^6,x]","\frac{\sec ^5(c+d x) \sqrt{b \cos (c+d x)} \left(150 \sin (c+d x)+91 \sin (3 (c+d x))+21 \sin (5 (c+d x))-336 \cos ^{\frac{9}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{360 d}","\frac{2 b^5 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}+\frac{14 b^3 \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}+\frac{14 b \sin (c+d x)}{15 d \sqrt{b \cos (c+d x)}}-\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^5*(-336*Cos[c + d*x]^(9/2)*EllipticE[(c + d*x)/2, 2] + 150*Sin[c + d*x] + 91*Sin[3*(c + d*x)] + 21*Sin[5*(c + d*x)]))/(360*d)","A",1
78,1,83,126,0.0980497,"\int \cos ^4(c+d x) (b \cos (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^4*(b*Cos[c + d*x])^(3/2),x]","\frac{(b \cos (c+d x))^{3/2} \left(240 F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(290 \sin (c+d x)+57 \sin (3 (c+d x))+7 \sin (5 (c+d x))) \sqrt{\cos (c+d x)}\right)}{616 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^3 d}+\frac{30 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{77 d \sqrt{b \cos (c+d x)}}+\frac{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 b d}+\frac{30 b \sin (c+d x) \sqrt{b \cos (c+d x)}}{77 d}",1,"((b*Cos[c + d*x])^(3/2)*(240*EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(290*Sin[c + d*x] + 57*Sin[3*(c + d*x)] + 7*Sin[5*(c + d*x)])))/(616*d*Cos[c + d*x]^(3/2))","A",1
79,1,75,95,0.0987342,"\int \cos ^3(c+d x) (b \cos (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^3*(b*Cos[c + d*x])^(3/2),x]","\frac{(b \cos (c+d x))^{3/2} \left(168 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(38 \sin (2 (c+d x))+5 \sin (4 (c+d x))) \sqrt{\cos (c+d x)}\right)}{180 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^2 d}+\frac{14 \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}+\frac{14 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(3/2)*(168*EllipticE[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(38*Sin[2*(c + d*x)] + 5*Sin[4*(c + d*x)])))/(180*d*Cos[c + d*x]^(3/2))","A",1
80,1,73,98,0.0967017,"\int \cos ^2(c+d x) (b \cos (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^2*(b*Cos[c + d*x])^(3/2),x]","\frac{(b \cos (c+d x))^{3/2} \left(20 F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(23 \sin (c+d x)+3 \sin (3 (c+d x))) \sqrt{\cos (c+d x)}\right)}{42 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{10 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b d}+\frac{10 b \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}",1,"((b*Cos[c + d*x])^(3/2)*(20*EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(23*Sin[c + d*x] + 3*Sin[3*(c + d*x)])))/(42*d*Cos[c + d*x]^(3/2))","A",1
81,1,65,67,0.0844556,"\int \cos (c+d x) (b \cos (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]*(b*Cos[c + d*x])^(3/2),x]","\frac{(b \cos (c+d x))^{5/2} \left(6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+\sin (2 (c+d x)) \sqrt{\cos (c+d x)}\right)}{5 b d \cos ^{\frac{5}{2}}(c+d x)}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}+\frac{6 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*(6*EllipticE[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*Sin[2*(c + d*x)]))/(5*b*d*Cos[c + d*x]^(5/2))","A",1
82,1,58,70,0.0149972,"\int (b \cos (c+d x))^{3/2} \, dx","Integrate[(b*Cos[c + d*x])^(3/2),x]","\frac{2 (b \cos (c+d x))^{3/2} \left(F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+\sin (c+d x) \sqrt{\cos (c+d x)}\right)}{3 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*(b*Cos[c + d*x])^(3/2)*(EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*Sin[c + d*x]))/(3*d*Cos[c + d*x]^(3/2))","A",1
83,1,39,39,0.0139134,"\int (b \cos (c+d x))^{3/2} \sec (c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x],x]","\frac{2 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(2*b*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]])","A",1
84,1,41,41,0.0203754,"\int (b \cos (c+d x))^{3/2} \sec ^2(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^2,x]","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(2*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]])","A",1
85,1,50,66,0.0526117,"\int (b \cos (c+d x))^{3/2} \sec ^3(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^3,x]","\frac{2 b^2 \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 b^2 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(2*b^2*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/(d*Sqrt[b*Cos[c + d*x]])","A",1
86,1,51,72,0.06432,"\int (b \cos (c+d x))^{3/2} \sec ^4(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^4,x]","\frac{2 b^2 \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 b^3 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*b^2*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*d*Sqrt[b*Cos[c + d*x]])","A",1
87,1,69,98,0.1125225,"\int (b \cos (c+d x))^{3/2} \sec ^5(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^5,x]","\frac{\sec ^4(c+d x) (b \cos (c+d x))^{3/2} \left(7 \sin (c+d x)+3 \sin (3 (c+d x))-12 \cos ^{\frac{5}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","\frac{2 b^4 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b^2 \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^4*(-12*Cos[c + d*x]^(5/2)*EllipticE[(c + d*x)/2, 2] + 7*Sin[c + d*x] + 3*Sin[3*(c + d*x)]))/(10*d)","A",1
88,1,69,100,0.1243011,"\int (b \cos (c+d x))^{3/2} \sec ^6(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^6,x]","\frac{\sec ^4(c+d x) (b \cos (c+d x))^{3/2} \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 d}","\frac{2 b^5 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{10 b^3 \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{10 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"((b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^4*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*d)","A",1
89,1,79,126,0.1734005,"\int (b \cos (c+d x))^{3/2} \sec ^7(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^7,x]","\frac{\sec ^6(c+d x) (b \cos (c+d x))^{3/2} \left(150 \sin (c+d x)+91 \sin (3 (c+d x))+21 \sin (5 (c+d x))-336 \cos ^{\frac{9}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{360 d}","\frac{2 b^6 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}+\frac{14 b^4 \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}+\frac{14 b^2 \sin (c+d x)}{15 d \sqrt{b \cos (c+d x)}}-\frac{14 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^6*(-336*Cos[c + d*x]^(9/2)*EllipticE[(c + d*x)/2, 2] + 150*Sin[c + d*x] + 91*Sin[3*(c + d*x)] + 21*Sin[5*(c + d*x)]))/(360*d)","A",1
90,1,83,125,0.132858,"\int \cos ^3(c+d x) (b \cos (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^3*(b*Cos[c + d*x])^(5/2),x]","\frac{(b \cos (c+d x))^{5/2} \left(240 F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(290 \sin (c+d x)+57 \sin (3 (c+d x))+7 \sin (5 (c+d x))) \sqrt{\cos (c+d x)}\right)}{616 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{30 b^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{77 d \sqrt{b \cos (c+d x)}}+\frac{2 \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^2 d}+\frac{30 b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{77 d}+\frac{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 d}",1,"((b*Cos[c + d*x])^(5/2)*(240*EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(290*Sin[c + d*x] + 57*Sin[3*(c + d*x)] + 7*Sin[5*(c + d*x)])))/(616*d*Cos[c + d*x]^(5/2))","A",1
91,1,75,98,0.1003012,"\int \cos ^2(c+d x) (b \cos (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^2*(b*Cos[c + d*x])^(5/2),x]","\frac{(b \cos (c+d x))^{5/2} \left(168 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(38 \sin (2 (c+d x))+5 \sin (4 (c+d x))) \sqrt{\cos (c+d x)}\right)}{180 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{14 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}+\frac{2 \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b d}+\frac{14 b \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 d}",1,"((b*Cos[c + d*x])^(5/2)*(168*EllipticE[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(38*Sin[2*(c + d*x)] + 5*Sin[4*(c + d*x)])))/(180*d*Cos[c + d*x]^(5/2))","A",1
92,1,76,97,0.0933837,"\int \cos (c+d x) (b \cos (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]*(b*Cos[c + d*x])^(5/2),x]","\frac{b^2 \sqrt{b \cos (c+d x)} \left(20 F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(23 \sin (c+d x)+3 \sin (3 (c+d x))) \sqrt{\cos (c+d x)}\right)}{42 d \sqrt{\cos (c+d x)}}","\frac{10 b^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{10 b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}",1,"(b^2*Sqrt[b*Cos[c + d*x]]*(20*EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(23*Sin[c + d*x] + 3*Sin[3*(c + d*x)])))/(42*d*Sqrt[Cos[c + d*x]])","A",1
93,1,62,70,0.0146245,"\int (b \cos (c+d x))^{5/2} \, dx","Integrate[(b*Cos[c + d*x])^(5/2),x]","\frac{(b \cos (c+d x))^{5/2} \left(6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+\sin (2 (c+d x)) \sqrt{\cos (c+d x)}\right)}{5 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{6 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}+\frac{2 b \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 d}",1,"((b*Cos[c + d*x])^(5/2)*(6*EllipticE[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*Sin[2*(c + d*x)]))/(5*d*Cos[c + d*x]^(5/2))","A",1
94,1,59,72,0.0221025,"\int (b \cos (c+d x))^{5/2} \sec (c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x],x]","\frac{2 b (b \cos (c+d x))^{3/2} \left(F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+\sin (c+d x) \sqrt{\cos (c+d x)}\right)}{3 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 b^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}+\frac{2 b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}",1,"(2*b*(b*Cos[c + d*x])^(3/2)*(EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*Sin[c + d*x]))/(3*d*Cos[c + d*x]^(3/2))","A",1
95,1,41,41,0.0143915,"\int (b \cos (c+d x))^{5/2} \sec ^2(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^2,x]","\frac{2 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{2 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(2*b^2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]])","A",1
96,1,38,41,0.0442261,"\int (b \cos (c+d x))^{5/2} \sec ^3(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^3,x]","\frac{2 F\left(\left.\frac{1}{2} (c+d x)\right|2\right) (b \cos (c+d x))^{5/2}}{d \cos ^{\frac{5}{2}}(c+d x)}","\frac{2 b^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(2*(b*Cos[c + d*x])^(5/2)*EllipticF[(c + d*x)/2, 2])/(d*Cos[c + d*x]^(5/2))","A",1
97,1,50,68,0.0546229,"\int (b \cos (c+d x))^{5/2} \sec ^4(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^4,x]","\frac{2 b^3 \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 b^3 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(2*b^3*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/(d*Sqrt[b*Cos[c + d*x]])","A",1
98,1,51,72,0.064493,"\int (b \cos (c+d x))^{5/2} \sec ^5(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^5,x]","\frac{2 b^3 \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 b^4 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 b^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*b^3*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*d*Sqrt[b*Cos[c + d*x]])","A",1
99,1,69,100,0.1514638,"\int (b \cos (c+d x))^{5/2} \sec ^6(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^6,x]","\frac{\sec ^5(c+d x) (b \cos (c+d x))^{5/2} \left(7 \sin (c+d x)+3 \sin (3 (c+d x))-12 \cos ^{\frac{5}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","\frac{2 b^5 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 b^3 \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^5*(-12*Cos[c + d*x]^(5/2)*EllipticE[(c + d*x)/2, 2] + 7*Sin[c + d*x] + 3*Sin[3*(c + d*x)]))/(10*d)","A",1
100,1,69,100,0.1770449,"\int (b \cos (c+d x))^{5/2} \sec ^7(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^7,x]","\frac{\sec ^5(c+d x) (b \cos (c+d x))^{5/2} \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 d}","\frac{2 b^6 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{10 b^4 \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{10 b^3 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^5*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*d)","A",1
101,1,79,128,0.2407181,"\int (b \cos (c+d x))^{5/2} \sec ^8(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^8,x]","\frac{\sec ^7(c+d x) (b \cos (c+d x))^{5/2} \left(150 \sin (c+d x)+91 \sin (3 (c+d x))+21 \sin (5 (c+d x))-336 \cos ^{\frac{9}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{360 d}","\frac{2 b^7 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}+\frac{14 b^5 \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}+\frac{14 b^3 \sin (c+d x)}{15 d \sqrt{b \cos (c+d x)}}-\frac{14 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^7*(-336*Cos[c + d*x]^(9/2)*EllipticE[(c + d*x)/2, 2] + 150*Sin[c + d*x] + 91*Sin[3*(c + d*x)] + 21*Sin[5*(c + d*x)]))/(360*d)","A",1
102,1,76,98,0.0183567,"\int (b \cos (c+d x))^{7/2} \, dx","Integrate[(b*Cos[c + d*x])^(7/2),x]","\frac{b^3 \sqrt{b \cos (c+d x)} \left(20 F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(23 \sin (c+d x)+3 \sin (3 (c+d x))) \sqrt{\cos (c+d x)}\right)}{42 d \sqrt{\cos (c+d x)}}","\frac{10 b^4 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}+\frac{10 b^3 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\frac{2 b \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}",1,"(b^3*Sqrt[b*Cos[c + d*x]]*(20*EllipticF[(c + d*x)/2, 2] + Sqrt[Cos[c + d*x]]*(23*Sin[c + d*x] + 3*Sin[3*(c + d*x)])))/(42*d*Sqrt[Cos[c + d*x]])","A",1
103,1,73,125,0.1323404,"\int \frac{\cos ^6(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^6/Sqrt[b*Cos[c + d*x]],x]","\frac{347 \sin (2 (c+d x))+64 \sin (4 (c+d x))+7 \sin (6 (c+d x))+480 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{1232 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^5 d}+\frac{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 b^3 d}+\frac{30 \sin (c+d x) \sqrt{b \cos (c+d x)}}{77 b d}+\frac{30 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{77 d \sqrt{b \cos (c+d x)}}",1,"(480*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 347*Sin[2*(c + d*x)] + 64*Sin[4*(c + d*x)] + 7*Sin[6*(c + d*x)])/(1232*d*Sqrt[b*Cos[c + d*x]])","A",1
104,1,71,100,0.1156219,"\int \frac{\cos ^5(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^5/Sqrt[b*Cos[c + d*x]],x]","\frac{(38 \sin (2 (c+d x))+5 \sin (4 (c+d x))) \cos (c+d x)+168 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{180 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^4 d}+\frac{14 \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^2 d}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}",1,"(168*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]*(38*Sin[2*(c + d*x)] + 5*Sin[4*(c + d*x)]))/(180*d*Sqrt[b*Cos[c + d*x]])","A",1
105,1,63,97,0.1019929,"\int \frac{\cos ^4(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^4/Sqrt[b*Cos[c + d*x]],x]","\frac{26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{84 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^3 d}+\frac{10 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b d}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)])/(84*d*Sqrt[b*Cos[c + d*x]])","A",1
106,1,58,72,0.056483,"\int \frac{\cos ^3(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^3/Sqrt[b*Cos[c + d*x]],x]","\frac{\sin (2 (c+d x)) \cos (c+d x)+6 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^2 d}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}",1,"(6*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]*Sin[2*(c + d*x)])/(5*d*Sqrt[b*Cos[c + d*x]])","A",1
107,1,51,69,0.0464349,"\int \frac{\cos ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^2/Sqrt[b*Cos[c + d*x]],x]","\frac{\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b d}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)])/(3*d*Sqrt[b*Cos[c + d*x]])","A",1
108,1,41,41,0.0155438,"\int \frac{\cos (c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]/Sqrt[b*Cos[c + d*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}",1,"(2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]])","A",1
109,1,38,38,0.0135005,"\int \frac{1}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[1/Sqrt[b*Cos[c + d*x]],x]","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{b \cos (c+d x)}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]])","A",1
110,1,47,65,0.0378761,"\int \frac{\sec (c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]/Sqrt[b*Cos[c + d*x]],x]","\frac{2 \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x)}{d \sqrt{b \cos (c+d x)}}-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b d \sqrt{\cos (c+d x)}}",1,"(2*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/(d*Sqrt[b*Cos[c + d*x]])","A",1
111,1,48,67,0.0599652,"\int \frac{\sec ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]^2/Sqrt[b*Cos[c + d*x]],x]","\frac{2 \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d \sqrt{b \cos (c+d x)}}","\frac{2 b \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 d \sqrt{b \cos (c+d x)}}",1,"(2*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*d*Sqrt[b*Cos[c + d*x]])","A",1
112,1,65,97,0.0892338,"\int \frac{\sec ^3(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]^3/Sqrt[b*Cos[c + d*x]],x]","\frac{6 \sin (c+d x)-6 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \sec (c+d x)}{5 d \sqrt{b \cos (c+d x)}}","\frac{2 b^2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}+\frac{6 \sin (c+d x)}{5 d \sqrt{b \cos (c+d x)}}-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b d \sqrt{\cos (c+d x)}}",1,"(-6*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + 6*Sin[c + d*x] + 2*Sec[c + d*x]*Tan[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",1
113,1,63,95,0.1357374,"\int \frac{\sec ^4(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]^4/Sqrt[b*Cos[c + d*x]],x]","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \left(3 \sec ^2(c+d x)+5\right)}{21 d \sqrt{b \cos (c+d x)}}","\frac{2 b^3 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{10 b \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 d \sqrt{b \cos (c+d x)}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 2*(5 + 3*Sec[c + d*x]^2)*Tan[c + d*x])/(21*d*Sqrt[b*Cos[c + d*x]])","A",1
114,1,77,125,0.2987222,"\int \frac{\sec ^5(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]^5/Sqrt[b*Cos[c + d*x]],x]","\frac{42 \sin (c+d x)-42 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \sec (c+d x) \left(5 \sec ^2(c+d x)+7\right)}{45 d \sqrt{b \cos (c+d x)}}","\frac{2 b^4 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}+\frac{14 b^2 \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}+\frac{14 \sin (c+d x)}{15 d \sqrt{b \cos (c+d x)}}-\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b d \sqrt{\cos (c+d x)}}",1,"(-42*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + 42*Sin[c + d*x] + 2*Sec[c + d*x]*(7 + 5*Sec[c + d*x]^2)*Tan[c + d*x])/(45*d*Sqrt[b*Cos[c + d*x]])","A",1
115,1,76,128,0.087717,"\int \frac{\cos ^7(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^7/(b*Cos[c + d*x])^(3/2),x]","\frac{347 \sin (2 (c+d x))+64 \sin (4 (c+d x))+7 \sin (6 (c+d x))+480 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{1232 b d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^6 d}+\frac{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 b^4 d}+\frac{30 \sin (c+d x) \sqrt{b \cos (c+d x)}}{77 b^2 d}+\frac{30 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{77 b d \sqrt{b \cos (c+d x)}}",1,"(480*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 347*Sin[2*(c + d*x)] + 64*Sin[4*(c + d*x)] + 7*Sin[6*(c + d*x)])/(1232*b*d*Sqrt[b*Cos[c + d*x]])","A",1
116,1,74,100,0.0507468,"\int \frac{\cos ^6(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^6/(b*Cos[c + d*x])^(3/2),x]","\frac{(38 \sin (2 (c+d x))+5 \sin (4 (c+d x))) \cos (c+d x)+168 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{180 b d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^5 d}+\frac{14 \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^3 d}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^2 d \sqrt{\cos (c+d x)}}",1,"(168*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]*(38*Sin[2*(c + d*x)] + 5*Sin[4*(c + d*x)]))/(180*b*d*Sqrt[b*Cos[c + d*x]])","A",1
117,1,66,100,0.0485271,"\int \frac{\cos ^5(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^5/(b*Cos[c + d*x])^(3/2),x]","\frac{26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{84 b d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^4 d}+\frac{10 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^2 d}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}",1,"(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)])/(84*b*d*Sqrt[b*Cos[c + d*x]])","A",1
118,1,61,72,0.035829,"\int \frac{\cos ^4(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^4/(b*Cos[c + d*x])^(3/2),x]","\frac{\sin (2 (c+d x)) \cos (c+d x)+6 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^3 d}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}",1,"(6*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]*Sin[2*(c + d*x)])/(5*b*d*Sqrt[b*Cos[c + d*x]])","A",1
119,1,54,72,0.03368,"\int \frac{\cos ^3(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^3/(b*Cos[c + d*x])^(3/2),x]","\frac{\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^2 d}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)])/(3*b*d*Sqrt[b*Cos[c + d*x]])","A",1
120,1,41,41,0.0148998,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^2/(b*Cos[c + d*x])^(3/2),x]","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}",1,"(2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]])","A",1
121,1,41,41,0.0183779,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]/(b*Cos[c + d*x])^(3/2),x]","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{b \cos (c+d x)}}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{b \cos (c+d x)}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(b*d*Sqrt[b*Cos[c + d*x]])","A",1
122,1,50,68,0.0148712,"\int \frac{1}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[(b*Cos[c + d*x])^(-3/2),x]","\frac{2 \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{b d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x)}{b d \sqrt{b \cos (c+d x)}}-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^2 d \sqrt{\cos (c+d x)}}",1,"(2*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/(b*d*Sqrt[b*Cos[c + d*x]])","A",1
123,1,51,69,0.0250755,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]/(b*Cos[c + d*x])^(3/2),x]","\frac{2 \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 b d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x)}{3 d (b \cos (c+d x))^{3/2}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b d \sqrt{b \cos (c+d x)}}",1,"(2*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*b*d*Sqrt[b*Cos[c + d*x]])","A",1
124,1,68,98,0.0511737,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^2/(b*Cos[c + d*x])^(3/2),x]","\frac{6 \sin (c+d x)-6 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \sec (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}","-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^2 d \sqrt{\cos (c+d x)}}+\frac{6 \sin (c+d x)}{5 b d \sqrt{b \cos (c+d x)}}+\frac{2 b \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}",1,"(-6*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + 6*Sin[c + d*x] + 2*Sec[c + d*x]*Tan[c + d*x])/(5*b*d*Sqrt[b*Cos[c + d*x]])","A",1
125,1,66,97,0.0441573,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^3/(b*Cos[c + d*x])^(3/2),x]","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \left(3 \sec ^2(c+d x)+5\right)}{21 b d \sqrt{b \cos (c+d x)}}","\frac{2 b^2 \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}+\frac{10 \sin (c+d x)}{21 d (b \cos (c+d x))^{3/2}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b d \sqrt{b \cos (c+d x)}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 2*(5 + 3*Sec[c + d*x]^2)*Tan[c + d*x])/(21*b*d*Sqrt[b*Cos[c + d*x]])","A",1
126,1,80,126,0.0399394,"\int \frac{\sec ^4(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^4/(b*Cos[c + d*x])^(3/2),x]","\frac{42 \sin (c+d x)-42 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \sec (c+d x) \left(5 \sec ^2(c+d x)+7\right)}{45 b d \sqrt{b \cos (c+d x)}}","\frac{2 b^3 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}-\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^2 d \sqrt{\cos (c+d x)}}+\frac{14 b \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}+\frac{14 \sin (c+d x)}{15 b d \sqrt{b \cos (c+d x)}}",1,"(-42*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + 42*Sin[c + d*x] + 2*Sec[c + d*x]*(7 + 5*Sec[c + d*x]^2)*Tan[c + d*x])/(45*b*d*Sqrt[b*Cos[c + d*x]])","A",1
127,1,76,128,0.052119,"\int \frac{\cos ^8(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^8/(b*Cos[c + d*x])^(5/2),x]","\frac{347 \sin (2 (c+d x))+64 \sin (4 (c+d x))+7 \sin (6 (c+d x))+480 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{1232 b^2 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{9/2}}{11 b^7 d}+\frac{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 b^5 d}+\frac{30 \sin (c+d x) \sqrt{b \cos (c+d x)}}{77 b^3 d}+\frac{30 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{77 b^2 d \sqrt{b \cos (c+d x)}}",1,"(480*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 347*Sin[2*(c + d*x)] + 64*Sin[4*(c + d*x)] + 7*Sin[6*(c + d*x)])/(1232*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
128,1,74,100,0.0568416,"\int \frac{\cos ^7(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^7/(b*Cos[c + d*x])^(5/2),x]","\frac{(38 \sin (2 (c+d x))+5 \sin (4 (c+d x))) \cos (c+d x)+168 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{180 b^2 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{7/2}}{9 b^6 d}+\frac{14 \sin (c+d x) (b \cos (c+d x))^{3/2}}{45 b^4 d}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^3 d \sqrt{\cos (c+d x)}}",1,"(168*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]*(38*Sin[2*(c + d*x)] + 5*Sin[4*(c + d*x)]))/(180*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
129,1,66,100,0.0410464,"\int \frac{\cos ^6(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^6/(b*Cos[c + d*x])^(5/2),x]","\frac{26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{84 b^2 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 b^5 d}+\frac{10 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 b^3 d}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}",1,"(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)])/(84*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
130,1,61,72,0.0326083,"\int \frac{\cos ^5(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^5/(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (2 (c+d x)) \cos (c+d x)+6 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^2 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^{3/2}}{5 b^4 d}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}",1,"(6*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]*Sin[2*(c + d*x)])/(5*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
131,1,54,72,0.0285511,"\int \frac{\cos ^4(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^4/(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 b^3 d}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)])/(3*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
132,1,41,41,0.0129974,"\int \frac{\cos ^3(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^3/(b*Cos[c + d*x])^(5/2),x]","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}",1,"(2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^3*d*Sqrt[Cos[c + d*x]])","A",1
133,1,38,41,0.0499964,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^2/(b*Cos[c + d*x])^(5/2),x]","\frac{2 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d (b \cos (c+d x))^{5/2}}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b^2 d \sqrt{b \cos (c+d x)}}",1,"(2*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2])/(d*(b*Cos[c + d*x])^(5/2))","A",1
134,1,50,68,0.0213999,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]/(b*Cos[c + d*x])^(5/2),x]","\frac{2 \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{b^2 d \sqrt{b \cos (c+d x)}}","\frac{2 \sin (c+d x)}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{b^3 d \sqrt{\cos (c+d x)}}",1,"(2*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
135,1,51,72,0.0161019,"\int \frac{1}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[(b*Cos[c + d*x])^(-5/2),x]","\frac{2 \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{3 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 \sin (c+d x)}{3 b d (b \cos (c+d x))^{3/2}}",1,"(2*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
136,1,68,97,0.0263366,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]/(b*Cos[c + d*x])^(5/2),x]","\frac{6 \sin (c+d x)-6 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \sec (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}","-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^3 d \sqrt{\cos (c+d x)}}+\frac{6 \sin (c+d x)}{5 b^2 d \sqrt{b \cos (c+d x)}}+\frac{2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}",1,"(-6*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + 6*Sin[c + d*x] + 2*Sec[c + d*x]*Tan[c + d*x])/(5*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
137,1,66,98,0.0617778,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^2/(b*Cos[c + d*x])^(5/2),x]","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \left(3 \sec ^2(c+d x)+5\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{21 b^2 d \sqrt{b \cos (c+d x)}}+\frac{10 \sin (c+d x)}{21 b d (b \cos (c+d x))^{3/2}}+\frac{2 b \sin (c+d x)}{7 d (b \cos (c+d x))^{7/2}}",1,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 2*(5 + 3*Sec[c + d*x]^2)*Tan[c + d*x])/(21*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
138,1,80,125,0.041357,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^3/(b*Cos[c + d*x])^(5/2),x]","\frac{42 \sin (c+d x)-42 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \sec (c+d x) \left(5 \sec ^2(c+d x)+7\right)}{45 b^2 d \sqrt{b \cos (c+d x)}}","-\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{15 b^3 d \sqrt{\cos (c+d x)}}+\frac{2 b^2 \sin (c+d x)}{9 d (b \cos (c+d x))^{9/2}}+\frac{14 \sin (c+d x)}{15 b^2 d \sqrt{b \cos (c+d x)}}+\frac{14 \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}",1,"(-42*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + 42*Sin[c + d*x] + 2*Sec[c + d*x]*(7 + 5*Sec[c + d*x]^2)*Tan[c + d*x])/(45*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
139,1,68,100,0.0163379,"\int \frac{1}{(b \cos (c+d x))^{7/2}} \, dx","Integrate[(b*Cos[c + d*x])^(-7/2),x]","\frac{6 \sin (c+d x)-6 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+2 \tan (c+d x) \sec (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}","-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \cos (c+d x)}}{5 b^4 d \sqrt{\cos (c+d x)}}+\frac{6 \sin (c+d x)}{5 b^3 d \sqrt{b \cos (c+d x)}}+\frac{2 \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}",1,"(-6*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + 6*Sin[c + d*x] + 2*Sec[c + d*x]*Tan[c + d*x])/(5*b^3*d*Sqrt[b*Cos[c + d*x]])","A",1
140,1,55,98,0.08402,"\int \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]],x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) \sqrt{b \cos (c+d x)}}{32 d \sqrt{\cos (c+d x)}}","\frac{3 x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{\sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}",1,"(Sqrt[b*Cos[c + d*x]]*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*Sqrt[Cos[c + d*x]])","A",1
141,1,45,70,0.0852793,"\int \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]],x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) \sqrt{b \cos (c+d x)}}{6 d \sqrt{\cos (c+d x)}}","\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(5 + Cos[2*(c + d*x)])*Sin[c + d*x])/(6*d*Sqrt[Cos[c + d*x]])","A",1
142,1,45,63,0.0533169,"\int \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]],x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \sqrt{b \cos (c+d x)}}{4 d \sqrt{\cos (c+d x)}}","\frac{x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{\sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"(Sqrt[b*Cos[c + d*x]]*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Sqrt[Cos[c + d*x]])","A",1
143,1,32,32,0.0240751,"\int \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)} \, dx","Integrate[Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]],x]","\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",1
144,1,24,24,0.0098553,"\int \frac{\sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}} \, dx","Integrate[Sqrt[b*Cos[c + d*x]]/Sqrt[Cos[c + d*x]],x]","\frac{x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]]","A",1
145,1,33,33,0.0110111,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(3/2),x]","\frac{\sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}","\frac{\sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]])","A",1
146,1,32,32,0.017289,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(5/2),x]","\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"(Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",1
147,1,52,72,0.0423753,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(7/2),x]","\frac{\sqrt{b \cos (c+d x)} \left(\sin (c+d x)+\cos ^2(c+d x) \tanh ^{-1}(\sin (c+d x))\right)}{2 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{\sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^2 + Sin[c + d*x]))/(2*d*Cos[c + d*x]^(5/2))","A",1
148,1,45,70,0.0818985,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(9/2),x]","\frac{\left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{\sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"(Sqrt[b*Cos[c + d*x]]*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*Sqrt[Cos[c + d*x]])","A",1
149,1,66,107,0.0999349,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(11/2),x]","\frac{\sqrt{b \cos (c+d x)} \left(\sin (c+d x) \left(3 \cos ^2(c+d x)+2\right)+3 \cos ^4(c+d x) \tanh ^{-1}(\sin (c+d x))\right)}{8 d \cos ^{\frac{9}{2}}(c+d x)}","\frac{3 \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{\sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{3 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(3*ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^4 + (2 + 3*Cos[c + d*x]^2)*Sin[c + d*x]))/(8*d*Cos[c + d*x]^(9/2))","A",1
150,1,55,101,0.0781693,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(3/2),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) (b \cos (c+d x))^{3/2}}{32 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{3 b x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 b \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}",1,"((b*Cos[c + d*x])^(3/2)*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*Cos[c + d*x]^(3/2))","A",1
151,1,45,72,0.1085982,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) (b \cos (c+d x))^{3/2}}{6 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{b \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(3/2)*(5 + Cos[2*(c + d*x)])*Sin[c + d*x])/(6*d*Cos[c + d*x]^(3/2))","A",1
152,1,45,65,0.051098,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2} \, dx","Integrate[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) (b \cos (c+d x))^{3/2}}{4 d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"((b*Cos[c + d*x])^(3/2)*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Cos[c + d*x]^(3/2))","A",1
153,1,32,33,0.0374736,"\int \frac{(b \cos (c+d x))^{3/2}}{\sqrt{\cos (c+d x)}} \, dx","Integrate[(b*Cos[c + d*x])^(3/2)/Sqrt[Cos[c + d*x]],x]","\frac{\sin (c+d x) (b \cos (c+d x))^{3/2}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",1
154,1,24,25,0.0145876,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(3/2),x]","\frac{x (b \cos (c+d x))^{3/2}}{\cos ^{\frac{3}{2}}(c+d x)}","\frac{b x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(x*(b*Cos[c + d*x])^(3/2))/Cos[c + d*x]^(3/2)","A",1
155,1,33,34,0.0142952,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(5/2),x]","\frac{(b \cos (c+d x))^{3/2} \tanh ^{-1}(\sin (c+d x))}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*(b*Cos[c + d*x])^(3/2))/(d*Cos[c + d*x]^(3/2))","A",1
156,1,32,33,0.016495,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(7/2),x]","\frac{\sin (c+d x) (b \cos (c+d x))^{3/2}}{d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"((b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(d*Cos[c + d*x]^(5/2))","A",1
157,1,52,74,0.0473503,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(9/2),x]","\frac{(b \cos (c+d x))^{3/2} \left(\sin (c+d x)+\cos ^2(c+d x) \tanh ^{-1}(\sin (c+d x))\right)}{2 d \cos ^{\frac{7}{2}}(c+d x)}","\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(3/2)*(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^2 + Sin[c + d*x]))/(2*d*Cos[c + d*x]^(7/2))","A",1
158,1,45,72,0.0485898,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(11/2),x]","\frac{\left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right) (b \cos (c+d x))^{3/2}}{d \cos ^{\frac{3}{2}}(c+d x)}","\frac{b \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"((b*Cos[c + d*x])^(3/2)*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*Cos[c + d*x]^(3/2))","A",1
159,1,67,110,0.0820665,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(13/2),x]","\frac{b \sqrt{b \cos (c+d x)} \left(\sin (c+d x) \left(3 \cos ^2(c+d x)+2\right)+3 \cos ^4(c+d x) \tanh ^{-1}(\sin (c+d x))\right)}{8 d \cos ^{\frac{9}{2}}(c+d x)}","\frac{3 b \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{3 b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}",1,"(b*Sqrt[b*Cos[c + d*x]]*(3*ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^4 + (2 + 3*Cos[c + d*x]^2)*Sin[c + d*x]))/(8*d*Cos[c + d*x]^(9/2))","A",1
160,1,57,116,0.1157642,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \left(3 \sin ^4(c+d x)-10 \sin ^2(c+d x)+15\right) (b \cos (c+d x))^{5/2}}{15 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin ^5(c+d x) \sqrt{b \cos (c+d x)}}{5 d \sqrt{\cos (c+d x)}}-\frac{2 b^2 \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}+\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*Sin[c + d*x]*(15 - 10*Sin[c + d*x]^2 + 3*Sin[c + d*x]^4))/(15*d*Cos[c + d*x]^(5/2))","A",1
161,1,55,107,0.0810795,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(5/2),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) (b \cos (c+d x))^{5/2}}{32 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{3 b^2 x \sqrt{b \cos (c+d x)}}{8 \sqrt{\cos (c+d x)}}+\frac{b^2 \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}{4 d}+\frac{3 b^2 \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{8 d}",1,"((b*Cos[c + d*x])^(5/2)*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*Cos[c + d*x]^(5/2))","A",1
162,1,45,76,0.12584,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2} \, dx","Integrate[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) (b \cos (c+d x))^{5/2}}{6 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}-\frac{b^2 \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*(5 + Cos[2*(c + d*x)])*Sin[c + d*x])/(6*d*Cos[c + d*x]^(5/2))","A",1
163,1,45,69,0.0670317,"\int \frac{(b \cos (c+d x))^{5/2}}{\sqrt{\cos (c+d x)}} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Sqrt[Cos[c + d*x]],x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) (b \cos (c+d x))^{5/2}}{4 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 x \sqrt{b \cos (c+d x)}}{2 \sqrt{\cos (c+d x)}}+\frac{b^2 \sin (c+d x) \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}{2 d}",1,"((b*Cos[c + d*x])^(5/2)*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Cos[c + d*x]^(5/2))","A",1
164,1,32,35,0.0489169,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(3/2),x]","\frac{\sin (c+d x) (b \cos (c+d x))^{5/2}}{d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(d*Cos[c + d*x]^(5/2))","A",1
165,1,24,27,0.0123119,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(5/2),x]","\frac{x (b \cos (c+d x))^{5/2}}{\cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(x*(b*Cos[c + d*x])^(5/2))/Cos[c + d*x]^(5/2)","A",1
166,1,33,36,0.0213525,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(7/2),x]","\frac{(b \cos (c+d x))^{5/2} \tanh ^{-1}(\sin (c+d x))}{d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*(b*Cos[c + d*x])^(5/2))/(d*Cos[c + d*x]^(5/2))","A",1
167,1,32,35,0.0182469,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(9/2),x]","\frac{\sin (c+d x) (b \cos (c+d x))^{5/2}}{d \cos ^{\frac{7}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"((b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(d*Cos[c + d*x]^(7/2))","A",1
168,1,52,78,0.0522851,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(11/2),x]","\frac{(b \cos (c+d x))^{5/2} \left(\sin (c+d x)+\cos ^2(c+d x) \tanh ^{-1}(\sin (c+d x))\right)}{2 d \cos ^{\frac{9}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{2 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^2 + Sin[c + d*x]))/(2*d*Cos[c + d*x]^(9/2))","A",1
169,1,45,76,0.0519421,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(13/2),x]","\frac{\left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right) (b \cos (c+d x))^{5/2}}{d \cos ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 d \cos ^{\frac{7}{2}}(c+d x)}+\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{2}}(c+d x)}",1,"((b*Cos[c + d*x])^(5/2)*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*Cos[c + d*x]^(5/2))","A",1
170,1,66,116,0.1013961,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{15}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(15/2),x]","\frac{(b \cos (c+d x))^{5/2} \left(\sin (c+d x) \left(3 \cos ^2(c+d x)+2\right)+3 \cos ^4(c+d x) \tanh ^{-1}(\sin (c+d x))\right)}{8 d \cos ^{\frac{13}{2}}(c+d x)}","\frac{3 b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{8 d \cos ^{\frac{5}{2}}(c+d x)}+\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{4 d \cos ^{\frac{9}{2}}(c+d x)}+\frac{3 b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\cos (c+d x)}}",1,"((b*Cos[c + d*x])^(5/2)*(3*ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^4 + (2 + 3*Cos[c + d*x]^2)*Sin[c + d*x]))/(8*d*Cos[c + d*x]^(13/2))","A",1
171,1,57,107,0.1031774,"\int \frac{\cos ^{\frac{11}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^(11/2)/Sqrt[b*Cos[c + d*x]],x]","\frac{\sin (c+d x) \left(3 \sin ^4(c+d x)-10 \sin ^2(c+d x)+15\right) \sqrt{\cos (c+d x)}}{15 d \sqrt{b \cos (c+d x)}}","\frac{\sin ^5(c+d x) \sqrt{\cos (c+d x)}}{5 d \sqrt{b \cos (c+d x)}}-\frac{2 \sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*Sin[c + d*x]*(15 - 10*Sin[c + d*x]^2 + 3*Sin[c + d*x]^4))/(15*d*Sqrt[b*Cos[c + d*x]])","A",1
172,1,55,98,0.0650351,"\int \frac{\cos ^{\frac{9}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^(9/2)/Sqrt[b*Cos[c + d*x]],x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) \sqrt{\cos (c+d x)}}{32 d \sqrt{b \cos (c+d x)}}","\frac{3 x \sqrt{\cos (c+d x)}}{8 \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 d \sqrt{b \cos (c+d x)}}+\frac{3 \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*Sqrt[b*Cos[c + d*x]])","A",1
173,1,45,70,0.0655754,"\int \frac{\cos ^{\frac{7}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^(7/2)/Sqrt[b*Cos[c + d*x]],x]","\frac{\sin (c+d x) \sqrt{\cos (c+d x)} (\cos (2 (c+d x))+5)}{6 d \sqrt{b \cos (c+d x)}}","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*(5 + Cos[2*(c + d*x)])*Sin[c + d*x])/(6*d*Sqrt[b*Cos[c + d*x]])","A",1
174,1,45,63,0.05159,"\int \frac{\cos ^{\frac{5}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^(5/2)/Sqrt[b*Cos[c + d*x]],x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \sqrt{\cos (c+d x)}}{4 d \sqrt{b \cos (c+d x)}}","\frac{x \sqrt{\cos (c+d x)}}{2 \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Sqrt[b*Cos[c + d*x]])","A",1
175,1,32,32,0.0245447,"\int \frac{\cos ^{\frac{3}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^(3/2)/Sqrt[b*Cos[c + d*x]],x]","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",1
176,1,24,24,0.0105112,"\int \frac{\sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}} \, dx","Integrate[Sqrt[Cos[c + d*x]]/Sqrt[b*Cos[c + d*x]],x]","\frac{x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}","\frac{x \sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}}",1,"(x*Sqrt[Cos[c + d*x]])/Sqrt[b*Cos[c + d*x]]","A",1
177,1,33,33,0.0114674,"\int \frac{1}{\sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}} \, dx","Integrate[1/(Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]),x]","\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}","\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(d*Sqrt[b*Cos[c + d*x]])","A",1
178,1,32,32,0.0207963,"\int \frac{1}{\cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Integrate[1/(Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{\sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}","\frac{\sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"Sin[c + d*x]/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",1
179,1,52,72,0.0351297,"\int \frac{1}{\cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Integrate[1/(Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{\sin (c+d x)+\cos ^2(c+d x) \tanh ^{-1}(\sin (c+d x))}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{\sin (c+d x)}{2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^2 + Sin[c + d*x])/(2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",1
180,1,45,70,0.0582236,"\int \frac{1}{\cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Integrate[1/(Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{\sqrt{\cos (c+d x)} \left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right)}{d \sqrt{b \cos (c+d x)}}","\frac{\sin ^3(c+d x)}{3 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x)}{d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*Sqrt[b*Cos[c + d*x]])","A",1
181,1,66,107,0.0558575,"\int \frac{1}{\cos ^{\frac{9}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Integrate[1/(Cos[c + d*x]^(9/2)*Sqrt[b*Cos[c + d*x]]),x]","\frac{\sin (c+d x) \left(3 \cos ^2(c+d x)+2\right)+3 \cos ^4(c+d x) \tanh ^{-1}(\sin (c+d x))}{8 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}","\frac{3 \sin (c+d x)}{8 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x)}{4 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{3 \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{b \cos (c+d x)}}",1,"(3*ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^4 + (2 + 3*Cos[c + d*x]^2)*Sin[c + d*x])/(8*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]])","A",1
182,1,55,107,0.0501756,"\int \frac{\cos ^{\frac{11}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^(11/2)/(b*Cos[c + d*x])^(3/2),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) \cos ^{\frac{3}{2}}(c+d x)}{32 d (b \cos (c+d x))^{3/2}}","\frac{3 x \sqrt{\cos (c+d x)}}{8 b \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b d \sqrt{b \cos (c+d x)}}+\frac{3 \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b d \sqrt{b \cos (c+d x)}}",1,"(Cos[c + d*x]^(3/2)*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*(b*Cos[c + d*x])^(3/2))","A",1
183,1,45,76,0.0480606,"\int \frac{\cos ^{\frac{9}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^(9/2)/(b*Cos[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (\cos (2 (c+d x))+5)}{6 d (b \cos (c+d x))^{3/2}}","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b d \sqrt{b \cos (c+d x)}}",1,"(Cos[c + d*x]^(3/2)*(5 + Cos[2*(c + d*x)])*Sin[c + d*x])/(6*d*(b*Cos[c + d*x])^(3/2))","A",1
184,1,45,69,0.0368663,"\int \frac{\cos ^{\frac{7}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^(7/2)/(b*Cos[c + d*x])^(3/2),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \cos ^{\frac{3}{2}}(c+d x)}{4 d (b \cos (c+d x))^{3/2}}","\frac{x \sqrt{\cos (c+d x)}}{2 b \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b d \sqrt{b \cos (c+d x)}}",1,"(Cos[c + d*x]^(3/2)*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*(b*Cos[c + d*x])^(3/2))","A",1
185,1,32,35,0.0350383,"\int \frac{\cos ^{\frac{5}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^(5/2)/(b*Cos[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{d (b \cos (c+d x))^{3/2}}","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}",1,"(Cos[c + d*x]^(3/2)*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(3/2))","A",1
186,1,24,27,0.0116522,"\int \frac{\cos ^{\frac{3}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^(3/2)/(b*Cos[c + d*x])^(3/2),x]","\frac{x \cos ^{\frac{3}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}}","\frac{x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}",1,"(x*Cos[c + d*x]^(3/2))/(b*Cos[c + d*x])^(3/2)","A",1
187,1,33,36,0.0124929,"\int \frac{\sqrt{\cos (c+d x)}}{(b \cos (c+d x))^{3/2}} \, dx","Integrate[Sqrt[Cos[c + d*x]]/(b*Cos[c + d*x])^(3/2),x]","\frac{\cos ^{\frac{3}{2}}(c+d x) \tanh ^{-1}(\sin (c+d x))}{d (b \cos (c+d x))^{3/2}}","\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^(3/2))/(d*(b*Cos[c + d*x])^(3/2))","A",1
188,1,32,35,0.0122058,"\int \frac{1}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2}} \, dx","Integrate[1/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2)),x]","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{d (b \cos (c+d x))^{3/2}}","\frac{\sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(3/2))","A",1
189,1,52,78,0.0283905,"\int \frac{1}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Integrate[1/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{\sin (c+d x)+\cos ^2(c+d x) \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2}}","\frac{\sin (c+d x)}{2 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^2 + Sin[c + d*x])/(2*d*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2))","A",1
190,1,45,76,0.0225916,"\int \frac{1}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Integrate[1/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{\cos ^{\frac{3}{2}}(c+d x) \left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right)}{d (b \cos (c+d x))^{3/2}}","\frac{\sin ^3(c+d x)}{3 b d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x)}{b d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"(Cos[c + d*x]^(3/2)*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*(b*Cos[c + d*x])^(3/2))","A",1
191,1,66,116,0.0387845,"\int \frac{1}{\cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Integrate[1/(Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^(3/2)),x]","\frac{\sin (c+d x) \left(3 \cos ^2(c+d x)+2\right)+3 \cos ^4(c+d x) \tanh ^{-1}(\sin (c+d x))}{8 d \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{3/2}}","\frac{3 \sin (c+d x)}{8 b d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x)}{4 b d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{3 \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b d \sqrt{b \cos (c+d x)}}",1,"(3*ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^4 + (2 + 3*Cos[c + d*x]^2)*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(3/2))","A",1
192,1,58,107,0.0689889,"\int \frac{\cos ^{\frac{13}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^(13/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) \sqrt{\cos (c+d x)}}{32 b^2 d \sqrt{b \cos (c+d x)}}","\frac{3 x \sqrt{\cos (c+d x)}}{8 b^2 \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x) \cos ^{\frac{7}{2}}(c+d x)}{4 b^2 d \sqrt{b \cos (c+d x)}}+\frac{3 \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{8 b^2 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
193,1,48,76,0.043064,"\int \frac{\cos ^{\frac{11}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^(11/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \sqrt{\cos (c+d x)} (\cos (2 (c+d x))+5)}{6 b^2 d \sqrt{b \cos (c+d x)}}","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\cos (c+d x)}}{3 b^2 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*(5 + Cos[2*(c + d*x)])*Sin[c + d*x])/(6*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
194,1,48,69,0.0395011,"\int \frac{\cos ^{\frac{9}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^(9/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \sqrt{\cos (c+d x)}}{4 b^2 d \sqrt{b \cos (c+d x)}}","\frac{x \sqrt{\cos (c+d x)}}{2 b^2 \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{2 b^2 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
195,1,35,35,0.021283,"\int \frac{\cos ^{\frac{7}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^(7/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{b^2 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",1
196,1,24,27,0.0113847,"\int \frac{\cos ^{\frac{5}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^(5/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{x \cos ^{\frac{5}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}}","\frac{x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}",1,"(x*Cos[c + d*x]^(5/2))/(b*Cos[c + d*x])^(5/2)","A",1
197,1,33,36,0.01921,"\int \frac{\cos ^{\frac{3}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^(3/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{\cos ^{\frac{5}{2}}(c+d x) \tanh ^{-1}(\sin (c+d x))}{d (b \cos (c+d x))^{5/2}}","\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^(5/2))/(d*(b*Cos[c + d*x])^(5/2))","A",1
198,1,32,35,0.0132405,"\int \frac{\sqrt{\cos (c+d x)}}{(b \cos (c+d x))^{5/2}} \, dx","Integrate[Sqrt[Cos[c + d*x]]/(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \cos ^{\frac{3}{2}}(c+d x)}{d (b \cos (c+d x))^{5/2}}","\frac{\sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"(Cos[c + d*x]^(3/2)*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(5/2))","A",1
199,1,55,78,0.0415196,"\int \frac{1}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2}} \, dx","Integrate[1/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2)),x]","\frac{\sqrt{b \cos (c+d x)} \left(\sin (c+d x)+\cos ^2(c+d x) \tanh ^{-1}(\sin (c+d x))\right)}{2 b^3 d \cos ^{\frac{5}{2}}(c+d x)}","\frac{\sin (c+d x)}{2 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[b*Cos[c + d*x]]*(ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^2 + Sin[c + d*x]))/(2*b^3*d*Cos[c + d*x]^(5/2))","A",1
200,1,45,76,0.0251722,"\int \frac{1}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Integrate[1/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(5/2)),x]","\frac{\cos ^{\frac{5}{2}}(c+d x) \left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right)}{d (b \cos (c+d x))^{5/2}}","\frac{\sin ^3(c+d x)}{3 b^2 d \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}}",1,"(Cos[c + d*x]^(5/2)*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*(b*Cos[c + d*x])^(5/2))","A",1
201,1,66,116,0.0430483,"\int \frac{1}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Integrate[1/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(5/2)),x]","\frac{\sin (c+d x) \left(3 \cos ^2(c+d x)+2\right)+3 \cos ^4(c+d x) \tanh ^{-1}(\sin (c+d x))}{8 d \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{5/2}}","\frac{3 \sin (c+d x)}{8 b^2 d \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{\sin (c+d x)}{4 b^2 d \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}}+\frac{3 \sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 b^2 d \sqrt{b \cos (c+d x)}}",1,"(3*ArcTanh[Sin[c + d*x]]*Cos[c + d*x]^4 + (2 + 3*Cos[c + d*x]^2)*Sin[c + d*x])/(8*d*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(5/2))","A",1
202,1,82,82,0.099469,"\int \cos ^m(c+d x) \sqrt[3]{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^m*(b*Cos[c + d*x])^(1/3),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{4}{3}\right);\frac{1}{2} \left(m+\frac{10}{3}\right);\cos ^2(c+d x)\right)}{d \left(m+\frac{4}{3}\right)}","-\frac{3 \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+4);\frac{1}{6} (3 m+10);\cos ^2(c+d x)\right)}{d (3 m+4) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(1/3)*Csc[c + d*x]*Hypergeometric2F1[1/2, (4/3 + m)/2, (10/3 + m)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(4/3 + m)))","A",1
203,1,63,58,0.0584527,"\int \cos ^2(c+d x) \sqrt[3]{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]^2*(b*Cos[c + d*x])^(1/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cos ^2(c+d x) \cot (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cos[c + d*x]^2*(b*Cos[c + d*x])^(1/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(10*d)","A",1
204,1,58,58,0.0512153,"\int \cos (c+d x) \sqrt[3]{b \cos (c+d x)} \, dx","Integrate[Cos[c + d*x]*(b*Cos[c + d*x])^(1/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 b d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(4/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(7*b*d)","A",1
205,1,55,58,0.0361799,"\int \sqrt[3]{b \cos (c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^(1/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 b d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(1/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(4*d)","A",1
206,1,54,53,0.0461369,"\int \sqrt[3]{b \cos (c+d x)} \sec (c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(1/3)*Sec[c + d*x],x]","-\frac{3 b \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d (b \cos (c+d x))^{2/3}}","-\frac{3 \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}",1,"(-3*b*Cot[c + d*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(b*Cos[c + d*x])^(2/3))","A",1
207,1,56,56,0.0584686,"\int \sqrt[3]{b \cos (c+d x)} \sec ^2(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(1/3)*Sec[c + d*x]^2,x]","\frac{3 b \sqrt{\sin ^2(c+d x)} \csc (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d (b \cos (c+d x))^{2/3}}","\frac{3 b \sin (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"(3*b*Csc[c + d*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(2*d*(b*Cos[c + d*x])^(2/3))","A",1
208,1,63,58,0.0426991,"\int \sqrt[3]{b \cos (c+d x)} \sec ^3(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(1/3)*Sec[c + d*x]^3,x]","\frac{3 \sqrt{\sin ^2(c+d x)} \csc (c+d x) \sec ^2(c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};\cos ^2(c+d x)\right)}{5 d}","\frac{3 b^2 \sin (c+d x) \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{5/3}}",1,"(3*(b*Cos[c + d*x])^(1/3)*Csc[c + d*x]*Hypergeometric2F1[-5/6, 1/2, 1/6, Cos[c + d*x]^2]*Sec[c + d*x]^2*Sqrt[Sin[c + d*x]^2])/(5*d)","A",1
209,1,82,82,0.1119479,"\int \cos ^m(c+d x) (b \cos (c+d x))^{2/3} \, dx","Integrate[Cos[c + d*x]^m*(b*Cos[c + d*x])^(2/3),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{5}{3}\right);\frac{1}{2} \left(m+\frac{11}{3}\right);\cos ^2(c+d x)\right)}{d \left(m+\frac{5}{3}\right)}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{2/3} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+5);\frac{1}{6} (3 m+11);\cos ^2(c+d x)\right)}{d (3 m+5) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(2/3)*Csc[c + d*x]*Hypergeometric2F1[1/2, (5/3 + m)/2, (11/3 + m)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(5/3 + m)))","A",1
210,1,63,58,0.0568709,"\int \cos ^2(c+d x) (b \cos (c+d x))^{2/3} \, dx","Integrate[Cos[c + d*x]^2*(b*Cos[c + d*x])^(2/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cos ^2(c+d x) \cot (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{11/3} \, _2F_1\left(\frac{1}{2},\frac{11}{6};\frac{17}{6};\cos ^2(c+d x)\right)}{11 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cos[c + d*x]^2*(b*Cos[c + d*x])^(2/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 11/6, 17/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(11*d)","A",1
211,1,58,58,0.0508665,"\int \cos (c+d x) (b \cos (c+d x))^{2/3} \, dx","Integrate[Cos[c + d*x]*(b*Cos[c + d*x])^(2/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(5/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(8*b*d)","A",1
212,1,55,58,0.0353588,"\int (b \cos (c+d x))^{2/3} \, dx","Integrate[(b*Cos[c + d*x])^(2/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(2/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(5*d)","A",1
213,1,56,55,0.0445838,"\int (b \cos (c+d x))^{2/3} \sec (c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(2/3)*Sec[c + d*x],x]","-\frac{3 b \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt[3]{b \cos (c+d x)}}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*b*Cot[c + d*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(2*d*(b*Cos[c + d*x])^(1/3))","A",1
214,1,54,54,0.0549732,"\int (b \cos (c+d x))^{2/3} \sec ^2(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(2/3)*Sec[c + d*x]^2,x]","\frac{3 b \sqrt{\sin ^2(c+d x)} \csc (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt[3]{b \cos (c+d x)}}","\frac{3 b \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*b*Csc[c + d*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(b*Cos[c + d*x])^(1/3))","A",1
215,1,63,58,0.0424942,"\int (b \cos (c+d x))^{2/3} \sec ^3(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(2/3)*Sec[c + d*x]^3,x]","\frac{3 \sqrt{\sin ^2(c+d x)} \csc (c+d x) \sec ^2(c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d}","\frac{3 b^2 \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}",1,"(3*(b*Cos[c + d*x])^(2/3)*Csc[c + d*x]*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sec[c + d*x]^2*Sqrt[Sin[c + d*x]^2])/(4*d)","A",1
216,1,82,83,0.1656269,"\int \cos ^m(c+d x) (b \cos (c+d x))^{4/3} \, dx","Integrate[Cos[c + d*x]^m*(b*Cos[c + d*x])^(4/3),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) (b \cos (c+d x))^{4/3} \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{7}{3}\right);\frac{1}{2} \left(m+\frac{13}{3}\right);\cos ^2(c+d x)\right)}{d \left(m+\frac{7}{3}\right)}","-\frac{3 b \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \cos ^{m+2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+7);\frac{1}{6} (3 m+13);\cos ^2(c+d x)\right)}{d (3 m+7) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(4/3)*Csc[c + d*x]*Hypergeometric2F1[1/2, (7/3 + m)/2, (13/3 + m)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(7/3 + m)))","A",1
217,1,63,58,0.0732463,"\int \cos ^2(c+d x) (b \cos (c+d x))^{4/3} \, dx","Integrate[Cos[c + d*x]^2*(b*Cos[c + d*x])^(4/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cos ^2(c+d x) \cot (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{13 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{13/3} \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{13 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cos[c + d*x]^2*(b*Cos[c + d*x])^(4/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 13/6, 19/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(13*d)","A",1
218,1,58,58,0.067577,"\int \cos (c+d x) (b \cos (c+d x))^{4/3} \, dx","Integrate[Cos[c + d*x]*(b*Cos[c + d*x])^(4/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 b d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{10/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(7/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(10*b*d)","A",1
219,1,55,58,0.0026655,"\int (b \cos (c+d x))^{4/3} \, dx","Integrate[(b*Cos[c + d*x])^(4/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(4/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(7*d)","A",1
220,1,56,55,0.0047321,"\int (b \cos (c+d x))^{4/3} \sec (c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(4/3)*Sec[c + d*x],x]","-\frac{3 b \sqrt{\sin ^2(c+d x)} \cot (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*b*(b*Cos[c + d*x])^(1/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(4*d)","A",1
221,1,56,54,0.0087519,"\int (b \cos (c+d x))^{4/3} \sec ^2(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(4/3)*Sec[c + d*x]^2,x]","-\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d (b \cos (c+d x))^{2/3}}","-\frac{3 b \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)}}",1,"(-3*b^2*Cot[c + d*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(b*Cos[c + d*x])^(2/3))","A",1
222,1,58,58,0.0557002,"\int (b \cos (c+d x))^{4/3} \sec ^3(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^(4/3)*Sec[c + d*x]^3,x]","\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \csc (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d (b \cos (c+d x))^{2/3}}","\frac{3 b^2 \sin (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"(3*b^2*Csc[c + d*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(2*d*(b*Cos[c + d*x])^(2/3))","A",1
223,1,82,82,0.107765,"\int \frac{\cos ^m(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^m/(b*Cos[c + d*x])^(1/3),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{2}{3}\right);\frac{1}{2} \left(m+\frac{8}{3}\right);\cos ^2(c+d x)\right)}{d \left(m+\frac{2}{3}\right) \sqrt[3]{b \cos (c+d x)}}","-\frac{3 \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+2);\frac{1}{6} (3 m+8);\cos ^2(c+d x)\right)}{d (3 m+2) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"-((Cos[c + d*x]^(1 + m)*Csc[c + d*x]*Hypergeometric2F1[1/2, (2/3 + m)/2, (8/3 + m)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(2/3 + m)*(b*Cos[c + d*x])^(1/3)))","A",1
224,1,63,58,0.0678322,"\int \frac{\cos ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]^2/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cos ^2(c+d x) \cot (c+d x) \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 d \sqrt[3]{b \cos (c+d x)}}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cos[c + d*x]^2*Cot[c + d*x]*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(8*d*(b*Cos[c + d*x])^(1/3))","A",1
225,1,58,58,0.0045954,"\int \frac{\cos (c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Integrate[Cos[c + d*x]/(b*Cos[c + d*x])^(1/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(2/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(5*b*d)","A",1
226,1,55,58,0.0031437,"\int \frac{1}{\sqrt[3]{b \cos (c+d x)}} \, dx","Integrate[(b*Cos[c + d*x])^(-1/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 d \sqrt[3]{b \cos (c+d x)}}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 b d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cot[c + d*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(2*d*(b*Cos[c + d*x])^(1/3))","A",1
227,1,54,53,0.0435952,"\int \frac{\sec (c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]/(b*Cos[c + d*x])^(1/3),x]","\frac{3 b \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d (b \cos (c+d x))^{4/3}}","\frac{3 \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*b*Cot[c + d*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(b*Cos[c + d*x])^(4/3))","A",1
228,1,58,56,0.0482578,"\int \frac{\sec ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]^2/(b*Cos[c + d*x])^(1/3),x]","\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d (b \cos (c+d x))^{7/3}}","\frac{3 b \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}",1,"(3*b^2*Cot[c + d*x]*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(4*d*(b*Cos[c + d*x])^(7/3))","A",1
229,1,58,58,0.100597,"\int \frac{\sec ^3(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Integrate[Sec[c + d*x]^3/(b*Cos[c + d*x])^(1/3),x]","\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \csc (c+d x) \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\cos ^2(c+d x)\right)}{7 d (b \cos (c+d x))^{7/3}}","\frac{3 b^2 \sin (c+d x) \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{7/3}}",1,"(3*b^2*Csc[c + d*x]*Hypergeometric2F1[-7/6, 1/2, -1/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(7*d*(b*Cos[c + d*x])^(7/3))","A",1
230,1,82,82,0.1026734,"\int \frac{\cos ^m(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Integrate[Cos[c + d*x]^m/(b*Cos[c + d*x])^(2/3),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{1}{3}\right);\frac{1}{2} \left(m+\frac{7}{3}\right);\cos ^2(c+d x)\right)}{d \left(m+\frac{1}{3}\right) (b \cos (c+d x))^{2/3}}","-\frac{3 \sin (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m+1);\frac{1}{6} (3 m+7);\cos ^2(c+d x)\right)}{d (3 m+1) \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"-((Cos[c + d*x]^(1 + m)*Csc[c + d*x]*Hypergeometric2F1[1/2, (1/3 + m)/2, (7/3 + m)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(1/3 + m)*(b*Cos[c + d*x])^(2/3)))","A",1
231,1,63,58,0.0691239,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Integrate[Cos[c + d*x]^2/(b*Cos[c + d*x])^(2/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cos ^2(c+d x) \cot (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d (b \cos (c+d x))^{2/3}}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cos[c + d*x]^2*Cot[c + d*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(7*d*(b*Cos[c + d*x])^(2/3))","A",1
232,1,58,58,0.0041643,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Integrate[Cos[c + d*x]/(b*Cos[c + d*x])^(2/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 b d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\cos ^2(c+d x)\right)}{4 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(1/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(4*b*d)","A",1
233,1,53,56,0.003394,"\int \frac{1}{(b \cos (c+d x))^{2/3}} \, dx","Integrate[(b*Cos[c + d*x])^(-2/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{d (b \cos (c+d x))^{2/3}}","-\frac{3 \sin (c+d x) \sqrt[3]{b \cos (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cot[c + d*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(b*Cos[c + d*x])^(2/3))","A",1
234,1,56,55,0.0439173,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Integrate[Sec[c + d*x]/(b*Cos[c + d*x])^(2/3),x]","\frac{3 b \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d (b \cos (c+d x))^{5/3}}","\frac{3 \sin (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{2/3}}",1,"(3*b*Cot[c + d*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(2*d*(b*Cos[c + d*x])^(5/3))","A",1
235,1,58,56,0.0524738,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Integrate[Sec[c + d*x]^2/(b*Cos[c + d*x])^(2/3),x]","\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};\cos ^2(c+d x)\right)}{5 d (b \cos (c+d x))^{8/3}}","\frac{3 b \sin (c+d x) \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{5/3}}",1,"(3*b^2*Cot[c + d*x]*Hypergeometric2F1[-5/6, 1/2, 1/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(5*d*(b*Cos[c + d*x])^(8/3))","A",1
236,1,58,58,0.0974886,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Integrate[Sec[c + d*x]^3/(b*Cos[c + d*x])^(2/3),x]","\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \csc (c+d x) \, _2F_1\left(-\frac{4}{3},\frac{1}{2};-\frac{1}{3};\cos ^2(c+d x)\right)}{8 d (b \cos (c+d x))^{8/3}}","\frac{3 b^2 \sin (c+d x) \, _2F_1\left(-\frac{4}{3},\frac{1}{2};-\frac{1}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{8/3}}",1,"(3*b^2*Csc[c + d*x]*Hypergeometric2F1[-4/3, 1/2, -1/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(8*d*(b*Cos[c + d*x])^(8/3))","A",1
237,1,82,83,0.1026,"\int \frac{\cos ^m(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Integrate[Cos[c + d*x]^m/(b*Cos[c + d*x])^(4/3),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) \cos ^{m+1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m-\frac{1}{3}\right);\frac{1}{2} \left(m+\frac{5}{3}\right);\cos ^2(c+d x)\right)}{d \left(m-\frac{1}{3}\right) (b \cos (c+d x))^{4/3}}","\frac{3 \sin (c+d x) \cos ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (3 m-1);\frac{1}{6} (3 m+5);\cos ^2(c+d x)\right)}{b d (1-3 m) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"-((Cos[c + d*x]^(1 + m)*Csc[c + d*x]*Hypergeometric2F1[1/2, (-1/3 + m)/2, (5/3 + m)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(-1/3 + m)*(b*Cos[c + d*x])^(4/3)))","A",1
238,1,58,58,0.0043309,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Integrate[Cos[c + d*x]^2/(b*Cos[c + d*x])^(4/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^2 d}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 b^3 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(2/3)*Cot[c + d*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(5*b^2*d)","A",1
239,1,58,58,0.0077834,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Integrate[Cos[c + d*x]/(b*Cos[c + d*x])^(4/3),x]","-\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 b d \sqrt[3]{b \cos (c+d x)}}","-\frac{3 \sin (c+d x) (b \cos (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\cos ^2(c+d x)\right)}{2 b^2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*Cot[c + d*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(2*b*d*(b*Cos[c + d*x])^(1/3))","A",1
240,1,53,56,0.0031406,"\int \frac{1}{(b \cos (c+d x))^{4/3}} \, dx","Integrate[(b*Cos[c + d*x])^(-4/3),x]","\frac{3 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{d (b \cos (c+d x))^{4/3}}","\frac{3 \sin (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\cos ^2(c+d x)\right)}{b d \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \cos (c+d x)}}",1,"(3*Cot[c + d*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(b*Cos[c + d*x])^(4/3))","A",1
241,1,56,55,0.008255,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Integrate[Sec[c + d*x]/(b*Cos[c + d*x])^(4/3),x]","\frac{3 b \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d (b \cos (c+d x))^{7/3}}","\frac{3 \sin (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{4/3}}",1,"(3*b*Cot[c + d*x]*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(4*d*(b*Cos[c + d*x])^(7/3))","A",1
242,1,58,56,0.0580556,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Integrate[Sec[c + d*x]^2/(b*Cos[c + d*x])^(4/3),x]","\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\cos ^2(c+d x)\right)}{7 d (b \cos (c+d x))^{10/3}}","\frac{3 b \sin (c+d x) \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{7/3}}",1,"(3*b^2*Cot[c + d*x]*Hypergeometric2F1[-7/6, 1/2, -1/6, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(7*d*(b*Cos[c + d*x])^(10/3))","A",1
243,1,58,58,0.1036678,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Integrate[Sec[c + d*x]^3/(b*Cos[c + d*x])^(4/3),x]","\frac{3 b^2 \sqrt{\sin ^2(c+d x)} \csc (c+d x) \, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};\cos ^2(c+d x)\right)}{10 d (b \cos (c+d x))^{10/3}}","\frac{3 b^2 \sin (c+d x) \, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)} (b \cos (c+d x))^{10/3}}",1,"(3*b^2*Csc[c + d*x]*Hypergeometric2F1[-5/3, 1/2, -2/3, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(10*d*(b*Cos[c + d*x])^(10/3))","A",1
244,1,77,82,0.0839309,"\int (a \cos (e+f x))^m (b \cos (e+f x))^n \, dx","Integrate[(a*Cos[e + f*x])^m*(b*Cos[e + f*x])^n,x]","-\frac{\sqrt{\sin ^2(e+f x)} \cot (e+f x) (a \cos (e+f x))^m (b \cos (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(e+f x)\right)}{f (m+n+1)}","-\frac{\sin (e+f x) (a \cos (e+f x))^{m+1} (b \cos (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\cos ^2(e+f x)\right)}{a f (m+n+1) \sqrt{\sin ^2(e+f x)}}",1,"-(((a*Cos[e + f*x])^m*(b*Cos[e + f*x])^n*Cot[e + f*x]*Hypergeometric2F1[1/2, (1 + m + n)/2, (3 + m + n)/2, Cos[e + f*x]^2]*Sqrt[Sin[e + f*x]^2])/(f*(1 + m + n)))","A",1
245,1,72,69,0.0722236,"\int \cos ^2(c+d x) (b \cos (c+d x))^n \, dx","Integrate[Cos[c + d*x]^2*(b*Cos[c + d*x])^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cos ^2(c+d x) \cot (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{d (n+3)}","-\frac{\sin (c+d x) (b \cos (c+d x))^{n+3} \, _2F_1\left(\frac{1}{2},\frac{n+3}{2};\frac{n+5}{2};\cos ^2(c+d x)\right)}{b^3 d (n+3) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]^2*(b*Cos[c + d*x])^n*Cot[c + d*x]*Hypergeometric2F1[1/2, (3 + n)/2, (5 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(3 + n)))","A",1
246,1,70,69,0.0509426,"\int \cos (c+d x) (b \cos (c+d x))^n \, dx","Integrate[Cos[c + d*x]*(b*Cos[c + d*x])^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cos (c+d x) \cot (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{d (n+2)}","-\frac{\sin (c+d x) (b \cos (c+d x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\cos ^2(c+d x)\right)}{b^2 d (n+2) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]*(b*Cos[c + d*x])^n*Cot[c + d*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(2 + n)))","A",1
247,1,64,69,0.0415331,"\int (b \cos (c+d x))^n \, dx","Integrate[(b*Cos[c + d*x])^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{d (n+1)}","-\frac{\sin (c+d x) (b \cos (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}",1,"-(((b*Cos[c + d*x])^n*Cot[c + d*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(1 + n)))","A",1
248,1,63,60,0.0551178,"\int (b \cos (c+d x))^n \sec (c+d x) \, dx","Integrate[(b*Cos[c + d*x])^n*Sec[c + d*x],x]","-\frac{b \sqrt{\sin ^2(c+d x)} \cot (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n}","-\frac{\sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}",1,"-((b*(b*Cos[c + d*x])^(-1 + n)*Cot[c + d*x]*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*n))","A",1
249,1,67,68,0.0634136,"\int (b \cos (c+d x))^n \sec ^2(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^n*Sec[c + d*x]^2,x]","-\frac{b \sqrt{\sin ^2(c+d x)} \csc (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (n-1)}","\frac{b \sin (c+d x) (b \cos (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}",1,"-((b*(b*Cos[c + d*x])^(-1 + n)*Csc[c + d*x]*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(-1 + n)))","A",1
250,1,70,68,0.0464602,"\int (b \cos (c+d x))^n \sec ^3(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^n*Sec[c + d*x]^3,x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) \sec ^2(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (n-2)}","\frac{b^2 \sin (c+d x) (b \cos (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}",1,"-(((b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (-2 + n)/2, n/2, Cos[c + d*x]^2]*Sec[c + d*x]^2*Sqrt[Sin[c + d*x]^2])/(d*(-2 + n)))","A",1
251,1,72,70,0.0529496,"\int (b \cos (c+d x))^n \sec ^4(c+d x) \, dx","Integrate[(b*Cos[c + d*x])^n*Sec[c + d*x]^4,x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) \sec ^3(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n-3}{2};\frac{n-1}{2};\cos ^2(c+d x)\right)}{d (n-3)}","\frac{b^3 \sin (c+d x) (b \cos (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{n-3}{2};\frac{n-1}{2};\cos ^2(c+d x)\right)}{d (3-n) \sqrt{\sin ^2(c+d x)}}",1,"-(((b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (-3 + n)/2, (-1 + n)/2, Cos[c + d*x]^2]*Sec[c + d*x]^3*Sqrt[Sin[c + d*x]^2])/(d*(-3 + n)))","A",1
252,1,80,80,0.130044,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, dx","Integrate[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cos ^{\frac{7}{2}}(c+d x) \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n+\frac{7}{2}\right);\frac{1}{2} \left(n+\frac{11}{2}\right);\cos ^2(c+d x)\right)}{d \left(n+\frac{7}{2}\right)}","-\frac{2 \sin (c+d x) \cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+7);\frac{1}{4} (2 n+11);\cos ^2(c+d x)\right)}{d (2 n+7) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (7/2 + n)/2, (11/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(7/2 + n)))","A",1
253,1,80,80,0.1102838,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, dx","Integrate[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x) \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n+\frac{5}{2}\right);\frac{1}{2} \left(n+\frac{9}{2}\right);\cos ^2(c+d x)\right)}{d \left(n+\frac{5}{2}\right)}","-\frac{2 \sin (c+d x) \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+5);\frac{1}{4} (2 n+9);\cos ^2(c+d x)\right)}{d (2 n+5) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (5/2 + n)/2, (9/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(5/2 + n)))","A",1
254,1,80,80,0.0837877,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, dx","Integrate[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n,x]","-\frac{\sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x) \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n+\frac{3}{2}\right);\frac{1}{2} \left(n+\frac{7}{2}\right);\cos ^2(c+d x)\right)}{d \left(n+\frac{3}{2}\right)}","-\frac{2 \sin (c+d x) \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}",1,"-((Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (3/2 + n)/2, (7/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(3/2 + n)))","A",1
255,1,80,80,0.054286,"\int \frac{(b \cos (c+d x))^n}{\sqrt{\cos (c+d x)}} \, dx","Integrate[(b*Cos[c + d*x])^n/Sqrt[Cos[c + d*x]],x]","-\frac{\sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)} \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n+\frac{1}{2}\right);\frac{1}{2} \left(n+\frac{5}{2}\right);\cos ^2(c+d x)\right)}{d \left(n+\frac{1}{2}\right)}","-\frac{2 \sin (c+d x) \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}",1,"-((Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (1/2 + n)/2, (5/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(1/2 + n)))","A",1
256,1,80,80,0.0776405,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^n/Cos[c + d*x]^(3/2),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n-\frac{1}{2}\right);\frac{1}{2} \left(n+\frac{3}{2}\right);\cos ^2(c+d x)\right)}{d \left(n-\frac{1}{2}\right) \sqrt{\cos (c+d x)}}","\frac{2 \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-1);\frac{1}{4} (2 n+3);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\cos (c+d x)}}",1,"-(((b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (-1/2 + n)/2, (3/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(-1/2 + n)*Sqrt[Cos[c + d*x]]))","A",1
257,1,80,80,0.0821885,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^n/Cos[c + d*x]^(5/2),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n-\frac{3}{2}\right);\frac{1}{2} \left(n+\frac{1}{2}\right);\cos ^2(c+d x)\right)}{d \left(n-\frac{3}{2}\right) \cos ^{\frac{3}{2}}(c+d x)}","\frac{2 \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{3}{2}}(c+d x)}",1,"-(((b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (-3/2 + n)/2, (1/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(-3/2 + n)*Cos[c + d*x]^(3/2)))","A",1
258,1,80,80,0.0804602,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^n/Cos[c + d*x]^(7/2),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n-\frac{5}{2}\right);\frac{1}{2} \left(n-\frac{1}{2}\right);\cos ^2(c+d x)\right)}{d \left(n-\frac{5}{2}\right) \cos ^{\frac{5}{2}}(c+d x)}","\frac{2 \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-5);\frac{1}{4} (2 n-1);\cos ^2(c+d x)\right)}{d (5-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{5}{2}}(c+d x)}",1,"-(((b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (-5/2 + n)/2, (-1/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(-5/2 + n)*Cos[c + d*x]^(5/2)))","A",1
259,1,80,80,0.0832757,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Integrate[(b*Cos[c + d*x])^n/Cos[c + d*x]^(9/2),x]","-\frac{\sqrt{\sin ^2(c+d x)} \csc (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n-\frac{7}{2}\right);\frac{1}{2} \left(n-\frac{3}{2}\right);\cos ^2(c+d x)\right)}{d \left(n-\frac{7}{2}\right) \cos ^{\frac{7}{2}}(c+d x)}","\frac{2 \sin (c+d x) (b \cos (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (2 n-7);\frac{1}{4} (2 n-3);\cos ^2(c+d x)\right)}{d (7-2 n) \sqrt{\sin ^2(c+d x)} \cos ^{\frac{7}{2}}(c+d x)}",1,"-(((b*Cos[c + d*x])^n*Csc[c + d*x]*Hypergeometric2F1[1/2, (-7/2 + n)/2, (-3/2 + n)/2, Cos[c + d*x]^2]*Sqrt[Sin[c + d*x]^2])/(d*(-7/2 + n)*Cos[c + d*x]^(7/2)))","A",1
260,1,89,88,10.9064392,"\int (a \cos (e+f x))^m (b \sec (e+f x))^n \, dx","Integrate[(a*Cos[e + f*x])^m*(b*Sec[e + f*x])^n,x]","-\frac{\sin (e+f x) \cos (e+f x) (a \cos (e+f x))^m (b \sec (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m-n+1);\frac{1}{2} (m-n+3);\cos ^2(e+f x)\right)}{f (m-n+1) \sqrt{\sin ^2(e+f x)}}","-\frac{\sin (e+f x) (a \cos (e+f x))^{m+1} (b \sec (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m-n+1);\frac{1}{2} (m-n+3);\cos ^2(e+f x)\right)}{a f (m-n+1) \sqrt{\sin ^2(e+f x)}}",1,"-((Cos[e + f*x]*(a*Cos[e + f*x])^m*Hypergeometric2F1[1/2, (1 + m - n)/2, (3 + m - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^n*Sin[e + f*x])/(f*(1 + m - n)*Sqrt[Sin[e + f*x]^2]))","A",1
261,1,15,15,0.0202339,"\int \cos (a+b x) \sqrt{\csc (a+b x)} \, dx","Integrate[Cos[a + b*x]*Sqrt[Csc[a + b*x]],x]","\frac{2}{b \sqrt{\csc (a+b x)}}","\frac{2}{b \sqrt{\csc (a+b x)}}",1,"2/(b*Sqrt[Csc[a + b*x]])","A",1
262,1,17,17,0.0231547,"\int \frac{\cos (a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Cos[a + b*x]/Sqrt[Csc[a + b*x]],x]","\frac{2}{3 b \csc ^{\frac{3}{2}}(a+b x)}","\frac{2}{3 b \csc ^{\frac{3}{2}}(a+b x)}",1,"2/(3*b*Csc[a + b*x]^(3/2))","A",1
263,1,53,67,0.0973397,"\int \cos ^2(a+b x) \sqrt{\csc (a+b x)} \, dx","Integrate[Cos[a + b*x]^2*Sqrt[Csc[a + b*x]],x]","\frac{\sqrt{\csc (a+b x)} \left(\sin (2 (a+b x))-4 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{4} (-2 a-2 b x+\pi )\right|2\right)\right)}{3 b}","\frac{2 \cos (a+b x)}{3 b \sqrt{\csc (a+b x)}}+\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}",1,"(Sqrt[Csc[a + b*x]]*(-4*EllipticF[(-2*a + Pi - 2*b*x)/4, 2]*Sqrt[Sin[a + b*x]] + Sin[2*(a + b*x)]))/(3*b)","A",1
264,1,61,67,0.1450575,"\int \frac{\cos ^2(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Cos[a + b*x]^2/Sqrt[Csc[a + b*x]],x]","-\frac{2 \sqrt{\csc (a+b x)} \left(2 \sqrt{\sin (a+b x)} E\left(\left.\frac{1}{4} (-2 a-2 b x+\pi )\right|2\right)-\sin ^2(a+b x) \cos (a+b x)\right)}{5 b}","\frac{2 \cos (a+b x)}{5 b \csc ^{\frac{3}{2}}(a+b x)}+\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}",1,"(-2*Sqrt[Csc[a + b*x]]*(2*EllipticE[(-2*a + Pi - 2*b*x)/4, 2]*Sqrt[Sin[a + b*x]] - Cos[a + b*x]*Sin[a + b*x]^2))/(5*b)","A",1
265,1,18,21,0.0250981,"\int \cos ^3(x) \csc ^{\frac{9}{2}}(x) \, dx","Integrate[Cos[x]^3*Csc[x]^(9/2),x]","\frac{2}{21} \csc ^{\frac{3}{2}}(x) \left(7-3 \csc ^2(x)\right)","\frac{2}{3} \csc ^{\frac{3}{2}}(x)-\frac{2}{7} \csc ^{\frac{7}{2}}(x)",1,"(2*Csc[x]^(3/2)*(7 - 3*Csc[x]^2))/21","A",1
266,1,27,33,0.0617509,"\int \cos ^3(a+b x) \sqrt{\csc (a+b x)} \, dx","Integrate[Cos[a + b*x]^3*Sqrt[Csc[a + b*x]],x]","\frac{\cos (2 (a+b x))+9}{5 b \sqrt{\csc (a+b x)}}","\frac{2}{b \sqrt{\csc (a+b x)}}-\frac{2}{5 b \csc ^{\frac{5}{2}}(a+b x)}",1,"(9 + Cos[2*(a + b*x)])/(5*b*Sqrt[Csc[a + b*x]])","A",1
267,1,29,35,0.0648906,"\int \frac{\cos ^3(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Cos[a + b*x]^3/Sqrt[Csc[a + b*x]],x]","\frac{2 \left(7 \csc ^2(a+b x)-3\right)}{21 b \csc ^{\frac{7}{2}}(a+b x)}","\frac{2}{3 b \csc ^{\frac{3}{2}}(a+b x)}-\frac{2}{7 b \csc ^{\frac{7}{2}}(a+b x)}",1,"(2*(-3 + 7*Csc[a + b*x]^2))/(21*b*Csc[a + b*x]^(7/2))","A",1
268,1,63,92,0.1362235,"\int \cos ^4(a+b x) \sqrt{\csc (a+b x)} \, dx","Integrate[Cos[a + b*x]^4*Sqrt[Csc[a + b*x]],x]","\frac{\sqrt{\csc (a+b x)} \left(10 \sin (2 (a+b x))+\sin (4 (a+b x))-32 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{4} (-2 a-2 b x+\pi )\right|2\right)\right)}{28 b}","\frac{2 \cos ^3(a+b x)}{7 b \sqrt{\csc (a+b x)}}+\frac{4 \cos (a+b x)}{7 b \sqrt{\csc (a+b x)}}+\frac{8 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{7 b}",1,"(Sqrt[Csc[a + b*x]]*(-32*EllipticF[(-2*a + Pi - 2*b*x)/4, 2]*Sqrt[Sin[a + b*x]] + 10*Sin[2*(a + b*x)] + Sin[4*(a + b*x)]))/(28*b)","A",1
269,1,63,92,0.4060465,"\int \frac{\cos ^4(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Cos[a + b*x]^4/Sqrt[Csc[a + b*x]],x]","\frac{39 \cos (a+b x)+5 \cos (3 (a+b x))-\frac{48 E\left(\left.\frac{1}{4} (-2 a-2 b x+\pi )\right|2\right)}{\sin ^{\frac{3}{2}}(a+b x)}}{90 b \csc ^{\frac{3}{2}}(a+b x)}","\frac{2 \cos ^3(a+b x)}{9 b \csc ^{\frac{3}{2}}(a+b x)}+\frac{4 \cos (a+b x)}{15 b \csc ^{\frac{3}{2}}(a+b x)}+\frac{8 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{15 b}",1,"(39*Cos[a + b*x] + 5*Cos[3*(a + b*x)] - (48*EllipticE[(-2*a + Pi - 2*b*x)/4, 2])/Sin[a + b*x]^(3/2))/(90*b*Csc[a + b*x]^(3/2))","A",1
270,1,10,10,0.0075914,"\int \cos (x) \csc ^{\frac{7}{3}}(x) \, dx","Integrate[Cos[x]*Csc[x]^(7/3),x]","-\frac{3}{4} \csc ^{\frac{4}{3}}(x)","-\frac{3}{4} \csc ^{\frac{4}{3}}(x)",1,"(-3*Csc[x]^(4/3))/4","A",1
271,1,47,32,0.0291248,"\int \sqrt{\csc (a+b x)} \sec (a+b x) \, dx","Integrate[Sqrt[Csc[a + b*x]]*Sec[a + b*x],x]","\frac{\sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} \left(\tan ^{-1}\left(\sqrt{\sin (a+b x)}\right)+\tanh ^{-1}\left(\sqrt{\sin (a+b x)}\right)\right)}{b}","\frac{\tanh ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{b}-\frac{\tan ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{b}",1,"((ArcTan[Sqrt[Sin[a + b*x]]] + ArcTanh[Sqrt[Sin[a + b*x]]])*Sqrt[Csc[a + b*x]]*Sqrt[Sin[a + b*x]])/b","A",1
272,1,50,31,0.0326801,"\int \frac{\sec (a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Sec[a + b*x]/Sqrt[Csc[a + b*x]],x]","-\frac{\sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} \left(\tan ^{-1}\left(\sqrt{\sin (a+b x)}\right)-\tanh ^{-1}\left(\sqrt{\sin (a+b x)}\right)\right)}{b}","\frac{\tan ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{b}+\frac{\tanh ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{b}",1,"-(((ArcTan[Sqrt[Sin[a + b*x]]] - ArcTanh[Sqrt[Sin[a + b*x]]])*Sqrt[Csc[a + b*x]]*Sqrt[Sin[a + b*x]])/b)","A",1
273,1,49,61,0.1422686,"\int \sqrt{\csc (a+b x)} \sec ^2(a+b x) \, dx","Integrate[Sqrt[Csc[a + b*x]]*Sec[a + b*x]^2,x]","\frac{\sec (a+b x)+\frac{F\left(\left.\frac{1}{4} (2 a+2 b x-\pi )\right|2\right)}{\sqrt{\sin (a+b x)}}}{b \sqrt{\csc (a+b x)}}","\frac{\sec (a+b x)}{b \sqrt{\csc (a+b x)}}+\frac{\sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(Sec[a + b*x] + EllipticF[(2*a - Pi + 2*b*x)/4, 2]/Sqrt[Sin[a + b*x]])/(b*Sqrt[Csc[a + b*x]])","A",1
274,1,54,62,0.1481491,"\int \frac{\sec ^2(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Sec[a + b*x]^2/Sqrt[Csc[a + b*x]],x]","\frac{\sqrt{\csc (a+b x)} \left(\sin (a+b x) \tan (a+b x)+\sqrt{\sin (a+b x)} E\left(\left.\frac{1}{4} (-2 a-2 b x+\pi )\right|2\right)\right)}{b}","\frac{\sec (a+b x)}{b \csc ^{\frac{3}{2}}(a+b x)}-\frac{\sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(Sqrt[Csc[a + b*x]]*(EllipticE[(-2*a + Pi - 2*b*x)/4, 2]*Sqrt[Sin[a + b*x]] + Sin[a + b*x]*Tan[a + b*x]))/b","A",1
275,1,73,62,0.112319,"\int \sqrt{\csc (a+b x)} \sec ^3(a+b x) \, dx","Integrate[Sqrt[Csc[a + b*x]]*Sec[a + b*x]^3,x]","\frac{\sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} \left(2 \sqrt{\sin (a+b x)} \sec ^2(a+b x)+3 \left(\tan ^{-1}\left(\sqrt{\sin (a+b x)}\right)+\tanh ^{-1}\left(\sqrt{\sin (a+b x)}\right)\right)\right)}{4 b}","-\frac{3 \tan ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{4 b}+\frac{\sec ^2(a+b x)}{2 b \sqrt{\csc (a+b x)}}+\frac{3 \tanh ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{4 b}",1,"(Sqrt[Csc[a + b*x]]*(3*(ArcTan[Sqrt[Sin[a + b*x]]] + ArcTanh[Sqrt[Sin[a + b*x]]]) + 2*Sec[a + b*x]^2*Sqrt[Sin[a + b*x]])*Sqrt[Sin[a + b*x]])/(4*b)","A",1
276,1,33,62,0.0279045,"\int \frac{\sec ^3(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Sec[a + b*x]^3/Sqrt[Csc[a + b*x]],x]","\frac{2 \, _2F_1\left(\frac{3}{4},2;\frac{7}{4};\sin ^2(a+b x)\right)}{3 b \csc ^{\frac{3}{2}}(a+b x)}","\frac{\sec ^2(a+b x)}{2 b \csc ^{\frac{3}{2}}(a+b x)}+\frac{\tan ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{4 b}+\frac{\tanh ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{4 b}",1,"(2*Hypergeometric2F1[3/4, 2, 7/4, Sin[a + b*x]^2])/(3*b*Csc[a + b*x]^(3/2))","C",1
277,1,64,92,0.3778848,"\int \sqrt{\csc (a+b x)} \sec ^4(a+b x) \, dx","Integrate[Sqrt[Csc[a + b*x]]*Sec[a + b*x]^4,x]","\frac{\sqrt{\csc (a+b x)} \left(\tan (a+b x) \left(2 \sec ^2(a+b x)+5\right)-5 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{4} (-2 a-2 b x+\pi )\right|2\right)\right)}{6 b}","\frac{\sec ^3(a+b x)}{3 b \sqrt{\csc (a+b x)}}+\frac{5 \sec (a+b x)}{6 b \sqrt{\csc (a+b x)}}+\frac{5 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{6 b}",1,"(Sqrt[Csc[a + b*x]]*(-5*EllipticF[(-2*a + Pi - 2*b*x)/4, 2]*Sqrt[Sin[a + b*x]] + (5 + 2*Sec[a + b*x]^2)*Tan[a + b*x]))/(6*b)","A",1
278,1,76,92,0.2319842,"\int \frac{\sec ^4(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Integrate[Sec[a + b*x]^4/Sqrt[Csc[a + b*x]],x]","\frac{\cos (a+b x) \sqrt{\csc (a+b x)} \left(2 \sec ^4(a+b x)+\sec ^2(a+b x)+3 \sqrt{\sin (a+b x)} \sec (a+b x) E\left(\left.\frac{1}{4} (-2 a-2 b x+\pi )\right|2\right)-3\right)}{6 b}","\frac{\sec ^3(a+b x)}{3 b \csc ^{\frac{3}{2}}(a+b x)}+\frac{\sec (a+b x)}{2 b \csc ^{\frac{3}{2}}(a+b x)}-\frac{\sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{2 b}",1,"(Cos[a + b*x]*Sqrt[Csc[a + b*x]]*(-3 + Sec[a + b*x]^2 + 2*Sec[a + b*x]^4 + 3*EllipticE[(-2*a + Pi - 2*b*x)/4, 2]*Sec[a + b*x]*Sqrt[Sin[a + b*x]]))/(6*b)","A",1
279,1,105,76,0.6803648,"\int (d \cos (a+b x))^{3/2} \csc ^p(a+b x) \, dx","Integrate[(d*Cos[a + b*x])^(3/2)*Csc[a + b*x]^p,x]","-\frac{2 (d \cos (a+b x))^{5/2} \sin ^2(a+b x)^{\frac{p-1}{2}} \csc ^{p-1}(a+b x) \left(5 \cos ^2(a+b x) \, _2F_1\left(\frac{9}{4},\frac{p+1}{2};\frac{13}{4};\cos ^2(a+b x)\right)+9 \, _2F_1\left(\frac{5}{4},\frac{p-1}{2};\frac{9}{4};\cos ^2(a+b x)\right)\right)}{45 b d}","\frac{d \sqrt{d \cos (a+b x)} \csc ^{p-1}(a+b x) \, _2F_1\left(-\frac{1}{4},\frac{1-p}{2};\frac{3-p}{2};\sin ^2(a+b x)\right)}{b (1-p) \sqrt[4]{\cos ^2(a+b x)}}",1,"(-2*(d*Cos[a + b*x])^(5/2)*Csc[a + b*x]^(-1 + p)*(9*Hypergeometric2F1[5/4, (-1 + p)/2, 9/4, Cos[a + b*x]^2] + 5*Cos[a + b*x]^2*Hypergeometric2F1[9/4, (1 + p)/2, 13/4, Cos[a + b*x]^2])*(Sin[a + b*x]^2)^((-1 + p)/2))/(45*b*d)","A",1
280,1,70,76,0.1698038,"\int \sqrt{d \cos (a+b x)} \csc ^p(a+b x) \, dx","Integrate[Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^p,x]","-\frac{2 (d \cos (a+b x))^{3/2} \sin ^2(a+b x)^{\frac{p-1}{2}} \csc ^{p-1}(a+b x) \, _2F_1\left(\frac{3}{4},\frac{p+1}{2};\frac{7}{4};\cos ^2(a+b x)\right)}{3 b d}","\frac{d \sqrt[4]{\cos ^2(a+b x)} \csc ^{p-1}(a+b x) \, _2F_1\left(\frac{1}{4},\frac{1-p}{2};\frac{3-p}{2};\sin ^2(a+b x)\right)}{b (1-p) \sqrt{d \cos (a+b x)}}",1,"(-2*(d*Cos[a + b*x])^(3/2)*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[3/4, (1 + p)/2, 7/4, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^((-1 + p)/2))/(3*b*d)","A",1
281,1,68,76,0.220082,"\int \frac{\csc ^p(a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Integrate[Csc[a + b*x]^p/Sqrt[d*Cos[a + b*x]],x]","-\frac{2 \sqrt{d \cos (a+b x)} \sin ^2(a+b x)^{\frac{p+1}{2}} \csc ^{p+1}(a+b x) \, _2F_1\left(\frac{1}{4},\frac{p+1}{2};\frac{5}{4};\cos ^2(a+b x)\right)}{b d}","\frac{d \cos ^2(a+b x)^{3/4} \csc ^{p-1}(a+b x) \, _2F_1\left(\frac{3}{4},\frac{1-p}{2};\frac{3-p}{2};\sin ^2(a+b x)\right)}{b (1-p) (d \cos (a+b x))^{3/2}}",1,"(-2*Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^(1 + p)*Hypergeometric2F1[1/4, (1 + p)/2, 5/4, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^((1 + p)/2))/(b*d)","A",1
282,1,68,78,0.2596998,"\int \frac{\csc ^p(a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Integrate[Csc[a + b*x]^p/(d*Cos[a + b*x])^(3/2),x]","\frac{2 \sin ^2(a+b x)^{\frac{p-1}{2}} \csc ^{p-1}(a+b x) \, _2F_1\left(-\frac{1}{4},\frac{p+1}{2};\frac{3}{4};\cos ^2(a+b x)\right)}{b d \sqrt{d \cos (a+b x)}}","\frac{\sqrt[4]{\cos ^2(a+b x)} \csc ^{p-1}(a+b x) \, _2F_1\left(\frac{5}{4},\frac{1-p}{2};\frac{3-p}{2};\sin ^2(a+b x)\right)}{b d (1-p) \sqrt{d \cos (a+b x)}}",1,"(2*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[-1/4, (1 + p)/2, 3/4, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^((-1 + p)/2))/(b*d*Sqrt[d*Cos[a + b*x]])","A",1
283,1,70,78,0.2800172,"\int \frac{\csc ^p(a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Integrate[Csc[a + b*x]^p/(d*Cos[a + b*x])^(5/2),x]","\frac{2 \sin ^2(a+b x)^{\frac{p-1}{2}} \csc ^{p-1}(a+b x) \, _2F_1\left(-\frac{3}{4},\frac{p+1}{2};\frac{1}{4};\cos ^2(a+b x)\right)}{3 b d (d \cos (a+b x))^{3/2}}","\frac{\cos ^2(a+b x)^{3/4} \csc ^{p-1}(a+b x) \, _2F_1\left(\frac{7}{4},\frac{1-p}{2};\frac{3-p}{2};\sin ^2(a+b x)\right)}{b d (1-p) (d \cos (a+b x))^{3/2}}",1,"(2*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[-3/4, (1 + p)/2, 1/4, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^((-1 + p)/2))/(3*b*d*(d*Cos[a + b*x])^(3/2))","A",1
284,1,312,85,1.9655409,"\int \cos ^m(e+f x) \csc ^n(e+f x) \, dx","Integrate[Cos[e + f*x]^m*Csc[e + f*x]^n,x]","-\frac{2 (n-3) \sin \left(\frac{1}{2} (e+f x)\right) \cos ^3\left(\frac{1}{2} (e+f x)\right) \cos ^m(e+f x) \csc ^n(e+f x) F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left(2 \sin ^2\left(\frac{1}{2} (e+f x)\right) \left(m F_1\left(\frac{3}{2}-\frac{n}{2};1-m,m-n+1;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+(m-n+1) F_1\left(\frac{3}{2}-\frac{n}{2};-m,m-n+2;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)+(n-3) \cos ^2\left(\frac{1}{2} (e+f x)\right) F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)}","\frac{\cos ^{m-1}(e+f x) \cos ^2(e+f x)^{\frac{1-m}{2}} \csc ^{n-1}(e+f x) \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(-2*(-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^3*Cos[e + f*x]^m*Csc[e + f*x]^n*Sin[(e + f*x)/2])/(f*(-1 + n)*((-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^2 + 2*(m*AppellF1[3/2 - n/2, 1 - m, 1 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + (1 + m - n)*AppellF1[3/2 - n/2, -m, 2 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Sin[(e + f*x)/2]^2))","C",0
285,1,314,88,0.2268882,"\int (a \cos (e+f x))^m \csc ^n(e+f x) \, dx","Integrate[(a*Cos[e + f*x])^m*Csc[e + f*x]^n,x]","-\frac{2 (n-3) \sin \left(\frac{1}{2} (e+f x)\right) \cos ^3\left(\frac{1}{2} (e+f x)\right) \csc ^n(e+f x) (a \cos (e+f x))^m F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left(2 \sin ^2\left(\frac{1}{2} (e+f x)\right) \left(m F_1\left(\frac{3}{2}-\frac{n}{2};1-m,m-n+1;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+(m-n+1) F_1\left(\frac{3}{2}-\frac{n}{2};-m,m-n+2;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)+(n-3) \cos ^2\left(\frac{1}{2} (e+f x)\right) F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)}","\frac{a \cos ^2(e+f x)^{\frac{1-m}{2}} \csc ^{n-1}(e+f x) (a \cos (e+f x))^{m-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(-2*(-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^3*(a*Cos[e + f*x])^m*Csc[e + f*x]^n*Sin[(e + f*x)/2])/(f*(-1 + n)*((-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^2 + 2*(m*AppellF1[3/2 - n/2, 1 - m, 1 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + (1 + m - n)*AppellF1[3/2 - n/2, -m, 2 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Sin[(e + f*x)/2]^2))","C",0
286,1,314,88,0.2365766,"\int \cos ^m(e+f x) (b \csc (e+f x))^n \, dx","Integrate[Cos[e + f*x]^m*(b*Csc[e + f*x])^n,x]","-\frac{2 (n-3) \sin \left(\frac{1}{2} (e+f x)\right) \cos ^3\left(\frac{1}{2} (e+f x)\right) \cos ^m(e+f x) (b \csc (e+f x))^n F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left(2 \sin ^2\left(\frac{1}{2} (e+f x)\right) \left(m F_1\left(\frac{3}{2}-\frac{n}{2};1-m,m-n+1;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+(m-n+1) F_1\left(\frac{3}{2}-\frac{n}{2};-m,m-n+2;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)+(n-3) \cos ^2\left(\frac{1}{2} (e+f x)\right) F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)}","\frac{b \cos ^{m-1}(e+f x) \cos ^2(e+f x)^{\frac{1-m}{2}} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(-2*(-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^3*Cos[e + f*x]^m*(b*Csc[e + f*x])^n*Sin[(e + f*x)/2])/(f*(-1 + n)*((-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^2 + 2*(m*AppellF1[3/2 - n/2, 1 - m, 1 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + (1 + m - n)*AppellF1[3/2 - n/2, -m, 2 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Sin[(e + f*x)/2]^2))","C",0
287,1,316,91,0.2272921,"\int (a \cos (e+f x))^m (b \csc (e+f x))^n \, dx","Integrate[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^n,x]","-\frac{2 (n-3) \sin \left(\frac{1}{2} (e+f x)\right) \cos ^3\left(\frac{1}{2} (e+f x)\right) (a \cos (e+f x))^m (b \csc (e+f x))^n F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left(2 \sin ^2\left(\frac{1}{2} (e+f x)\right) \left(m F_1\left(\frac{3}{2}-\frac{n}{2};1-m,m-n+1;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+(m-n+1) F_1\left(\frac{3}{2}-\frac{n}{2};-m,m-n+2;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)+(n-3) \cos ^2\left(\frac{1}{2} (e+f x)\right) F_1\left(\frac{1}{2}-\frac{n}{2};-m,m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)}","\frac{a b \cos ^2(e+f x)^{\frac{1-m}{2}} (a \cos (e+f x))^{m-1} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"(-2*(-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^3*(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^n*Sin[(e + f*x)/2])/(f*(-1 + n)*((-3 + n)*AppellF1[1/2 - n/2, -m, 1 + m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^2 + 2*(m*AppellF1[3/2 - n/2, 1 - m, 1 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + (1 + m - n)*AppellF1[3/2 - n/2, -m, 2 + m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Sin[(e + f*x)/2]^2))","C",0
288,1,94,78,7.909287,"\int (a \cos (e+f x))^m (b \csc (e+f x))^{7/2} \, dx","Integrate[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^(7/2),x]","\frac{2 a b (b \csc (e+f x))^{5/2} \left(-\cot ^2(e+f x)\right)^{\frac{1-m}{2}} (a \cos (e+f x))^{m-1} \, _2F_1\left(\frac{1}{4} (7-2 m),\frac{1-m}{2};\frac{1}{4} (11-2 m);\csc ^2(e+f x)\right)}{f (2 m-7)}","-\frac{b^3 \sqrt[4]{\sin ^2(e+f x)} \sqrt{b \csc (e+f x)} (a \cos (e+f x))^{m+1} \, _2F_1\left(\frac{9}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a f (m+1)}",1,"(2*a*b*(a*Cos[e + f*x])^(-1 + m)*(-Cot[e + f*x]^2)^((1 - m)/2)*(b*Csc[e + f*x])^(5/2)*Hypergeometric2F1[(7 - 2*m)/4, (1 - m)/2, (11 - 2*m)/4, Csc[e + f*x]^2])/(f*(-7 + 2*m))","A",1
289,1,94,76,2.3855029,"\int (a \cos (e+f x))^m (b \csc (e+f x))^{5/2} \, dx","Integrate[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^(5/2),x]","\frac{2 a b (b \csc (e+f x))^{3/2} \left(-\cot ^2(e+f x)\right)^{\frac{1-m}{2}} (a \cos (e+f x))^{m-1} \, _2F_1\left(\frac{1}{4} (5-2 m),\frac{1-m}{2};\frac{1}{4} (9-2 m);\csc ^2(e+f x)\right)}{f (2 m-5)}","-\frac{b \sin ^2(e+f x)^{3/4} (b \csc (e+f x))^{3/2} (a \cos (e+f x))^{m+1} \, _2F_1\left(\frac{7}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a f (m+1)}",1,"(2*a*b*(a*Cos[e + f*x])^(-1 + m)*(-Cot[e + f*x]^2)^((1 - m)/2)*(b*Csc[e + f*x])^(3/2)*Hypergeometric2F1[(5 - 2*m)/4, (1 - m)/2, (9 - 2*m)/4, Csc[e + f*x]^2])/(f*(-5 + 2*m))","A",1
290,1,94,76,1.2400228,"\int (a \cos (e+f x))^m (b \csc (e+f x))^{3/2} \, dx","Integrate[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^(3/2),x]","\frac{2 a b \sqrt{b \csc (e+f x)} \left(-\cot ^2(e+f x)\right)^{\frac{1-m}{2}} (a \cos (e+f x))^{m-1} \, _2F_1\left(\frac{1}{4} (3-2 m),\frac{1-m}{2};\frac{1}{4} (7-2 m);\csc ^2(e+f x)\right)}{f (2 m-3)}","-\frac{b \sqrt[4]{\sin ^2(e+f x)} \sqrt{b \csc (e+f x)} (a \cos (e+f x))^{m+1} \, _2F_1\left(\frac{5}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a f (m+1)}",1,"(2*a*b*(a*Cos[e + f*x])^(-1 + m)*(-Cot[e + f*x]^2)^((1 - m)/2)*Sqrt[b*Csc[e + f*x]]*Hypergeometric2F1[(3 - 2*m)/4, (1 - m)/2, (7 - 2*m)/4, Csc[e + f*x]^2])/(f*(-3 + 2*m))","A",1
291,1,96,78,1.0498353,"\int (a \cos (e+f x))^m \sqrt{b \csc (e+f x)} \, dx","Integrate[(a*Cos[e + f*x])^m*Sqrt[b*Csc[e + f*x]],x]","\frac{2 \tan (e+f x) \sqrt{b \csc (e+f x)} \left(-\cot ^2(e+f x)\right)^{\frac{1-m}{2}} (a \cos (e+f x))^m \, _2F_1\left(\frac{1}{4} (1-2 m),\frac{1-m}{2};\frac{1}{4} (5-2 m);\csc ^2(e+f x)\right)}{f (2 m-1)}","-\frac{\sin ^2(e+f x)^{3/4} (b \csc (e+f x))^{3/2} (a \cos (e+f x))^{m+1} \, _2F_1\left(\frac{3}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a b f (m+1)}",1,"(2*(a*Cos[e + f*x])^m*(-Cot[e + f*x]^2)^((1 - m)/2)*Sqrt[b*Csc[e + f*x]]*Hypergeometric2F1[(1 - 2*m)/4, (1 - m)/2, (5 - 2*m)/4, Csc[e + f*x]^2]*Tan[e + f*x])/(f*(-1 + 2*m))","A",1
292,1,225,78,1.6385196,"\int \frac{(a \cos (e+f x))^m}{\sqrt{b \csc (e+f x)}} \, dx","Integrate[(a*Cos[e + f*x])^m/Sqrt[b*Csc[e + f*x]],x]","\frac{14 b (a \cos (e+f x))^m F_1\left(\frac{3}{4};-m,m+\frac{3}{2};\frac{7}{4};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{3 f (b \csc (e+f x))^{3/2} \left(7 F_1\left(\frac{3}{4};-m,m+\frac{3}{2};\frac{7}{4};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-2 \tan ^2\left(\frac{1}{2} (e+f x)\right) \left(2 m F_1\left(\frac{7}{4};1-m,m+\frac{3}{2};\frac{11}{4};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+(2 m+3) F_1\left(\frac{7}{4};-m,m+\frac{5}{2};\frac{11}{4};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)\right)}","-\frac{\sqrt[4]{\sin ^2(e+f x)} \sqrt{b \csc (e+f x)} (a \cos (e+f x))^{m+1} \, _2F_1\left(\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a b f (m+1)}",1,"(14*b*AppellF1[3/4, -m, 3/2 + m, 7/4, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*(a*Cos[e + f*x])^m)/(3*f*(b*Csc[e + f*x])^(3/2)*(7*AppellF1[3/4, -m, 3/2 + m, 7/4, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] - 2*(2*m*AppellF1[7/4, 1 - m, 3/2 + m, 11/4, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + (3 + 2*m)*AppellF1[7/4, -m, 5/2 + m, 11/4, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Tan[(e + f*x)/2]^2))","C",0
293,1,116,78,6.448788,"\int \frac{(a \cos (e+f x))^m}{(b \csc (e+f x))^{3/2}} \, dx","Integrate[(a*Cos[e + f*x])^m/(b*Csc[e + f*x])^(3/2),x]","\frac{2 a \cos (2 (e+f x)) \left(-\cot ^2(e+f x)\right)^{\frac{1-m}{2}} (a \cos (e+f x))^{m-1} \, _2F_1\left(\frac{1}{4} (-2 m-3),\frac{1-m}{2};\frac{1}{4} (1-2 m);\csc ^2(e+f x)\right)}{b f (2 m+3) \left(\csc ^2(e+f x)-2\right) \sqrt{b \csc (e+f x)}}","-\frac{(a \cos (e+f x))^{m+1} \, _2F_1\left(-\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a b f (m+1) \sqrt[4]{\sin ^2(e+f x)} \sqrt{b \csc (e+f x)}}",1,"(2*a*(a*Cos[e + f*x])^(-1 + m)*Cos[2*(e + f*x)]*(-Cot[e + f*x]^2)^((1 - m)/2)*Hypergeometric2F1[(-3 - 2*m)/4, (1 - m)/2, (1 - 2*m)/4, Csc[e + f*x]^2])/(b*f*(3 + 2*m)*Sqrt[b*Csc[e + f*x]]*(-2 + Csc[e + f*x]^2))","A",1
294,1,125,78,1.0601246,"\int \frac{(a \cos (e+f x))^m}{(b \csc (e+f x))^{5/2}} \, dx","Integrate[(a*Cos[e + f*x])^m/(b*Csc[e + f*x])^(5/2),x]","\frac{2 (2 \cos (2 (e+f x))+1) \tan (e+f x) \left(-\cot ^2(e+f x)\right)^{\frac{1-m}{2}} (a \cos (e+f x))^m \, _2F_1\left(\frac{1}{4} (-2 m-5),\frac{1-m}{2};\frac{1}{4} (-2 m-1);\csc ^2(e+f x)\right)}{b^2 f (2 m+5) \left(3 \csc ^2(e+f x)-4\right) \sqrt{b \csc (e+f x)}}","-\frac{\sqrt[4]{\sin ^2(e+f x)} \sqrt{b \csc (e+f x)} (a \cos (e+f x))^{m+1} \, _2F_1\left(-\frac{3}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a b^3 f (m+1)}",1,"(2*(a*Cos[e + f*x])^m*(1 + 2*Cos[2*(e + f*x)])*(-Cot[e + f*x]^2)^((1 - m)/2)*Hypergeometric2F1[(-5 - 2*m)/4, (1 - m)/2, (-1 - 2*m)/4, Csc[e + f*x]^2]*Tan[e + f*x])/(b^2*f*(5 + 2*m)*Sqrt[b*Csc[e + f*x]]*(-4 + 3*Csc[e + f*x]^2))","A",1