1,1,10,0,0.0041908,"\int \cos (a+b x) \, dx","Int[Cos[a + b*x],x]","\frac{\sin (a+b x)}{b}","\frac{\sin (a+b x)}{b}",1,"Sin[a + b*x]/b","A",1,1,6,0.1667,1,"{2637}"
2,1,25,0,0.0089483,"\int \cos ^2(a+b x) \, dx","Int[Cos[a + b*x]^2,x]","\frac{\sin (a+b x) \cos (a+b x)}{2 b}+\frac{x}{2}","\frac{\sin (a+b x) \cos (a+b x)}{2 b}+\frac{x}{2}",1,"x/2 + (Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",2,2,8,0.2500,1,"{2635, 8}"
3,1,26,0,0.0112665,"\int \cos ^3(a+b x) \, dx","Int[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",2,1,8,0.1250,1,"{2633}"
4,1,46,0,0.0208342,"\int \cos ^4(a+b x) \, dx","Int[Cos[a + b*x]^4,x]","\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}","\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,"(3*x)/8 + (3*Cos[a + b*x]*Sin[a + b*x])/(8*b) + (Cos[a + b*x]^3*Sin[a + b*x])/(4*b)","A",3,2,8,0.2500,1,"{2635, 8}"
5,1,41,0,0.0129965,"\int \cos ^5(a+b x) \, dx","Int[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",2,1,8,0.1250,1,"{2633}"
6,1,67,0,0.0331819,"\int \cos ^6(a+b x) \, dx","Int[Cos[a + b*x]^6,x]","\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}","\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,"(5*x)/16 + (5*Cos[a + b*x]*Sin[a + b*x])/(16*b) + (5*Cos[a + b*x]^3*Sin[a + b*x])/(24*b) + (Cos[a + b*x]^5*Sin[a + b*x])/(6*b)","A",4,2,8,0.2500,1,"{2635, 8}"
7,1,54,0,0.0163204,"\int \cos ^7(a+b x) \, dx","Int[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",2,1,8,0.1250,1,"{2633}"
8,1,88,0,0.0469793,"\int \cos ^8(a+b x) \, dx","Int[Cos[a + b*x]^8,x]","\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}","\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,"(35*x)/128 + (35*Cos[a + b*x]*Sin[a + b*x])/(128*b) + (35*Cos[a + b*x]^3*Sin[a + b*x])/(192*b) + (7*Cos[a + b*x]^5*Sin[a + b*x])/(48*b) + (Cos[a + b*x]^7*Sin[a + b*x])/(8*b)","A",5,2,8,0.2500,1,"{2635, 8}"
9,1,65,0,0.0316657,"\int \cos ^{\frac{7}{2}}(a+b x) \, dx","Int[Cos[a + b*x]^(7/2),x]","\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}","\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,"(10*EllipticF[(a + b*x)/2, 2])/(21*b) + (10*Sqrt[Cos[a + b*x]]*Sin[a + b*x])/(21*b) + (2*Cos[a + b*x]^(5/2)*Sin[a + b*x])/(7*b)","A",3,2,10,0.2000,1,"{2635, 2641}"
10,1,42,0,0.0181638,"\int \cos ^{\frac{5}{2}}(a+b x) \, dx","Int[Cos[a + b*x]^(5/2),x]","\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}","\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])/(5*b) + (2*Cos[a + b*x]^(3/2)*Sin[a + b*x])/(5*b)","A",2,2,10,0.2000,1,"{2635, 2639}"
11,1,42,0,0.0182761,"\int \cos ^{\frac{3}{2}}(a+b x) \, dx","Int[Cos[a + b*x]^(3/2),x]","\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}","\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])/(3*b) + (2*Sqrt[Cos[a + b*x]]*Sin[a + b*x])/(3*b)","A",2,2,10,0.2000,1,"{2635, 2641}"
12,1,16,0,0.0086084,"\int \sqrt{\cos (a+b x)} \, dx","Int[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",1,1,10,0.1000,1,"{2639}"
13,1,16,0,0.0091156,"\int \frac{1}{\sqrt{\cos (a+b x)}} \, dx","Int[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",1,1,10,0.1000,1,"{2641}"
14,1,38,0,0.0177816,"\int \frac{1}{\cos ^{\frac{3}{2}}(a+b x)} \, dx","Int[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",2,2,10,0.2000,1,"{2636, 2639}"
15,1,42,0,0.0183912,"\int \frac{1}{\cos ^{\frac{5}{2}}(a+b x)} \, dx","Int[Cos[a + b*x]^(-5/2),x]","\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)}","\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])/(3*b) + (2*Sin[a + b*x])/(3*b*Cos[a + b*x]^(3/2))","A",2,2,10,0.2000,1,"{2636, 2641}"
16,1,65,0,0.0292644,"\int \frac{1}{\cos ^{\frac{7}{2}}(a+b x)} \, dx","Int[Cos[a + b*x]^(-7/2),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)}}","-\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*EllipticE[(a + b*x)/2, 2])/(5*b) + (2*Sin[a + b*x])/(5*b*Cos[a + b*x]^(5/2)) + (6*Sin[a + b*x])/(5*b*Sqrt[Cos[a + b*x]])","A",3,2,10,0.2000,1,"{2636, 2639}"
17,1,98,0,0.0586644,"\int (c \cos (a+b x))^{7/2} \, dx","Int[(c*Cos[a + b*x])^(7/2),x]","\frac{10 c^3 \sin (a+b x) \sqrt{c \cos (a+b x)}}{21 b}+\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{2 c \sin (a+b x) (c \cos (a+b x))^{5/2}}{7 b}","\frac{10 c^3 \sin (a+b x) \sqrt{c \cos (a+b x)}}{21 b}+\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{2 c \sin (a+b x) (c \cos (a+b x))^{5/2}}{7 b}",1,"(10*c^4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(21*b*Sqrt[c*Cos[a + b*x]]) + (10*c^3*Sqrt[c*Cos[a + b*x]]*Sin[a + b*x])/(21*b) + (2*c*(c*Cos[a + b*x])^(5/2)*Sin[a + b*x])/(7*b)","A",4,3,12,0.2500,1,"{2635, 2642, 2641}"
18,1,70,0,0.0364114,"\int (c \cos (a+b x))^{5/2} \, dx","Int[(c*Cos[a + b*x])^(5/2),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}","\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,"(6*c^2*Sqrt[c*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*Sqrt[Cos[a + b*x]]) + (2*c*(c*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(5*b)","A",3,3,12,0.2500,1,"{2635, 2640, 2639}"
19,1,70,0,0.0365162,"\int (c \cos (a+b x))^{3/2} \, dx","Int[(c*Cos[a + b*x])^(3/2),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}","\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^2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(3*b*Sqrt[c*Cos[a + b*x]]) + (2*c*Sqrt[c*Cos[a + b*x]]*Sin[a + b*x])/(3*b)","A",3,3,12,0.2500,1,"{2635, 2642, 2641}"
20,1,38,0,0.0215331,"\int \sqrt{c \cos (a+b x)} \, dx","Int[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",2,2,12,0.1667,1,"{2640, 2639}"
21,1,38,0,0.0226469,"\int \frac{1}{\sqrt{c \cos (a+b x)}} \, dx","Int[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",2,2,12,0.1667,1,"{2642, 2641}"
22,1,68,0,0.0360195,"\int \frac{1}{(c \cos (a+b x))^{3/2}} \, dx","Int[(c*Cos[a + b*x])^(-3/2),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)}}","\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[c*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(b*c^2*Sqrt[Cos[a + b*x]]) + (2*Sin[a + b*x])/(b*c*Sqrt[c*Cos[a + b*x]])","A",3,3,12,0.2500,1,"{2636, 2640, 2639}"
23,1,72,0,0.0353468,"\int \frac{1}{(c \cos (a+b x))^{5/2}} \, dx","Int[(c*Cos[a + b*x])^(-5/2),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}}","\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])/(3*b*c^2*Sqrt[c*Cos[a + b*x]]) + (2*Sin[a + b*x])/(3*b*c*(c*Cos[a + b*x])^(3/2))","A",3,3,12,0.2500,1,"{2636, 2642, 2641}"
24,1,100,0,0.0556972,"\int \frac{1}{(c \cos (a+b x))^{7/2}} \, dx","Int[(c*Cos[a + b*x])^(-7/2),x]","\frac{6 \sin (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{2 \sin (a+b x)}{5 b c (c \cos (a+b x))^{5/2}}","\frac{6 \sin (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{2 \sin (a+b x)}{5 b c (c \cos (a+b x))^{5/2}}",1,"(-6*Sqrt[c*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*c^4*Sqrt[Cos[a + b*x]]) + (2*Sin[a + b*x])/(5*b*c*(c*Cos[a + b*x])^(5/2)) + (6*Sin[a + b*x])/(5*b*c^3*Sqrt[c*Cos[a + b*x]])","A",4,3,12,0.2500,1,"{2636, 2640, 2639}"
25,1,53,0,0.0125782,"\int \cos ^{\frac{4}{3}}(a+b x) \, dx","Int[Cos[a + b*x]^(4/3),x]","-\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)}}","-\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)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[a + b*x]^2]*Sin[a + b*x])/(7*b*Sqrt[Sin[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
26,1,53,0,0.0120525,"\int \cos ^{\frac{2}{3}}(a+b x) \, dx","Int[Cos[a + b*x]^(2/3),x]","-\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)}}","-\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)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[a + b*x]^2]*Sin[a + b*x])/(5*b*Sqrt[Sin[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
27,1,53,0,0.0117492,"\int \sqrt[3]{\cos (a+b x)} \, dx","Int[Cos[a + b*x]^(1/3),x]","-\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)}}","-\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)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[a + b*x]^2]*Sin[a + b*x])/(4*b*Sqrt[Sin[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
28,1,53,0,0.012273,"\int \frac{1}{\sqrt[3]{\cos (a+b x)}} \, dx","Int[Cos[a + b*x]^(-1/3),x]","-\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)}}","-\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)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[a + b*x]^2]*Sin[a + b*x])/(2*b*Sqrt[Sin[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
29,1,51,0,0.0118621,"\int \frac{1}{\cos ^{\frac{2}{3}}(a+b x)} \, dx","Int[Cos[a + b*x]^(-2/3),x]","-\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)}}","-\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)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[a + b*x]^2]*Sin[a + b*x])/(b*Sqrt[Sin[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
30,1,51,0,0.0119056,"\int \frac{1}{\cos ^{\frac{4}{3}}(a+b x)} \, dx","Int[Cos[a + b*x]^(-4/3),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)}}","\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*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[a + b*x]^2]*Sin[a + b*x])/(b*Cos[a + b*x]^(1/3)*Sqrt[Sin[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
31,1,58,0,0.0142855,"\int (c \cos (a+b x))^{4/3} \, dx","Int[(c*Cos[a + b*x])^(4/3),x]","-\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)}}","-\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])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[a + b*x]^2]*Sin[a + b*x])/(7*b*c*Sqrt[Sin[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
32,1,58,0,0.01522,"\int (c \cos (a+b x))^{2/3} \, dx","Int[(c*Cos[a + b*x])^(2/3),x]","-\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)}}","-\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])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[a + b*x]^2]*Sin[a + b*x])/(5*b*c*Sqrt[Sin[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
33,1,58,0,0.0154246,"\int \sqrt[3]{c \cos (a+b x)} \, dx","Int[(c*Cos[a + b*x])^(1/3),x]","-\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)}}","-\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])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[a + b*x]^2]*Sin[a + b*x])/(4*b*c*Sqrt[Sin[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
34,1,58,0,0.0153915,"\int \frac{1}{\sqrt[3]{c \cos (a+b x)}} \, dx","Int[(c*Cos[a + b*x])^(-1/3),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)}}","-\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*(c*Cos[a + b*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[a + b*x]^2]*Sin[a + b*x])/(2*b*c*Sqrt[Sin[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
35,1,56,0,0.0148829,"\int \frac{1}{(c \cos (a+b x))^{2/3}} \, dx","Int[(c*Cos[a + b*x])^(-2/3),x]","-\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)}}","-\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*(c*Cos[a + b*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[a + b*x]^2]*Sin[a + b*x])/(b*c*Sqrt[Sin[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
36,1,56,0,0.0250676,"\int \frac{1}{(c \cos (a+b x))^{4/3}} \, dx","Int[(c*Cos[a + b*x])^(-4/3),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 c \sqrt{\sin ^2(a+b x)} \sqrt[3]{c \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 c \sqrt{\sin ^2(a+b x)} \sqrt[3]{c \cos (a+b x)}}",1,"(3*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[a + b*x]^2]*Sin[a + b*x])/(b*c*(c*Cos[a + b*x])^(1/3)*Sqrt[Sin[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
37,1,64,0,0.0170212,"\int \cos ^n(a+b x) \, dx","Int[Cos[a + b*x]^n,x]","-\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)}}","-\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)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sin[a + b*x])/(b*(1 + n)*Sqrt[Sin[a + b*x]^2]))","A",1,1,8,0.1250,1,"{2643}"
38,1,69,0,0.0203006,"\int (c \cos (a+b x))^n \, dx","Int[(c*Cos[a + b*x])^n,x]","-\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)}}","-\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])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sin[a + b*x])/(b*c*(1 + n)*Sqrt[Sin[a + b*x]^2]))","A",1,1,10,0.1000,1,"{2643}"
39,1,53,0,0.0387325,"\int \left(a \cos ^2(x)\right)^{5/2} \, dx","Int[(a*Cos[x]^2)^(5/2),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}","\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,"(8*a^2*Sqrt[a*Cos[x]^2]*Tan[x])/15 + (4*a*(a*Cos[x]^2)^(3/2)*Tan[x])/15 + ((a*Cos[x]^2)^(5/2)*Tan[x])/5","A",4,3,10,0.3000,1,"{3203, 3207, 2637}"
40,1,34,0,0.0268519,"\int \left(a \cos ^2(x)\right)^{3/2} \, dx","Int[(a*Cos[x]^2)^(3/2),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)}","\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,"(2*a*Sqrt[a*Cos[x]^2]*Tan[x])/3 + ((a*Cos[x]^2)^(3/2)*Tan[x])/3","A",3,3,10,0.3000,1,"{3203, 3207, 2637}"
41,1,13,0,0.0112618,"\int \sqrt{a \cos ^2(x)} \, dx","Int[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",2,2,10,0.2000,1,"{3207, 2637}"
42,1,16,0,0.0140495,"\int \frac{1}{\sqrt{a \cos ^2(x)}} \, dx","Int[1/Sqrt[a*Cos[x]^2],x]","\frac{\cos (x) \tanh ^{-1}(\sin (x))}{\sqrt{a \cos ^2(x)}}","\frac{\cos (x) \tanh ^{-1}(\sin (x))}{\sqrt{a \cos ^2(x)}}",1,"(ArcTanh[Sin[x]]*Cos[x])/Sqrt[a*Cos[x]^2]","A",2,2,10,0.2000,1,"{3207, 3770}"
43,1,42,0,0.0223124,"\int \frac{1}{\left(a \cos ^2(x)\right)^{3/2}} \, dx","Int[(a*Cos[x]^2)^(-3/2),x]","\frac{\tan (x)}{2 a \sqrt{a \cos ^2(x)}}+\frac{\cos (x) \tanh ^{-1}(\sin (x))}{2 a \sqrt{a \cos ^2(x)}}","\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,"(ArcTanh[Sin[x]]*Cos[x])/(2*a*Sqrt[a*Cos[x]^2]) + Tan[x]/(2*a*Sqrt[a*Cos[x]^2])","A",3,3,10,0.3000,1,"{3204, 3207, 3770}"
44,1,61,0,0.0437965,"\int \frac{1}{\left(a \cos ^2(x)\right)^{5/2}} \, dx","Int[(a*Cos[x]^2)^(-5/2),x]","\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}}","\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,"(3*ArcTanh[Sin[x]]*Cos[x])/(8*a^2*Sqrt[a*Cos[x]^2]) + Tan[x]/(4*a*(a*Cos[x]^2)^(3/2)) + (3*Tan[x])/(8*a^2*Sqrt[a*Cos[x]^2])","A",4,3,10,0.3000,1,"{3204, 3207, 3770}"
45,1,117,0,0.065901,"\int \left(a \cos ^3(x)\right)^{5/2} \, dx","Int[(a*Cos[x]^3)^(5/2),x]","\frac{2}{15} a^2 \sin (x) \cos ^5(x) \sqrt{a \cos ^3(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)}+\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)}",1,"(26*a^2*Sqrt[a*Cos[x]^3]*EllipticF[x/2, 2])/(77*Cos[x]^(3/2)) + (78*a^2*Cos[x]*Sqrt[a*Cos[x]^3]*Sin[x])/385 + (26*a^2*Cos[x]^3*Sqrt[a*Cos[x]^3]*Sin[x])/165 + (2*a^2*Cos[x]^5*Sqrt[a*Cos[x]^3]*Sin[x])/15 + (26*a^2*Sqrt[a*Cos[x]^3]*Tan[x])/77","A",6,3,10,0.3000,1,"{3207, 2635, 2641}"
46,1,67,0,0.0408263,"\int \left(a \cos ^3(x)\right)^{3/2} \, dx","Int[(a*Cos[x]^3)^(3/2),x]","\frac{2}{9} a \sin (x) \cos ^2(x) \sqrt{a \cos ^3(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)}+\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)}",1,"(14*a*Sqrt[a*Cos[x]^3]*EllipticE[x/2, 2])/(15*Cos[x]^(3/2)) + (14*a*Sqrt[a*Cos[x]^3]*Sin[x])/45 + (2*a*Cos[x]^2*Sqrt[a*Cos[x]^3]*Sin[x])/9","A",4,3,10,0.3000,1,"{3207, 2635, 2639}"
47,1,44,0,0.0283456,"\int \sqrt{a \cos ^3(x)} \, dx","Int[Sqrt[a*Cos[x]^3],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)}","\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])/(3*Cos[x]^(3/2)) + (2*Sqrt[a*Cos[x]^3]*Tan[x])/3","A",3,3,10,0.3000,1,"{3207, 2635, 2641}"
48,1,42,0,0.0234349,"\int \frac{1}{\sqrt{a \cos ^3(x)}} \, dx","Int[1/Sqrt[a*Cos[x]^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)}}","\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])/Sqrt[a*Cos[x]^3] + (2*Cos[x]*Sin[x])/Sqrt[a*Cos[x]^3]","A",3,3,10,0.3000,1,"{3207, 2636, 2639}"
49,1,71,0,0.0303169,"\int \frac{1}{\left(a \cos ^3(x)\right)^{3/2}} \, dx","Int[(a*Cos[x]^3)^(-3/2),x]","\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)}}","\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,"(10*Cos[x]^(3/2)*EllipticF[x/2, 2])/(21*a*Sqrt[a*Cos[x]^3]) + (10*Sin[x])/(21*a*Sqrt[a*Cos[x]^3]) + (2*Sec[x]*Tan[x])/(7*a*Sqrt[a*Cos[x]^3])","A",4,3,10,0.3000,1,"{3207, 2636, 2641}"
50,1,117,0,0.0509484,"\int \frac{1}{\left(a \cos ^3(x)\right)^{5/2}} \, dx","Int[(a*Cos[x]^3)^(-5/2),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)}}","\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,"(-154*Cos[x]^(3/2)*EllipticE[x/2, 2])/(195*a^2*Sqrt[a*Cos[x]^3]) + (154*Cos[x]*Sin[x])/(195*a^2*Sqrt[a*Cos[x]^3]) + (154*Tan[x])/(585*a^2*Sqrt[a*Cos[x]^3]) + (22*Sec[x]^2*Tan[x])/(117*a^2*Sqrt[a*Cos[x]^3]) + (2*Sec[x]^4*Tan[x])/(13*a^2*Sqrt[a*Cos[x]^3])","A",6,3,10,0.3000,1,"{3207, 2636, 2639}"
51,1,132,0,0.0510577,"\int \left(a \cos ^4(x)\right)^{5/2} \, dx","Int[(a*Cos[x]^4)^(5/2),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)}+\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)}+\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)}",1,"(63*a^2*x*Sqrt[a*Cos[x]^4]*Sec[x]^2)/256 + (21*a^2*Cos[x]*Sqrt[a*Cos[x]^4]*Sin[x])/128 + (21*a^2*Cos[x]^3*Sqrt[a*Cos[x]^4]*Sin[x])/160 + (9*a^2*Cos[x]^5*Sqrt[a*Cos[x]^4]*Sin[x])/80 + (a^2*Cos[x]^7*Sqrt[a*Cos[x]^4]*Sin[x])/10 + (63*a^2*Sqrt[a*Cos[x]^4]*Tan[x])/256","A",7,3,10,0.3000,1,"{3207, 2635, 8}"
52,1,78,0,0.0319987,"\int \left(a \cos ^4(x)\right)^{3/2} \, dx","Int[(a*Cos[x]^4)^(3/2),x]","\frac{1}{6} a \sin (x) \cos ^3(x) \sqrt{a \cos ^4(x)}+\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)}+\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)}",1,"(5*a*x*Sqrt[a*Cos[x]^4]*Sec[x]^2)/16 + (5*a*Cos[x]*Sqrt[a*Cos[x]^4]*Sin[x])/24 + (a*Cos[x]^3*Sqrt[a*Cos[x]^4]*Sin[x])/6 + (5*a*Sqrt[a*Cos[x]^4]*Tan[x])/16","A",5,3,10,0.3000,1,"{3207, 2635, 8}"
53,1,36,0,0.0153305,"\int \sqrt{a \cos ^4(x)} \, dx","Int[Sqrt[a*Cos[x]^4],x]","\frac{1}{2} \tan (x) \sqrt{a \cos ^4(x)}+\frac{1}{2} x \sec ^2(x) \sqrt{a \cos ^4(x)}","\frac{1}{2} \tan (x) \sqrt{a \cos ^4(x)}+\frac{1}{2} x \sec ^2(x) \sqrt{a \cos ^4(x)}",1,"(x*Sqrt[a*Cos[x]^4]*Sec[x]^2)/2 + (Sqrt[a*Cos[x]^4]*Tan[x])/2","A",3,3,10,0.3000,1,"{3207, 2635, 8}"
54,1,15,0,0.0140777,"\int \frac{1}{\sqrt{a \cos ^4(x)}} \, dx","Int[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",3,3,10,0.3000,1,"{3207, 3767, 8}"
55,1,67,0,0.0214227,"\int \frac{1}{\left(a \cos ^4(x)\right)^{3/2}} \, dx","Int[(a*Cos[x]^4)^(-3/2),x]","\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)}}","\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]*Sin[x])/(a*Sqrt[a*Cos[x]^4]) + (2*Sin[x]^2*Tan[x])/(3*a*Sqrt[a*Cos[x]^4]) + (Sin[x]^2*Tan[x]^3)/(5*a*Sqrt[a*Cos[x]^4])","A",3,2,10,0.2000,1,"{3207, 3767}"
56,1,117,0,0.0321276,"\int \frac{1}{\left(a \cos ^4(x)\right)^{5/2}} \, dx","Int[(a*Cos[x]^4)^(-5/2),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)}}","\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,"(Cos[x]*Sin[x])/(a^2*Sqrt[a*Cos[x]^4]) + (4*Sin[x]^2*Tan[x])/(3*a^2*Sqrt[a*Cos[x]^4]) + (6*Sin[x]^2*Tan[x]^3)/(5*a^2*Sqrt[a*Cos[x]^4]) + (4*Sin[x]^2*Tan[x]^5)/(7*a^2*Sqrt[a*Cos[x]^4]) + (Sin[x]^2*Tan[x]^7)/(9*a^2*Sqrt[a*Cos[x]^4])","A",3,2,10,0.2000,1,"{3207, 3767}"
57,1,78,0,0.0347181,"\int \left(b \cos ^m(c+d x)\right)^n \, dx","Int[(b*Cos[c + d*x]^m)^n,x]","-\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)}}","-\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,"-((Cos[c + d*x]*(b*Cos[c + d*x]^m)^n*Hypergeometric2F1[1/2, (1 + m*n)/2, (3 + m*n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + m*n)*Sqrt[Sin[c + d*x]^2]))","A",2,2,12,0.1667,1,"{3208, 2643}"
58,1,89,0,0.0400767,"\int \left(c \cos ^m(a+b x)\right)^{5/2} \, dx","Int[(c*Cos[a + b*x]^m)^(5/2),x]","-\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)}}","-\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^2*Cos[a + b*x]^(1 + 2*m)*Sqrt[c*Cos[a + b*x]^m]*Hypergeometric2F1[1/2, (2 + 5*m)/4, (6 + 5*m)/4, Cos[a + b*x]^2]*Sin[a + b*x])/(b*(2 + 5*m)*Sqrt[Sin[a + b*x]^2])","A",2,2,14,0.1429,1,"{3208, 2643}"
59,1,83,0,0.039055,"\int \left(c \cos ^m(a+b x)\right)^{3/2} \, dx","Int[(c*Cos[a + b*x]^m)^(3/2),x]","-\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)}}","-\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]^(1 + m)*Sqrt[c*Cos[a + b*x]^m]*Hypergeometric2F1[1/2, (2 + 3*m)/4, (3*(2 + m))/4, Cos[a + b*x]^2]*Sin[a + b*x])/(b*(2 + 3*m)*Sqrt[Sin[a + b*x]^2])","A",2,2,14,0.1429,1,"{3208, 2643}"
60,1,74,0,0.0392015,"\int \sqrt{c \cos ^m(a+b x)} \, dx","Int[Sqrt[c*Cos[a + b*x]^m],x]","-\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)}}","-\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*Cos[a + b*x]*Sqrt[c*Cos[a + b*x]^m]*Hypergeometric2F1[1/2, (2 + m)/4, (6 + m)/4, Cos[a + b*x]^2]*Sin[a + b*x])/(b*(2 + m)*Sqrt[Sin[a + b*x]^2])","A",2,2,14,0.1429,1,"{3208, 2643}"
61,1,80,0,0.0466379,"\int \frac{1}{\sqrt{c \cos ^m(a+b x)}} \, dx","Int[1/Sqrt[c*Cos[a + b*x]^m],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)}}","-\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*Cos[a + b*x]*Hypergeometric2F1[1/2, (2 - m)/4, (6 - m)/4, Cos[a + b*x]^2]*Sin[a + b*x])/(b*(2 - m)*Sqrt[c*Cos[a + b*x]^m]*Sqrt[Sin[a + b*x]^2])","A",2,2,14,0.1429,1,"{3208, 2643}"
62,1,89,0,0.0465239,"\int \frac{1}{\left(c \cos ^m(a+b x)\right)^{3/2}} \, dx","Int[(c*Cos[a + b*x]^m)^(-3/2),x]","-\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)}}","-\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,"(-2*Cos[a + b*x]^(1 - m)*Hypergeometric2F1[1/2, (2 - 3*m)/4, (3*(2 - m))/4, Cos[a + b*x]^2]*Sin[a + b*x])/(b*c*(2 - 3*m)*Sqrt[c*Cos[a + b*x]^m]*Sqrt[Sin[a + b*x]^2])","A",2,2,14,0.1429,1,"{3208, 2643}"
63,1,89,0,0.0453095,"\int \frac{1}{\left(c \cos ^m(a+b x)\right)^{5/2}} \, dx","Int[(c*Cos[a + b*x]^m)^(-5/2),x]","-\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)}}","-\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,"(-2*Cos[a + b*x]^(1 - 2*m)*Hypergeometric2F1[1/2, (2 - 5*m)/4, (6 - 5*m)/4, Cos[a + b*x]^2]*Sin[a + b*x])/(b*c^2*(2 - 5*m)*Sqrt[c*Cos[a + b*x]^m]*Sqrt[Sin[a + b*x]^2])","A",2,2,14,0.1429,1,"{3208, 2643}"
64,1,24,0,0.0198843,"\int \left(c \cos ^m(a+b x)\right)^{\frac{1}{m}} \, dx","Int[(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",2,2,14,0.1429,1,"{3208, 2637}"
65,1,80,0,0.0461189,"\int \left(a (b \cos (c+d x))^p\right)^n \, dx","Int[(a*(b*Cos[c + d*x])^p)^n,x]","-\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)}}","-\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,"-((Cos[c + d*x]*(a*(b*Cos[c + d*x])^p)^n*Hypergeometric2F1[1/2, (1 + n*p)/2, (3 + n*p)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + n*p)*Sqrt[Sin[c + d*x]^2]))","A",2,2,14,0.1429,1,"{3208, 2643}"
66,1,123,0,0.0900455,"\int \cos ^5(c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^5*Sqrt[b*Cos[c + d*x]],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)}}","\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,"(30*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(77*d*Sqrt[b*Cos[c + d*x]]) + (30*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(77*d) + (18*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(77*b^2*d) + (2*(b*Cos[c + d*x])^(9/2)*Sin[c + d*x])/(11*b^4*d)","A",6,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
67,1,97,0,0.069299,"\int \cos ^4(c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^4*Sqrt[b*Cos[c + d*x]],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)}}","\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,"(14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (14*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b*d) + (2*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^3*d)","A",5,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
68,1,95,0,0.0658559,"\int \cos ^3(c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^3*Sqrt[b*Cos[c + d*x]],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)}}","\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,"(10*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^2*d)","A",5,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
69,1,69,0,0.0409837,"\int \cos ^2(c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^2*Sqrt[b*Cos[c + d*x]],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)}}","\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,"(6*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b*d)","A",4,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
70,1,67,0,0.0428716,"\int \cos (c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]*Sqrt[b*Cos[c + d*x]],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)}}","\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*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",4,4,19,0.2105,1,"{16, 2635, 2642, 2641}"
71,1,38,0,0.0200229,"\int \sqrt{b \cos (c+d x)} \, dx","Int[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",2,2,12,0.1667,1,"{2640, 2639}"
72,1,39,0,0.0292921,"\int \sqrt{b \cos (c+d x)} \sec (c+d x) \, dx","Int[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",3,3,19,0.1579,1,"{16, 2642, 2641}"
73,1,63,0,0.0546447,"\int \sqrt{b \cos (c+d x)} \sec ^2(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^2,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)}}","\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*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
74,1,70,0,0.0568187,"\int \sqrt{b \cos (c+d x)} \sec ^3(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^3,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)}}","\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])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
75,1,95,0,0.0734399,"\int \sqrt{b \cos (c+d x)} \sec ^4(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^4,x]","\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)}}","\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,"(-6*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^3*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (6*b*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
76,1,98,0,0.0723142,"\int \sqrt{b \cos (c+d x)} \sec ^5(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^5,x]","\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)}}","\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,"(10*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b^4*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (10*b^2*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
77,1,123,0,0.0969328,"\int \sqrt{b \cos (c+d x)} \sec ^6(c+d x) \, dx","Int[Sqrt[b*Cos[c + d*x]]*Sec[c + d*x]^6,x]","\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)}}","\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,"(-14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (2*b^5*Sin[c + d*x])/(9*d*(b*Cos[c + d*x])^(9/2)) + (14*b^3*Sin[c + d*x])/(45*d*(b*Cos[c + d*x])^(5/2)) + (14*b*Sin[c + d*x])/(15*d*Sqrt[b*Cos[c + d*x]])","A",6,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
78,1,126,0,0.0859398,"\int \cos ^4(c+d x) (b \cos (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^4*(b*Cos[c + d*x])^(3/2),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}","\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,"(30*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(77*d*Sqrt[b*Cos[c + d*x]]) + (30*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(77*d) + (18*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(77*b*d) + (2*(b*Cos[c + d*x])^(9/2)*Sin[c + d*x])/(11*b^3*d)","A",6,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
79,1,95,0,0.0601152,"\int \cos ^3(c+d x) (b \cos (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^3*(b*Cos[c + d*x])^(3/2),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)}}","\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,"(14*b*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (14*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*d) + (2*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^2*d)","A",5,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
80,1,98,0,0.0605094,"\int \cos ^2(c+d x) (b \cos (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(3/2),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}","\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,"(10*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b*d)","A",5,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
81,1,67,0,0.039129,"\int \cos (c+d x) (b \cos (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(3/2),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)}}","\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,"(6*b*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",4,4,19,0.2105,1,"{16, 2635, 2640, 2639}"
82,1,70,0,0.0333971,"\int (b \cos (c+d x))^{3/2} \, dx","Int[(b*Cos[c + d*x])^(3/2),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}","\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^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",3,3,12,0.2500,1,"{2635, 2642, 2641}"
83,1,39,0,0.0291086,"\int (b \cos (c+d x))^{3/2} \sec (c+d x) \, dx","Int[(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",3,3,19,0.1579,1,"{16, 2640, 2639}"
84,1,41,0,0.0380161,"\int (b \cos (c+d x))^{3/2} \sec ^2(c+d x) \, dx","Int[(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",3,3,21,0.1429,1,"{16, 2642, 2641}"
85,1,66,0,0.0544,"\int (b \cos (c+d x))^{3/2} \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^3,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)}}","\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*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^2*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
86,1,72,0,0.0537292,"\int (b \cos (c+d x))^{3/2} \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^4,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)}}","\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])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b^3*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
87,1,98,0,0.0737354,"\int (b \cos (c+d x))^{3/2} \sec ^5(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^5,x]","\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)}}","\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,"(-6*b*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^4*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (6*b^2*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
88,1,100,0,0.0734373,"\int (b \cos (c+d x))^{3/2} \sec ^6(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^6,x]","\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)}}","\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,"(10*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b^5*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (10*b^3*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
89,1,126,0,0.0945455,"\int (b \cos (c+d x))^{3/2} \sec ^7(c+d x) \, dx","Int[(b*Cos[c + d*x])^(3/2)*Sec[c + d*x]^7,x]","\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)}}","\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,"(-14*b*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (2*b^6*Sin[c + d*x])/(9*d*(b*Cos[c + d*x])^(9/2)) + (14*b^4*Sin[c + d*x])/(45*d*(b*Cos[c + d*x])^(5/2)) + (14*b^2*Sin[c + d*x])/(15*d*Sqrt[b*Cos[c + d*x]])","A",6,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
90,1,125,0,0.0804959,"\int \cos ^3(c+d x) (b \cos (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^3*(b*Cos[c + d*x])^(5/2),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{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{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 d}","\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{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{18 \sin (c+d x) (b \cos (c+d x))^{5/2}}{77 d}",1,"(30*b^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(77*d*Sqrt[b*Cos[c + d*x]]) + (30*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(77*d) + (18*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(77*d) + (2*(b*Cos[c + d*x])^(9/2)*Sin[c + d*x])/(11*b^2*d)","A",6,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
91,1,98,0,0.0589,"\int \cos ^2(c+d x) (b \cos (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(5/2),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}","\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,"(14*b^2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (14*b*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*d) + (2*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b*d)","A",5,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
92,1,97,0,0.0579795,"\int \cos (c+d x) (b \cos (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(5/2),x]","\frac{10 b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\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{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}","\frac{10 b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\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{2 \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}",1,"(10*b^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*d)","A",5,4,19,0.2105,1,"{16, 2635, 2642, 2641}"
93,1,70,0,0.0327125,"\int (b \cos (c+d x))^{5/2} \, dx","Int[(b*Cos[c + d*x])^(5/2),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}","\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,"(6*b^2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*d)","A",3,3,12,0.2500,1,"{2635, 2640, 2639}"
94,1,72,0,0.0481798,"\int (b \cos (c+d x))^{5/2} \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x],x]","\frac{2 b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{3 d}+\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}+\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])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*d)","A",4,4,19,0.2105,1,"{16, 2635, 2642, 2641}"
95,1,41,0,0.0394378,"\int (b \cos (c+d x))^{5/2} \sec ^2(c+d x) \, dx","Int[(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",3,3,21,0.1429,1,"{16, 2640, 2639}"
96,1,41,0,0.0380636,"\int (b \cos (c+d x))^{5/2} \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^3,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)}}","\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^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(d*Sqrt[b*Cos[c + d*x]])","A",3,3,21,0.1429,1,"{16, 2642, 2641}"
97,1,68,0,0.055213,"\int (b \cos (c+d x))^{5/2} \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^4,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)}}","\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^2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]) + (2*b^3*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
98,1,72,0,0.0563395,"\int (b \cos (c+d x))^{5/2} \sec ^5(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^5,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)}}","\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])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b^4*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
99,1,100,0,0.07335,"\int (b \cos (c+d x))^{5/2} \sec ^6(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^6,x]","\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)}}","\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,"(-6*b^2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*d*Sqrt[Cos[c + d*x]]) + (2*b^5*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (6*b^3*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
100,1,100,0,0.0741106,"\int (b \cos (c+d x))^{5/2} \sec ^7(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^7,x]","\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)}}","\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,"(10*b^3*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b^6*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (10*b^4*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
101,1,128,0,0.0948979,"\int (b \cos (c+d x))^{5/2} \sec ^8(c+d x) \, dx","Int[(b*Cos[c + d*x])^(5/2)*Sec[c + d*x]^8,x]","\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)}}","\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,"(-14*b^2*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*d*Sqrt[Cos[c + d*x]]) + (2*b^7*Sin[c + d*x])/(9*d*(b*Cos[c + d*x])^(9/2)) + (14*b^5*Sin[c + d*x])/(45*d*(b*Cos[c + d*x])^(5/2)) + (14*b^3*Sin[c + d*x])/(15*d*Sqrt[b*Cos[c + d*x]])","A",6,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
102,1,98,0,0.0505346,"\int (b \cos (c+d x))^{7/2} \, dx","Int[(b*Cos[c + d*x])^(7/2),x]","\frac{10 b^3 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\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{2 b \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}","\frac{10 b^3 \sin (c+d x) \sqrt{b \cos (c+d x)}}{21 d}+\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{2 b \sin (c+d x) (b \cos (c+d x))^{5/2}}{7 d}",1,"(10*b^4*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*b^3*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*d) + (2*b*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*d)","A",4,3,12,0.2500,1,"{2635, 2642, 2641}"
103,1,125,0,0.0913516,"\int \frac{\cos ^6(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^6/Sqrt[b*Cos[c + d*x]],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)}}","\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,"(30*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(77*d*Sqrt[b*Cos[c + d*x]]) + (30*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(77*b*d) + (18*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(77*b^3*d) + (2*(b*Cos[c + d*x])^(9/2)*Sin[c + d*x])/(11*b^5*d)","A",6,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
104,1,100,0,0.0589798,"\int \frac{\cos ^5(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^5/Sqrt[b*Cos[c + d*x]],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)}}","\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,"(14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b*d*Sqrt[Cos[c + d*x]]) + (14*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^2*d) + (2*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^4*d)","A",5,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
105,1,97,0,0.0617787,"\int \frac{\cos ^4(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^4/Sqrt[b*Cos[c + d*x]],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)}}","\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,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*d*Sqrt[b*Cos[c + d*x]]) + (10*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b*d) + (2*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^3*d)","A",5,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
106,1,72,0,0.039397,"\int \frac{\cos ^3(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^3/Sqrt[b*Cos[c + d*x]],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)}}","\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^2*d)","A",4,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
107,1,69,0,0.039005,"\int \frac{\cos ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^2/Sqrt[b*Cos[c + d*x]],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)}}","\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])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b*d)","A",4,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
108,1,41,0,0.0234976,"\int \frac{\cos (c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[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",3,3,19,0.1579,1,"{16, 2640, 2639}"
109,1,38,0,0.0192094,"\int \frac{1}{\sqrt{b \cos (c+d x)}} \, dx","Int[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",2,2,12,0.1667,1,"{2642, 2641}"
110,1,65,0,0.0444571,"\int \frac{\sec (c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]/Sqrt[b*Cos[c + d*x]],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)}}","\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]) + (2*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]])","A",4,4,19,0.2105,1,"{16, 2636, 2640, 2639}"
111,1,67,0,0.0514868,"\int \frac{\sec ^2(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]^2/Sqrt[b*Cos[c + d*x]],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)}}","\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])/(3*d*Sqrt[b*Cos[c + d*x]]) + (2*b*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
112,1,97,0,0.0732165,"\int \frac{\sec ^3(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]^3/Sqrt[b*Cos[c + d*x]],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)}}","\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b*d*Sqrt[Cos[c + d*x]]) + (2*b^2*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (6*Sin[c + d*x])/(5*d*Sqrt[b*Cos[c + d*x]])","A",5,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
113,1,95,0,0.0718351,"\int \frac{\sec ^4(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]^4/Sqrt[b*Cos[c + d*x]],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)}}","\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])/(21*d*Sqrt[b*Cos[c + d*x]]) + (2*b^3*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (10*b*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
114,1,125,0,0.0937142,"\int \frac{\sec ^5(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]^5/Sqrt[b*Cos[c + d*x]],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)}}","\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,"(-14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b*d*Sqrt[Cos[c + d*x]]) + (2*b^4*Sin[c + d*x])/(9*d*(b*Cos[c + d*x])^(9/2)) + (14*b^2*Sin[c + d*x])/(45*d*(b*Cos[c + d*x])^(5/2)) + (14*Sin[c + d*x])/(15*d*Sqrt[b*Cos[c + d*x]])","A",6,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
115,1,128,0,0.0825005,"\int \frac{\cos ^7(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^7/(b*Cos[c + d*x])^(3/2),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)}}","\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,"(30*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(77*b*d*Sqrt[b*Cos[c + d*x]]) + (30*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(77*b^2*d) + (18*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(77*b^4*d) + (2*(b*Cos[c + d*x])^(9/2)*Sin[c + d*x])/(11*b^6*d)","A",6,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
116,1,100,0,0.0580826,"\int \frac{\cos ^6(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^6/(b*Cos[c + d*x])^(3/2),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)}}","\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,"(14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^2*d*Sqrt[Cos[c + d*x]]) + (14*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^3*d) + (2*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^5*d)","A",5,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
117,1,100,0,0.0602144,"\int \frac{\cos ^5(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^5/(b*Cos[c + d*x])^(3/2),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)}}","\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,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b*d*Sqrt[b*Cos[c + d*x]]) + (10*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^2*d) + (2*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^4*d)","A",5,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
118,1,72,0,0.0396234,"\int \frac{\cos ^4(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^4/(b*Cos[c + d*x])^(3/2),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)}}","\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^3*d)","A",4,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
119,1,72,0,0.0406043,"\int \frac{\cos ^3(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^3/(b*Cos[c + d*x])^(3/2),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)}}","\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])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^2*d)","A",4,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
120,1,41,0,0.0233109,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[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",3,3,21,0.1429,1,"{16, 2640, 2639}"
121,1,41,0,0.0238076,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[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",3,3,19,0.1579,1,"{16, 2642, 2641}"
122,1,68,0,0.0336752,"\int \frac{1}{(b \cos (c+d x))^{3/2}} \, dx","Int[(b*Cos[c + d*x])^(-3/2),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)}}","\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^2*d*Sqrt[Cos[c + d*x]]) + (2*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",3,3,12,0.2500,1,"{2636, 2640, 2639}"
123,1,69,0,0.0477973,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]/(b*Cos[c + d*x])^(3/2),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)}}","\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])/(3*b*d*Sqrt[b*Cos[c + d*x]]) + (2*Sin[c + d*x])/(3*d*(b*Cos[c + d*x])^(3/2))","A",4,4,19,0.2105,1,"{16, 2636, 2642, 2641}"
124,1,98,0,0.0761207,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^2/(b*Cos[c + d*x])^(3/2),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}}","-\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^2*d*Sqrt[Cos[c + d*x]]) + (2*b*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (6*Sin[c + d*x])/(5*b*d*Sqrt[b*Cos[c + d*x]])","A",5,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
125,1,97,0,0.0747481,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^3/(b*Cos[c + d*x])^(3/2),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)}}","\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])/(21*b*d*Sqrt[b*Cos[c + d*x]]) + (2*b^2*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (10*Sin[c + d*x])/(21*d*(b*Cos[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
126,1,126,0,0.0961565,"\int \frac{\sec ^4(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Sec[c + d*x]^4/(b*Cos[c + d*x])^(3/2),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)}}","\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,"(-14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^2*d*Sqrt[Cos[c + d*x]]) + (2*b^3*Sin[c + d*x])/(9*d*(b*Cos[c + d*x])^(9/2)) + (14*b*Sin[c + d*x])/(45*d*(b*Cos[c + d*x])^(5/2)) + (14*Sin[c + d*x])/(15*b*d*Sqrt[b*Cos[c + d*x]])","A",6,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
127,1,128,0,0.0823867,"\int \frac{\cos ^8(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^8/(b*Cos[c + d*x])^(5/2),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)}}","\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,"(30*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(77*b^2*d*Sqrt[b*Cos[c + d*x]]) + (30*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(77*b^3*d) + (18*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(77*b^5*d) + (2*(b*Cos[c + d*x])^(9/2)*Sin[c + d*x])/(11*b^7*d)","A",6,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
128,1,100,0,0.0599299,"\int \frac{\cos ^7(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^7/(b*Cos[c + d*x])^(5/2),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)}}","\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,"(14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^3*d*Sqrt[Cos[c + d*x]]) + (14*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(45*b^4*d) + (2*(b*Cos[c + d*x])^(7/2)*Sin[c + d*x])/(9*b^6*d)","A",5,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
129,1,100,0,0.0601368,"\int \frac{\cos ^6(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^6/(b*Cos[c + d*x])^(5/2),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)}}","\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,"(10*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(21*b^2*d*Sqrt[b*Cos[c + d*x]]) + (10*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(21*b^3*d) + (2*(b*Cos[c + d*x])^(5/2)*Sin[c + d*x])/(7*b^5*d)","A",5,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
130,1,72,0,0.0402655,"\int \frac{\cos ^5(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^5/(b*Cos[c + d*x])^(5/2),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)}}","\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*(b*Cos[c + d*x])^(3/2)*Sin[c + d*x])/(5*b^4*d)","A",4,4,21,0.1905,1,"{16, 2635, 2640, 2639}"
131,1,72,0,0.0407445,"\int \frac{\cos ^4(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^4/(b*Cos[c + d*x])^(5/2),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)}}","\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])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(3*b^3*d)","A",4,4,21,0.1905,1,"{16, 2635, 2642, 2641}"
132,1,41,0,0.0228908,"\int \frac{\cos ^3(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[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",3,3,21,0.1429,1,"{16, 2640, 2639}"
133,1,41,0,0.0255456,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^2/(b*Cos[c + d*x])^(5/2),x]","\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)}}","\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*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",3,3,21,0.1429,1,"{16, 2642, 2641}"
134,1,68,0,0.0422722,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]/(b*Cos[c + d*x])^(5/2),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)}}","\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[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(b^3*d*Sqrt[Cos[c + d*x]]) + (2*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",4,4,19,0.2105,1,"{16, 2636, 2640, 2639}"
135,1,72,0,0.0353592,"\int \frac{1}{(b \cos (c+d x))^{5/2}} \, dx","Int[(b*Cos[c + d*x])^(-5/2),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}}","\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])/(3*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*Sin[c + d*x])/(3*b*d*(b*Cos[c + d*x])^(3/2))","A",3,3,12,0.2500,1,"{2636, 2642, 2641}"
136,1,97,0,0.0696084,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]/(b*Cos[c + d*x])^(5/2),x]","\frac{6 \sin (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{2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}","\frac{6 \sin (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{2 \sin (c+d x)}{5 d (b \cos (c+d x))^{5/2}}",1,"(-6*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^3*d*Sqrt[Cos[c + d*x]]) + (2*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/2)) + (6*Sin[c + d*x])/(5*b^2*d*Sqrt[b*Cos[c + d*x]])","A",5,4,19,0.2105,1,"{16, 2636, 2640, 2639}"
137,1,98,0,0.0792451,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[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)}{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}}","\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])/(21*b^2*d*Sqrt[b*Cos[c + d*x]]) + (2*b*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/2)) + (10*Sin[c + d*x])/(21*b*d*(b*Cos[c + d*x])^(3/2))","A",5,4,21,0.1905,1,"{16, 2636, 2642, 2641}"
138,1,125,0,0.0979237,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Sec[c + d*x]^3/(b*Cos[c + d*x])^(5/2),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 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{14 \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}","\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 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{14 \sin (c+d x)}{45 d (b \cos (c+d x))^{5/2}}",1,"(-14*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(15*b^3*d*Sqrt[Cos[c + d*x]]) + (2*b^2*Sin[c + d*x])/(9*d*(b*Cos[c + d*x])^(9/2)) + (14*Sin[c + d*x])/(45*d*(b*Cos[c + d*x])^(5/2)) + (14*Sin[c + d*x])/(15*b^2*d*Sqrt[b*Cos[c + d*x]])","A",6,4,21,0.1905,1,"{16, 2636, 2640, 2639}"
139,1,100,0,0.0531143,"\int \frac{1}{(b \cos (c+d x))^{7/2}} \, dx","Int[(b*Cos[c + d*x])^(-7/2),x]","\frac{6 \sin (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{2 \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}","\frac{6 \sin (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{2 \sin (c+d x)}{5 b d (b \cos (c+d x))^{5/2}}",1,"(-6*Sqrt[b*Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2])/(5*b^4*d*Sqrt[Cos[c + d*x]]) + (2*Sin[c + d*x])/(5*b*d*(b*Cos[c + d*x])^(5/2)) + (6*Sin[c + d*x])/(5*b^3*d*Sqrt[b*Cos[c + d*x]])","A",4,3,12,0.2500,1,"{2636, 2640, 2639}"
140,1,98,0,0.0271258,"\int \cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]],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}","\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,"(3*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (3*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,3,23,0.1304,1,"{17, 2635, 8}"
141,1,70,0,0.0172808,"\int \cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^(5/2)*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 ^3(c+d x) \sqrt{b \cos (c+d x)}}{3 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]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
142,1,63,0,0.0141595,"\int \cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]],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}","\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,"(x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",3,3,23,0.1304,1,"{17, 2635, 8}"
143,1,32,0,0.0067261,"\int \sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)} \, dx","Int[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",2,2,23,0.08696,1,"{17, 2637}"
144,1,24,0,0.0025662,"\int \frac{\sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}} \, dx","Int[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",2,2,23,0.08696,1,"{17, 8}"
145,1,33,0,0.0077919,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[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",2,2,23,0.08696,1,"{17, 3770}"
146,1,32,0,0.0118561,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[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",3,3,23,0.1304,1,"{17, 3767, 8}"
147,1,72,0,0.0206031,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(7/2),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)}}","\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,"(ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2))","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
148,1,70,0,0.018236,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(9/2),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)}","\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]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2)) + (Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Cos[c + d*x]^(7/2))","A",3,2,23,0.08696,1,"{17, 3767}"
149,1,107,0,0.0359618,"\int \frac{\sqrt{b \cos (c+d x)}}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[Sqrt[b*Cos[c + d*x]]/Cos[c + d*x]^(11/2),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)}}","\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,"(3*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + (3*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2))","A",4,3,23,0.1304,1,"{17, 3768, 3770}"
150,1,101,0,0.0286958,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(3/2),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}","\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,"(3*b*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (3*b*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,3,23,0.1304,1,"{17, 2635, 8}"
151,1,72,0,0.0182427,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2} \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2),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)}}","\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*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
152,1,65,0,0.014842,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2} \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2),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}","\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*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",3,3,23,0.1304,1,"{17, 2635, 8}"
153,1,33,0,0.0069987,"\int \frac{(b \cos (c+d x))^{3/2}}{\sqrt{\cos (c+d x)}} \, dx","Int[(b*Cos[c + d*x])^(3/2)/Sqrt[Cos[c + d*x]],x]","\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}","\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \sqrt{\cos (c+d x)}}",1,"(b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
154,1,25,0,0.0027328,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(3/2),x]","\frac{b x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{b x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(b*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]]","A",2,2,23,0.08696,1,"{17, 8}"
155,1,34,0,0.007926,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(5/2),x]","\frac{b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}","\frac{b \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (c+d x)}}",1,"(b*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
156,1,33,0,0.012162,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(7/2),x]","\frac{b \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{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*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",3,3,23,0.1304,1,"{17, 3767, 8}"
157,1,74,0,0.0210489,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(9/2),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)}}","\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*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2))","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
158,1,72,0,0.0183373,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(11/2),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)}","\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*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2)) + (b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Cos[c + d*x]^(7/2))","A",3,2,23,0.08696,1,"{17, 3767}"
159,1,110,0,0.0392478,"\int \frac{(b \cos (c+d x))^{3/2}}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(3/2)/Cos[c + d*x]^(13/2),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)}}","\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,"(3*b*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + (3*b*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2))","A",4,3,23,0.1304,1,"{17, 3768, 3770}"
160,1,116,0,0.025976,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(5/2),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)}}","\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^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (2*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]]) + (b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^5)/(5*d*Sqrt[Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
161,1,107,0,0.0299723,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{5/2} \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(5/2),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}","\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,"(3*b^2*x*Sqrt[b*Cos[c + d*x]])/(8*Sqrt[Cos[c + d*x]]) + (3*b^2*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d) + (b^2*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d)","A",4,3,23,0.1304,1,"{17, 2635, 8}"
162,1,76,0,0.0181426,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2} \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2),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)}}","\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^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]]) - (b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
163,1,69,0,0.0155617,"\int \frac{(b \cos (c+d x))^{5/2}}{\sqrt{\cos (c+d x)}} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Sqrt[Cos[c + d*x]],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}","\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^2*x*Sqrt[b*Cos[c + d*x]])/(2*Sqrt[Cos[c + d*x]]) + (b^2*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d)","A",3,3,23,0.1304,1,"{17, 2635, 8}"
164,1,35,0,0.008181,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(3/2),x]","\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{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^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
165,1,27,0,0.0027092,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(5/2),x]","\frac{b^2 x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}","\frac{b^2 x \sqrt{b \cos (c+d x)}}{\sqrt{\cos (c+d x)}}",1,"(b^2*x*Sqrt[b*Cos[c + d*x]])/Sqrt[Cos[c + d*x]]","A",2,2,23,0.08696,1,"{17, 8}"
166,1,36,0,0.0094418,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(7/2),x]","\frac{b^2 \sqrt{b \cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\cos (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,"(b^2*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(d*Sqrt[Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
167,1,35,0,0.0123448,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(9/2),x]","\frac{b^2 \sin (c+d x) \sqrt{b \cos (c+d x)}}{d \cos ^{\frac{3}{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^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2))","A",3,3,23,0.1304,1,"{17, 3767, 8}"
168,1,78,0,0.0212637,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{11}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(11/2),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)}}","\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^2*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(2*d*Sqrt[Cos[c + d*x]]) + (b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(2*d*Cos[c + d*x]^(5/2))","A",3,3,23,0.1304,1,"{17, 3768, 3770}"
169,1,76,0,0.0191562,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{13}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(13/2),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)}","\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^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(d*Cos[c + d*x]^(3/2)) + (b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Cos[c + d*x]^(7/2))","A",3,2,23,0.08696,1,"{17, 3767}"
170,1,116,0,0.0358522,"\int \frac{(b \cos (c+d x))^{5/2}}{\cos ^{\frac{15}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^(5/2)/Cos[c + d*x]^(15/2),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)}}","\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,"(3*b^2*ArcTanh[Sin[c + d*x]]*Sqrt[b*Cos[c + d*x]])/(8*d*Sqrt[Cos[c + d*x]]) + (b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(4*d*Cos[c + d*x]^(9/2)) + (3*b^2*Sqrt[b*Cos[c + d*x]]*Sin[c + d*x])/(8*d*Cos[c + d*x]^(5/2))","A",4,3,23,0.1304,1,"{17, 3768, 3770}"
171,1,107,0,0.0239209,"\int \frac{\cos ^{\frac{11}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^(11/2)/Sqrt[b*Cos[c + d*x]],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)}}","\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])/(d*Sqrt[b*Cos[c + d*x]]) - (2*Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[b*Cos[c + d*x]]) + (Sqrt[Cos[c + d*x]]*Sin[c + d*x]^5)/(5*d*Sqrt[b*Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
172,1,98,0,0.027159,"\int \frac{\cos ^{\frac{9}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^(9/2)/Sqrt[b*Cos[c + d*x]],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)}}","\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,"(3*x*Sqrt[Cos[c + d*x]])/(8*Sqrt[b*Cos[c + d*x]]) + (3*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*d*Sqrt[b*Cos[c + d*x]]) + (Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*d*Sqrt[b*Cos[c + d*x]])","A",4,3,23,0.1304,1,"{17, 2635, 8}"
173,1,70,0,0.0168504,"\int \frac{\cos ^{\frac{7}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^(7/2)/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 ^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)}}-\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]]*Sin[c + d*x])/(d*Sqrt[b*Cos[c + d*x]]) - (Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*d*Sqrt[b*Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
174,1,63,0,0.0146331,"\int \frac{\cos ^{\frac{5}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^(5/2)/Sqrt[b*Cos[c + d*x]],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)}}","\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,"(x*Sqrt[Cos[c + d*x]])/(2*Sqrt[b*Cos[c + d*x]]) + (Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*d*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{17, 2635, 8}"
175,1,32,0,0.0068127,"\int \frac{\cos ^{\frac{3}{2}}(c+d x)}{\sqrt{b \cos (c+d x)}} \, dx","Int[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",2,2,23,0.08696,1,"{17, 2637}"
176,1,24,0,0.0025845,"\int \frac{\sqrt{\cos (c+d x)}}{\sqrt{b \cos (c+d x)}} \, dx","Int[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",2,2,23,0.08696,1,"{17, 8}"
177,1,33,0,0.0072366,"\int \frac{1}{\sqrt{\cos (c+d x)} \sqrt{b \cos (c+d x)}} \, dx","Int[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",2,2,23,0.08696,1,"{18, 3770}"
178,1,32,0,0.0122905,"\int \frac{1}{\cos ^{\frac{3}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[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",3,3,23,0.1304,1,"{18, 3767, 8}"
179,1,72,0,0.0217717,"\int \frac{1}{\cos ^{\frac{5}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[1/(Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]]),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)}}","\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]]*Sqrt[Cos[c + d*x]])/(2*d*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]/(2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{18, 3768, 3770}"
180,1,70,0,0.0179936,"\int \frac{1}{\cos ^{\frac{7}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[1/(Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]),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)}}","\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,"Sin[c + d*x]/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]^3/(3*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]])","A",3,2,23,0.08696,1,"{18, 3767}"
181,1,107,0,0.0349813,"\int \frac{1}{\cos ^{\frac{9}{2}}(c+d x) \sqrt{b \cos (c+d x)}} \, dx","Int[1/(Cos[c + d*x]^(9/2)*Sqrt[b*Cos[c + d*x]]),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)}}","\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]]*Sqrt[Cos[c + d*x]])/(8*d*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]/(4*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + (3*Sin[c + d*x])/(8*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",4,3,23,0.1304,1,"{18, 3768, 3770}"
182,1,107,0,0.0290272,"\int \frac{\cos ^{\frac{11}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^(11/2)/(b*Cos[c + d*x])^(3/2),x]","\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)}}","\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,"(3*x*Sqrt[Cos[c + d*x]])/(8*b*Sqrt[b*Cos[c + d*x]]) + (3*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*b*d*Sqrt[b*Cos[c + d*x]]) + (Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*b*d*Sqrt[b*Cos[c + d*x]])","A",4,3,23,0.1304,1,"{17, 2635, 8}"
183,1,76,0,0.0190838,"\int \frac{\cos ^{\frac{9}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^(9/2)/(b*Cos[c + d*x])^(3/2),x]","\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)}}","\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,"(Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]]) - (Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*b*d*Sqrt[b*Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
184,1,69,0,0.0164085,"\int \frac{\cos ^{\frac{7}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^(7/2)/(b*Cos[c + d*x])^(3/2),x]","\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)}}","\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,"(x*Sqrt[Cos[c + d*x]])/(2*b*Sqrt[b*Cos[c + d*x]]) + (Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b*d*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{17, 2635, 8}"
185,1,35,0,0.0072789,"\int \frac{\cos ^{\frac{5}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^(5/2)/(b*Cos[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}","\frac{\sin (c+d x) \sqrt{\cos (c+d x)}}{b d \sqrt{b \cos (c+d x)}}",1,"(Sqrt[Cos[c + d*x]]*Sin[c + d*x])/(b*d*Sqrt[b*Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 2637}"
186,1,27,0,0.002648,"\int \frac{\cos ^{\frac{3}{2}}(c+d x)}{(b \cos (c+d x))^{3/2}} \, dx","Int[Cos[c + d*x]^(3/2)/(b*Cos[c + d*x])^(3/2),x]","\frac{x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}","\frac{x \sqrt{\cos (c+d x)}}{b \sqrt{b \cos (c+d x)}}",1,"(x*Sqrt[Cos[c + d*x]])/(b*Sqrt[b*Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 8}"
187,1,36,0,0.0084481,"\int \frac{\sqrt{\cos (c+d x)}}{(b \cos (c+d x))^{3/2}} \, dx","Int[Sqrt[Cos[c + d*x]]/(b*Cos[c + d*x])^(3/2),x]","\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \cos (c+d x)}}","\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]]*Sqrt[Cos[c + d*x]])/(b*d*Sqrt[b*Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
188,1,35,0,0.01258,"\int \frac{1}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{3/2}} \, dx","Int[1/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(3/2)),x]","\frac{\sin (c+d x)}{b d \sqrt{\cos (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,"Sin[c + d*x]/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{18, 3767, 8}"
189,1,78,0,0.021936,"\int \frac{1}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[1/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(3/2)),x]","\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)}}","\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]]*Sqrt[Cos[c + d*x]])/(2*b*d*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]/(2*b*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{18, 3768, 3770}"
190,1,76,0,0.01873,"\int \frac{1}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[1/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(3/2)),x]","\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)}}","\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,"Sin[c + d*x]/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]^3/(3*b*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]])","A",3,2,23,0.08696,1,"{18, 3767}"
191,1,116,0,0.0366223,"\int \frac{1}{\cos ^{\frac{7}{2}}(c+d x) (b \cos (c+d x))^{3/2}} \, dx","Int[1/(Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^(3/2)),x]","\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)}}","\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]]*Sqrt[Cos[c + d*x]])/(8*b*d*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]/(4*b*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + (3*Sin[c + d*x])/(8*b*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",4,3,23,0.1304,1,"{18, 3768, 3770}"
192,1,107,0,0.0278996,"\int \frac{\cos ^{\frac{13}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^(13/2)/(b*Cos[c + d*x])^(5/2),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)}}","\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,"(3*x*Sqrt[Cos[c + d*x]])/(8*b^2*Sqrt[b*Cos[c + d*x]]) + (3*Cos[c + d*x]^(3/2)*Sin[c + d*x])/(8*b^2*d*Sqrt[b*Cos[c + d*x]]) + (Cos[c + d*x]^(7/2)*Sin[c + d*x])/(4*b^2*d*Sqrt[b*Cos[c + d*x]])","A",4,3,23,0.1304,1,"{17, 2635, 8}"
193,1,76,0,0.0176209,"\int \frac{\cos ^{\frac{11}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^(11/2)/(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 ^3(c+d x) \sqrt{\cos (c+d x)}}{3 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]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Cos[c + d*x]]) - (Sqrt[Cos[c + d*x]]*Sin[c + d*x]^3)/(3*b^2*d*Sqrt[b*Cos[c + d*x]])","A",3,2,23,0.08696,1,"{17, 2633}"
194,1,69,0,0.0148098,"\int \frac{\cos ^{\frac{9}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^(9/2)/(b*Cos[c + d*x])^(5/2),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)}}","\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,"(x*Sqrt[Cos[c + d*x]])/(2*b^2*Sqrt[b*Cos[c + d*x]]) + (Cos[c + d*x]^(3/2)*Sin[c + d*x])/(2*b^2*d*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{17, 2635, 8}"
195,1,35,0,0.0072171,"\int \frac{\cos ^{\frac{7}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[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",2,2,23,0.08696,1,"{17, 2637}"
196,1,27,0,0.0026813,"\int \frac{\cos ^{\frac{5}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^(5/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}","\frac{x \sqrt{\cos (c+d x)}}{b^2 \sqrt{b \cos (c+d x)}}",1,"(x*Sqrt[Cos[c + d*x]])/(b^2*Sqrt[b*Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 8}"
197,1,36,0,0.0077614,"\int \frac{\cos ^{\frac{3}{2}}(c+d x)}{(b \cos (c+d x))^{5/2}} \, dx","Int[Cos[c + d*x]^(3/2)/(b*Cos[c + d*x])^(5/2),x]","\frac{\sqrt{\cos (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \cos (c+d x)}}","\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]]*Sqrt[Cos[c + d*x]])/(b^2*d*Sqrt[b*Cos[c + d*x]])","A",2,2,23,0.08696,1,"{17, 3770}"
198,1,35,0,0.0132257,"\int \frac{\sqrt{\cos (c+d x)}}{(b \cos (c+d x))^{5/2}} \, dx","Int[Sqrt[Cos[c + d*x]]/(b*Cos[c + d*x])^(5/2),x]","\frac{\sin (c+d x)}{b^2 d \sqrt{\cos (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,"Sin[c + d*x]/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{17, 3767, 8}"
199,1,78,0,0.0220886,"\int \frac{1}{\sqrt{\cos (c+d x)} (b \cos (c+d x))^{5/2}} \, dx","Int[1/(Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^(5/2)),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)}}","\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,"(ArcTanh[Sin[c + d*x]]*Sqrt[Cos[c + d*x]])/(2*b^2*d*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]/(2*b^2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",3,3,23,0.1304,1,"{18, 3768, 3770}"
200,1,76,0,0.01834,"\int \frac{1}{\cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Int[1/(Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^(5/2)),x]","\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)}}","\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,"Sin[c + d*x]/(b^2*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]^3/(3*b^2*d*Cos[c + d*x]^(5/2)*Sqrt[b*Cos[c + d*x]])","A",3,2,23,0.08696,1,"{18, 3767}"
201,1,116,0,0.0365752,"\int \frac{1}{\cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^{5/2}} \, dx","Int[1/(Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^(5/2)),x]","\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)}}","\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]]*Sqrt[Cos[c + d*x]])/(8*b^2*d*Sqrt[b*Cos[c + d*x]]) + Sin[c + d*x]/(4*b^2*d*Cos[c + d*x]^(7/2)*Sqrt[b*Cos[c + d*x]]) + (3*Sin[c + d*x])/(8*b^2*d*Cos[c + d*x]^(3/2)*Sqrt[b*Cos[c + d*x]])","A",4,3,23,0.1304,1,"{18, 3768, 3770}"
202,1,82,0,0.0261172,"\int \cos ^m(c+d x) \sqrt[3]{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(1/3),x]","-\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)}}","-\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,"(-3*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (4 + 3*m)/6, (10 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(4 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
203,1,58,0,0.019846,"\int \cos ^2(c+d x) \sqrt[3]{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(1/3),x]","-\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)}}","-\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*(b*Cos[c + d*x])^(10/3)*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*b^3*d*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
204,1,58,0,0.0204174,"\int \cos (c+d x) \sqrt[3]{b \cos (c+d x)} \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(1/3),x]","-\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)}}","-\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])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*b^2*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
205,1,58,0,0.013692,"\int \sqrt[3]{b \cos (c+d x)} \, dx","Int[(b*Cos[c + d*x])^(1/3),x]","-\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)}}","-\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])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*b*d*Sqrt[Sin[c + d*x]^2])","A",1,1,12,0.08333,1,"{2643}"
206,1,53,0,0.0244257,"\int \sqrt[3]{b \cos (c+d x)} \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(1/3)*Sec[c + d*x],x]","-\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)}}","-\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*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
207,1,56,0,0.0308035,"\int \sqrt[3]{b \cos (c+d x)} \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(1/3)*Sec[c + d*x]^2,x]","\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}}","\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*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
208,1,58,0,0.0316683,"\int \sqrt[3]{b \cos (c+d x)} \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(1/3)*Sec[c + d*x]^3,x]","\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}}","\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^2*Hypergeometric2F1[-5/6, 1/2, 1/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
209,1,82,0,0.0278641,"\int \cos ^m(c+d x) (b \cos (c+d x))^{2/3} \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(2/3),x]","-\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)}}","-\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,"(-3*Cos[c + d*x]^(1 + m)*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/2, (5 + 3*m)/6, (11 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
210,1,58,0,0.0199932,"\int \cos ^2(c+d x) (b \cos (c+d x))^{2/3} \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(2/3),x]","-\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)}}","-\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*(b*Cos[c + d*x])^(11/3)*Hypergeometric2F1[1/2, 11/6, 17/6, Cos[c + d*x]^2]*Sin[c + d*x])/(11*b^3*d*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
211,1,58,0,0.0199726,"\int \cos (c+d x) (b \cos (c+d x))^{2/3} \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(2/3),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^2 d \sqrt{\sin ^2(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^2 d \sqrt{\sin ^2(c+d x)}}",1,"(-3*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^2*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
212,1,58,0,0.0144588,"\int (b \cos (c+d x))^{2/3} \, dx","Int[(b*Cos[c + d*x])^(2/3),x]","-\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)}}","-\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])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b*d*Sqrt[Sin[c + d*x]^2])","A",1,1,12,0.08333,1,"{2643}"
213,1,55,0,0.0265928,"\int (b \cos (c+d x))^{2/3} \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*Sec[c + d*x],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)}}","-\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*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
214,1,54,0,0.0360375,"\int (b \cos (c+d x))^{2/3} \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*Sec[c + d*x]^2,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)}}","\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*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
215,1,58,0,0.0356666,"\int (b \cos (c+d x))^{2/3} \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(2/3)*Sec[c + d*x]^3,x]","\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}}","\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^2*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
216,1,83,0,0.0263632,"\int \cos ^m(c+d x) (b \cos (c+d x))^{4/3} \, dx","Int[Cos[c + d*x]^m*(b*Cos[c + d*x])^(4/3),x]","-\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)}}","-\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,"(-3*b*Cos[c + d*x]^(2 + m)*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/2, (7 + 3*m)/6, (13 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 3*m)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
217,1,58,0,0.0198179,"\int \cos ^2(c+d x) (b \cos (c+d x))^{4/3} \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^(4/3),x]","-\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)}}","-\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*(b*Cos[c + d*x])^(13/3)*Hypergeometric2F1[1/2, 13/6, 19/6, Cos[c + d*x]^2]*Sin[c + d*x])/(13*b^3*d*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
218,1,58,0,0.0196422,"\int \cos (c+d x) (b \cos (c+d x))^{4/3} \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^(4/3),x]","-\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)}}","-\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])^(10/3)*Hypergeometric2F1[1/2, 5/3, 8/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*b^2*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
219,1,58,0,0.0143119,"\int (b \cos (c+d x))^{4/3} \, dx","Int[(b*Cos[c + d*x])^(4/3),x]","-\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)}}","-\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])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*b*d*Sqrt[Sin[c + d*x]^2])","A",1,1,12,0.08333,1,"{2643}"
220,1,55,0,0.0251622,"\int (b \cos (c+d x))^{4/3} \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*Sec[c + d*x],x]","-\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)}}","-\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*Cos[c + d*x])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
221,1,54,0,0.0355324,"\int (b \cos (c+d x))^{4/3} \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*Sec[c + d*x]^2,x]","-\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)}}","-\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*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
222,1,58,0,0.0367279,"\int (b \cos (c+d x))^{4/3} \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^(4/3)*Sec[c + d*x]^3,x]","\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}}","\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*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
223,1,82,0,0.0263166,"\int \frac{\cos ^m(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^m/(b*Cos[c + d*x])^(1/3),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)}}","-\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,"(-3*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (2 + 3*m)/6, (8 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(2 + 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
224,1,58,0,0.019733,"\int \frac{\cos ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]^2/(b*Cos[c + d*x])^(1/3),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)}}","-\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*(b*Cos[c + d*x])^(8/3)*Hypergeometric2F1[1/2, 4/3, 7/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*b^3*d*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
225,1,58,0,0.0195851,"\int \frac{\cos (c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[Cos[c + d*x]/(b*Cos[c + d*x])^(1/3),x]","-\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)}}","-\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])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^2*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
226,1,58,0,0.0144522,"\int \frac{1}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[(b*Cos[c + d*x])^(-1/3),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)}}","-\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*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*b*d*Sqrt[Sin[c + d*x]^2])","A",1,1,12,0.08333,1,"{2643}"
227,1,53,0,0.0259716,"\int \frac{\sec (c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]/(b*Cos[c + d*x])^(1/3),x]","\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)}}","\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*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
228,1,56,0,0.0338812,"\int \frac{\sec ^2(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]^2/(b*Cos[c + d*x])^(1/3),x]","\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}}","\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*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
229,1,58,0,0.0324211,"\int \frac{\sec ^3(c+d x)}{\sqrt[3]{b \cos (c+d x)}} \, dx","Int[Sec[c + d*x]^3/(b*Cos[c + d*x])^(1/3),x]","\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}}","\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*Hypergeometric2F1[-7/6, 1/2, -1/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
230,1,82,0,0.0246889,"\int \frac{\cos ^m(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[Cos[c + d*x]^m/(b*Cos[c + d*x])^(2/3),x]","-\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}}","-\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,"(-3*Cos[c + d*x]^(1 + m)*Hypergeometric2F1[1/2, (1 + 3*m)/6, (7 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 3*m)*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
231,1,58,0,0.0200931,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[Cos[c + d*x]^2/(b*Cos[c + d*x])^(2/3),x]","-\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)}}","-\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*(b*Cos[c + d*x])^(7/3)*Hypergeometric2F1[1/2, 7/6, 13/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*b^3*d*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
232,1,58,0,0.0201501,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[Cos[c + d*x]/(b*Cos[c + d*x])^(2/3),x]","-\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)}}","-\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])^(4/3)*Hypergeometric2F1[1/2, 2/3, 5/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*b^2*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
233,1,56,0,0.0151921,"\int \frac{1}{(b \cos (c+d x))^{2/3}} \, dx","Int[(b*Cos[c + d*x])^(-2/3),x]","-\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)}}","-\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*(b*Cos[c + d*x])^(1/3)*Hypergeometric2F1[1/6, 1/2, 7/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*Sqrt[Sin[c + d*x]^2])","A",1,1,12,0.08333,1,"{2643}"
234,1,55,0,0.0263834,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[Sec[c + d*x]/(b*Cos[c + d*x])^(2/3),x]","\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}}","\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*Hypergeometric2F1[-1/3, 1/2, 2/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*d*(b*Cos[c + d*x])^(2/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
235,1,56,0,0.0373004,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[Sec[c + d*x]^2/(b*Cos[c + d*x])^(2/3),x]","\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}}","\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*Hypergeometric2F1[-5/6, 1/2, 1/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*d*(b*Cos[c + d*x])^(5/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
236,1,58,0,0.0453945,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{2/3}} \, dx","Int[Sec[c + d*x]^3/(b*Cos[c + d*x])^(2/3),x]","\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}}","\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*Hypergeometric2F1[-4/3, 1/2, -1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(8*d*(b*Cos[c + d*x])^(8/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
237,1,83,0,0.0311037,"\int \frac{\cos ^m(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[Cos[c + d*x]^m/(b*Cos[c + d*x])^(4/3),x]","\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)}}","\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,"(3*Cos[c + d*x]^m*Hypergeometric2F1[1/2, (-1 + 3*m)/6, (5 + 3*m)/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 - 3*m)*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
238,1,58,0,0.0211971,"\int \frac{\cos ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[Cos[c + d*x]^2/(b*Cos[c + d*x])^(4/3),x]","-\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)}}","-\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])^(5/3)*Hypergeometric2F1[1/2, 5/6, 11/6, Cos[c + d*x]^2]*Sin[c + d*x])/(5*b^3*d*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
239,1,58,0,0.0205319,"\int \frac{\cos (c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[Cos[c + d*x]/(b*Cos[c + d*x])^(4/3),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)}}","-\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*(b*Cos[c + d*x])^(2/3)*Hypergeometric2F1[1/3, 1/2, 4/3, Cos[c + d*x]^2]*Sin[c + d*x])/(2*b^2*d*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
240,1,56,0,0.0155542,"\int \frac{1}{(b \cos (c+d x))^{4/3}} \, dx","Int[(b*Cos[c + d*x])^(-4/3),x]","\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)}}","\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*Hypergeometric2F1[-1/6, 1/2, 5/6, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(b*Cos[c + d*x])^(1/3)*Sqrt[Sin[c + d*x]^2])","A",1,1,12,0.08333,1,"{2643}"
241,1,55,0,0.0267245,"\int \frac{\sec (c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[Sec[c + d*x]/(b*Cos[c + d*x])^(4/3),x]","\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}}","\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*Hypergeometric2F1[-2/3, 1/2, 1/3, Cos[c + d*x]^2]*Sin[c + d*x])/(4*d*(b*Cos[c + d*x])^(4/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
242,1,56,0,0.0585996,"\int \frac{\sec ^2(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[Sec[c + d*x]^2/(b*Cos[c + d*x])^(4/3),x]","\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}}","\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*Hypergeometric2F1[-7/6, 1/2, -1/6, Cos[c + d*x]^2]*Sin[c + d*x])/(7*d*(b*Cos[c + d*x])^(7/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
243,1,58,0,0.0424405,"\int \frac{\sec ^3(c+d x)}{(b \cos (c+d x))^{4/3}} \, dx","Int[Sec[c + d*x]^3/(b*Cos[c + d*x])^(4/3),x]","\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}}","\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*Hypergeometric2F1[-5/3, 1/2, -2/3, Cos[c + d*x]^2]*Sin[c + d*x])/(10*d*(b*Cos[c + d*x])^(10/3)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{16, 2643}"
244,1,82,0,0.0343084,"\int (a \cos (e+f x))^m (b \cos (e+f x))^n \, dx","Int[(a*Cos[e + f*x])^m*(b*Cos[e + f*x])^n,x]","-\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)}}","-\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])^(1 + m)*(b*Cos[e + f*x])^n*Hypergeometric2F1[1/2, (1 + m + n)/2, (3 + m + n)/2, Cos[e + f*x]^2]*Sin[e + f*x])/(a*f*(1 + m + n)*Sqrt[Sin[e + f*x]^2]))","A",2,2,21,0.09524,1,"{20, 2643}"
245,1,69,0,0.0330704,"\int \cos ^2(c+d x) (b \cos (c+d x))^n \, dx","Int[Cos[c + d*x]^2*(b*Cos[c + d*x])^n,x]","-\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)}}","-\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,"-(((b*Cos[c + d*x])^(3 + n)*Hypergeometric2F1[1/2, (3 + n)/2, (5 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^3*d*(3 + n)*Sqrt[Sin[c + d*x]^2]))","A",2,2,19,0.1053,1,"{16, 2643}"
246,1,69,0,0.0491827,"\int \cos (c+d x) (b \cos (c+d x))^n \, dx","Int[Cos[c + d*x]*(b*Cos[c + d*x])^n,x]","-\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)}}","-\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,"-(((b*Cos[c + d*x])^(2 + n)*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b^2*d*(2 + n)*Sqrt[Sin[c + d*x]^2]))","A",2,2,17,0.1176,1,"{16, 2643}"
247,1,69,0,0.02375,"\int (b \cos (c+d x))^n \, dx","Int[(b*Cos[c + d*x])^n,x]","-\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)}}","-\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])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(b*d*(1 + n)*Sqrt[Sin[c + d*x]^2]))","A",1,1,10,0.1000,1,"{2643}"
248,1,60,0,0.0302036,"\int (b \cos (c+d x))^n \sec (c+d x) \, dx","Int[(b*Cos[c + d*x])^n*Sec[c + d*x],x]","-\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)}}","-\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*Cos[c + d*x])^n*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*n*Sqrt[Sin[c + d*x]^2]))","A",2,2,17,0.1176,1,"{16, 2643}"
249,1,68,0,0.0447606,"\int (b \cos (c+d x))^n \sec ^2(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*Sec[c + d*x]^2,x]","\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)}}","\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)*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n)*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
250,1,68,0,0.0418703,"\int (b \cos (c+d x))^n \sec ^3(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*Sec[c + d*x]^3,x]","\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)}}","\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^2*(b*Cos[c + d*x])^(-2 + n)*Hypergeometric2F1[1/2, (-2 + n)/2, n/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(2 - n)*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
251,1,70,0,0.0420231,"\int (b \cos (c+d x))^n \sec ^4(c+d x) \, dx","Int[(b*Cos[c + d*x])^n*Sec[c + d*x]^4,x]","\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)}}","\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^3*(b*Cos[c + d*x])^(-3 + n)*Hypergeometric2F1[1/2, (-3 + n)/2, (-1 + n)/2, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 - n)*Sqrt[Sin[c + d*x]^2])","A",2,2,19,0.1053,1,"{16, 2643}"
252,1,80,0,0.0270646,"\int \cos ^{\frac{5}{2}}(c+d x) (b \cos (c+d x))^n \, dx","Int[Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n,x]","-\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)}}","-\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,"(-2*Cos[c + d*x]^(7/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (7 + 2*n)/4, (11 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
253,1,80,0,0.0284351,"\int \cos ^{\frac{3}{2}}(c+d x) (b \cos (c+d x))^n \, dx","Int[Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n,x]","-\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)}}","-\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,"(-2*Cos[c + d*x]^(5/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (5 + 2*n)/4, (9 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
254,1,80,0,0.0266442,"\int \sqrt{\cos (c+d x)} (b \cos (c+d x))^n \, dx","Int[Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n,x]","-\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)}}","-\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,"(-2*Cos[c + d*x]^(3/2)*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (3 + 2*n)/4, (7 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
255,1,80,0,0.0266147,"\int \frac{(b \cos (c+d x))^n}{\sqrt{\cos (c+d x)}} \, dx","Int[(b*Cos[c + d*x])^n/Sqrt[Cos[c + d*x]],x]","-\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)}}","-\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,"(-2*Sqrt[Cos[c + d*x]]*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (1 + 2*n)/4, (5 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 + 2*n)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
256,1,80,0,0.0285066,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{3}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^n/Cos[c + d*x]^(3/2),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)}}","\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,"(2*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-1 + 2*n)/4, (3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(1 - 2*n)*Sqrt[Cos[c + d*x]]*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
257,1,80,0,0.0284384,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{5}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^n/Cos[c + d*x]^(5/2),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)}","\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,"(2*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-3 + 2*n)/4, (1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(3 - 2*n)*Cos[c + d*x]^(3/2)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
258,1,80,0,0.0279148,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{7}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^n/Cos[c + d*x]^(7/2),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)}","\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,"(2*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-5 + 2*n)/4, (-1 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(5 - 2*n)*Cos[c + d*x]^(5/2)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
259,1,80,0,0.0289639,"\int \frac{(b \cos (c+d x))^n}{\cos ^{\frac{9}{2}}(c+d x)} \, dx","Int[(b*Cos[c + d*x])^n/Cos[c + d*x]^(9/2),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)}","\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,"(2*(b*Cos[c + d*x])^n*Hypergeometric2F1[1/2, (-7 + 2*n)/4, (-3 + 2*n)/4, Cos[c + d*x]^2]*Sin[c + d*x])/(d*(7 - 2*n)*Cos[c + d*x]^(7/2)*Sqrt[Sin[c + d*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
260,1,88,0,0.070436,"\int (a \cos (e+f x))^m (b \sec (e+f x))^n \, dx","Int[(a*Cos[e + f*x])^m*(b*Sec[e + f*x])^n,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)}}","-\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,"-(((a*Cos[e + f*x])^(1 + 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])/(a*f*(1 + m - n)*Sqrt[Sin[e + f*x]^2]))","A",2,2,21,0.09524,1,"{2588, 2643}"
261,1,15,0,0.0246537,"\int \cos (a+b x) \sqrt{\csc (a+b x)} \, dx","Int[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",2,2,17,0.1176,1,"{2621, 30}"
262,1,17,0,0.0247542,"\int \frac{\cos (a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[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",2,2,17,0.1176,1,"{2621, 30}"
263,1,67,0,0.0505877,"\int \cos ^2(a+b x) \sqrt{\csc (a+b x)} \, dx","Int[Cos[a + b*x]^2*Sqrt[Csc[a + b*x]],x]","\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}","\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,"(2*Cos[a + b*x])/(3*b*Sqrt[Csc[a + b*x]]) + (4*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b)","A",3,3,19,0.1579,1,"{2628, 3771, 2641}"
264,1,67,0,0.0483108,"\int \frac{\cos ^2(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[Cos[a + b*x]^2/Sqrt[Csc[a + b*x]],x]","\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}","\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*Cos[a + b*x])/(5*b*Csc[a + b*x]^(3/2)) + (4*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(5*b)","A",3,3,19,0.1579,1,"{2628, 3771, 2639}"
265,1,21,0,0.0240884,"\int \cos ^3(x) \csc ^{\frac{9}{2}}(x) \, dx","Int[Cos[x]^3*Csc[x]^(9/2),x]","\frac{2}{3} \csc ^{\frac{3}{2}}(x)-\frac{2}{7} \csc ^{\frac{7}{2}}(x)","\frac{2}{3} \csc ^{\frac{3}{2}}(x)-\frac{2}{7} \csc ^{\frac{7}{2}}(x)",1,"(2*Csc[x]^(3/2))/3 - (2*Csc[x]^(7/2))/7","A",3,2,11,0.1818,1,"{2621, 14}"
266,1,33,0,0.0326656,"\int \cos ^3(a+b x) \sqrt{\csc (a+b x)} \, dx","Int[Cos[a + b*x]^3*Sqrt[Csc[a + b*x]],x]","\frac{2}{b \sqrt{\csc (a+b x)}}-\frac{2}{5 b \csc ^{\frac{5}{2}}(a+b x)}","\frac{2}{b \sqrt{\csc (a+b x)}}-\frac{2}{5 b \csc ^{\frac{5}{2}}(a+b x)}",1,"-2/(5*b*Csc[a + b*x]^(5/2)) + 2/(b*Sqrt[Csc[a + b*x]])","A",3,2,19,0.1053,1,"{2621, 14}"
267,1,35,0,0.0327947,"\int \frac{\cos ^3(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[Cos[a + b*x]^3/Sqrt[Csc[a + b*x]],x]","\frac{2}{3 b \csc ^{\frac{3}{2}}(a+b x)}-\frac{2}{7 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/(7*b*Csc[a + b*x]^(7/2)) + 2/(3*b*Csc[a + b*x]^(3/2))","A",3,2,19,0.1053,1,"{2621, 14}"
268,1,92,0,0.0801452,"\int \cos ^4(a+b x) \sqrt{\csc (a+b x)} \, dx","Int[Cos[a + b*x]^4*Sqrt[Csc[a + b*x]],x]","\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}","\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,"(4*Cos[a + b*x])/(7*b*Sqrt[Csc[a + b*x]]) + (2*Cos[a + b*x]^3)/(7*b*Sqrt[Csc[a + b*x]]) + (8*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(7*b)","A",4,3,19,0.1579,1,"{2628, 3771, 2641}"
269,1,92,0,0.0788764,"\int \frac{\cos ^4(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[Cos[a + b*x]^4/Sqrt[Csc[a + b*x]],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}","\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,"(4*Cos[a + b*x])/(15*b*Csc[a + b*x]^(3/2)) + (2*Cos[a + b*x]^3)/(9*b*Csc[a + b*x]^(3/2)) + (8*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(15*b)","A",4,3,19,0.1579,1,"{2628, 3771, 2639}"
270,1,10,0,0.0165183,"\int \cos (x) \csc ^{\frac{7}{3}}(x) \, dx","Int[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",2,2,9,0.2222,1,"{2621, 30}"
271,1,32,0,0.0278043,"\int \sqrt{\csc (a+b x)} \sec (a+b x) \, dx","Int[Sqrt[Csc[a + b*x]]*Sec[a + b*x],x]","\frac{\tanh ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{b}-\frac{\tan ^{-1}\left(\sqrt{\csc (a+b x)}\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[Csc[a + b*x]]]/b) + ArcTanh[Sqrt[Csc[a + b*x]]]/b","A",5,5,17,0.2941,1,"{2621, 329, 298, 203, 206}"
272,1,31,0,0.0287734,"\int \frac{\sec (a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[Sec[a + b*x]/Sqrt[Csc[a + b*x]],x]","\frac{\tan ^{-1}\left(\sqrt{\csc (a+b x)}\right)}{b}+\frac{\tanh ^{-1}\left(\sqrt{\csc (a+b x)}\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[Csc[a + b*x]]]/b + ArcTanh[Sqrt[Csc[a + b*x]]]/b","A",5,5,17,0.2941,1,"{2621, 329, 212, 206, 203}"
273,1,61,0,0.0484402,"\int \sqrt{\csc (a+b x)} \sec ^2(a+b x) \, dx","Int[Sqrt[Csc[a + b*x]]*Sec[a + b*x]^2,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}","\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]/(b*Sqrt[Csc[a + b*x]]) + (Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b","A",3,3,19,0.1579,1,"{2626, 3771, 2641}"
274,1,62,0,0.0477514,"\int \frac{\sec ^2(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[Sec[a + b*x]^2/Sqrt[Csc[a + b*x]],x]","\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}","\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,"Sec[a + b*x]/(b*Csc[a + b*x]^(3/2)) - (Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b","A",3,3,19,0.1579,1,"{2626, 3771, 2639}"
275,1,62,0,0.0532984,"\int \sqrt{\csc (a+b x)} \sec ^3(a+b x) \, dx","Int[Sqrt[Csc[a + b*x]]*Sec[a + b*x]^3,x]","-\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}","-\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,"(-3*ArcTan[Sqrt[Csc[a + b*x]]])/(4*b) + (3*ArcTanh[Sqrt[Csc[a + b*x]]])/(4*b) + Sec[a + b*x]^2/(2*b*Sqrt[Csc[a + b*x]])","A",6,6,19,0.3158,1,"{2621, 288, 329, 298, 203, 206}"
276,1,62,0,0.0463736,"\int \frac{\sec ^3(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[Sec[a + b*x]^3/Sqrt[Csc[a + b*x]],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}","\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,"ArcTan[Sqrt[Csc[a + b*x]]]/(4*b) + ArcTanh[Sqrt[Csc[a + b*x]]]/(4*b) + Sec[a + b*x]^2/(2*b*Csc[a + b*x]^(3/2))","A",6,6,19,0.3158,1,"{2621, 288, 329, 212, 206, 203}"
277,1,92,0,0.0813144,"\int \sqrt{\csc (a+b x)} \sec ^4(a+b x) \, dx","Int[Sqrt[Csc[a + b*x]]*Sec[a + b*x]^4,x]","\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}","\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,"(5*Sec[a + b*x])/(6*b*Sqrt[Csc[a + b*x]]) + Sec[a + b*x]^3/(3*b*Sqrt[Csc[a + b*x]]) + (5*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(6*b)","A",4,3,19,0.1579,1,"{2626, 3771, 2641}"
278,1,92,0,0.0803564,"\int \frac{\sec ^4(a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[Sec[a + b*x]^4/Sqrt[Csc[a + b*x]],x]","\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}","\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,"Sec[a + b*x]/(2*b*Csc[a + b*x]^(3/2)) + Sec[a + b*x]^3/(3*b*Csc[a + b*x]^(3/2)) - (Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(2*b)","A",4,3,19,0.1579,1,"{2626, 3771, 2639}"
279,1,76,0,0.1054683,"\int (d \cos (a+b x))^{3/2} \csc ^p(a+b x) \, dx","Int[(d*Cos[a + b*x])^(3/2)*Csc[a + b*x]^p,x]","\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)}}","\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,"(d*Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[-1/4, (1 - p)/2, (3 - p)/2, Sin[a + b*x]^2])/(b*(1 - p)*(Cos[a + b*x]^2)^(1/4))","A",2,2,21,0.09524,1,"{2587, 2577}"
280,1,76,0,0.091963,"\int \sqrt{d \cos (a+b x)} \csc ^p(a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^p,x]","\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)}}","\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,"(d*(Cos[a + b*x]^2)^(1/4)*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[1/4, (1 - p)/2, (3 - p)/2, Sin[a + b*x]^2])/(b*(1 - p)*Sqrt[d*Cos[a + b*x]])","A",2,2,21,0.09524,1,"{2587, 2577}"
281,1,76,0,0.0973584,"\int \frac{\csc ^p(a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Csc[a + b*x]^p/Sqrt[d*Cos[a + b*x]],x]","\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}}","\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,"(d*(Cos[a + b*x]^2)^(3/4)*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[3/4, (1 - p)/2, (3 - p)/2, Sin[a + b*x]^2])/(b*(1 - p)*(d*Cos[a + b*x])^(3/2))","A",2,2,21,0.09524,1,"{2587, 2577}"
282,1,78,0,0.1110886,"\int \frac{\csc ^p(a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]^p/(d*Cos[a + b*x])^(3/2),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)}}","\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,"((Cos[a + b*x]^2)^(1/4)*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[5/4, (1 - p)/2, (3 - p)/2, Sin[a + b*x]^2])/(b*d*(1 - p)*Sqrt[d*Cos[a + b*x]])","A",2,2,21,0.09524,1,"{2587, 2577}"
283,1,78,0,0.1101075,"\int \frac{\csc ^p(a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]^p/(d*Cos[a + b*x])^(5/2),x]","\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}}","\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,"((Cos[a + b*x]^2)^(3/4)*Csc[a + b*x]^(-1 + p)*Hypergeometric2F1[7/4, (1 - p)/2, (3 - p)/2, Sin[a + b*x]^2])/(b*d*(1 - p)*(d*Cos[a + b*x])^(3/2))","A",2,2,21,0.09524,1,"{2587, 2577}"
284,1,85,0,0.0825669,"\int \cos ^m(e+f x) \csc ^n(e+f x) \, dx","Int[Cos[e + f*x]^m*Csc[e + f*x]^n,x]","\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)}","\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,"(Cos[e + f*x]^(-1 + m)*(Cos[e + f*x]^2)^((1 - m)/2)*Csc[e + f*x]^(-1 + n)*Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(1 - n))","A",2,2,17,0.1176,1,"{2587, 2577}"
285,1,88,0,0.0912086,"\int (a \cos (e+f x))^m \csc ^n(e+f x) \, dx","Int[(a*Cos[e + f*x])^m*Csc[e + f*x]^n,x]","\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)}","\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,"(a*(a*Cos[e + f*x])^(-1 + m)*(Cos[e + f*x]^2)^((1 - m)/2)*Csc[e + f*x]^(-1 + n)*Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(1 - n))","A",2,2,19,0.1053,1,"{2587, 2577}"
286,1,88,0,0.0921135,"\int \cos ^m(e+f x) (b \csc (e+f x))^n \, dx","Int[Cos[e + f*x]^m*(b*Csc[e + f*x])^n,x]","\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)}","\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,"(b*Cos[e + f*x]^(-1 + m)*(Cos[e + f*x]^2)^((1 - m)/2)*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(1 - n))","A",2,2,19,0.1053,1,"{2587, 2577}"
287,1,91,0,0.0987331,"\int (a \cos (e+f x))^m (b \csc (e+f x))^n \, dx","Int[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^n,x]","\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)}","\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,"(a*b*(a*Cos[e + f*x])^(-1 + m)*(Cos[e + f*x]^2)^((1 - m)/2)*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(1 - n))","A",2,2,21,0.09524,1,"{2587, 2577}"
288,1,76,0,0.1175665,"\int (a \cos (e+f x))^m (b \csc (e+f x))^{7/2} \, dx","Int[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^(7/2),x]","-\frac{b \sin ^2(e+f x)^{5/4} (b \csc (e+f x))^{5/2} (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)}","-\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,"-((b*(a*Cos[e + f*x])^(1 + m)*(b*Csc[e + f*x])^(5/2)*Hypergeometric2F1[9/4, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^(5/4))/(a*f*(1 + m)))","A",2,2,23,0.08696,1,"{2587, 2576}"
289,1,76,0,0.1158171,"\int (a \cos (e+f x))^m (b \csc (e+f x))^{5/2} \, dx","Int[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^(5/2),x]","-\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)}","-\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,"-((b*(a*Cos[e + f*x])^(1 + m)*(b*Csc[e + f*x])^(3/2)*Hypergeometric2F1[7/4, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^(3/4))/(a*f*(1 + m)))","A",2,2,23,0.08696,1,"{2587, 2576}"
290,1,76,0,0.1120164,"\int (a \cos (e+f x))^m (b \csc (e+f x))^{3/2} \, dx","Int[(a*Cos[e + f*x])^m*(b*Csc[e + f*x])^(3/2),x]","-\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)}","-\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,"-((b*(a*Cos[e + f*x])^(1 + m)*Sqrt[b*Csc[e + f*x]]*Hypergeometric2F1[5/4, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^(1/4))/(a*f*(1 + m)))","A",2,2,23,0.08696,1,"{2587, 2576}"
291,1,78,0,0.0984332,"\int (a \cos (e+f x))^m \sqrt{b \csc (e+f x)} \, dx","Int[(a*Cos[e + f*x])^m*Sqrt[b*Csc[e + f*x]],x]","-\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)}","-\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,"-(((a*Cos[e + f*x])^(1 + m)*(b*Csc[e + f*x])^(3/2)*Hypergeometric2F1[3/4, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^(3/4))/(a*b*f*(1 + m)))","A",2,2,23,0.08696,1,"{2586, 2576}"
292,1,78,0,0.097994,"\int \frac{(a \cos (e+f x))^m}{\sqrt{b \csc (e+f x)}} \, dx","Int[(a*Cos[e + f*x])^m/Sqrt[b*Csc[e + f*x]],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{1}{4},\frac{m+1}{2};\frac{m+3}{2};\cos ^2(e+f x)\right)}{a b f (m+1)}","-\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,"-(((a*Cos[e + f*x])^(1 + m)*Sqrt[b*Csc[e + f*x]]*Hypergeometric2F1[1/4, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2]*(Sin[e + f*x]^2)^(1/4))/(a*b*f*(1 + m)))","A",2,2,23,0.08696,1,"{2586, 2576}"
293,1,78,0,0.1116701,"\int \frac{(a \cos (e+f x))^m}{(b \csc (e+f x))^{3/2}} \, dx","Int[(a*Cos[e + f*x])^m/(b*Csc[e + f*x])^(3/2),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)}}","-\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,"-(((a*Cos[e + f*x])^(1 + m)*Hypergeometric2F1[-1/4, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2])/(a*b*f*(1 + m)*Sqrt[b*Csc[e + f*x]]*(Sin[e + f*x]^2)^(1/4)))","A",2,2,23,0.08696,1,"{2586, 2576}"
294,1,78,0,0.1112427,"\int \frac{(a \cos (e+f x))^m}{(b \csc (e+f x))^{5/2}} \, dx","Int[(a*Cos[e + f*x])^m/(b*Csc[e + f*x])^(5/2),x]","-\frac{(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) \sin ^2(e+f x)^{3/4} (b \csc (e+f x))^{3/2}}","-\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,"-(((a*Cos[e + f*x])^(1 + m)*Hypergeometric2F1[-3/4, (1 + m)/2, (3 + m)/2, Cos[e + f*x]^2])/(a*b*f*(1 + m)*(b*Csc[e + f*x])^(3/2)*(Sin[e + f*x]^2)^(3/4)))","A",2,2,23,0.08696,1,"{2586, 2576}"