1,1,11,11,0.0023884,"\int \sec (a+b x) \, dx","Integrate[Sec[a + b*x],x]","\frac{\tanh ^{-1}(\sin (a+b x))}{b}","\frac{\tanh ^{-1}(\sin (a+b x))}{b}",1,"ArcTanh[Sin[a + b*x]]/b","A",1
2,1,10,10,0.0039624,"\int \sec ^2(a+b x) \, dx","Integrate[Sec[a + b*x]^2,x]","\frac{\tan (a+b x)}{b}","\frac{\tan (a+b x)}{b}",1,"Tan[a + b*x]/b","A",1
3,1,34,34,0.0101392,"\int \sec ^3(a+b x) \, dx","Integrate[Sec[a + b*x]^3,x]","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\tan (a+b x) \sec (a+b x)}{2 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\tan (a+b x) \sec (a+b x)}{2 b}",1,"ArcTanh[Sin[a + b*x]]/(2*b) + (Sec[a + b*x]*Tan[a + b*x])/(2*b)","A",1
4,1,23,26,0.0474664,"\int \sec ^4(a+b x) \, dx","Integrate[Sec[a + b*x]^4,x]","\frac{\frac{1}{3} \tan ^3(a+b x)+\tan (a+b x)}{b}","\frac{\tan ^3(a+b x)}{3 b}+\frac{\tan (a+b x)}{b}",1,"(Tan[a + b*x] + Tan[a + b*x]^3/3)/b","A",1
5,1,42,55,0.0761561,"\int \sec ^5(a+b x) \, dx","Integrate[Sec[a + b*x]^5,x]","\frac{3 \tanh ^{-1}(\sin (a+b x))+\tan (a+b x) \sec (a+b x) \left(2 \sec ^2(a+b x)+3\right)}{8 b}","\frac{3 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\tan (a+b x) \sec ^3(a+b x)}{4 b}+\frac{3 \tan (a+b x) \sec (a+b x)}{8 b}",1,"(3*ArcTanh[Sin[a + b*x]] + Sec[a + b*x]*(3 + 2*Sec[a + b*x]^2)*Tan[a + b*x])/(8*b)","A",1
6,1,35,41,0.1097353,"\int \sec ^6(a+b x) \, dx","Integrate[Sec[a + b*x]^6,x]","\frac{\frac{1}{5} \tan ^5(a+b x)+\frac{2}{3} \tan ^3(a+b x)+\tan (a+b x)}{b}","\frac{\tan ^5(a+b x)}{5 b}+\frac{2 \tan ^3(a+b x)}{3 b}+\frac{\tan (a+b x)}{b}",1,"(Tan[a + b*x] + (2*Tan[a + b*x]^3)/3 + Tan[a + b*x]^5/5)/b","A",1
7,1,52,76,0.1351904,"\int \sec ^7(a+b x) \, dx","Integrate[Sec[a + b*x]^7,x]","\frac{15 \tanh ^{-1}(\sin (a+b x))+\tan (a+b x) \sec (a+b x) \left(8 \sec ^4(a+b x)+10 \sec ^2(a+b x)+15\right)}{48 b}","\frac{5 \tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan (a+b x) \sec ^5(a+b x)}{6 b}+\frac{5 \tan (a+b x) \sec ^3(a+b x)}{24 b}+\frac{5 \tan (a+b x) \sec (a+b x)}{16 b}",1,"(15*ArcTanh[Sin[a + b*x]] + Sec[a + b*x]*(15 + 10*Sec[a + b*x]^2 + 8*Sec[a + b*x]^4)*Tan[a + b*x])/(48*b)","A",1
8,1,43,53,0.1858242,"\int \sec ^8(a+b x) \, dx","Integrate[Sec[a + b*x]^8,x]","\frac{\frac{1}{7} \tan ^7(a+b x)+\frac{3}{5} \tan ^5(a+b x)+\tan ^3(a+b x)+\tan (a+b x)}{b}","\frac{\tan ^7(a+b x)}{7 b}+\frac{3 \tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{b}+\frac{\tan (a+b x)}{b}",1,"(Tan[a + b*x] + Tan[a + b*x]^3 + (3*Tan[a + b*x]^5)/5 + Tan[a + b*x]^7/7)/b","A",1
9,1,59,85,0.1718609,"\int \sec ^{\frac{7}{2}}(a+b x) \, dx","Integrate[Sec[a + b*x]^(7/2),x]","\frac{\sec ^{\frac{5}{2}}(a+b x) \left(7 \sin (a+b x)+3 \sin (3 (a+b x))-12 \cos ^{\frac{5}{2}}(a+b x) E\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{10 b}","\frac{2 \sin (a+b x) \sec ^{\frac{5}{2}}(a+b x)}{5 b}+\frac{6 \sin (a+b x) \sqrt{\sec (a+b x)}}{5 b}-\frac{6 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}",1,"(Sec[a + b*x]^(5/2)*(-12*Cos[a + b*x]^(5/2)*EllipticE[(a + b*x)/2, 2] + 7*Sin[a + b*x] + 3*Sin[3*(a + b*x)]))/(10*b)","A",1
10,1,46,62,0.0590403,"\int \sec ^{\frac{5}{2}}(a+b x) \, dx","Integrate[Sec[a + b*x]^(5/2),x]","\frac{2 \sec ^{\frac{3}{2}}(a+b x) \left(\sin (a+b x)+\cos ^{\frac{3}{2}}(a+b x) F\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{3 b}","\frac{2 \sin (a+b x) \sec ^{\frac{3}{2}}(a+b x)}{3 b}+\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}",1,"(2*Sec[a + b*x]^(3/2)*(Cos[a + b*x]^(3/2)*EllipticF[(a + b*x)/2, 2] + Sin[a + b*x]))/(3*b)","A",1
11,1,45,58,0.0373067,"\int \sec ^{\frac{3}{2}}(a+b x) \, dx","Integrate[Sec[a + b*x]^(3/2),x]","\frac{2 \sqrt{\sec (a+b x)} \left(\sin (a+b x)-\sqrt{\cos (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{b}","\frac{2 \sin (a+b x) \sqrt{\sec (a+b x)}}{b}-\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*Sqrt[Sec[a + b*x]]*(-(Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]) + Sin[a + b*x]))/b","A",1
12,1,36,36,0.0199695,"\int \sqrt{\sec (a+b x)} \, dx","Integrate[Sqrt[Sec[a + b*x]],x]","\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/b","A",1
13,1,36,36,0.0260018,"\int \frac{1}{\sqrt{\sec (a+b x)}} \, dx","Integrate[1/Sqrt[Sec[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)}}","\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*EllipticE[(a + b*x)/2, 2])/(b*Sqrt[Cos[a + b*x]]*Sqrt[Sec[a + b*x]])","A",1
14,1,49,62,0.0440026,"\int \frac{1}{\sec ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[Sec[a + b*x]^(-3/2),x]","\frac{\sqrt{\sec (a+b x)} \left(\sin (2 (a+b x))+2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{3 b}","\frac{2 \sin (a+b x)}{3 b \sqrt{\sec (a+b x)}}+\frac{2 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}",1,"(Sqrt[Sec[a + b*x]]*(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2] + Sin[2*(a + b*x)]))/(3*b)","A",1
15,1,55,62,0.0615971,"\int \frac{1}{\sec ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Sec[a + b*x]^(-5/2),x]","\frac{\sqrt{\sec (a+b x)} \left(\sin (a+b x)+\sin (3 (a+b x))+12 \sqrt{\cos (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{10 b}","\frac{2 \sin (a+b x)}{5 b \sec ^{\frac{3}{2}}(a+b x)}+\frac{6 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b}",1,"(Sqrt[Sec[a + b*x]]*(12*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2] + Sin[a + b*x] + Sin[3*(a + b*x)]))/(10*b)","A",1
16,1,61,85,0.1006785,"\int \frac{1}{\sec ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[Sec[a + b*x]^(-7/2),x]","\frac{\sqrt{\sec (a+b x)} \left(26 \sin (2 (a+b x))+3 \sin (4 (a+b x))+40 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{84 b}","\frac{2 \sin (a+b x)}{7 b \sec ^{\frac{5}{2}}(a+b x)}+\frac{10 \sin (a+b x)}{21 b \sqrt{\sec (a+b x)}}+\frac{10 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b}",1,"(Sqrt[Sec[a + b*x]]*(40*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2] + 26*Sin[2*(a + b*x)] + 3*Sin[4*(a + b*x)]))/(84*b)","A",1
17,1,62,98,0.1704863,"\int (c \sec (a+b x))^{7/2} \, dx","Integrate[(c*Sec[a + b*x])^(7/2),x]","\frac{c (c \sec (a+b x))^{5/2} \left(7 \sin (a+b x)+3 \sin (3 (a+b x))-12 \cos ^{\frac{5}{2}}(a+b x) E\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{10 b}","-\frac{6 c^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}+\frac{6 c^3 \sin (a+b x) \sqrt{c \sec (a+b x)}}{5 b}+\frac{2 c \sin (a+b x) (c \sec (a+b x))^{5/2}}{5 b}",1,"(c*(c*Sec[a + b*x])^(5/2)*(-12*Cos[a + b*x]^(5/2)*EllipticE[(a + b*x)/2, 2] + 7*Sin[a + b*x] + 3*Sin[3*(a + b*x)]))/(10*b)","A",1
18,1,51,70,0.0700573,"\int (c \sec (a+b x))^{5/2} \, dx","Integrate[(c*Sec[a + b*x])^(5/2),x]","\frac{2 c^2 \sqrt{c \sec (a+b x)} \left(\tan (a+b x)+\sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{3 b}","\frac{2 c^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{3 b}+\frac{2 c \sin (a+b x) (c \sec (a+b x))^{3/2}}{3 b}",1,"(2*c^2*Sqrt[c*Sec[a + b*x]]*(Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2] + Tan[a + b*x]))/(3*b)","A",1
19,1,48,66,0.0410235,"\int (c \sec (a+b x))^{3/2} \, dx","Integrate[(c*Sec[a + b*x])^(3/2),x]","\frac{2 c \sqrt{c \sec (a+b x)} \left(\sin (a+b x)-\sqrt{\cos (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{b}","\frac{2 c \sin (a+b x) \sqrt{c \sec (a+b x)}}{b}-\frac{2 c^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}",1,"(2*c*Sqrt[c*Sec[a + b*x]]*(-(Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]) + Sin[a + b*x]))/b","A",1
20,1,38,38,0.0205491,"\int \sqrt{c \sec (a+b x)} \, dx","Integrate[Sqrt[c*Sec[a + b*x]],x]","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{b}","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{b}",1,"(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[c*Sec[a + b*x]])/b","A",1
21,1,38,38,0.0297335,"\int \frac{1}{\sqrt{c \sec (a+b x)}} \, dx","Integrate[1/Sqrt[c*Sec[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}",1,"(2*EllipticE[(a + b*x)/2, 2])/(b*Sqrt[Cos[a + b*x]]*Sqrt[c*Sec[a + b*x]])","A",1
22,1,59,72,0.0600694,"\int \frac{1}{(c \sec (a+b x))^{3/2}} \, dx","Integrate[(c*Sec[a + b*x])^(-3/2),x]","\frac{\sec ^2(a+b x) \left(\sin (2 (a+b x))+2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{3 b (c \sec (a+b x))^{3/2}}","\frac{2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{3 b c^2}+\frac{2 \sin (a+b x)}{3 b c \sqrt{c \sec (a+b x)}}",1,"(Sec[a + b*x]^2*(2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2] + Sin[2*(a + b*x)]))/(3*b*(c*Sec[a + b*x])^(3/2))","A",1
23,1,60,72,0.0735042,"\int \frac{1}{(c \sec (a+b x))^{5/2}} \, dx","Integrate[(c*Sec[a + b*x])^(-5/2),x]","\frac{\sqrt{c \sec (a+b x)} \left(\sin (a+b x)+\sin (3 (a+b x))+12 \sqrt{\cos (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{10 b c^3}","\frac{6 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{5 b c^2 \sqrt{\cos (a+b x)} \sqrt{c \sec (a+b x)}}+\frac{2 \sin (a+b x)}{5 b c (c \sec (a+b x))^{3/2}}",1,"(Sqrt[c*Sec[a + b*x]]*(12*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2] + Sin[a + b*x] + Sin[3*(a + b*x)]))/(10*b*c^3)","A",1
24,1,66,100,0.1019586,"\int \frac{1}{(c \sec (a+b x))^{7/2}} \, dx","Integrate[(c*Sec[a + b*x])^(-7/2),x]","\frac{\sqrt{c \sec (a+b x)} \left(26 \sin (2 (a+b x))+3 \sin (4 (a+b x))+40 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)\right)}{84 b c^4}","\frac{10 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{c \sec (a+b x)}}{21 b c^4}+\frac{10 \sin (a+b x)}{21 b c^3 \sqrt{c \sec (a+b x)}}+\frac{2 \sin (a+b x)}{7 b c (c \sec (a+b x))^{5/2}}",1,"(Sqrt[c*Sec[a + b*x]]*(40*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2] + 26*Sin[2*(a + b*x)] + 3*Sin[4*(a + b*x)]))/(84*b*c^4)","A",1
25,1,55,51,0.0514787,"\int \sec ^{\frac{4}{3}}(a+b x) \, dx","Integrate[Sec[a + b*x]^(4/3),x]","\frac{3 \sqrt{-\tan ^2(a+b x)} \csc (a+b x) \sqrt[3]{\sec (a+b x)} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sec ^2(a+b x)\right)}{4 b}","\frac{3 \sin (a+b x) \sqrt[3]{\sec (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)}}",1,"(3*Csc[a + b*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sec[a + b*x]^2]*Sec[a + b*x]^(1/3)*Sqrt[-Tan[a + b*x]^2])/(4*b)","A",1
26,1,55,51,0.0371868,"\int \sec ^{\frac{2}{3}}(a+b x) \, dx","Integrate[Sec[a + b*x]^(2/3),x]","\frac{3 \sqrt{-\tan ^2(a+b x)} \csc (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sec ^2(a+b x)\right)}{2 b \sqrt[3]{\sec (a+b x)}}","-\frac{3 \sin (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)} \sqrt[3]{\sec (a+b x)}}",1,"(3*Csc[a + b*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(2*b*Sec[a + b*x]^(1/3))","A",1
27,1,53,53,0.0388461,"\int \sqrt[3]{\sec (a+b x)} \, dx","Integrate[Sec[a + b*x]^(1/3),x]","\frac{3 \sqrt{-\tan ^2(a+b x)} \csc (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sec ^2(a+b x)\right)}{b \sec ^{\frac{2}{3}}(a+b x)}","-\frac{3 \sin (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)} \sec ^{\frac{2}{3}}(a+b x)}",1,"(3*Csc[a + b*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(b*Sec[a + b*x]^(2/3))","A",1
28,1,53,53,0.0835019,"\int \frac{1}{\sqrt[3]{\sec (a+b x)}} \, dx","Integrate[Sec[a + b*x]^(-1/3),x]","-\frac{3 \sqrt{-\tan ^2(a+b x)} \csc (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sec ^2(a+b x)\right)}{b \sec ^{\frac{4}{3}}(a+b x)}","-\frac{3 \sin (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)} \sec ^{\frac{4}{3}}(a+b x)}",1,"(-3*Csc[a + b*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(b*Sec[a + b*x]^(4/3))","A",1
29,1,55,53,0.0844347,"\int \frac{1}{\sec ^{\frac{2}{3}}(a+b x)} \, dx","Integrate[Sec[a + b*x]^(-2/3),x]","-\frac{3 \sqrt{-\tan ^2(a+b x)} \csc (a+b x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\sec ^2(a+b x)\right)}{2 b \sec ^{\frac{5}{3}}(a+b x)}","-\frac{3 \sin (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)} \sec ^{\frac{5}{3}}(a+b x)}",1,"(-3*Csc[a + b*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(2*b*Sec[a + b*x]^(5/3))","A",1
30,1,55,53,0.0678372,"\int \frac{1}{\sec ^{\frac{4}{3}}(a+b x)} \, dx","Integrate[Sec[a + b*x]^(-4/3),x]","-\frac{3 \sqrt{-\tan ^2(a+b x)} \csc (a+b x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\sec ^2(a+b x)\right)}{4 b \sec ^{\frac{7}{3}}(a+b x)}","-\frac{3 \sin (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)} \sec ^{\frac{7}{3}}(a+b x)}",1,"(-3*Csc[a + b*x]*Hypergeometric2F1[-2/3, 1/2, 1/3, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(4*b*Sec[a + b*x]^(7/3))","A",1
31,1,57,54,0.0459742,"\int (c \sec (a+b x))^{4/3} \, dx","Integrate[(c*Sec[a + b*x])^(4/3),x]","\frac{3 \sqrt{-\tan ^2(a+b x)} \cot (a+b x) (c \sec (a+b x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sec ^2(a+b x)\right)}{4 b}","\frac{3 c \sin (a+b x) \sqrt[3]{c \sec (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)}}",1,"(3*Cot[a + b*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sec[a + b*x]^2]*(c*Sec[a + b*x])^(4/3)*Sqrt[-Tan[a + b*x]^2])/(4*b)","A",1
32,1,57,54,0.0429261,"\int (c \sec (a+b x))^{2/3} \, dx","Integrate[(c*Sec[a + b*x])^(2/3),x]","\frac{3 \sqrt{-\tan ^2(a+b x)} \cot (a+b x) (c \sec (a+b x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sec ^2(a+b x)\right)}{2 b}","-\frac{3 c \sin (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)} \sqrt[3]{c \sec (a+b x)}}",1,"(3*Cot[a + b*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sec[a + b*x]^2]*(c*Sec[a + b*x])^(2/3)*Sqrt[-Tan[a + b*x]^2])/(2*b)","A",1
33,1,55,56,0.0416285,"\int \sqrt[3]{c \sec (a+b x)} \, dx","Integrate[(c*Sec[a + b*x])^(1/3),x]","\frac{3 \sqrt{-\tan ^2(a+b x)} \cot (a+b x) \sqrt[3]{c \sec (a+b x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sec ^2(a+b x)\right)}{b}","-\frac{3 c \sin (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)} (c \sec (a+b x))^{2/3}}",1,"(3*Cot[a + b*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Sec[a + b*x]^2]*(c*Sec[a + b*x])^(1/3)*Sqrt[-Tan[a + b*x]^2])/b","A",1
34,1,55,56,0.0545929,"\int \frac{1}{\sqrt[3]{c \sec (a+b x)}} \, dx","Integrate[(c*Sec[a + b*x])^(-1/3),x]","-\frac{3 \sqrt{-\tan ^2(a+b x)} \cot (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sec ^2(a+b x)\right)}{b \sqrt[3]{c \sec (a+b x)}}","-\frac{3 c \sin (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)} (c \sec (a+b x))^{4/3}}",1,"(-3*Cot[a + b*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(b*(c*Sec[a + b*x])^(1/3))","A",1
35,1,57,56,0.0548888,"\int \frac{1}{(c \sec (a+b x))^{2/3}} \, dx","Integrate[(c*Sec[a + b*x])^(-2/3),x]","-\frac{3 \sqrt{-\tan ^2(a+b x)} \cot (a+b x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\sec ^2(a+b x)\right)}{2 b (c \sec (a+b x))^{2/3}}","-\frac{3 c \sin (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)} (c \sec (a+b x))^{5/3}}",1,"(-3*Cot[a + b*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(2*b*(c*Sec[a + b*x])^(2/3))","A",1
36,1,57,56,0.0719732,"\int \frac{1}{(c \sec (a+b x))^{4/3}} \, dx","Integrate[(c*Sec[a + b*x])^(-4/3),x]","-\frac{3 \sqrt{-\tan ^2(a+b x)} \cot (a+b x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\sec ^2(a+b x)\right)}{4 b (c \sec (a+b x))^{4/3}}","-\frac{3 c \sin (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)} (c \sec (a+b x))^{7/3}}",1,"(-3*Cot[a + b*x]*Hypergeometric2F1[-2/3, 1/2, 1/3, Sec[a + b*x]^2]*Sqrt[-Tan[a + b*x]^2])/(4*b*(c*Sec[a + b*x])^(4/3))","A",1
37,1,61,70,0.0526939,"\int \sec ^n(a+b x) \, dx","Integrate[Sec[a + b*x]^n,x]","\frac{\sqrt{-\tan ^2(a+b x)} \csc (a+b x) \sec ^{n-1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\sec ^2(a+b x)\right)}{b n}","-\frac{\sin (a+b x) \sec ^{n-1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{b (1-n) \sqrt{\sin ^2(a+b x)}}",1,"(Csc[a + b*x]*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Sec[a + b*x]^2]*Sec[a + b*x]^(-1 + n)*Sqrt[-Tan[a + b*x]^2])/(b*n)","A",1
38,1,61,73,0.0459471,"\int (c \sec (a+b x))^n \, dx","Integrate[(c*Sec[a + b*x])^n,x]","\frac{\sqrt{-\tan ^2(a+b x)} \cot (a+b x) (c \sec (a+b x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\sec ^2(a+b x)\right)}{b n}","-\frac{c \sin (a+b x) (c \sec (a+b x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{b (1-n) \sqrt{\sin ^2(a+b x)}}",1,"(Cot[a + b*x]*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Sec[a + b*x]^2]*(c*Sec[a + b*x])^n*Sqrt[-Tan[a + b*x]^2])/(b*n)","A",1
39,1,74,50,0.3044272,"\int \sec ^2(x)^{7/2} \, dx","Integrate[(Sec[x]^2)^(7/2),x]","\frac{1}{96} \cos (x) \sqrt{\sec ^2(x)} \left(\frac{1}{8} (198 \sin (x)+85 \sin (3 x)+15 \sin (5 x)) \sec ^6(x)-30 \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+30 \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{1}{6} \tan (x) \sec ^2(x)^{5/2}+\frac{5}{24} \tan (x) \sec ^2(x)^{3/2}+\frac{5}{16} \tan (x) \sqrt{\sec ^2(x)}+\frac{5}{16} \sinh ^{-1}(\tan (x))",1,"(Cos[x]*Sqrt[Sec[x]^2]*(-30*Log[Cos[x/2] - Sin[x/2]] + 30*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^6*(198*Sin[x] + 85*Sin[3*x] + 15*Sin[5*x]))/8))/96","A",1
40,1,68,36,0.1578941,"\int \sec ^2(x)^{5/2} \, dx","Integrate[(Sec[x]^2)^(5/2),x]","\frac{1}{16} \cos (x) \sqrt{\sec ^2(x)} \left(\frac{1}{2} (11 \sin (x)+3 \sin (3 x)) \sec ^4(x)-6 \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+6 \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{1}{4} \tan (x) \sec ^2(x)^{3/2}+\frac{3}{8} \tan (x) \sqrt{\sec ^2(x)}+\frac{3}{8} \sinh ^{-1}(\tan (x))",1,"(Cos[x]*Sqrt[Sec[x]^2]*(-6*Log[Cos[x/2] - Sin[x/2]] + 6*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^4*(11*Sin[x] + 3*Sin[3*x]))/2))/16","A",1
41,1,52,22,0.0634903,"\int \sec ^2(x)^{3/2} \, dx","Integrate[(Sec[x]^2)^(3/2),x]","\frac{1}{2} \cos (x) \sqrt{\sec ^2(x)} \left(\tan (x) \sec (x)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{1}{2} \tan (x) \sqrt{\sec ^2(x)}+\frac{1}{2} \sinh ^{-1}(\tan (x))",1,"(Cos[x]*Sqrt[Sec[x]^2]*(-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]] + Sec[x]*Tan[x]))/2","B",1
42,1,44,3,0.00995,"\int \sqrt{\sec ^2(x)} \, dx","Integrate[Sqrt[Sec[x]^2],x]","\cos (x) \sqrt{\sec ^2(x)} \left(\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)\right)","\sinh ^{-1}(\tan (x))",1,"Cos[x]*(-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]])*Sqrt[Sec[x]^2]","B",1
43,1,11,11,0.0067097,"\int \frac{1}{\sqrt{\sec ^2(x)}} \, dx","Integrate[1/Sqrt[Sec[x]^2],x]","\frac{\tan (x)}{\sqrt{\sec ^2(x)}}","\frac{\tan (x)}{\sqrt{\sec ^2(x)}}",1,"Tan[x]/Sqrt[Sec[x]^2]","A",1
44,1,23,29,0.0152884,"\int \frac{1}{\sec ^2(x)^{3/2}} \, dx","Integrate[(Sec[x]^2)^(-3/2),x]","\frac{(9 \sin (x)+\sin (3 x)) \sec (x)}{12 \sqrt{\sec ^2(x)}}","\frac{2 \tan (x)}{3 \sqrt{\sec ^2(x)}}+\frac{\tan (x)}{3 \sec ^2(x)^{3/2}}",1,"(Sec[x]*(9*Sin[x] + Sin[3*x]))/(12*Sqrt[Sec[x]^2])","A",1
45,1,31,43,0.0260596,"\int \frac{1}{\sec ^2(x)^{5/2}} \, dx","Integrate[(Sec[x]^2)^(-5/2),x]","\frac{(150 \sin (x)+25 \sin (3 x)+3 \sin (5 x)) \sec (x)}{240 \sqrt{\sec ^2(x)}}","\frac{8 \tan (x)}{15 \sqrt{\sec ^2(x)}}+\frac{4 \tan (x)}{15 \sec ^2(x)^{3/2}}+\frac{\tan (x)}{5 \sec ^2(x)^{5/2}}",1,"(Sec[x]*(150*Sin[x] + 25*Sin[3*x] + 3*Sin[5*x]))/(240*Sqrt[Sec[x]^2])","A",1
46,1,37,57,0.0402503,"\int \frac{1}{\sec ^2(x)^{7/2}} \, dx","Integrate[(Sec[x]^2)^(-7/2),x]","\frac{(1225 \sin (x)+245 \sin (3 x)+49 \sin (5 x)+5 \sin (7 x)) \sec (x)}{2240 \sqrt{\sec ^2(x)}}","\frac{16 \tan (x)}{35 \sqrt{\sec ^2(x)}}+\frac{8 \tan (x)}{35 \sec ^2(x)^{3/2}}+\frac{6 \tan (x)}{35 \sec ^2(x)^{5/2}}+\frac{\tan (x)}{7 \sec ^2(x)^{7/2}}",1,"(Sec[x]*(1225*Sin[x] + 245*Sin[3*x] + 49*Sin[5*x] + 5*Sin[7*x]))/(2240*Sqrt[Sec[x]^2])","A",1
47,1,78,84,0.1402704,"\int \left(a \sec ^2(x)\right)^{7/2} \, dx","Integrate[(a*Sec[x]^2)^(7/2),x]","\frac{1}{96} \cos ^7(x) \left(a \sec ^2(x)\right)^{7/2} \left(\frac{1}{8} (198 \sin (x)+85 \sin (3 x)+15 \sin (5 x)) \sec ^6(x)-30 \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+30 \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{5}{16} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{5}{16} a^3 \tan (x) \sqrt{a \sec ^2(x)}+\frac{5}{24} a^2 \tan (x) \left(a \sec ^2(x)\right)^{3/2}+\frac{1}{6} a \tan (x) \left(a \sec ^2(x)\right)^{5/2}",1,"(Cos[x]^7*(a*Sec[x]^2)^(7/2)*(-30*Log[Cos[x/2] - Sin[x/2]] + 30*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^6*(198*Sin[x] + 85*Sin[3*x] + 15*Sin[5*x]))/8))/96","A",1
48,1,72,65,0.1317468,"\int \left(a \sec ^2(x)\right)^{5/2} \, dx","Integrate[(a*Sec[x]^2)^(5/2),x]","\frac{1}{16} \cos ^5(x) \left(a \sec ^2(x)\right)^{5/2} \left(\frac{1}{2} (11 \sin (x)+3 \sin (3 x)) \sec ^4(x)-6 \log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+6 \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{3}{8} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{3}{8} a^2 \tan (x) \sqrt{a \sec ^2(x)}+\frac{1}{4} a \tan (x) \left(a \sec ^2(x)\right)^{3/2}",1,"(Cos[x]^5*(a*Sec[x]^2)^(5/2)*(-6*Log[Cos[x/2] - Sin[x/2]] + 6*Log[Cos[x/2] + Sin[x/2]] + (Sec[x]^4*(11*Sin[x] + 3*Sin[3*x]))/2))/16","A",1
49,1,55,46,0.0536399,"\int \left(a \sec ^2(x)\right)^{3/2} \, dx","Integrate[(a*Sec[x]^2)^(3/2),x]","\frac{1}{2} a \cos (x) \sqrt{a \sec ^2(x)} \left(\tan (x) \sec (x)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)+\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)\right)","\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)+\frac{1}{2} a \tan (x) \sqrt{a \sec ^2(x)}",1,"(a*Cos[x]*Sqrt[a*Sec[x]^2]*(-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]] + Sec[x]*Tan[x]))/2","A",1
50,1,46,25,0.008967,"\int \sqrt{a \sec ^2(x)} \, dx","Integrate[Sqrt[a*Sec[x]^2],x]","\cos (x) \sqrt{a \sec ^2(x)} \left(\log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\log \left(\cos \left(\frac{x}{2}\right)-\sin \left(\frac{x}{2}\right)\right)\right)","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \tan (x)}{\sqrt{a \sec ^2(x)}}\right)",1,"Cos[x]*(-Log[Cos[x/2] - Sin[x/2]] + Log[Cos[x/2] + Sin[x/2]])*Sqrt[a*Sec[x]^2]","A",1
51,1,13,13,0.0062592,"\int \frac{1}{\sqrt{a \sec ^2(x)}} \, dx","Integrate[1/Sqrt[a*Sec[x]^2],x]","\frac{\tan (x)}{\sqrt{a \sec ^2(x)}}","\frac{\tan (x)}{\sqrt{a \sec ^2(x)}}",1,"Tan[x]/Sqrt[a*Sec[x]^2]","A",1
52,1,27,36,0.0201923,"\int \frac{1}{\left(a \sec ^2(x)\right)^{3/2}} \, dx","Integrate[(a*Sec[x]^2)^(-3/2),x]","\frac{(9 \sin (x)+\sin (3 x)) \sec ^3(x)}{12 \left(a \sec ^2(x)\right)^{3/2}}","\frac{2 \tan (x)}{3 a \sqrt{a \sec ^2(x)}}+\frac{\tan (x)}{3 \left(a \sec ^2(x)\right)^{3/2}}",1,"(Sec[x]^3*(9*Sin[x] + Sin[3*x]))/(12*(a*Sec[x]^2)^(3/2))","A",1
53,1,36,55,0.0295718,"\int \frac{1}{\left(a \sec ^2(x)\right)^{5/2}} \, dx","Integrate[(a*Sec[x]^2)^(-5/2),x]","\frac{(150 \sin (x)+25 \sin (3 x)+3 \sin (5 x)) \cos (x) \sqrt{a \sec ^2(x)}}{240 a^3}","\frac{8 \tan (x)}{15 a^2 \sqrt{a \sec ^2(x)}}+\frac{4 \tan (x)}{15 a \left(a \sec ^2(x)\right)^{3/2}}+\frac{\tan (x)}{5 \left(a \sec ^2(x)\right)^{5/2}}",1,"(Cos[x]*Sqrt[a*Sec[x]^2]*(150*Sin[x] + 25*Sin[3*x] + 3*Sin[5*x]))/(240*a^3)","A",1
54,1,42,74,0.0296016,"\int \frac{1}{\left(a \sec ^2(x)\right)^{7/2}} \, dx","Integrate[(a*Sec[x]^2)^(-7/2),x]","\frac{(1225 \sin (x)+245 \sin (3 x)+49 \sin (5 x)+5 \sin (7 x)) \cos (x) \sqrt{a \sec ^2(x)}}{2240 a^4}","\frac{16 \tan (x)}{35 a^3 \sqrt{a \sec ^2(x)}}+\frac{8 \tan (x)}{35 a^2 \left(a \sec ^2(x)\right)^{3/2}}+\frac{6 \tan (x)}{35 a \left(a \sec ^2(x)\right)^{5/2}}+\frac{\tan (x)}{7 \left(a \sec ^2(x)\right)^{7/2}}",1,"(Cos[x]*Sqrt[a*Sec[x]^2]*(1225*Sin[x] + 245*Sin[3*x] + 49*Sin[5*x] + 5*Sin[7*x]))/(2240*a^4)","A",1
55,1,59,117,0.1009483,"\int \left(a \sec ^3(x)\right)^{5/2} \, dx","Integrate[(a*Sec[x]^3)^(5/2),x]","-\frac{2}{585} a \sec (x) \left(a \sec ^3(x)\right)^{3/2} \left(-45 \tan (x)+231 \cos ^{\frac{11}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right)-231 \sin (x) \cos ^5(x)-77 \sin (x) \cos ^3(x)-55 \sin (x) \cos (x)\right)","\frac{154}{585} a^2 \tan (x) \sqrt{a \sec ^3(x)}+\frac{2}{13} a^2 \tan (x) \sec ^4(x) \sqrt{a \sec ^3(x)}+\frac{22}{117} a^2 \tan (x) \sec ^2(x) \sqrt{a \sec ^3(x)}-\frac{154}{195} a^2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}+\frac{154}{195} a^2 \sin (x) \cos (x) \sqrt{a \sec ^3(x)}",1,"(-2*a*Sec[x]*(a*Sec[x]^3)^(3/2)*(231*Cos[x]^(11/2)*EllipticE[x/2, 2] - 55*Cos[x]*Sin[x] - 77*Cos[x]^3*Sin[x] - 231*Cos[x]^5*Sin[x] - 45*Tan[x]))/585","A",1
56,1,43,65,0.0394135,"\int \left(a \sec ^3(x)\right)^{3/2} \, dx","Integrate[(a*Sec[x]^3)^(3/2),x]","\frac{2}{21} a \sec (x) \sqrt{a \sec ^3(x)} \left(3 \tan (x)+5 \cos ^{\frac{5}{2}}(x) F\left(\left.\frac{x}{2}\right|2\right)+5 \sin (x) \cos (x)\right)","\frac{10}{21} a \sin (x) \sqrt{a \sec ^3(x)}+\frac{2}{7} a \tan (x) \sec (x) \sqrt{a \sec ^3(x)}+\frac{10}{21} a \cos ^{\frac{3}{2}}(x) F\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}",1,"(2*a*Sec[x]*Sqrt[a*Sec[x]^3]*(5*Cos[x]^(5/2)*EllipticF[x/2, 2] + 5*Cos[x]*Sin[x] + 3*Tan[x]))/21","A",1
57,1,32,42,0.0191803,"\int \sqrt{a \sec ^3(x)} \, dx","Integrate[Sqrt[a*Sec[x]^3],x]","2 \cos (x) \sqrt{a \sec ^3(x)} \left(\sin (x)-\sqrt{\cos (x)} E\left(\left.\frac{x}{2}\right|2\right)\right)","2 \sin (x) \cos (x) \sqrt{a \sec ^3(x)}-2 \cos ^{\frac{3}{2}}(x) E\left(\left.\frac{x}{2}\right|2\right) \sqrt{a \sec ^3(x)}",1,"2*Cos[x]*Sqrt[a*Sec[x]^3]*(-(Sqrt[Cos[x]]*EllipticE[x/2, 2]) + Sin[x])","A",1
58,1,31,44,0.0433925,"\int \frac{1}{\sqrt{a \sec ^3(x)}} \, dx","Integrate[1/Sqrt[a*Sec[x]^3],x]","\frac{2 \left(\tan (x)+\frac{F\left(\left.\frac{x}{2}\right|2\right)}{\cos ^{\frac{3}{2}}(x)}\right)}{3 \sqrt{a \sec ^3(x)}}","\frac{2 \tan (x)}{3 \sqrt{a \sec ^3(x)}}+\frac{2 F\left(\left.\frac{x}{2}\right|2\right)}{3 \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}",1,"(2*(EllipticF[x/2, 2]/Cos[x]^(3/2) + Tan[x]))/(3*Sqrt[a*Sec[x]^3])","A",1
59,1,43,73,0.1023811,"\int \frac{1}{\left(a \sec ^3(x)\right)^{3/2}} \, dx","Integrate[(a*Sec[x]^3)^(-3/2),x]","\frac{33 \sin (x)+5 \sin (3 x)+\frac{84 E\left(\left.\frac{x}{2}\right|2\right)}{\cos ^{\frac{3}{2}}(x)}}{90 a \sqrt{a \sec ^3(x)}}","\frac{14 \sin (x)}{45 a \sqrt{a \sec ^3(x)}}+\frac{14 E\left(\left.\frac{x}{2}\right|2\right)}{15 a \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}+\frac{2 \sin (x) \cos ^2(x)}{9 a \sqrt{a \sec ^3(x)}}",1,"((84*EllipticE[x/2, 2])/Cos[x]^(3/2) + 33*Sin[x] + 5*Sin[3*x])/(90*a*Sqrt[a*Sec[x]^3])","A",1
60,1,59,117,0.1032655,"\int \frac{1}{\left(a \sec ^3(x)\right)^{5/2}} \, dx","Integrate[(a*Sec[x]^3)^(-5/2),x]","\frac{\cos (x) \sqrt{a \sec ^3(x)} \left(19122 \sin (2 x)+4406 \sin (4 x)+826 \sin (6 x)+77 \sin (8 x)+24960 \sqrt{\cos (x)} F\left(\left.\frac{x}{2}\right|2\right)\right)}{73920 a^3}","\frac{26 \tan (x)}{77 a^2 \sqrt{a \sec ^3(x)}}+\frac{26 F\left(\left.\frac{x}{2}\right|2\right)}{77 a^2 \cos ^{\frac{3}{2}}(x) \sqrt{a \sec ^3(x)}}+\frac{2 \sin (x) \cos ^5(x)}{15 a^2 \sqrt{a \sec ^3(x)}}+\frac{26 \sin (x) \cos ^3(x)}{165 a^2 \sqrt{a \sec ^3(x)}}+\frac{78 \sin (x) \cos (x)}{385 a^2 \sqrt{a \sec ^3(x)}}",1,"(Cos[x]*Sqrt[a*Sec[x]^3]*(24960*Sqrt[Cos[x]]*EllipticF[x/2, 2] + 19122*Sin[2*x] + 4406*Sin[4*x] + 826*Sin[6*x] + 77*Sin[8*x]))/(73920*a^3)","A",1
61,1,54,163,0.1791948,"\int \left(a \sec ^4(x)\right)^{7/2} \, dx","Integrate[(a*Sec[x]^4)^(7/2),x]","\frac{\sin (x) \cos (x) (2380 \cos (2 x)+1093 \cos (4 x)+378 \cos (6 x)+92 \cos (8 x)+14 \cos (10 x)+\cos (12 x)+2048) \left(a \sec ^4(x)\right)^{7/2}}{6006}","a^3 \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{13} a^3 \sin ^2(x) \tan ^{11}(x) \sqrt{a \sec ^4(x)}+\frac{6}{11} a^3 \sin ^2(x) \tan ^9(x) \sqrt{a \sec ^4(x)}+\frac{5}{3} a^3 \sin ^2(x) \tan ^7(x) \sqrt{a \sec ^4(x)}+\frac{20}{7} a^3 \sin ^2(x) \tan ^5(x) \sqrt{a \sec ^4(x)}+3 a^3 \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+2 a^3 \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}",1,"(Cos[x]*(2048 + 2380*Cos[2*x] + 1093*Cos[4*x] + 378*Cos[6*x] + 92*Cos[8*x] + 14*Cos[10*x] + Cos[12*x])*(a*Sec[x]^4)^(7/2)*Sin[x])/6006","A",1
62,1,42,117,0.1000013,"\int \left(a \sec ^4(x)\right)^{5/2} \, dx","Integrate[(a*Sec[x]^4)^(5/2),x]","\frac{1}{315} \sin (x) \cos (x) (130 \cos (2 x)+46 \cos (4 x)+10 \cos (6 x)+\cos (8 x)+128) \left(a \sec ^4(x)\right)^{5/2}","a^2 \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{9} a^2 \sin ^2(x) \tan ^7(x) \sqrt{a \sec ^4(x)}+\frac{4}{7} a^2 \sin ^2(x) \tan ^5(x) \sqrt{a \sec ^4(x)}+\frac{6}{5} a^2 \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+\frac{4}{3} a^2 \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}",1,"(Cos[x]*(128 + 130*Cos[2*x] + 46*Cos[4*x] + 10*Cos[6*x] + Cos[8*x])*(a*Sec[x]^4)^(5/2)*Sin[x])/315","A",1
63,1,30,61,0.063406,"\int \left(a \sec ^4(x)\right)^{3/2} \, dx","Integrate[(a*Sec[x]^4)^(3/2),x]","\frac{1}{15} \sin (x) \cos (x) (6 \cos (2 x)+\cos (4 x)+8) \left(a \sec ^4(x)\right)^{3/2}","a \sin (x) \cos (x) \sqrt{a \sec ^4(x)}+\frac{1}{5} a \sin ^2(x) \tan ^3(x) \sqrt{a \sec ^4(x)}+\frac{2}{3} a \sin ^2(x) \tan (x) \sqrt{a \sec ^4(x)}",1,"(Cos[x]*(8 + 6*Cos[2*x] + Cos[4*x])*(a*Sec[x]^4)^(3/2)*Sin[x])/15","A",1
64,1,15,15,0.0057768,"\int \sqrt{a \sec ^4(x)} \, dx","Integrate[Sqrt[a*Sec[x]^4],x]","\sin (x) \cos (x) \sqrt{a \sec ^4(x)}","\sin (x) \cos (x) \sqrt{a \sec ^4(x)}",1,"Cos[x]*Sqrt[a*Sec[x]^4]*Sin[x]","A",1
65,1,23,36,0.0246513,"\int \frac{1}{\sqrt{a \sec ^4(x)}} \, dx","Integrate[1/Sqrt[a*Sec[x]^4],x]","\frac{\tan (x)+x \sec ^2(x)}{2 \sqrt{a \sec ^4(x)}}","\frac{x \sec ^2(x)}{2 \sqrt{a \sec ^4(x)}}+\frac{\tan (x)}{2 \sqrt{a \sec ^4(x)}}",1,"(x*Sec[x]^2 + Tan[x])/(2*Sqrt[a*Sec[x]^4])","A",1
66,1,38,86,0.0425113,"\int \frac{1}{\left(a \sec ^4(x)\right)^{3/2}} \, dx","Integrate[(a*Sec[x]^4)^(-3/2),x]","\frac{(60 x+45 \sin (2 x)+9 \sin (4 x)+\sin (6 x)) \sec ^6(x)}{192 \left(a \sec ^4(x)\right)^{3/2}}","\frac{5 x \sec ^2(x)}{16 a \sqrt{a \sec ^4(x)}}+\frac{5 \tan (x)}{16 a \sqrt{a \sec ^4(x)}}+\frac{\sin (x) \cos ^3(x)}{6 a \sqrt{a \sec ^4(x)}}+\frac{5 \sin (x) \cos (x)}{24 a \sqrt{a \sec ^4(x)}}",1,"(Sec[x]^6*(60*x + 45*Sin[2*x] + 9*Sin[4*x] + Sin[6*x]))/(192*(a*Sec[x]^4)^(3/2))","A",1
67,1,55,132,0.0913819,"\int \frac{1}{\left(a \sec ^4(x)\right)^{5/2}} \, dx","Integrate[(a*Sec[x]^4)^(-5/2),x]","\frac{(2520 x+2100 \sin (2 x)+600 \sin (4 x)+150 \sin (6 x)+25 \sin (8 x)+2 \sin (10 x)) \cos ^2(x) \sqrt{a \sec ^4(x)}}{10240 a^3}","\frac{63 x \sec ^2(x)}{256 a^2 \sqrt{a \sec ^4(x)}}+\frac{63 \tan (x)}{256 a^2 \sqrt{a \sec ^4(x)}}+\frac{\sin (x) \cos ^7(x)}{10 a^2 \sqrt{a \sec ^4(x)}}+\frac{9 \sin (x) \cos ^5(x)}{80 a^2 \sqrt{a \sec ^4(x)}}+\frac{21 \sin (x) \cos ^3(x)}{160 a^2 \sqrt{a \sec ^4(x)}}+\frac{21 \sin (x) \cos (x)}{128 a^2 \sqrt{a \sec ^4(x)}}",1,"(Cos[x]^2*Sqrt[a*Sec[x]^4]*(2520*x + 2100*Sin[2*x] + 600*Sin[4*x] + 150*Sin[6*x] + 25*Sin[8*x] + 2*Sin[10*x]))/(10240*a^3)","A",1
68,1,69,81,0.1004458,"\int \left((b \sec (c+d x))^p\right)^n \, dx","Integrate[((b*Sec[c + d*x])^p)^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \cot (c+d x) \left((b \sec (c+d x))^p\right)^n \, _2F_1\left(\frac{1}{2},\frac{n p}{2};\frac{1}{2} (n p+2);\sec ^2(c+d x)\right)}{d n p}","-\frac{\sin (c+d x) \cos (c+d x) \left((b \sec (c+d x))^p\right)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\cos ^2(c+d x)\right)}{d (1-n p) \sqrt{\sin ^2(c+d x)}}",1,"(Cot[c + d*x]*Hypergeometric2F1[1/2, (n*p)/2, (2 + n*p)/2, Sec[c + d*x]^2]*((b*Sec[c + d*x])^p)^n*Sqrt[-Tan[c + d*x]^2])/(d*n*p)","A",1
69,1,71,83,0.0783723,"\int \left(a (b \sec (c+d x))^p\right)^n \, dx","Integrate[(a*(b*Sec[c + d*x])^p)^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(\frac{1}{2},\frac{n p}{2};\frac{1}{2} (n p+2);\sec ^2(c+d x)\right) \left(a (b \sec (c+d x))^p\right)^n}{d n p}","-\frac{\sin (c+d x) \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\cos ^2(c+d x)\right) \left(a (b \sec (c+d x))^p\right)^n}{d (1-n p) \sqrt{\sin ^2(c+d x)}}",1,"(Cot[c + d*x]*Hypergeometric2F1[1/2, (n*p)/2, (2 + n*p)/2, Sec[c + d*x]^2]*(a*(b*Sec[c + d*x])^p)^n*Sqrt[-Tan[c + d*x]^2])/(d*n*p)","A",1
70,1,69,97,0.2168156,"\int \sec ^4(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^4*Sqrt[b*Sec[c + d*x]],x]","\frac{\sec ^2(c+d x) \sqrt{b \sec (c+d x)} \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^3 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b d}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}",1,"(Sec[c + d*x]^2*Sqrt[b*Sec[c + d*x]]*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*d)","A",1
71,1,69,95,0.1746325,"\int \sec ^3(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^3*Sqrt[b*Sec[c + d*x]],x]","\frac{\sec ^2(c+d x) \sqrt{b \sec (c+d x)} \left(7 \sin (c+d x)+3 \sin (3 (c+d x))-12 \cos ^{\frac{5}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^2 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}-\frac{6 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^2*Sqrt[b*Sec[c + d*x]]*(-12*Cos[c + d*x]^(5/2)*EllipticE[(c + d*x)/2, 2] + 7*Sin[c + d*x] + 3*Sin[3*(c + d*x)]))/(10*d)","A",1
72,1,51,69,0.086922,"\int \sec ^2(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^2*Sqrt[b*Sec[c + d*x]],x]","\frac{2 (b \sec (c+d x))^{3/2} \left(\sin (c+d x)+\cos ^{\frac{3}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 b d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b d}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}",1,"(2*(b*Sec[c + d*x])^(3/2)*(Cos[c + d*x]^(3/2)*EllipticF[(c + d*x)/2, 2] + Sin[c + d*x]))/(3*b*d)","A",1
73,1,47,63,0.0523358,"\int \sec (c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]*Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sqrt{b \sec (c+d x)} \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{d}","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*Sqrt[b*Sec[c + d*x]]*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/d","A",1
74,1,38,38,0.0220807,"\int \sqrt{b \sec (c+d x)} \, dx","Integrate[Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/d","A",1
75,1,39,39,0.0366845,"\int \cos (c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Cos[c + d*x]*Sqrt[b*Sec[c + d*x]],x]","\frac{2 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*b*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",1
76,1,51,67,0.057027,"\int \cos ^2(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Cos[c + d*x]^2*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left(\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d}","\frac{2 b \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}",1,"(Sqrt[b*Sec[c + d*x]]*(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)]))/(3*d)","A",1
77,1,57,70,0.0647819,"\int \cos ^3(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Cos[c + d*x]^3*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left(\sin (c+d x)+\sin (3 (c+d x))+12 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","\frac{2 b^2 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*(12*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Sin[c + d*x] + Sin[3*(c + d*x)]))/(10*d)","A",1
78,1,63,95,0.0928852,"\int \cos ^4(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Cos[c + d*x]^4*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left(26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{84 d}","\frac{2 b^3 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}",1,"(Sqrt[b*Sec[c + d*x]]*(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)]))/(84*d)","A",1
79,1,71,98,0.2509831,"\int \cos ^5(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Cos[c + d*x]^5*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left((33 \sin (c+d x)+5 \sin (3 (c+d x))) \cos ^2(c+d x)+84 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{90 d}","\frac{2 b^4 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^2 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*(84*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]^2*(33*Sin[c + d*x] + 5*Sin[3*(c + d*x)])))/(90*d)","A",1
80,1,64,95,0.1866966,"\int \sec ^3(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Sec[c + d*x]^3*(b*Sec[c + d*x])^(3/2),x]","\frac{(b \sec (c+d x))^{5/2} \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 b d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^2 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}+\frac{10 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}",1,"((b*Sec[c + d*x])^(5/2)*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*b*d)","A",1
81,1,64,98,0.1770112,"\int \sec ^2(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Sec[c + d*x]^2*(b*Sec[c + d*x])^(3/2),x]","\frac{(b \sec (c+d x))^{5/2} \left(7 \sin (c+d x)+3 \sin (3 (c+d x))-12 \cos ^{\frac{5}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 b d}","-\frac{6 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b d}+\frac{6 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}",1,"((b*Sec[c + d*x])^(5/2)*(-12*Cos[c + d*x]^(5/2)*EllipticE[(c + d*x)/2, 2] + 7*Sin[c + d*x] + 3*Sin[3*(c + d*x)]))/(10*b*d)","A",1
82,1,49,67,0.0781455,"\int \sec (c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Sec[c + d*x]*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b \sqrt{b \sec (c+d x)} \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}+\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}",1,"(2*b*Sqrt[b*Sec[c + d*x]]*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*d)","A",1
83,1,48,66,0.0339002,"\int (b \sec (c+d x))^{3/2} \, dx","Integrate[(b*Sec[c + d*x])^(3/2),x]","\frac{2 b \sqrt{b \sec (c+d x)} \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{d}","\frac{2 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*b*Sqrt[b*Sec[c + d*x]]*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/d","A",1
84,1,39,39,0.0202008,"\int \cos (c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}","\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}",1,"(2*b*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/d","A",1
85,1,41,41,0.022079,"\int \cos ^2(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^2*(b*Sec[c + d*x])^(3/2),x]","\frac{2 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*b^2*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",1
86,1,52,70,0.0485591,"\int \cos ^3(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^3*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sqrt{b \sec (c+d x)} \left(\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d}","\frac{2 b^2 \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}",1,"(b*Sqrt[b*Sec[c + d*x]]*(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)]))/(3*d)","A",1
87,1,58,72,0.0486586,"\int \cos ^4(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^4*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sqrt{b \sec (c+d x)} \left(\sin (c+d x)+\sin (3 (c+d x))+12 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","\frac{2 b^3 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(b*Sqrt[b*Sec[c + d*x]]*(12*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Sin[c + d*x] + Sin[3*(c + d*x)]))/(10*d)","A",1
88,1,64,98,0.0770912,"\int \cos ^5(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^5*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sqrt{b \sec (c+d x)} \left(26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{84 d}","\frac{2 b^4 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b^2 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 b \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}",1,"(b*Sqrt[b*Sec[c + d*x]]*(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)]))/(84*d)","A",1
89,1,72,100,0.1547566,"\int \cos ^6(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Cos[c + d*x]^6*(b*Sec[c + d*x])^(3/2),x]","\frac{b \sqrt{b \sec (c+d x)} \left((33 \sin (c+d x)+5 \sin (3 (c+d x))) \cos ^2(c+d x)+84 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{90 d}","\frac{2 b^5 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^3 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b^2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(b*Sqrt[b*Sec[c + d*x]]*(84*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]^2*(33*Sin[c + d*x] + 5*Sin[3*(c + d*x)])))/(90*d)","A",1
90,1,61,98,0.1934663,"\int \sec ^2(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Sec[c + d*x]^2*(b*Sec[c + d*x])^(5/2),x]","\frac{(b \sec (c+d x))^{5/2} \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 d}","\frac{10 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}+\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b d}+\frac{10 b \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 d}",1,"((b*Sec[c + d*x])^(5/2)*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*d)","A",1
91,1,61,97,0.181097,"\int \sec (c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Sec[c + d*x]*(b*Sec[c + d*x])^(5/2),x]","\frac{(b \sec (c+d x))^{5/2} \left(7 \sin (c+d x)+3 \sin (3 (c+d x))-12 \cos ^{\frac{5}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","-\frac{6 b^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{6 b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 d}",1,"((b*Sec[c + d*x])^(5/2)*(-12*Cos[c + d*x]^(5/2)*EllipticE[(c + d*x)/2, 2] + 7*Sin[c + d*x] + 3*Sin[3*(c + d*x)]))/(10*d)","A",1
92,1,51,70,0.0176317,"\int (b \sec (c+d x))^{5/2} \, dx","Integrate[(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^2 \sqrt{b \sec (c+d x)} \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d}","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}+\frac{2 b \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 d}",1,"(2*b^2*Sqrt[b*Sec[c + d*x]]*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*d)","A",1
93,1,50,68,0.0244062,"\int \cos (c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^2 \sqrt{b \sec (c+d x)} \left(\sin (c+d x)-\sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{d}","\frac{2 b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d}-\frac{2 b^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*b^2*Sqrt[b*Sec[c + d*x]]*(-(Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2]) + Sin[c + d*x]))/d","A",1
94,1,41,41,0.0168049,"\int \cos ^2(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^2*(b*Sec[c + d*x])^(5/2),x]","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}","\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{d}",1,"(2*b^2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/d","A",1
95,1,38,41,0.0428193,"\int \cos ^3(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^3*(b*Sec[c + d*x])^(5/2),x]","\frac{2 \cos ^{\frac{5}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right) (b \sec (c+d x))^{5/2}}{d}","\frac{2 b^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*Cos[c + d*x]^(5/2)*EllipticE[(c + d*x)/2, 2]*(b*Sec[c + d*x])^(5/2))/d","A",1
96,1,54,72,0.0542659,"\int \cos ^4(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^4*(b*Sec[c + d*x])^(5/2),x]","\frac{b^2 \sqrt{b \sec (c+d x)} \left(\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d}","\frac{2 b^3 \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 d}",1,"(b^2*Sqrt[b*Sec[c + d*x]]*(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)]))/(3*d)","A",1
97,1,60,72,0.0531952,"\int \cos ^5(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^5*(b*Sec[c + d*x])^(5/2),x]","\frac{b^2 \sqrt{b \sec (c+d x)} \left(\sin (c+d x)+\sin (3 (c+d x))+12 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","\frac{2 b^4 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 b^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(b^2*Sqrt[b*Sec[c + d*x]]*(12*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Sin[c + d*x] + Sin[3*(c + d*x)]))/(10*d)","A",1
98,1,66,100,0.0779537,"\int \cos ^6(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^6*(b*Sec[c + d*x])^(5/2),x]","\frac{b^2 \sqrt{b \sec (c+d x)} \left(26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{84 d}","\frac{2 b^5 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 b^3 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 b^2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 d}",1,"(b^2*Sqrt[b*Sec[c + d*x]]*(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)]))/(84*d)","A",1
99,1,74,100,0.1819468,"\int \cos ^7(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Cos[c + d*x]^7*(b*Sec[c + d*x])^(5/2),x]","\frac{b^2 \sqrt{b \sec (c+d x)} \left((33 \sin (c+d x)+5 \sin (3 (c+d x))) \cos ^2(c+d x)+84 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{90 d}","\frac{2 b^6 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b^4 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 b^3 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(b^2*Sqrt[b*Sec[c + d*x]]*(84*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]^2*(33*Sin[c + d*x] + 5*Sin[3*(c + d*x)])))/(90*d)","A",1
100,1,62,98,0.089497,"\int (b \sec (c+d x))^{7/2} \, dx","Integrate[(b*Sec[c + d*x])^(7/2),x]","\frac{b (b \sec (c+d x))^{5/2} \left(7 \sin (c+d x)+3 \sin (3 (c+d x))-12 \cos ^{\frac{5}{2}}(c+d x) E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 d}","-\frac{6 b^4 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{6 b^3 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 b \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 d}",1,"(b*(b*Sec[c + d*x])^(5/2)*(-12*Cos[c + d*x]^(5/2)*EllipticE[(c + d*x)/2, 2] + 7*Sin[c + d*x] + 3*Sin[3*(c + d*x)]))/(10*d)","A",1
101,1,69,100,0.0871291,"\int \frac{\sec ^5(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^5/Sqrt[b*Sec[c + d*x]],x]","\frac{\sec ^3(c+d x) \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 d \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^4 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^2 d}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b d}",1,"(Sec[c + d*x]^3*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*d*Sqrt[b*Sec[c + d*x]])","A",1
102,1,61,97,0.2384,"\int \frac{\sec ^4(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^4/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \tan (c+d x) \left(\sec ^2(c+d x)+3\right)-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{5 d \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^3 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b d}-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"((-6*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 2*(3 + Sec[c + d*x]^2)*Tan[c + d*x])/(5*d*Sqrt[b*Sec[c + d*x]])","A",1
103,1,51,72,0.0773791,"\int \frac{\sec ^3(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^3/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sqrt{b \sec (c+d x)} \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 b d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^2 d}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b d}",1,"(2*Sqrt[b*Sec[c + d*x]]*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*b*d)","A",1
104,1,48,65,0.0806168,"\int \frac{\sec ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^2/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \tan (c+d x)-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{d \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b d}-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"((-2*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 2*Tan[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",1
105,1,41,41,0.017421,"\int \frac{\sec (c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]/Sqrt[b*Sec[c + d*x]],x]","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b d}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b*d)","A",1
106,1,38,38,0.0158277,"\int \frac{1}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[1/Sqrt[b*Sec[c + d*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*EllipticE[(c + d*x)/2, 2])/(d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",1
107,1,60,69,0.0752802,"\int \frac{\cos (c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Cos[c + d*x]/Sqrt[b*Sec[c + d*x]],x]","\frac{b \sec ^2(c+d x) \left(\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d (b \sec (c+d x))^{3/2}}","\frac{2 \sin (c+d x)}{3 d \sqrt{b \sec (c+d x)}}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b d}",1,"(b*Sec[c + d*x]^2*(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)]))/(3*d*(b*Sec[c + d*x])^(3/2))","A",1
108,1,60,67,0.088417,"\int \frac{\cos ^2(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Cos[c + d*x]^2/Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left(\sin (c+d x)+\sin (3 (c+d x))+12 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 b d}","\frac{2 b \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*(12*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Sin[c + d*x] + Sin[3*(c + d*x)]))/(10*b*d)","A",1
109,1,66,97,0.0876792,"\int \frac{\cos ^3(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Cos[c + d*x]^3/Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left(26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{84 b d}","\frac{2 b^2 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}+\frac{10 \sin (c+d x)}{21 d \sqrt{b \sec (c+d x)}}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b d}",1,"(Sqrt[b*Sec[c + d*x]]*(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)]))/(84*b*d)","A",1
110,1,70,95,0.1956929,"\int \frac{\cos ^4(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Cos[c + d*x]^4/Sqrt[b*Sec[c + d*x]],x]","\frac{4 (33 \sin (c+d x)+5 \sin (3 (c+d x))) \cos (c+d x)+\frac{336 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{360 d \sqrt{b \sec (c+d x)}}","\frac{2 b^3 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 b \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"((336*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 4*Cos[c + d*x]*(33*Sin[c + d*x] + 5*Sin[3*(c + d*x)]))/(360*d*Sqrt[b*Sec[c + d*x]])","A",1
111,1,69,100,0.1731606,"\int \frac{\sec ^6(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^6/(b*Sec[c + d*x])^(3/2),x]","\frac{\sec ^4(c+d x) \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 d (b \sec (c+d x))^{3/2}}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^5 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^3 d}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^2 d}",1,"(Sec[c + d*x]^4*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*d*(b*Sec[c + d*x])^(3/2))","A",1
112,1,64,100,0.0560091,"\int \frac{\sec ^5(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^5/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \tan (c+d x) \left(\sec ^2(c+d x)+3\right)-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{5 b d \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^4 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b^2 d}-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"((-6*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 2*(3 + Sec[c + d*x]^2)*Tan[c + d*x])/(5*b*d*Sqrt[b*Sec[c + d*x]])","A",1
113,1,56,72,0.0944732,"\int \frac{\sec ^4(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^4/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \sec ^3(c+d x) \left(\sin (c+d x)+\cos ^{\frac{3}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d (b \sec (c+d x))^{3/2}}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^3 d}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^2 d}",1,"(2*Sec[c + d*x]^3*(Cos[c + d*x]^(3/2)*EllipticF[(c + d*x)/2, 2] + Sin[c + d*x]))/(3*d*(b*Sec[c + d*x])^(3/2))","A",1
114,1,51,68,0.0576823,"\int \frac{\sec ^3(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^3/(b*Sec[c + d*x])^(3/2),x]","\frac{2 \tan (c+d x)-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{b d \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b^2 d}-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"((-2*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 2*Tan[c + d*x])/(b*d*Sqrt[b*Sec[c + d*x]])","A",1
115,1,41,41,0.0234681,"\int \frac{\sec ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^2/(b*Sec[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) \sqrt{b \sec (c+d x)}}{b^2 d}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b^2 d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b^2*d)","A",1
116,1,41,41,0.0333395,"\int \frac{\sec (c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]/(b*Sec[c + d*x])^(3/2),x]","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*EllipticE[(c + d*x)/2, 2])/(b*d*Sqrt[Cos[c + d*x]]*Sqrt[b*Sec[c + d*x]])","A",1
117,1,59,72,0.0493183,"\int \frac{1}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[(b*Sec[c + d*x])^(-3/2),x]","\frac{\sec ^2(c+d x) \left(\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 d (b \sec (c+d x))^{3/2}}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^2 d}+\frac{2 \sin (c+d x)}{3 b d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^2*(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)]))/(3*d*(b*Sec[c + d*x])^(3/2))","A",1
118,1,60,69,0.0313905,"\int \frac{\cos (c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]/(b*Sec[c + d*x])^(3/2),x]","\frac{\sqrt{b \sec (c+d x)} \left(\sin (c+d x)+\sin (3 (c+d x))+12 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 b^2 d}","\frac{2 \sin (c+d x)}{5 d (b \sec (c+d x))^{3/2}}+\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*(12*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Sin[c + d*x] + Sin[3*(c + d*x)]))/(10*b^2*d)","A",1
119,1,66,98,0.0987051,"\int \frac{\cos ^2(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^2/(b*Sec[c + d*x])^(3/2),x]","\frac{\sqrt{b \sec (c+d x)} \left(26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{84 b^2 d}","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^2 d}+\frac{10 \sin (c+d x)}{21 b d \sqrt{b \sec (c+d x)}}+\frac{2 b \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}",1,"(Sqrt[b*Sec[c + d*x]]*(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)]))/(84*b^2*d)","A",1
120,1,73,97,0.0817163,"\int \frac{\cos ^3(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Cos[c + d*x]^3/(b*Sec[c + d*x])^(3/2),x]","\frac{84 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)+(33 \sin (c+d x)+5 \sin (3 (c+d x))) \cos ^{\frac{3}{2}}(c+d x)}{90 d \cos ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{3/2}}","\frac{2 b^2 \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}+\frac{14 \sin (c+d x)}{45 d (b \sec (c+d x))^{3/2}}+\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(84*EllipticE[(c + d*x)/2, 2] + Cos[c + d*x]^(3/2)*(33*Sin[c + d*x] + 5*Sin[3*(c + d*x)]))/(90*d*Cos[c + d*x]^(3/2)*(b*Sec[c + d*x])^(3/2))","A",1
121,1,64,100,0.1447108,"\int \frac{\sec ^7(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^7/(b*Sec[c + d*x])^(5/2),x]","\frac{(b \sec (c+d x))^{5/2} \left(5 \sin (2 (c+d x))+6 \tan (c+d x)+10 \cos ^{\frac{5}{2}}(c+d x) F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{21 b^5 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{7/2}}{7 b^6 d}+\frac{10 \sin (c+d x) (b \sec (c+d x))^{3/2}}{21 b^4 d}+\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^3 d}",1,"((b*Sec[c + d*x])^(5/2)*(10*Cos[c + d*x]^(5/2)*EllipticF[(c + d*x)/2, 2] + 5*Sin[2*(c + d*x)] + 6*Tan[c + d*x]))/(21*b^5*d)","A",1
122,1,64,100,0.1171761,"\int \frac{\sec ^6(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^6/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \tan (c+d x) \left(\sec ^2(c+d x)+3\right)-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{5 b^2 d \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{5/2}}{5 b^5 d}+\frac{6 \sin (c+d x) \sqrt{b \sec (c+d x)}}{5 b^3 d}-\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"((-6*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 2*(3 + Sec[c + d*x]^2)*Tan[c + d*x])/(5*b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
123,1,51,72,0.0692695,"\int \frac{\sec ^5(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^5/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \sqrt{b \sec (c+d x)} \left(\tan (c+d x)+\sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 b^3 d}","\frac{2 \sin (c+d x) (b \sec (c+d x))^{3/2}}{3 b^4 d}+\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^3 d}",1,"(2*Sqrt[b*Sec[c + d*x]]*(Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Tan[c + d*x]))/(3*b^3*d)","A",1
124,1,51,68,0.0535037,"\int \frac{\sec ^4(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^4/(b*Sec[c + d*x])^(5/2),x]","\frac{2 \tan (c+d x)-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{b^2 d \sqrt{b \sec (c+d x)}}","\frac{2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{b^3 d}-\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"((-2*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 2*Tan[c + d*x])/(b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
125,1,41,41,0.0164935,"\int \frac{\sec ^3(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^3/(b*Sec[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) \sqrt{b \sec (c+d x)}}{b^3 d}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{b^3 d}",1,"(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2]*Sqrt[b*Sec[c + d*x]])/(b^3*d)","A",1
126,1,38,41,0.0380671,"\int \frac{\sec ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^2/(b*Sec[c + d*x])^(5/2),x]","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{d \cos ^{\frac{5}{2}}(c+d x) (b \sec (c+d x))^{5/2}}","\frac{2 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(2*EllipticE[(c + d*x)/2, 2])/(d*Cos[c + d*x]^(5/2)*(b*Sec[c + d*x])^(5/2))","A",1
127,1,62,72,0.03271,"\int \frac{\sec (c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]/(b*Sec[c + d*x])^(5/2),x]","\frac{\sec ^2(c+d x) \left(\sin (2 (c+d x))+2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{3 b d (b \sec (c+d x))^{3/2}}","\frac{2 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{3 b^3 d}+\frac{2 \sin (c+d x)}{3 b^2 d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^2*(2*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + Sin[2*(c + d*x)]))/(3*b*d*(b*Sec[c + d*x])^(3/2))","A",1
128,1,60,72,0.0192376,"\int \frac{1}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[(b*Sec[c + d*x])^(-5/2),x]","\frac{\sqrt{b \sec (c+d x)} \left(\sin (c+d x)+\sin (3 (c+d x))+12 \sqrt{\cos (c+d x)} E\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{10 b^3 d}","\frac{6 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{5 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{2 \sin (c+d x)}{5 b d (b \sec (c+d x))^{3/2}}",1,"(Sqrt[b*Sec[c + d*x]]*(12*Sqrt[Cos[c + d*x]]*EllipticE[(c + d*x)/2, 2] + Sin[c + d*x] + Sin[3*(c + d*x)]))/(10*b^3*d)","A",1
129,1,66,97,0.0405322,"\int \frac{\cos (c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]/(b*Sec[c + d*x])^(5/2),x]","\frac{\sqrt{b \sec (c+d x)} \left(26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{84 b^3 d}","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^3 d}+\frac{10 \sin (c+d x)}{21 b^2 d \sqrt{b \sec (c+d x)}}+\frac{2 \sin (c+d x)}{7 d (b \sec (c+d x))^{5/2}}",1,"(Sqrt[b*Sec[c + d*x]]*(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)]))/(84*b^3*d)","A",1
130,1,73,98,0.1264769,"\int \frac{\cos ^2(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Cos[c + d*x]^2/(b*Sec[c + d*x])^(5/2),x]","\frac{4 (33 \sin (c+d x)+5 \sin (3 (c+d x))) \cos (c+d x)+\frac{336 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{\sqrt{\cos (c+d x)}}}{360 b^2 d \sqrt{b \sec (c+d x)}}","\frac{14 E\left(\left.\frac{1}{2} (c+d x)\right|2\right)}{15 b^2 d \sqrt{\cos (c+d x)} \sqrt{b \sec (c+d x)}}+\frac{14 \sin (c+d x)}{45 b d (b \sec (c+d x))^{3/2}}+\frac{2 b \sin (c+d x)}{9 d (b \sec (c+d x))^{7/2}}",1,"((336*EllipticE[(c + d*x)/2, 2])/Sqrt[Cos[c + d*x]] + 4*Cos[c + d*x]*(33*Sin[c + d*x] + 5*Sin[3*(c + d*x)]))/(360*b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
131,1,66,100,0.0209363,"\int \frac{1}{(b \sec (c+d x))^{7/2}} \, dx","Integrate[(b*Sec[c + d*x])^(-7/2),x]","\frac{\sqrt{b \sec (c+d x)} \left(26 \sin (2 (c+d x))+3 \sin (4 (c+d x))+40 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right)\right)}{84 b^4 d}","\frac{10 \sqrt{\cos (c+d x)} F\left(\left.\frac{1}{2} (c+d x)\right|2\right) \sqrt{b \sec (c+d x)}}{21 b^4 d}+\frac{10 \sin (c+d x)}{21 b^3 d \sqrt{b \sec (c+d x)}}+\frac{2 \sin (c+d x)}{7 b d (b \sec (c+d x))^{5/2}}",1,"(Sqrt[b*Sec[c + d*x]]*(40*Sqrt[Cos[c + d*x]]*EllipticF[(c + d*x)/2, 2] + 26*Sin[2*(c + d*x)] + 3*Sin[4*(c + d*x)]))/(84*b^4*d)","A",1
132,1,64,107,0.1504135,"\int \sec ^{\frac{9}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^(9/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left(3 \tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x) \left(2 \sec ^2(c+d x)+3\right)\right)}{8 d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{4 d}+\frac{3 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{8 d}+\frac{3 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*(3*ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*(3 + 2*Sec[c + d*x]^2)*Tan[c + d*x]))/(8*d*Sqrt[Sec[c + d*x]])","A",1
133,1,45,70,0.0931459,"\int \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^(7/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}","\frac{\sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{\sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(Sqrt[b*Sec[c + d*x]]*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*Sqrt[Sec[c + d*x]])","A",1
134,1,50,72,0.057964,"\int \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \left(\tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x)\right)}{2 d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{\sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*(ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*Tan[c + d*x]))/(2*d*Sqrt[Sec[c + d*x]])","A",1
135,1,32,32,0.0187062,"\int \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]],x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"(Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/d","A",1
136,1,33,33,0.0127066,"\int \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)} \, dx","Integrate[Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}","\frac{\sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[b*Sec[c + d*x]])/(d*Sqrt[Sec[c + d*x]])","A",1
137,1,24,24,0.0158667,"\int \frac{\sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}} \, dx","Integrate[Sqrt[b*Sec[c + d*x]]/Sqrt[Sec[c + d*x]],x]","\frac{x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}","\frac{x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}",1,"(x*Sqrt[b*Sec[c + d*x]])/Sqrt[Sec[c + d*x]]","A",1
138,1,32,32,0.0376952,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(3/2),x]","\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}",1,"(Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]])","A",1
139,1,45,63,0.0709063,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(5/2),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \sqrt{b \sec (c+d x)}}{4 d \sqrt{\sec (c+d x)}}","\frac{x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}",1,"(Sqrt[b*Sec[c + d*x]]*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Sqrt[Sec[c + d*x]])","A",1
140,1,45,70,0.1161411,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{7}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(7/2),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) \sqrt{b \sec (c+d x)}}{6 d \sqrt{\sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}",1,"((5 + Cos[2*(c + d*x)])*Sqrt[b*Sec[c + d*x]]*Sin[c + d*x])/(6*d*Sqrt[Sec[c + d*x]])","A",1
141,1,55,98,0.1202984,"\int \frac{\sqrt{b \sec (c+d x)}}{\sec ^{\frac{9}{2}}(c+d x)} \, dx","Integrate[Sqrt[b*Sec[c + d*x]]/Sec[c + d*x]^(9/2),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) \sqrt{b \sec (c+d x)}}{32 d \sqrt{\sec (c+d x)}}","\frac{3 x \sqrt{b \sec (c+d x)}}{8 \sqrt{\sec (c+d x)}}+\frac{3 \sin (c+d x) \sqrt{b \sec (c+d x)}}{8 d \sec ^{\frac{3}{2}}(c+d x)}+\frac{\sin (c+d x) \sqrt{b \sec (c+d x)}}{4 d \sec ^{\frac{7}{2}}(c+d x)}",1,"(Sqrt[b*Sec[c + d*x]]*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*Sqrt[Sec[c + d*x]])","A",1
142,1,64,110,0.1168553,"\int \sec ^{\frac{7}{2}}(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Sec[c + d*x]^(7/2)*(b*Sec[c + d*x])^(3/2),x]","\frac{(b \sec (c+d x))^{3/2} \left(3 \tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x) \left(2 \sec ^2(c+d x)+3\right)\right)}{8 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b \sin (c+d x) \sec ^{\frac{7}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{4 d}+\frac{3 b \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{8 d}+\frac{3 b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{8 d \sqrt{\sec (c+d x)}}",1,"((b*Sec[c + d*x])^(3/2)*(3*ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*(3 + 2*Sec[c + d*x]^2)*Tan[c + d*x]))/(8*d*Sec[c + d*x]^(3/2))","A",1
143,1,45,72,0.0932127,"\int \sec ^{\frac{5}{2}}(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Sec[c + d*x]^(5/2)*(b*Sec[c + d*x])^(3/2),x]","\frac{\left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right) (b \sec (c+d x))^{3/2}}{d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"((b*Sec[c + d*x])^(3/2)*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*Sec[c + d*x]^(3/2))","A",1
144,1,50,74,0.0648427,"\int \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{3/2} \, dx","Integrate[Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(3/2),x]","\frac{(b \sec (c+d x))^{3/2} \left(\tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x)\right)}{2 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}",1,"((b*Sec[c + d*x])^(3/2)*(ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*Tan[c + d*x]))/(2*d*Sec[c + d*x]^(3/2))","A",1
145,1,32,33,0.0209877,"\int \sqrt{\sec (c+d x)} (b \sec (c+d x))^{3/2} \, dx","Integrate[Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(3/2),x]","\frac{\sin (c+d x) (b \sec (c+d x))^{3/2}}{d \sqrt{\sec (c+d x)}}","\frac{b \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"((b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(d*Sqrt[Sec[c + d*x]])","A",1
146,1,33,34,0.0193205,"\int \frac{(b \sec (c+d x))^{3/2}}{\sqrt{\sec (c+d x)}} \, dx","Integrate[(b*Sec[c + d*x])^(3/2)/Sqrt[Sec[c + d*x]],x]","\frac{(b \sec (c+d x))^{3/2} \tanh ^{-1}(\sin (c+d x))}{d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*(b*Sec[c + d*x])^(3/2))/(d*Sec[c + d*x]^(3/2))","A",1
147,1,24,25,0.0259734,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(3/2),x]","\frac{x (b \sec (c+d x))^{3/2}}{\sec ^{\frac{3}{2}}(c+d x)}","\frac{b x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}",1,"(x*(b*Sec[c + d*x])^(3/2))/Sec[c + d*x]^(3/2)","A",1
148,1,32,33,0.0471688,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(5/2),x]","\frac{\sin (c+d x) (b \sec (c+d x))^{3/2}}{d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}",1,"((b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(d*Sec[c + d*x]^(3/2))","A",1
149,1,45,65,0.0823492,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{7}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(7/2),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) (b \sec (c+d x))^{3/2}}{4 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}",1,"((b*Sec[c + d*x])^(3/2)*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Sec[c + d*x]^(3/2))","A",1
150,1,45,72,0.1439904,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{9}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(9/2),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) (b \sec (c+d x))^{3/2}}{6 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{b \sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}",1,"((5 + Cos[2*(c + d*x)])*(b*Sec[c + d*x])^(3/2)*Sin[c + d*x])/(6*d*Sec[c + d*x]^(3/2))","A",1
151,1,55,101,0.1635949,"\int \frac{(b \sec (c+d x))^{3/2}}{\sec ^{\frac{11}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(3/2)/Sec[c + d*x]^(11/2),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) (b \sec (c+d x))^{3/2}}{32 d \sec ^{\frac{3}{2}}(c+d x)}","\frac{3 b x \sqrt{b \sec (c+d x)}}{8 \sqrt{\sec (c+d x)}}+\frac{3 b \sin (c+d x) \sqrt{b \sec (c+d x)}}{8 d \sec ^{\frac{3}{2}}(c+d x)}+\frac{b \sin (c+d x) \sqrt{b \sec (c+d x)}}{4 d \sec ^{\frac{7}{2}}(c+d x)}",1,"((b*Sec[c + d*x])^(3/2)*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*Sec[c + d*x]^(3/2))","A",1
152,1,57,116,0.2254216,"\int \sec ^{\frac{7}{2}}(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Sec[c + d*x]^(7/2)*(b*Sec[c + d*x])^(5/2),x]","\frac{\left(\frac{1}{5} \tan ^5(c+d x)+\frac{2}{3} \tan ^3(c+d x)+\tan (c+d x)\right) (b \sec (c+d x))^{5/2}}{d \sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin ^5(c+d x) \sec ^{\frac{9}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{5 d}+\frac{2 b^2 \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"((b*Sec[c + d*x])^(5/2)*(Tan[c + d*x] + (2*Tan[c + d*x]^3)/3 + Tan[c + d*x]^5/5))/(d*Sec[c + d*x]^(5/2))","A",1
153,1,45,76,0.0887024,"\int \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{5/2} \, dx","Integrate[Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(5/2),x]","\frac{\left(\frac{1}{3} \tan ^3(c+d x)+\tan (c+d x)\right) (b \sec (c+d x))^{5/2}}{d \sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin ^3(c+d x) \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{3 d}+\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"((b*Sec[c + d*x])^(5/2)*(Tan[c + d*x] + Tan[c + d*x]^3/3))/(d*Sec[c + d*x]^(5/2))","A",1
154,1,50,78,0.0801488,"\int \sqrt{\sec (c+d x)} (b \sec (c+d x))^{5/2} \, dx","Integrate[Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(5/2),x]","\frac{(b \sec (c+d x))^{5/2} \left(\tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x)\right)}{2 d \sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}}{2 d}+\frac{b^2 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{\sec (c+d x)}}",1,"((b*Sec[c + d*x])^(5/2)*(ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*Tan[c + d*x]))/(2*d*Sec[c + d*x]^(5/2))","A",1
155,1,32,35,0.0311132,"\int \frac{(b \sec (c+d x))^{5/2}}{\sqrt{\sec (c+d x)}} \, dx","Integrate[(b*Sec[c + d*x])^(5/2)/Sqrt[Sec[c + d*x]],x]","\frac{\sin (c+d x) (b \sec (c+d x))^{5/2}}{d \sec ^{\frac{3}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}{d}",1,"((b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(d*Sec[c + d*x]^(3/2))","A",1
156,1,33,36,0.0335583,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(3/2),x]","\frac{(b \sec (c+d x))^{5/2} \tanh ^{-1}(\sin (c+d x))}{d \sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sqrt{b \sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{\sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*(b*Sec[c + d*x])^(5/2))/(d*Sec[c + d*x]^(5/2))","A",1
157,1,24,27,0.0199545,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(5/2),x]","\frac{x (b \sec (c+d x))^{5/2}}{\sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 x \sqrt{b \sec (c+d x)}}{\sqrt{\sec (c+d x)}}",1,"(x*(b*Sec[c + d*x])^(5/2))/Sec[c + d*x]^(5/2)","A",1
158,1,32,35,0.0690276,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{7}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(7/2),x]","\frac{\sin (c+d x) (b \sec (c+d x))^{5/2}}{d \sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}",1,"((b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(d*Sec[c + d*x]^(5/2))","A",1
159,1,45,69,0.1119737,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{9}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(9/2),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) (b \sec (c+d x))^{5/2}}{4 d \sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 x \sqrt{b \sec (c+d x)}}{2 \sqrt{\sec (c+d x)}}+\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{2 d \sec ^{\frac{3}{2}}(c+d x)}",1,"((b*Sec[c + d*x])^(5/2)*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Sec[c + d*x]^(5/2))","A",1
160,1,45,76,0.1667269,"\int \frac{(b \sec (c+d x))^{5/2}}{\sec ^{\frac{11}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(5/2)/Sec[c + d*x]^(11/2),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) (b \sec (c+d x))^{5/2}}{6 d \sec ^{\frac{5}{2}}(c+d x)}","\frac{b^2 \sin (c+d x) \sqrt{b \sec (c+d x)}}{d \sqrt{\sec (c+d x)}}-\frac{b^2 \sin ^3(c+d x) \sqrt{b \sec (c+d x)}}{3 d \sqrt{\sec (c+d x)}}",1,"((5 + Cos[2*(c + d*x)])*(b*Sec[c + d*x])^(5/2)*Sin[c + d*x])/(6*d*Sec[c + d*x]^(5/2))","A",1
161,1,50,72,0.0611959,"\int \frac{\sec ^{\frac{7}{2}}(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^(7/2)/Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{\sec (c+d x)} \left(\tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x)\right)}{2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*(ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*Tan[c + d*x]))/(2*d*Sqrt[b*Sec[c + d*x]])","A",1
162,1,32,32,0.0213374,"\int \frac{\sec ^{\frac{5}{2}}(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^(5/2)/Sqrt[b*Sec[c + d*x]],x]","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*Sin[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",1
163,1,33,33,0.0143329,"\int \frac{\sec ^{\frac{3}{2}}(c+d x)}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^(3/2)/Sqrt[b*Sec[c + d*x]],x]","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \sec (c+d x)}}","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sqrt[Sec[c + d*x]])/(d*Sqrt[b*Sec[c + d*x]])","A",1
164,1,24,24,0.0124069,"\int \frac{\sqrt{\sec (c+d x)}}{\sqrt{b \sec (c+d x)}} \, dx","Integrate[Sqrt[Sec[c + d*x]]/Sqrt[b*Sec[c + d*x]],x]","\frac{x \sqrt{\sec (c+d x)}}{\sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{\sqrt{b \sec (c+d x)}}",1,"(x*Sqrt[Sec[c + d*x]])/Sqrt[b*Sec[c + d*x]]","A",1
165,1,32,32,0.0313193,"\int \frac{1}{\sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}} \, dx","Integrate[1/(Sqrt[Sec[c + d*x]]*Sqrt[b*Sec[c + d*x]]),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(d*Sqrt[b*Sec[c + d*x]])","A",1
166,1,45,63,0.063888,"\int \frac{1}{\sec ^{\frac{3}{2}}(c+d x) \sqrt{b \sec (c+d x)}} \, dx","Integrate[1/(Sec[c + d*x]^(3/2)*Sqrt[b*Sec[c + d*x]]),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \sqrt{\sec (c+d x)}}{4 d \sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*Sqrt[b*Sec[c + d*x]])","A",1
167,1,45,70,0.0885017,"\int \frac{1}{\sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}} \, dx","Integrate[1/(Sec[c + d*x]^(5/2)*Sqrt[b*Sec[c + d*x]]),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) \sqrt{\sec (c+d x)}}{6 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 d \sqrt{b \sec (c+d x)}}",1,"((5 + Cos[2*(c + d*x)])*Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(6*d*Sqrt[b*Sec[c + d*x]])","A",1
168,1,50,78,0.0617363,"\int \frac{\sec ^{\frac{9}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^(9/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{\sec ^{\frac{3}{2}}(c+d x) \left(\tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x)\right)}{2 d (b \sec (c+d x))^{3/2}}","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 b d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*(ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*Tan[c + d*x]))/(2*d*(b*Sec[c + d*x])^(3/2))","A",1
169,1,32,35,0.0365104,"\int \frac{\sec ^{\frac{7}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^(7/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{d (b \sec (c+d x))^{3/2}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{b d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(5/2)*Sin[c + d*x])/(d*(b*Sec[c + d*x])^(3/2))","A",1
170,1,33,36,0.0273644,"\int \frac{\sec ^{\frac{5}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^(5/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{\sec ^{\frac{3}{2}}(c+d x) \tanh ^{-1}(\sin (c+d x))}{d (b \sec (c+d x))^{3/2}}","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sec[c + d*x]^(3/2))/(d*(b*Sec[c + d*x])^(3/2))","A",1
171,1,24,27,0.0257666,"\int \frac{\sec ^{\frac{3}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sec[c + d*x]^(3/2)/(b*Sec[c + d*x])^(3/2),x]","\frac{x \sec ^{\frac{3}{2}}(c+d x)}{(b \sec (c+d x))^{3/2}}","\frac{x \sqrt{\sec (c+d x)}}{b \sqrt{b \sec (c+d x)}}",1,"(x*Sec[c + d*x]^(3/2))/(b*Sec[c + d*x])^(3/2)","A",1
172,1,32,35,0.0425455,"\int \frac{\sqrt{\sec (c+d x)}}{(b \sec (c+d x))^{3/2}} \, dx","Integrate[Sqrt[Sec[c + d*x]]/(b*Sec[c + d*x])^(3/2),x]","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{d (b \sec (c+d x))^{3/2}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*Sin[c + d*x])/(d*(b*Sec[c + d*x])^(3/2))","A",1
173,1,45,69,0.0692819,"\int \frac{1}{\sqrt{\sec (c+d x)} (b \sec (c+d x))^{3/2}} \, dx","Integrate[1/(Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(3/2)),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \sec ^{\frac{3}{2}}(c+d x)}{4 d (b \sec (c+d x))^{3/2}}","\frac{x \sqrt{\sec (c+d x)}}{2 b \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 b d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*d*(b*Sec[c + d*x])^(3/2))","A",1
174,1,45,76,0.0980169,"\int \frac{1}{\sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{3/2}} \, dx","Integrate[1/(Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(3/2)),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) \sec ^{\frac{3}{2}}(c+d x)}{6 d (b \sec (c+d x))^{3/2}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 b d \sqrt{b \sec (c+d x)}}",1,"((5 + Cos[2*(c + d*x)])*Sec[c + d*x]^(3/2)*Sin[c + d*x])/(6*d*(b*Sec[c + d*x])^(3/2))","A",1
175,1,55,107,0.1211569,"\int \frac{1}{\sec ^{\frac{5}{2}}(c+d x) (b \sec (c+d x))^{3/2}} \, dx","Integrate[1/(Sec[c + d*x]^(5/2)*(b*Sec[c + d*x])^(3/2)),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) \sec ^{\frac{3}{2}}(c+d x)}{32 d (b \sec (c+d x))^{3/2}}","\frac{3 x \sqrt{\sec (c+d x)}}{8 b \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{4 b d \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}+\frac{3 \sin (c+d x)}{8 b d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(3/2)*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*d*(b*Sec[c + d*x])^(3/2))","A",1
176,1,53,78,0.0479059,"\int \frac{\sec ^{\frac{11}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^(11/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sqrt{\sec (c+d x)} \left(\tanh ^{-1}(\sin (c+d x))+\tan (c+d x) \sec (c+d x)\right)}{2 b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sec ^{\frac{5}{2}}(c+d x)}{2 b^2 d \sqrt{b \sec (c+d x)}}+\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{2 b^2 d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*(ArcTanh[Sin[c + d*x]] + Sec[c + d*x]*Tan[c + d*x]))/(2*b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
177,1,32,35,0.0333469,"\int \frac{\sec ^{\frac{9}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^(9/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \sec ^{\frac{7}{2}}(c+d x)}{d (b \sec (c+d x))^{5/2}}","\frac{\sin (c+d x) \sec ^{\frac{3}{2}}(c+d x)}{b^2 d \sqrt{b \sec (c+d x)}}",1,"(Sec[c + d*x]^(7/2)*Sin[c + d*x])/(d*(b*Sec[c + d*x])^(5/2))","A",1
178,1,33,36,0.0223533,"\int \frac{\sec ^{\frac{7}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^(7/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sec ^{\frac{5}{2}}(c+d x) \tanh ^{-1}(\sin (c+d x))}{d (b \sec (c+d x))^{5/2}}","\frac{\sqrt{\sec (c+d x)} \tanh ^{-1}(\sin (c+d x))}{b^2 d \sqrt{b \sec (c+d x)}}",1,"(ArcTanh[Sin[c + d*x]]*Sec[c + d*x]^(5/2))/(d*(b*Sec[c + d*x])^(5/2))","A",1
179,1,24,27,0.0201557,"\int \frac{\sec ^{\frac{5}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^(5/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{x \sec ^{\frac{5}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}}","\frac{x \sqrt{\sec (c+d x)}}{b^2 \sqrt{b \sec (c+d x)}}",1,"(x*Sec[c + d*x]^(5/2))/(b*Sec[c + d*x])^(5/2)","A",1
180,1,35,35,0.026109,"\int \frac{\sec ^{\frac{3}{2}}(c+d x)}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sec[c + d*x]^(3/2)/(b*Sec[c + d*x])^(5/2),x]","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b^2 d \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
181,1,48,69,0.0521823,"\int \frac{\sqrt{\sec (c+d x)}}{(b \sec (c+d x))^{5/2}} \, dx","Integrate[Sqrt[Sec[c + d*x]]/(b*Sec[c + d*x])^(5/2),x]","\frac{(2 (c+d x)+\sin (2 (c+d x))) \sqrt{\sec (c+d x)}}{4 b^2 d \sqrt{b \sec (c+d x)}}","\frac{x \sqrt{\sec (c+d x)}}{2 b^2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{2 b^2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*(2*(c + d*x) + Sin[2*(c + d*x)]))/(4*b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
182,1,48,76,0.0674139,"\int \frac{1}{\sqrt{\sec (c+d x)} (b \sec (c+d x))^{5/2}} \, dx","Integrate[1/(Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^(5/2)),x]","\frac{\sin (c+d x) (\cos (2 (c+d x))+5) \sqrt{\sec (c+d x)}}{6 b^2 d \sqrt{b \sec (c+d x)}}","\frac{\sin (c+d x) \sqrt{\sec (c+d x)}}{b^2 d \sqrt{b \sec (c+d x)}}-\frac{\sin ^3(c+d x) \sqrt{\sec (c+d x)}}{3 b^2 d \sqrt{b \sec (c+d x)}}",1,"((5 + Cos[2*(c + d*x)])*Sqrt[Sec[c + d*x]]*Sin[c + d*x])/(6*b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
183,1,58,107,0.0583371,"\int \frac{1}{\sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^{5/2}} \, dx","Integrate[1/(Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^(5/2)),x]","\frac{(12 (c+d x)+8 \sin (2 (c+d x))+\sin (4 (c+d x))) \sqrt{\sec (c+d x)}}{32 b^2 d \sqrt{b \sec (c+d x)}}","\frac{3 x \sqrt{\sec (c+d x)}}{8 b^2 \sqrt{b \sec (c+d x)}}+\frac{\sin (c+d x)}{4 b^2 d \sec ^{\frac{5}{2}}(c+d x) \sqrt{b \sec (c+d x)}}+\frac{3 \sin (c+d x)}{8 b^2 d \sqrt{\sec (c+d x)} \sqrt{b \sec (c+d x)}}",1,"(Sqrt[Sec[c + d*x]]*(12*(c + d*x) + 8*Sin[2*(c + d*x)] + Sin[4*(c + d*x)]))/(32*b^2*d*Sqrt[b*Sec[c + d*x]])","A",1
184,1,60,58,0.0718691,"\int \sec ^2(c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^2*(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sec ^2(c+d x)\right)}{7 b d}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\cos ^2(c+d x)\right)}{4 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*Csc[c + d*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(4/3)*Sqrt[-Tan[c + d*x]^2])/(7*b*d)","A",1
185,1,60,53,0.0478563,"\int \sec (c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]*(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sec ^2(c+d x)\right)}{4 b d}","\frac{3 \sin (c+d x) \sqrt[3]{b \sec (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)}}",1,"(3*Cot[c + d*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(4/3)*Sqrt[-Tan[c + d*x]^2])/(4*b*d)","A",1
186,1,55,56,0.0422675,"\int \sqrt[3]{b \sec (c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \sqrt[3]{b \sec (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sec ^2(c+d x)\right)}{d}","-\frac{3 b \sin (c+d x) \, _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)} (b \sec (c+d x))^{2/3}}",1,"(3*Cot[c + d*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(1/3)*Sqrt[-Tan[c + d*x]^2])/d","A",1
187,1,58,58,0.0646998,"\int \cos (c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Integrate[Cos[c + d*x]*(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\sec ^2(c+d x)\right)}{2 d (b \sec (c+d x))^{2/3}}","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{5/3}}",1,"(-3*b*Cot[c + d*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(2*d*(b*Sec[c + d*x])^(2/3))","A",1
188,1,59,58,0.1517568,"\int \cos ^2(c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Integrate[Cos[c + d*x]^2*(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sin (2 (c+d x)) \sqrt[3]{b \sec (c+d x)} \, _2F_1\left(-\frac{5}{6},\frac{1}{2};\frac{1}{6};\sec ^2(c+d x)\right)}{10 d \sqrt{-\tan ^2(c+d x)}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\cos ^2(c+d x)\right)}{8 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{8/3}}",1,"(3*Hypergeometric2F1[-5/6, 1/2, 1/6, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(1/3)*Sin[2*(c + d*x)])/(10*d*Sqrt[-Tan[c + d*x]^2])","A",1
189,1,60,58,0.0773856,"\int \sec ^2(c+d x) (b \sec (c+d x))^{4/3} \, dx","Integrate[Sec[c + d*x]^2*(b*Sec[c + d*x])^(4/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\sec ^2(c+d x)\right)}{10 b d}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{7/3} \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\cos ^2(c+d x)\right)}{7 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*Csc[c + d*x]*Hypergeometric2F1[1/2, 5/3, 8/3, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(7/3)*Sqrt[-Tan[c + d*x]^2])/(10*b*d)","A",1
190,1,60,55,0.0521668,"\int \sec (c+d x) (b \sec (c+d x))^{4/3} \, dx","Integrate[Sec[c + d*x]*(b*Sec[c + d*x])^(4/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sec ^2(c+d x)\right)}{7 b d}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{4/3} \, _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)}}",1,"(3*Cot[c + d*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(7/3)*Sqrt[-Tan[c + d*x]^2])/(7*b*d)","A",1
191,1,57,54,0.0055994,"\int (b \sec (c+d x))^{4/3} \, dx","Integrate[(b*Sec[c + d*x])^(4/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sec ^2(c+d x)\right)}{4 d}","\frac{3 b \sin (c+d x) \sqrt[3]{b \sec (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)}}",1,"(3*Cot[c + d*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(4/3)*Sqrt[-Tan[c + d*x]^2])/(4*d)","A",1
192,1,56,58,0.0064765,"\int \cos (c+d x) (b \sec (c+d x))^{4/3} \, dx","Integrate[Cos[c + d*x]*(b*Sec[c + d*x])^(4/3),x]","\frac{3 b \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \sqrt[3]{b \sec (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sec ^2(c+d x)\right)}{d}","-\frac{3 b^2 \sin (c+d x) \, _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)} (b \sec (c+d x))^{2/3}}",1,"(3*b*Cot[c + d*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(1/3)*Sqrt[-Tan[c + d*x]^2])/d","A",1
193,1,60,58,0.0117365,"\int \cos ^2(c+d x) (b \sec (c+d x))^{4/3} \, dx","Integrate[Cos[c + d*x]^2*(b*Sec[c + d*x])^(4/3),x]","-\frac{3 b^2 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\sec ^2(c+d x)\right)}{2 d (b \sec (c+d x))^{2/3}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\cos ^2(c+d x)\right)}{5 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{5/3}}",1,"(-3*b^2*Cot[c + d*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(2*d*(b*Sec[c + d*x])^(2/3))","A",1
194,1,60,58,0.0567473,"\int \frac{\sec ^2(c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^2/(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^{2/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\sec ^2(c+d x)\right)}{5 b d}","\frac{3 \sin (c+d x) (b \sec (c+d x))^{2/3} \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\cos ^2(c+d x)\right)}{2 b d \sqrt{\sin ^2(c+d x)}}",1,"(3*Csc[c + d*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(2/3)*Sqrt[-Tan[c + d*x]^2])/(5*b*d)","A",1
195,1,60,53,0.0458214,"\int \frac{\sec (c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]/(b*Sec[c + d*x])^(1/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sec ^2(c+d x)\right)}{2 b d}","-\frac{3 \sin (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)} \sqrt[3]{b \sec (c+d x)}}",1,"(3*Cot[c + d*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(2/3)*Sqrt[-Tan[c + d*x]^2])/(2*b*d)","A",1
196,1,55,56,0.0532547,"\int \frac{1}{\sqrt[3]{b \sec (c+d x)}} \, dx","Integrate[(b*Sec[c + d*x])^(-1/3),x]","-\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sec ^2(c+d x)\right)}{d \sqrt[3]{b \sec (c+d x)}}","-\frac{3 b \sin (c+d x) \, _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)} (b \sec (c+d x))^{4/3}}",1,"(-3*Cot[c + d*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(d*(b*Sec[c + d*x])^(1/3))","A",1
197,1,58,58,0.0840734,"\int \frac{\cos (c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Integrate[Cos[c + d*x]/(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\sec ^2(c+d x)\right)}{4 d (b \sec (c+d x))^{4/3}}","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{7/3}}",1,"(-3*b*Cot[c + d*x]*Hypergeometric2F1[-2/3, 1/2, 1/3, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(4*d*(b*Sec[c + d*x])^(4/3))","A",1
198,1,60,58,0.0680848,"\int \frac{\cos ^2(c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Integrate[Cos[c + d*x]^2/(b*Sec[c + d*x])^(1/3),x]","-\frac{3 b^2 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\sec ^2(c+d x)\right)}{7 d (b \sec (c+d x))^{7/3}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{10/3}}",1,"(-3*b^2*Cot[c + d*x]*Hypergeometric2F1[-7/6, 1/2, -1/6, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(7*d*(b*Sec[c + d*x])^(7/3))","A",1
199,1,60,56,0.007817,"\int \frac{\sec ^2(c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Integrate[Sec[c + d*x]^2/(b*Sec[c + d*x])^(4/3),x]","\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sec ^2(c+d x)\right)}{2 b^2 d}","-\frac{3 \sin (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)} \sqrt[3]{b \sec (c+d x)}}",1,"(3*Cot[c + d*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(2/3)*Sqrt[-Tan[c + d*x]^2])/(2*b^2*d)","A",1
200,1,58,55,0.014489,"\int \frac{\sec (c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Integrate[Sec[c + d*x]/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sec ^2(c+d x)\right)}{b d \sqrt[3]{b \sec (c+d x)}}","-\frac{3 \sin (c+d x) \, _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)} (b \sec (c+d x))^{4/3}}",1,"(-3*Cot[c + d*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(b*d*(b*Sec[c + d*x])^(1/3))","A",1
201,1,57,56,0.0036947,"\int \frac{1}{(b \sec (c+d x))^{4/3}} \, dx","Integrate[(b*Sec[c + d*x])^(-4/3),x]","-\frac{3 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{2}{3},\frac{1}{2};\frac{1}{3};\sec ^2(c+d x)\right)}{4 d (b \sec (c+d x))^{4/3}}","-\frac{3 b \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\cos ^2(c+d x)\right)}{7 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{7/3}}",1,"(-3*Cot[c + d*x]*Hypergeometric2F1[-2/3, 1/2, 1/3, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(4*d*(b*Sec[c + d*x])^(4/3))","A",1
202,1,58,58,0.0176232,"\int \frac{\cos (c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Integrate[Cos[c + d*x]/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 b \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{7}{6},\frac{1}{2};-\frac{1}{6};\sec ^2(c+d x)\right)}{7 d (b \sec (c+d x))^{7/3}}","-\frac{3 b^2 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{5}{3};\frac{8}{3};\cos ^2(c+d x)\right)}{10 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{10/3}}",1,"(-3*b*Cot[c + d*x]*Hypergeometric2F1[-7/6, 1/2, -1/6, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(7*d*(b*Sec[c + d*x])^(7/3))","A",1
203,1,60,58,0.087268,"\int \frac{\cos ^2(c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Integrate[Cos[c + d*x]^2/(b*Sec[c + d*x])^(4/3),x]","-\frac{3 b^2 \sqrt{-\tan ^2(c+d x)} \cot (c+d x) \, _2F_1\left(-\frac{5}{3},\frac{1}{2};-\frac{2}{3};\sec ^2(c+d x)\right)}{10 d (b \sec (c+d x))^{10/3}}","-\frac{3 b^3 \sin (c+d x) \, _2F_1\left(\frac{1}{2},\frac{13}{6};\frac{19}{6};\cos ^2(c+d x)\right)}{13 d \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{13/3}}",1,"(-3*b^2*Cot[c + d*x]*Hypergeometric2F1[-5/3, 1/2, -2/3, Sec[c + d*x]^2]*Sqrt[-Tan[c + d*x]^2])/(10*d*(b*Sec[c + d*x])^(10/3))","A",1
204,1,83,81,0.0952938,"\int \sec ^m(c+d x) (b \sec (c+d x))^{4/3} \, dx","Integrate[Sec[c + d*x]^m*(b*Sec[c + d*x])^(4/3),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^{4/3} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{4}{3}\right);\frac{1}{2} \left(m+\frac{10}{3}\right);\sec ^2(c+d x)\right)}{d \left(m+\frac{4}{3}\right)}","\frac{3 b \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \sec ^m(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (-3 m-1);\frac{1}{6} (5-3 m);\cos ^2(c+d x)\right)}{d (3 m+1) \sqrt{\sin ^2(c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (4/3 + m)/2, (10/3 + m)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*(b*Sec[c + d*x])^(4/3)*Sqrt[-Tan[c + d*x]^2])/(d*(4/3 + m))","A",1
205,1,83,82,0.1416782,"\int \sec ^m(c+d x) (b \sec (c+d x))^{2/3} \, dx","Integrate[Sec[c + d*x]^m*(b*Sec[c + d*x])^(2/3),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^{2/3} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{2}{3}\right);\frac{1}{2} \left(m+\frac{8}{3}\right);\sec ^2(c+d x)\right)}{d \left(m+\frac{2}{3}\right)}","-\frac{3 \sin (c+d x) (b \sec (c+d x))^{2/3} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (1-3 m);\frac{1}{6} (7-3 m);\cos ^2(c+d x)\right)}{d (1-3 m) \sqrt{\sin ^2(c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (2/3 + m)/2, (8/3 + m)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*(b*Sec[c + d*x])^(2/3)*Sqrt[-Tan[c + d*x]^2])/(d*(2/3 + m))","A",1
206,1,83,82,0.139204,"\int \sec ^m(c+d x) \sqrt[3]{b \sec (c+d x)} \, dx","Integrate[Sec[c + d*x]^m*(b*Sec[c + d*x])^(1/3),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sqrt[3]{b \sec (c+d x)} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m+\frac{1}{3}\right);\frac{1}{2} \left(m+\frac{7}{3}\right);\sec ^2(c+d x)\right)}{d \left(m+\frac{1}{3}\right)}","-\frac{3 \sin (c+d x) \sqrt[3]{b \sec (c+d x)} \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (2-3 m);\frac{1}{6} (8-3 m);\cos ^2(c+d x)\right)}{d (2-3 m) \sqrt{\sin ^2(c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (1/3 + m)/2, (7/3 + m)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*(b*Sec[c + d*x])^(1/3)*Sqrt[-Tan[c + d*x]^2])/(d*(1/3 + m))","A",1
207,1,83,82,0.1348138,"\int \frac{\sec ^m(c+d x)}{\sqrt[3]{b \sec (c+d x)}} \, dx","Integrate[Sec[c + d*x]^m/(b*Sec[c + d*x])^(1/3),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m-\frac{1}{3}\right);\frac{1}{2} \left(m+\frac{5}{3}\right);\sec ^2(c+d x)\right)}{d \left(m-\frac{1}{3}\right) \sqrt[3]{b \sec (c+d x)}}","-\frac{3 \sin (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (4-3 m);\frac{1}{6} (10-3 m);\cos ^2(c+d x)\right)}{d (4-3 m) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (-1/3 + m)/2, (5/3 + m)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*Sqrt[-Tan[c + d*x]^2])/(d*(-1/3 + m)*(b*Sec[c + d*x])^(1/3))","A",1
208,1,83,82,0.1355249,"\int \frac{\sec ^m(c+d x)}{(b \sec (c+d x))^{2/3}} \, dx","Integrate[Sec[c + d*x]^m/(b*Sec[c + d*x])^(2/3),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m-\frac{2}{3}\right);\frac{1}{2} \left(m+\frac{4}{3}\right);\sec ^2(c+d x)\right)}{d \left(m-\frac{2}{3}\right) (b \sec (c+d x))^{2/3}}","-\frac{3 \sin (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (5-3 m);\frac{1}{6} (11-3 m);\cos ^2(c+d x)\right)}{d (5-3 m) \sqrt{\sin ^2(c+d x)} (b \sec (c+d x))^{2/3}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (-2/3 + m)/2, (4/3 + m)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*Sqrt[-Tan[c + d*x]^2])/(d*(-2/3 + m)*(b*Sec[c + d*x])^(2/3))","A",1
209,1,83,85,0.1792936,"\int \frac{\sec ^m(c+d x)}{(b \sec (c+d x))^{4/3}} \, dx","Integrate[Sec[c + d*x]^m/(b*Sec[c + d*x])^(4/3),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sec ^{m-1}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(m-\frac{4}{3}\right);\frac{1}{2} \left(m+\frac{2}{3}\right);\sec ^2(c+d x)\right)}{d \left(m-\frac{4}{3}\right) (b \sec (c+d x))^{4/3}}","-\frac{3 \sin (c+d x) \sec ^{m-2}(c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{6} (7-3 m);\frac{1}{6} (13-3 m);\cos ^2(c+d x)\right)}{b d (7-3 m) \sqrt{\sin ^2(c+d x)} \sqrt[3]{b \sec (c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (-4/3 + m)/2, (2/3 + m)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*Sqrt[-Tan[c + d*x]^2])/(d*(-4/3 + m)*(b*Sec[c + d*x])^(4/3))","A",1
210,1,76,89,0.0682974,"\int \sec ^m(c+d x) (b \sec (c+d x))^n \, dx","Integrate[Sec[c + d*x]^m*(b*Sec[c + d*x])^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sec ^{m-1}(c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{m+n}{2};\frac{1}{2} (m+n+2);\sec ^2(c+d x)\right)}{d (m+n)}","-\frac{\sin (c+d x) \sec ^{m-1}(c+d x) (b \sec (c+d x))^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,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (m + n)/2, (2 + m + n)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(-1 + m)*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(m + n))","A",1
211,1,71,72,0.0486056,"\int \sec ^2(c+d x) (b \sec (c+d x))^n \, dx","Integrate[Sec[c + d*x]^2*(b*Sec[c + d*x])^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sec (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sec ^2(c+d x)\right)}{d (n+2)}","\frac{\sin (c+d x) (b \sec (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{1}{2} (-n-1);\frac{1-n}{2};\cos ^2(c+d x)\right)}{b d (n+1) \sqrt{\sin ^2(c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Sec[c + d*x]^2]*Sec[c + d*x]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(2 + n))","A",1
212,1,65,61,0.0375103,"\int \sec (c+d x) (b \sec (c+d x))^n \, dx","Integrate[Sec[c + d*x]*(b*Sec[c + d*x])^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sec ^2(c+d x)\right)}{d (n+1)}","\frac{\sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},-\frac{n}{2};\frac{2-n}{2};\cos ^2(c+d x)\right)}{d n \sqrt{\sin ^2(c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(1 + n))","A",1
213,1,61,73,0.0449208,"\int (b \sec (c+d x))^n \, dx","Integrate[(b*Sec[c + d*x])^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n}{2};\frac{n+2}{2};\sec ^2(c+d x)\right)}{d n}","-\frac{b \sin (c+d x) (b \sec (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(c+d x)\right)}{d (1-n) \sqrt{\sin ^2(c+d x)}}",1,"(Cot[c + d*x]*Hypergeometric2F1[1/2, n/2, (2 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*n)","A",1
214,1,68,75,0.0966751,"\int \cos (c+d x) (b \sec (c+d x))^n \, dx","Integrate[Cos[c + d*x]*(b*Sec[c + d*x])^n,x]","\frac{b \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{n-1}{2};\frac{n+1}{2};\sec ^2(c+d x)\right)}{d (n-1)}","-\frac{b^2 \sin (c+d x) (b \sec (c+d x))^{n-2} \, _2F_1\left(\frac{1}{2},\frac{2-n}{2};\frac{4-n}{2};\cos ^2(c+d x)\right)}{d (2-n) \sqrt{\sin ^2(c+d x)}}",1,"(b*Cot[c + d*x]*Hypergeometric2F1[1/2, (-1 + n)/2, (1 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^(-1 + n)*Sqrt[-Tan[c + d*x]^2])/(d*(-1 + n))","A",1
215,1,71,75,0.0769562,"\int \cos ^2(c+d x) (b \sec (c+d x))^n \, dx","Integrate[Cos[c + d*x]^2*(b*Sec[c + d*x])^n,x]","\frac{\cos ^2(c+d x) \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n-2}{2};\frac{n}{2};\sec ^2(c+d x)\right)}{d (n-2)}","-\frac{b^3 \sin (c+d x) (b \sec (c+d x))^{n-3} \, _2F_1\left(\frac{1}{2},\frac{3-n}{2};\frac{5-n}{2};\cos ^2(c+d x)\right)}{d (3-n) \sqrt{\sin ^2(c+d x)}}",1,"(Cos[c + d*x]^2*Cot[c + d*x]*Hypergeometric2F1[1/2, (-2 + n)/2, n/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(-2 + n))","A",1
216,1,73,75,0.1071734,"\int \cos ^3(c+d x) (b \sec (c+d x))^n \, dx","Integrate[Cos[c + d*x]^3*(b*Sec[c + d*x])^n,x]","\frac{\cos ^3(c+d x) \sqrt{-\tan ^2(c+d x)} \cot (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n-3}{2};\frac{n-1}{2};\sec ^2(c+d x)\right)}{d (n-3)}","-\frac{b^4 \sin (c+d x) (b \sec (c+d x))^{n-4} \, _2F_1\left(\frac{1}{2},\frac{4-n}{2};\frac{6-n}{2};\cos ^2(c+d x)\right)}{d (4-n) \sqrt{\sin ^2(c+d x)}}",1,"(Cos[c + d*x]^3*Cot[c + d*x]*Hypergeometric2F1[1/2, (-3 + n)/2, (-1 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(-3 + n))","A",1
217,1,81,80,0.098603,"\int \sec ^{\frac{5}{2}}(c+d x) (b \sec (c+d x))^n \, dx","Integrate[Sec[c + d*x]^(5/2)*(b*Sec[c + d*x])^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n+\frac{5}{2}\right);\frac{1}{2} \left(n+\frac{9}{2}\right);\sec ^2(c+d x)\right)}{d \left(n+\frac{5}{2}\right)}","\frac{2 \sin (c+d x) \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (-2 n-3);\frac{1}{4} (1-2 n);\cos ^2(c+d x)\right)}{d (2 n+3) \sqrt{\sin ^2(c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (5/2 + n)/2, (9/2 + n)/2, Sec[c + d*x]^2]*Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(5/2 + n))","A",1
218,1,81,80,0.0909031,"\int \sec ^{\frac{3}{2}}(c+d x) (b \sec (c+d x))^n \, dx","Integrate[Sec[c + d*x]^(3/2)*(b*Sec[c + d*x])^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) \sqrt{\sec (c+d x)} (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n+\frac{3}{2}\right);\frac{1}{2} \left(n+\frac{7}{2}\right);\sec ^2(c+d x)\right)}{d \left(n+\frac{3}{2}\right)}","\frac{2 \sin (c+d x) \sqrt{\sec (c+d x)} (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (-2 n-1);\frac{1}{4} (3-2 n);\cos ^2(c+d x)\right)}{d (2 n+1) \sqrt{\sin ^2(c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (3/2 + n)/2, (7/2 + n)/2, Sec[c + d*x]^2]*Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(3/2 + n))","A",1
219,1,81,80,0.0987281,"\int \sqrt{\sec (c+d x)} (b \sec (c+d x))^n \, dx","Integrate[Sqrt[Sec[c + d*x]]*(b*Sec[c + d*x])^n,x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n+\frac{1}{2}\right);\frac{1}{2} \left(n+\frac{5}{2}\right);\sec ^2(c+d x)\right)}{d \left(n+\frac{1}{2}\right) \sqrt{\sec (c+d x)}}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (1-2 n);\frac{1}{4} (5-2 n);\cos ^2(c+d x)\right)}{d (1-2 n) \sqrt{\sin ^2(c+d x)} \sqrt{\sec (c+d x)}}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (1/2 + n)/2, (5/2 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(1/2 + n)*Sqrt[Sec[c + d*x]])","A",1
220,1,81,80,0.1127797,"\int \frac{(b \sec (c+d x))^n}{\sqrt{\sec (c+d x)}} \, dx","Integrate[(b*Sec[c + d*x])^n/Sqrt[Sec[c + d*x]],x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n-\frac{1}{2}\right);\frac{1}{2} \left(n+\frac{3}{2}\right);\sec ^2(c+d x)\right)}{d \left(n-\frac{1}{2}\right) \sec ^{\frac{3}{2}}(c+d x)}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (3-2 n);\frac{1}{4} (7-2 n);\cos ^2(c+d x)\right)}{d (3-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{3}{2}}(c+d x)}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (-1/2 + n)/2, (3/2 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(-1/2 + n)*Sec[c + d*x]^(3/2))","A",1
221,1,81,80,0.1371689,"\int \frac{(b \sec (c+d x))^n}{\sec ^{\frac{3}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^n/Sec[c + d*x]^(3/2),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n-\frac{3}{2}\right);\frac{1}{2} \left(n+\frac{1}{2}\right);\sec ^2(c+d x)\right)}{d \left(n-\frac{3}{2}\right) \sec ^{\frac{5}{2}}(c+d x)}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (5-2 n);\frac{1}{4} (9-2 n);\cos ^2(c+d x)\right)}{d (5-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{5}{2}}(c+d x)}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (-3/2 + n)/2, (1/2 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(-3/2 + n)*Sec[c + d*x]^(5/2))","A",1
222,1,81,80,0.1729821,"\int \frac{(b \sec (c+d x))^n}{\sec ^{\frac{5}{2}}(c+d x)} \, dx","Integrate[(b*Sec[c + d*x])^n/Sec[c + d*x]^(5/2),x]","\frac{\sqrt{-\tan ^2(c+d x)} \csc (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(n-\frac{5}{2}\right);\frac{1}{2} \left(n-\frac{1}{2}\right);\sec ^2(c+d x)\right)}{d \left(n-\frac{5}{2}\right) \sec ^{\frac{7}{2}}(c+d x)}","-\frac{2 \sin (c+d x) (b \sec (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{4} (7-2 n);\frac{1}{4} (11-2 n);\cos ^2(c+d x)\right)}{d (7-2 n) \sqrt{\sin ^2(c+d x)} \sec ^{\frac{7}{2}}(c+d x)}",1,"(Csc[c + d*x]*Hypergeometric2F1[1/2, (-5/2 + n)/2, (-1/2 + n)/2, Sec[c + d*x]^2]*(b*Sec[c + d*x])^n*Sqrt[-Tan[c + d*x]^2])/(d*(-5/2 + n)*Sec[c + d*x]^(7/2))","A",1
223,1,20,20,0.0575442,"\int (d \sec (a+b x))^{7/2} \sin (a+b x) \, dx","Integrate[(d*Sec[a + b*x])^(7/2)*Sin[a + b*x],x]","\frac{2 d (d \sec (a+b x))^{5/2}}{5 b}","\frac{2 d (d \sec (a+b x))^{5/2}}{5 b}",1,"(2*d*(d*Sec[a + b*x])^(5/2))/(5*b)","A",1
224,1,20,20,0.0418086,"\int (d \sec (a+b x))^{5/2} \sin (a+b x) \, dx","Integrate[(d*Sec[a + b*x])^(5/2)*Sin[a + b*x],x]","\frac{2 d (d \sec (a+b x))^{3/2}}{3 b}","\frac{2 d (d \sec (a+b x))^{3/2}}{3 b}",1,"(2*d*(d*Sec[a + b*x])^(3/2))/(3*b)","A",1
225,1,18,18,0.0330533,"\int (d \sec (a+b x))^{3/2} \sin (a+b x) \, dx","Integrate[(d*Sec[a + b*x])^(3/2)*Sin[a + b*x],x]","\frac{2 d \sqrt{d \sec (a+b x)}}{b}","\frac{2 d \sqrt{d \sec (a+b x)}}{b}",1,"(2*d*Sqrt[d*Sec[a + b*x]])/b","A",1
226,1,18,18,0.03677,"\int \sqrt{d \sec (a+b x)} \sin (a+b x) \, dx","Integrate[Sqrt[d*Sec[a + b*x]]*Sin[a + b*x],x]","-\frac{2 d}{b \sqrt{d \sec (a+b x)}}","-\frac{2 d}{b \sqrt{d \sec (a+b x)}}",1,"(-2*d)/(b*Sqrt[d*Sec[a + b*x]])","A",1
227,1,20,20,0.0517084,"\int \frac{\sin (a+b x)}{\sqrt{d \sec (a+b x)}} \, dx","Integrate[Sin[a + b*x]/Sqrt[d*Sec[a + b*x]],x]","-\frac{2 d}{3 b (d \sec (a+b x))^{3/2}}","-\frac{2 d}{3 b (d \sec (a+b x))^{3/2}}",1,"(-2*d)/(3*b*(d*Sec[a + b*x])^(3/2))","A",1
228,1,32,41,0.2233073,"\int (d \sec (a+b x))^{5/2} \sin ^3(a+b x) \, dx","Integrate[(d*Sec[a + b*x])^(5/2)*Sin[a + b*x]^3,x]","\frac{d (3 \cos (2 (a+b x))+5) (d \sec (a+b x))^{3/2}}{3 b}","\frac{2 d^3}{b \sqrt{d \sec (a+b x)}}+\frac{2 d (d \sec (a+b x))^{3/2}}{3 b}",1,"(d*(5 + 3*Cos[2*(a + b*x)])*(d*Sec[a + b*x])^(3/2))/(3*b)","A",1
229,1,42,43,0.1080113,"\int (d \sec (a+b x))^{9/2} \sin ^3(a+b x) \, dx","Integrate[(d*Sec[a + b*x])^(9/2)*Sin[a + b*x]^3,x]","-\frac{d^4 (7 \cos (2 (a+b x))+1) \sec ^3(a+b x) \sqrt{d \sec (a+b x)}}{21 b}","\frac{2 d (d \sec (a+b x))^{7/2}}{7 b}-\frac{2 d^3 (d \sec (a+b x))^{3/2}}{3 b}",1,"-1/21*(d^4*(1 + 7*Cos[2*(a + b*x)])*Sec[a + b*x]^3*Sqrt[d*Sec[a + b*x]])/b","A",1
230,1,122,128,1.5063368,"\int (d \csc (a+b x))^{9/2} \sqrt{c \sec (a+b x)} \, dx","Integrate[(d*Csc[a + b*x])^(9/2)*Sqrt[c*Sec[a + b*x]],x]","\frac{2 d^4 \cos (2 (a+b x)) \cot (a+b x) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)} \left((\cos (2 (a+b x))-2) \csc ^4(a+b x)-2 \left(-\cot ^2(a+b x)\right)^{3/4} \sec ^2(a+b x) \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)\right)}{7 b \left(\csc ^2(a+b x)-2\right)}","\frac{4 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{7 b}-\frac{4 c d^3 (d \csc (a+b x))^{3/2}}{7 b \sqrt{c \sec (a+b x)}}-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b \sqrt{c \sec (a+b x)}}",1,"(2*d^4*Cos[2*(a + b*x)]*Cot[a + b*x]*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]*((-2 + Cos[2*(a + b*x)])*Csc[a + b*x]^4 - 2*(-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2]*Sec[a + b*x]^2))/(7*b*(-2 + Csc[a + b*x]^2))","C",1
231,1,56,69,0.1201891,"\int (d \csc (a+b x))^{7/2} \sqrt{c \sec (a+b x)} \, dx","Integrate[(d*Csc[a + b*x])^(7/2)*Sqrt[c*Sec[a + b*x]],x]","-\frac{2 d^3 \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)} (4 \cos (a+b x)+\cot (a+b x) \csc (a+b x))}{5 b}","-\frac{8 c d^3 \sqrt{d \csc (a+b x)}}{5 b \sqrt{c \sec (a+b x)}}-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b \sqrt{c \sec (a+b x)}}",1,"(-2*d^3*Sqrt[d*Csc[a + b*x]]*(4*Cos[a + b*x] + Cot[a + b*x]*Csc[a + b*x])*Sqrt[c*Sec[a + b*x]])/(5*b)","A",1
232,1,109,93,0.8858393,"\int (d \csc (a+b x))^{5/2} \sqrt{c \sec (a+b x)} \, dx","Integrate[(d*Csc[a + b*x])^(5/2)*Sqrt[c*Sec[a + b*x]],x]","-\frac{d (\cos (a+b x)+\cos (3 (a+b x))) \sec ^2(a+b x) \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2} \left(\left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)+\cot ^2(a+b x)\right)}{3 b \left(\csc ^2(a+b x)-2\right)}","\frac{2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}-\frac{2 c d (d \csc (a+b x))^{3/2}}{3 b \sqrt{c \sec (a+b x)}}",1,"-1/3*(d*(Cos[a + b*x] + Cos[3*(a + b*x)])*(d*Csc[a + b*x])^(3/2)*(Cot[a + b*x]^2 + (-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*Sec[a + b*x]^2*Sqrt[c*Sec[a + b*x]])/(b*(-2 + Csc[a + b*x]^2))","C",1
233,1,31,31,0.0658557,"\int (d \csc (a+b x))^{3/2} \sqrt{c \sec (a+b x)} \, dx","Integrate[(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]],x]","-\frac{2 c d \sqrt{d \csc (a+b x)}}{b \sqrt{c \sec (a+b x)}}","-\frac{2 c d \sqrt{d \csc (a+b x)}}{b \sqrt{c \sec (a+b x)}}",1,"(-2*c*d*Sqrt[d*Csc[a + b*x]])/(b*Sqrt[c*Sec[a + b*x]])","A",1
234,1,68,53,0.6749825,"\int \sqrt{d \csc (a+b x)} \sqrt{c \sec (a+b x)} \, dx","Integrate[Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]],x]","\frac{\tan ^3(a+b x) \left(-\cot ^2(a+b x)\right)^{7/4} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)}{b}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{b}",1,"((-Cot[a + b*x]^2)^(7/4)*Sqrt[d*Csc[a + b*x]]*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2]*Sqrt[c*Sec[a + b*x]]*Tan[a + b*x]^3)/b","C",1
235,1,171,270,1.3684161,"\int \frac{\sqrt{c \sec (a+b x)}}{\sqrt{d \csc (a+b x)}} \, dx","Integrate[Sqrt[c*Sec[a + b*x]]/Sqrt[d*Csc[a + b*x]],x]","\frac{\cot (a+b x) \sqrt{c \sec (a+b x)} \left(\log \left(\sqrt{\cot ^2(a+b x)}-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)-\log \left(\sqrt{\cot ^2(a+b x)}+\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)+2 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}\right)-2 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)\right)}{2 \sqrt{2} b \sqrt[4]{\cot ^2(a+b x)} \sqrt{d \csc (a+b x)}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}",1,"(Cot[a + b*x]*(2*ArcTan[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] - 2*ArcTan[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] + Log[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]] - Log[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]])*Sqrt[c*Sec[a + b*x]])/(2*Sqrt[2]*b*(Cot[a + b*x]^2)^(1/4)*Sqrt[d*Csc[a + b*x]])","A",1
236,1,80,93,0.691699,"\int \frac{\sqrt{c \sec (a+b x)}}{(d \csc (a+b x))^{3/2}} \, dx","Integrate[Sqrt[c*Sec[a + b*x]]/(d*Csc[a + b*x])^(3/2),x]","-\frac{(c \sec (a+b x))^{3/2} \left(\left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)+\cos (2 (a+b x))+1\right)}{2 b c d \sqrt{d \csc (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{2 b d^2}-\frac{c}{b d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"-1/2*((1 + Cos[2*(a + b*x)] + (-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*(c*Sec[a + b*x])^(3/2))/(b*c*d*Sqrt[d*Csc[a + b*x]])","C",1
237,1,222,322,1.8223604,"\int \frac{\sqrt{c \sec (a+b x)}}{(d \csc (a+b x))^{5/2}} \, dx","Integrate[Sqrt[c*Sec[a + b*x]]/(d*Csc[a + b*x])^(5/2),x]","\frac{c \sqrt{d \csc (a+b x)} \left(-4 \sqrt[4]{\cot ^2(a+b x)}+4 \cos (2 (a+b x)) \sqrt[4]{\cot ^2(a+b x)}+3 \sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)-3 \sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}+\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)+6 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}\right)-6 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)\right)}{16 b d^3 \sqrt[4]{\cot ^2(a+b x)} \sqrt{c \sec (a+b x)}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{2 b d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}",1,"(c*Sqrt[d*Csc[a + b*x]]*(6*Sqrt[2]*ArcTan[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] - 6*Sqrt[2]*ArcTan[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] - 4*(Cot[a + b*x]^2)^(1/4) + 4*Cos[2*(a + b*x)]*(Cot[a + b*x]^2)^(1/4) + 3*Sqrt[2]*Log[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]] - 3*Sqrt[2]*Log[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]]))/(16*b*d^3*(Cot[a + b*x]^2)^(1/4)*Sqrt[c*Sec[a + b*x]])","A",1
238,1,57,104,0.2940088,"\int (d \csc (a+b x))^{9/2} (c \sec (a+b x))^{3/2} \, dx","Integrate[(d*Csc[a + b*x])^(9/2)*(c*Sec[a + b*x])^(3/2),x]","-\frac{2 c d^5 \left(3 \csc ^4(a+b x)+8 \csc ^2(a+b x)-32\right) \sqrt{c \sec (a+b x)}}{21 b \sqrt{d \csc (a+b x)}}","\frac{64 c d^5 \sqrt{c \sec (a+b x)}}{21 b \sqrt{d \csc (a+b x)}}-\frac{16 c d^3 \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}{21 b}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{7/2}}{7 b}",1,"(-2*c*d^5*(-32 + 8*Csc[a + b*x]^2 + 3*Csc[a + b*x]^4)*Sqrt[c*Sec[a + b*x]])/(21*b*Sqrt[d*Csc[a + b*x]])","A",1
239,1,114,166,1.1414659,"\int (d \csc (a+b x))^{7/2} (c \sec (a+b x))^{3/2} \, dx","Integrate[(d*Csc[a + b*x])^(7/2)*(c*Sec[a + b*x])^(3/2),x]","-\frac{2 c d^3 \tan ^2(a+b x) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)} \left(12 \cos ^2(a+b x) \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)+\cot ^2(a+b x) \left(6 \cos (2 (a+b x))+\csc ^2(a+b x)\right)\right)}{5 b}","-\frac{24 c^2 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{24 c d^5 \sqrt{c \sec (a+b x)}}{5 b (d \csc (a+b x))^{3/2}}-\frac{12 c d^3 \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{5 b}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{5/2}}{5 b}",1,"(-2*c*d^3*Sqrt[d*Csc[a + b*x]]*(Cot[a + b*x]^2*(6*Cos[2*(a + b*x)] + Csc[a + b*x]^2) + 12*Cos[a + b*x]^2*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]]*Tan[a + b*x]^2)/(5*b)","C",1
240,1,45,69,0.1418782,"\int (d \csc (a+b x))^{5/2} (c \sec (a+b x))^{3/2} \, dx","Integrate[(d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(3/2),x]","-\frac{2 c d^3 \left(\csc ^2(a+b x)-4\right) \sqrt{c \sec (a+b x)}}{3 b \sqrt{d \csc (a+b x)}}","\frac{8 c d^3 \sqrt{c \sec (a+b x)}}{3 b \sqrt{d \csc (a+b x)}}-\frac{2 c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}{3 b}",1,"(-2*c*d^3*(-4 + Csc[a + b*x]^2)*Sqrt[c*Sec[a + b*x]])/(3*b*Sqrt[d*Csc[a + b*x]])","A",1
241,1,99,125,0.5194375,"\int (d \csc (a+b x))^{3/2} (c \sec (a+b x))^{3/2} \, dx","Integrate[(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2),x]","-\frac{2 c d \tan ^2(a+b x) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)} \left(2 \cos ^2(a+b x) \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)+\cos (2 (a+b x)) \cot ^2(a+b x)\right)}{b}","-\frac{4 c^2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{4 c d^3 \sqrt{c \sec (a+b x)}}{b (d \csc (a+b x))^{3/2}}-\frac{2 c d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{b}",1,"(-2*c*d*Sqrt[d*Csc[a + b*x]]*(Cos[2*(a + b*x)]*Cot[a + b*x]^2 + 2*Cos[a + b*x]^2*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]]*Tan[a + b*x]^2)/b","C",1
242,1,31,31,0.0653489,"\int \sqrt{d \csc (a+b x)} (c \sec (a+b x))^{3/2} \, dx","Integrate[Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2),x]","\frac{2 c d \sqrt{c \sec (a+b x)}}{b \sqrt{d \csc (a+b x)}}","\frac{2 c d \sqrt{c \sec (a+b x)}}{b \sqrt{d \csc (a+b x)}}",1,"(2*c*d*Sqrt[c*Sec[a + b*x]])/(b*Sqrt[d*Csc[a + b*x]])","A",1
243,1,66,89,0.3759296,"\int \frac{(c \sec (a+b x))^{3/2}}{\sqrt{d \csc (a+b x)}} \, dx","Integrate[(c*Sec[a + b*x])^(3/2)/Sqrt[d*Csc[a + b*x]],x]","-\frac{2 c d \sqrt{c \sec (a+b x)} \left(\sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)-1\right)}{b (d \csc (a+b x))^{3/2}}","\frac{2 c d \sqrt{c \sec (a+b x)}}{b (d \csc (a+b x))^{3/2}}-\frac{2 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"(-2*c*d*(-1 + (-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]])/(b*(d*Csc[a + b*x])^(3/2))","C",1
244,1,64,327,0.2482614,"\int \frac{(c \sec (a+b x))^{3/2}}{(d \csc (a+b x))^{3/2}} \, dx","Integrate[(c*Sec[a + b*x])^(3/2)/(d*Csc[a + b*x])^(3/2),x]","\frac{2 c \sqrt{c \sec (a+b x)} \left(\cot ^2(a+b x) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\cot ^2(a+b x)\right)+3\right)}{3 b d \sqrt{d \csc (a+b x)}}","\frac{c^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{2 c \sqrt{c \sec (a+b x)}}{b d \sqrt{d \csc (a+b x)}}",1,"(2*c*(3 + Cot[a + b*x]^2*Hypergeometric2F1[3/4, 1, 7/4, -Cot[a + b*x]^2])*Sqrt[c*Sec[a + b*x]])/(3*b*d*Sqrt[d*Csc[a + b*x]])","C",1
245,1,69,94,0.4151188,"\int \frac{(c \sec (a+b x))^{3/2}}{(d \csc (a+b x))^{5/2}} \, dx","Integrate[(c*Sec[a + b*x])^(3/2)/(d*Csc[a + b*x])^(5/2),x]","-\frac{c \sqrt{c \sec (a+b x)} \left(3 \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)-2\right)}{b d (d \csc (a+b x))^{3/2}}","\frac{2 c \sqrt{c \sec (a+b x)}}{b d (d \csc (a+b x))^{3/2}}-\frac{3 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"-((c*(-2 + 3*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]])/(b*d*(d*Csc[a + b*x])^(3/2)))","C",1
246,1,92,166,1.4545637,"\int (d \csc (a+b x))^{9/2} (c \sec (a+b x))^{5/2} \, dx","Integrate[(d*Csc[a + b*x])^(9/2)*(c*Sec[a + b*x])^(5/2),x]","-\frac{2 c d^5 (c \sec (a+b x))^{3/2} \left(20 \left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)+\cot ^2(a+b x) \left(3 \csc ^2(a+b x)+13\right)-7\right)}{21 b \sqrt{d \csc (a+b x)}}","\frac{40 c^2 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{21 b}+\frac{40 c d^5 (c \sec (a+b x))^{3/2}}{21 b \sqrt{d \csc (a+b x)}}-\frac{20 c d^3 (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}{21 b}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{7/2}}{7 b}",1,"(-2*c*d^5*(-7 + Cot[a + b*x]^2*(13 + 3*Csc[a + b*x]^2) + 20*(-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*(c*Sec[a + b*x])^(3/2))/(21*b*Sqrt[d*Csc[a + b*x]])","C",1
247,1,57,106,0.1932714,"\int (d \csc (a+b x))^{7/2} (c \sec (a+b x))^{5/2} \, dx","Integrate[(d*Csc[a + b*x])^(7/2)*(c*Sec[a + b*x])^(5/2),x]","-\frac{2 c d^3 (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)} \left(32 \cos ^2(a+b x)+3 \cot ^2(a+b x)-5\right)}{15 b}","-\frac{64 c^3 d^3 \sqrt{d \csc (a+b x)}}{15 b \sqrt{c \sec (a+b x)}}+\frac{16 c d^3 (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}{15 b}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{5/2}}{5 b}",1,"(-2*c*d^3*(-5 + 32*Cos[a + b*x]^2 + 3*Cot[a + b*x]^2)*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2))/(15*b)","A",1
248,1,87,131,0.6926223,"\int (d \csc (a+b x))^{5/2} (c \sec (a+b x))^{5/2} \, dx","Integrate[(d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(5/2),x]","-\frac{2 c^3 d \tan ^2(a+b x) (d \csc (a+b x))^{3/2} \left(2 \left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)+\cot ^2(a+b x)-1\right)}{3 b \sqrt{c \sec (a+b x)}}","\frac{4 c^2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}+\frac{4 c d^3 (c \sec (a+b x))^{3/2}}{3 b \sqrt{d \csc (a+b x)}}-\frac{2 c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}{3 b}",1,"(-2*c^3*d*(d*Csc[a + b*x])^(3/2)*(-1 + Cot[a + b*x]^2 + 2*(-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*Tan[a + b*x]^2)/(3*b*Sqrt[c*Sec[a + b*x]])","C",1
249,1,45,69,0.2144885,"\int (d \csc (a+b x))^{3/2} (c \sec (a+b x))^{5/2} \, dx","Integrate[(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(5/2),x]","-\frac{2 c d (2 \cos (2 (a+b x))+1) (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}{3 b}","\frac{2 c d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}{3 b}-\frac{8 c^3 d \sqrt{d \csc (a+b x)}}{3 b \sqrt{c \sec (a+b x)}}",1,"(-2*c*d*(1 + 2*Cos[2*(a + b*x)])*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2))/(3*b)","A",1
250,1,68,93,0.6024563,"\int \sqrt{d \csc (a+b x)} (c \sec (a+b x))^{5/2} \, dx","Integrate[Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(5/2),x]","-\frac{2 c d (c \sec (a+b x))^{3/2} \left(\left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)-1\right)}{3 b \sqrt{d \csc (a+b x)}}","\frac{2 c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b}+\frac{2 c d (c \sec (a+b x))^{3/2}}{3 b \sqrt{d \csc (a+b x)}}",1,"(-2*c*d*(-1 + (-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*(c*Sec[a + b*x])^(3/2))/(3*b*Sqrt[d*Csc[a + b*x]])","C",1
251,1,33,33,0.114504,"\int \frac{(c \sec (a+b x))^{5/2}}{\sqrt{d \csc (a+b x)}} \, dx","Integrate[(c*Sec[a + b*x])^(5/2)/Sqrt[d*Csc[a + b*x]],x]","\frac{2 c d (c \sec (a+b x))^{3/2}}{3 b (d \csc (a+b x))^{3/2}}","\frac{2 c d (c \sec (a+b x))^{3/2}}{3 b (d \csc (a+b x))^{3/2}}",1,"(2*c*d*(c*Sec[a + b*x])^(3/2))/(3*b*(d*Csc[a + b*x])^(3/2))","A",1
252,1,70,98,0.5315177,"\int \frac{(c \sec (a+b x))^{5/2}}{(d \csc (a+b x))^{3/2}} \, dx","Integrate[(c*Sec[a + b*x])^(5/2)/(d*Csc[a + b*x])^(3/2),x]","\frac{c (c \sec (a+b x))^{3/2} \left(\left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)+2\right)}{3 b d \sqrt{d \csc (a+b x)}}","\frac{2 c (c \sec (a+b x))^{3/2}}{3 b d \sqrt{d \csc (a+b x)}}-\frac{c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b d^2}",1,"(c*(2 + (-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*(c*Sec[a + b*x])^(3/2))/(3*b*d*Sqrt[d*Csc[a + b*x]])","C",1
253,1,280,329,1.7997027,"\int \frac{(c \sec (a+b x))^{5/2}}{(d \csc (a+b x))^{5/2}} \, dx","Integrate[(c*Sec[a + b*x])^(5/2)/(d*Csc[a + b*x])^(5/2),x]","-\frac{c (c \sec (a+b x))^{3/2} \left(8 \cos (a+b x) \sqrt[4]{\cot ^2(a+b x)} \cot (a+b x)-8 \sqrt[4]{\cot ^2(a+b x)} \csc (a+b x)+3 \sqrt{2} \cos (a+b x) \cot (a+b x) \log \left(\sqrt{\cot ^2(a+b x)}-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)-3 \sqrt{2} \cos (a+b x) \cot (a+b x) \log \left(\sqrt{\cot ^2(a+b x)}+\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)+6 \sqrt{2} \cos (a+b x) \cot (a+b x) \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}\right)-6 \sqrt{2} \cos (a+b x) \cot (a+b x) \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)\right)}{12 b d^2 \sqrt[4]{\cot ^2(a+b x)} \sqrt{d \csc (a+b x)}}","\frac{c^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{c^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{2 c (c \sec (a+b x))^{3/2}}{3 b d (d \csc (a+b x))^{3/2}}",1,"-1/12*(c*(6*Sqrt[2]*ArcTan[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4)]*Cos[a + b*x]*Cot[a + b*x] - 6*Sqrt[2]*ArcTan[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4)]*Cos[a + b*x]*Cot[a + b*x] + 8*Cos[a + b*x]*Cot[a + b*x]*(Cot[a + b*x]^2)^(1/4) - 8*(Cot[a + b*x]^2)^(1/4)*Csc[a + b*x] + 3*Sqrt[2]*Cos[a + b*x]*Cot[a + b*x]*Log[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]] - 3*Sqrt[2]*Cos[a + b*x]*Cot[a + b*x]*Log[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]])*(c*Sec[a + b*x])^(3/2))/(b*d^2*(Cot[a + b*x]^2)^(1/4)*Sqrt[d*Csc[a + b*x]])","A",1
254,1,45,69,0.2662009,"\int \frac{(d \csc (a+b x))^{9/2}}{\sqrt{c \sec (a+b x)}} \, dx","Integrate[(d*Csc[a + b*x])^(9/2)/Sqrt[c*Sec[a + b*x]],x]","\frac{2 c d (2 \cos (2 (a+b x))-5) (d \csc (a+b x))^{7/2}}{21 b (c \sec (a+b x))^{3/2}}","-\frac{8 c d^3 (d \csc (a+b x))^{3/2}}{21 b (c \sec (a+b x))^{3/2}}-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b (c \sec (a+b x))^{3/2}}",1,"(2*c*d*(-5 + 2*Cos[2*(a + b*x)])*(d*Csc[a + b*x])^(7/2))/(21*b*(c*Sec[a + b*x])^(3/2))","A",1
255,1,104,128,1.0848072,"\int \frac{(d \csc (a+b x))^{7/2}}{\sqrt{c \sec (a+b x)}} \, dx","Integrate[(d*Csc[a + b*x])^(7/2)/Sqrt[c*Sec[a + b*x]],x]","-\frac{2 d^2 \tan ^2(a+b x) (d \csc (a+b x))^{3/2} \left(\sin (2 (a+b x)) \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)-(\cos (2 (a+b x))-2) \cot ^3(a+b x)\right)}{5 b \sqrt{c \sec (a+b x)}}","-\frac{4 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{4 c d^3 \sqrt{d \csc (a+b x)}}{5 b (c \sec (a+b x))^{3/2}}-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b (c \sec (a+b x))^{3/2}}",1,"(-2*d^2*(d*Csc[a + b*x])^(3/2)*(-((-2 + Cos[2*(a + b*x)])*Cot[a + b*x]^3) + (-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2]*Sin[2*(a + b*x)])*Tan[a + b*x]^2)/(5*b*Sqrt[c*Sec[a + b*x]])","C",1
256,1,33,33,0.1152253,"\int \frac{(d \csc (a+b x))^{5/2}}{\sqrt{c \sec (a+b x)}} \, dx","Integrate[(d*Csc[a + b*x])^(5/2)/Sqrt[c*Sec[a + b*x]],x]","-\frac{2 c d (d \csc (a+b x))^{3/2}}{3 b (c \sec (a+b x))^{3/2}}","-\frac{2 c d (d \csc (a+b x))^{3/2}}{3 b (c \sec (a+b x))^{3/2}}",1,"(-2*c*d*(d*Csc[a + b*x])^(3/2))/(3*b*(c*Sec[a + b*x])^(3/2))","A",1
257,1,80,89,0.4825252,"\int \frac{(d \csc (a+b x))^{3/2}}{\sqrt{c \sec (a+b x)}} \, dx","Integrate[(d*Csc[a + b*x])^(3/2)/Sqrt[c*Sec[a + b*x]],x]","-\frac{2 d^2 \tan (a+b x) \left(\sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)+\cot ^2(a+b x)\right)}{b \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","-\frac{2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 c d \sqrt{d \csc (a+b x)}}{b (c \sec (a+b x))^{3/2}}",1,"(-2*d^2*(Cot[a + b*x]^2 + (-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Tan[a + b*x])/(b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]])","C",1
258,1,55,270,0.1291171,"\int \frac{\sqrt{d \csc (a+b x)}}{\sqrt{c \sec (a+b x)}} \, dx","Integrate[Sqrt[d*Csc[a + b*x]]/Sqrt[c*Sec[a + b*x]],x]","-\frac{2 \cot (a+b x) \sqrt{d \csc (a+b x)} \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\cot ^2(a+b x)\right)}{3 b \sqrt{c \sec (a+b x)}}","-\frac{\sqrt{\tan (a+b x)} \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{d \csc (a+b x)}}{\sqrt{2} b \sqrt{c \sec (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b \sqrt{c \sec (a+b x)}}-\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{c \sec (a+b x)}}+\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b \sqrt{c \sec (a+b x)}}",1,"(-2*Cot[a + b*x]*Sqrt[d*Csc[a + b*x]]*Hypergeometric2F1[3/4, 1, 7/4, -Cot[a + b*x]^2])/(3*b*Sqrt[c*Sec[a + b*x]])","C",1
259,1,66,53,0.223126,"\int \frac{1}{\sqrt{d \csc (a+b x)} \sqrt{c \sec (a+b x)}} \, dx","Integrate[1/(Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]]),x]","\frac{\tan (a+b x) \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)}{b \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"((-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2]*Tan[a + b*x])/(b*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]])","C",1
260,1,66,322,0.2645289,"\int \frac{1}{(d \csc (a+b x))^{3/2} \sqrt{c \sec (a+b x)}} \, dx","Integrate[1/((d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]]),x]","-\frac{\cot (a+b x) \left(\csc ^2(a+b x) \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\cot ^2(a+b x)\right)+3\right)}{6 b \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}+\frac{\sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b d^2 \sqrt{c \sec (a+b x)}}-\frac{c}{2 b d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}",1,"-1/6*(Cot[a + b*x]*(3 + Csc[a + b*x]^2*Hypergeometric2F1[3/4, 1, 7/4, -Cot[a + b*x]^2]))/(b*(d*Csc[a + b*x])^(3/2)*Sqrt[c*Sec[a + b*x]])","C",1
261,1,84,95,0.3625421,"\int \frac{1}{(d \csc (a+b x))^{5/2} \sqrt{c \sec (a+b x)}} \, dx","Integrate[1/((d*Csc[a + b*x])^(5/2)*Sqrt[c*Sec[a + b*x]]),x]","-\frac{\tan (a+b x) \left(-3 \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)+\cos (2 (a+b x))+1\right)}{6 b d^2 \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{3 b d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}",1,"-1/6*((1 + Cos[2*(a + b*x)] - 3*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Tan[a + b*x])/(b*d^2*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]])","C",1
262,1,57,110,0.2880428,"\int \frac{(d \csc (a+b x))^{11/2}}{(c \sec (a+b x))^{3/2}} \, dx","Integrate[(d*Csc[a + b*x])^(11/2)/(c*Sec[a + b*x])^(3/2),x]","\frac{2 d^3 (2 \cos (2 (a+b x))-7) \cot ^2(a+b x) (d \csc (a+b x))^{5/2}}{45 b c \sqrt{c \sec (a+b x)}}","\frac{8 d^5 \sqrt{d \csc (a+b x)}}{45 b c \sqrt{c \sec (a+b x)}}+\frac{2 d^3 (d \csc (a+b x))^{5/2}}{45 b c \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{9/2}}{9 b c \sqrt{c \sec (a+b x)}}",1,"(2*d^3*(-7 + 2*Cos[2*(a + b*x)])*Cot[a + b*x]^2*(d*Csc[a + b*x])^(5/2))/(45*b*c*Sqrt[c*Sec[a + b*x]])","A",1
263,1,119,135,1.4591157,"\int \frac{(d \csc (a+b x))^{9/2}}{(c \sec (a+b x))^{3/2}} \, dx","Integrate[(d*Csc[a + b*x])^(9/2)/(c*Sec[a + b*x])^(3/2),x]","-\frac{d^3 \cos (2 (a+b x)) (d \csc (a+b x))^{3/2} \left((\cos (2 (a+b x))+5) \csc ^4(a+b x)-2 \left(-\cot ^2(a+b x)\right)^{3/4} \sec ^2(a+b x) \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)\right)}{21 b c \left(\csc ^2(a+b x)-2\right) \sqrt{c \sec (a+b x)}}","-\frac{2 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{21 b c^2}+\frac{2 d^3 (d \csc (a+b x))^{3/2}}{21 b c \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{7/2}}{7 b c \sqrt{c \sec (a+b x)}}",1,"-1/21*(d^3*Cos[2*(a + b*x)]*(d*Csc[a + b*x])^(3/2)*((5 + Cos[2*(a + b*x)])*Csc[a + b*x]^4 - 2*(-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2]*Sec[a + b*x]^2))/(b*c*(-2 + Csc[a + b*x]^2)*Sqrt[c*Sec[a + b*x]])","C",1
264,1,45,33,0.1364277,"\int \frac{(d \csc (a+b x))^{7/2}}{(c \sec (a+b x))^{3/2}} \, dx","Integrate[(d*Csc[a + b*x])^(7/2)/(c*Sec[a + b*x])^(3/2),x]","-\frac{2 d^3 \cot ^2(a+b x) \sqrt{d \csc (a+b x)}}{5 b c \sqrt{c \sec (a+b x)}}","-\frac{2 c d (d \csc (a+b x))^{5/2}}{5 b (c \sec (a+b x))^{5/2}}",1,"(-2*d^3*Cot[a + b*x]^2*Sqrt[d*Csc[a + b*x]])/(5*b*c*Sqrt[c*Sec[a + b*x]])","A",1
265,1,105,98,0.8271364,"\int \frac{(d \csc (a+b x))^{5/2}}{(c \sec (a+b x))^{3/2}} \, dx","Integrate[(d*Csc[a + b*x])^(5/2)/(c*Sec[a + b*x])^(3/2),x]","-\frac{d \cos (2 (a+b x)) \sec ^3(a+b x) (d \csc (a+b x))^{3/2} \left(2 \cot ^2(a+b x)-\left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)\right)}{3 b \left(\csc ^2(a+b x)-2\right) (c \sec (a+b x))^{3/2}}","-\frac{d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{3 b c^2}-\frac{2 d (d \csc (a+b x))^{3/2}}{3 b c \sqrt{c \sec (a+b x)}}",1,"-1/3*(d*Cos[2*(a + b*x)]*(d*Csc[a + b*x])^(3/2)*(2*Cot[a + b*x]^2 - (-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*Sec[a + b*x]^3)/(b*(-2 + Csc[a + b*x]^2)*(c*Sec[a + b*x])^(3/2))","C",1
266,1,199,327,0.6722796,"\int \frac{(d \csc (a+b x))^{3/2}}{(c \sec (a+b x))^{3/2}} \, dx","Integrate[(d*Csc[a + b*x])^(3/2)/(c*Sec[a + b*x])^(3/2),x]","-\frac{d \sqrt{d \csc (a+b x)} \left(8 \sqrt[4]{\cot ^2(a+b x)}+\sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)-\sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}+\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)\right)}{4 b c \sqrt[4]{\cot ^2(a+b x)} \sqrt{c \sec (a+b x)}}","\frac{d^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{d^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{\sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{d^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d^2 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 d \sqrt{d \csc (a+b x)}}{b c \sqrt{c \sec (a+b x)}}",1,"-1/4*(d*Sqrt[d*Csc[a + b*x]]*(2*Sqrt[2]*ArcTan[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] + 8*(Cot[a + b*x]^2)^(1/4) + Sqrt[2]*Log[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]] - Sqrt[2]*Log[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]]))/(b*c*(Cot[a + b*x]^2)^(1/4)*Sqrt[c*Sec[a + b*x]])","A",1
267,1,84,92,0.6576543,"\int \frac{\sqrt{d \csc (a+b x)}}{(c \sec (a+b x))^{3/2}} \, dx","Integrate[Sqrt[d*Csc[a + b*x]]/(c*Sec[a + b*x])^(3/2),x]","\frac{d \sec ^3(a+b x) \left(-\left(-\cot ^2(a+b x)\right)^{3/4} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)+\cos (2 (a+b x))+1\right)}{2 b (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{2 b c^2}+\frac{d}{b c \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"(d*(1 + Cos[2*(a + b*x)] - (-Cot[a + b*x]^2)^(3/4)*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])*Sec[a + b*x]^3)/(2*b*Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2))","C",1
268,1,223,322,2.0192251,"\int \frac{1}{\sqrt{d \csc (a+b x)} (c \sec (a+b x))^{3/2}} \, dx","Integrate[1/(Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(3/2)),x]","\frac{\sqrt{d \csc (a+b x)} \left(4 \sqrt[4]{\cot ^2(a+b x)}-4 \cos (2 (a+b x)) \sqrt[4]{\cot ^2(a+b x)}+\sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)-\sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}+\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)+2 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}\right)-2 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)\right)}{16 b c d \sqrt[4]{\cot ^2(a+b x)} \sqrt{c \sec (a+b x)}}","-\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{\sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d}{2 b c \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}",1,"(Sqrt[d*Csc[a + b*x]]*(2*Sqrt[2]*ArcTan[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] - 2*Sqrt[2]*ArcTan[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] + 4*(Cot[a + b*x]^2)^(1/4) - 4*Cos[2*(a + b*x)]*(Cot[a + b*x]^2)^(1/4) + Sqrt[2]*Log[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]] - Sqrt[2]*Log[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]]))/(16*b*c*d*(Cot[a + b*x]^2)^(1/4)*Sqrt[c*Sec[a + b*x]])","A",1
269,1,89,135,0.5727274,"\int \frac{1}{(d \csc (a+b x))^{3/2} (c \sec (a+b x))^{3/2}} \, dx","Integrate[1/((d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2)),x]","\frac{\frac{\csc ^2(a+b x) \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{3}{2};\csc ^2(a+b x)\right)}{\sqrt[4]{-\cot ^2(a+b x)}}-2 \cos (2 (a+b x))}{12 b c d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}{12 b c^2 d^2}-\frac{c}{3 b d (c \sec (a+b x))^{5/2} \sqrt{d \csc (a+b x)}}+\frac{1}{6 b c d \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}",1,"(-2*Cos[2*(a + b*x)] + (Csc[a + b*x]^2*Hypergeometric2F1[1/2, 3/4, 3/2, Csc[a + b*x]^2])/(-Cot[a + b*x]^2)^(1/4))/(12*b*c*d*Sqrt[d*Csc[a + b*x]]*Sqrt[c*Sec[a + b*x]])","C",1
270,1,246,371,2.2828955,"\int \frac{1}{(d \csc (a+b x))^{5/2} (c \sec (a+b x))^{3/2}} \, dx","Integrate[1/((d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(3/2)),x]","\frac{\sqrt{d \csc (a+b x)} \left(8 \sqrt[4]{\cot ^2(a+b x)}-12 \cos (2 (a+b x)) \sqrt[4]{\cot ^2(a+b x)}+4 \cos (4 (a+b x)) \sqrt[4]{\cot ^2(a+b x)}+3 \sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)-3 \sqrt{2} \log \left(\sqrt{\cot ^2(a+b x)}+\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)+6 \sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}\right)-6 \sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt[4]{\cot ^2(a+b x)}+1\right)\right)}{128 b c d^3 \sqrt[4]{\cot ^2(a+b x)} \sqrt{c \sec (a+b x)}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{c \sec (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{c \sec (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{3 \sqrt{c \sec (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{4 b d (c \sec (a+b x))^{5/2} (d \csc (a+b x))^{3/2}}+\frac{3}{16 b c d \sqrt{c \sec (a+b x)} (d \csc (a+b x))^{3/2}}",1,"(Sqrt[d*Csc[a + b*x]]*(6*Sqrt[2]*ArcTan[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] - 6*Sqrt[2]*ArcTan[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4)] + 8*(Cot[a + b*x]^2)^(1/4) - 12*Cos[2*(a + b*x)]*(Cot[a + b*x]^2)^(1/4) + 4*Cos[4*(a + b*x)]*(Cot[a + b*x]^2)^(1/4) + 3*Sqrt[2]*Log[1 - Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]] - 3*Sqrt[2]*Log[1 + Sqrt[2]*(Cot[a + b*x]^2)^(1/4) + Sqrt[Cot[a + b*x]^2]]))/(128*b*c*d^3*(Cot[a + b*x]^2)^(1/4)*Sqrt[c*Sec[a + b*x]])","A",1
271,1,45,33,0.161551,"\int \frac{(d \csc (a+b x))^{9/2}}{(c \sec (a+b x))^{5/2}} \, dx","Integrate[(d*Csc[a + b*x])^(9/2)/(c*Sec[a + b*x])^(5/2),x]","-\frac{2 d^4 \cot ^3(a+b x) \sqrt{d \csc (a+b x)}}{7 b c^2 \sqrt{c \sec (a+b x)}}","-\frac{2 c d (d \csc (a+b x))^{7/2}}{7 b (c \sec (a+b x))^{7/2}}",1,"(-2*d^4*Cot[a + b*x]^3*Sqrt[d*Csc[a + b*x]])/(7*b*c^2*Sqrt[c*Sec[a + b*x]])","A",1
272,1,101,135,1.7716734,"\int \frac{(d \csc (a+b x))^{7/2}}{(c \sec (a+b x))^{5/2}} \, dx","Integrate[(d*Csc[a + b*x])^(7/2)/(c*Sec[a + b*x])^(5/2),x]","\frac{d^5 \sqrt{c \sec (a+b x)} \left(6 \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)+(1-3 \cos (2 (a+b x))) \cot ^2(a+b x) \csc ^2(a+b x)\right)}{5 b c^3 (d \csc (a+b x))^{3/2}}","\frac{6 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{5 b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{6 d^3 \sqrt{d \csc (a+b x)}}{5 b c (c \sec (a+b x))^{3/2}}-\frac{2 d (d \csc (a+b x))^{5/2}}{5 b c (c \sec (a+b x))^{3/2}}",1,"(d^5*((1 - 3*Cos[2*(a + b*x)])*Cot[a + b*x]^2*Csc[a + b*x]^2 + 6*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]])/(5*b*c^3*(d*Csc[a + b*x])^(3/2))","C",1
273,1,55,329,0.2040866,"\int \frac{(d \csc (a+b x))^{5/2}}{(c \sec (a+b x))^{5/2}} \, dx","Integrate[(d*Csc[a + b*x])^(5/2)/(c*Sec[a + b*x])^(5/2),x]","\frac{2 d (d \csc (a+b x))^{3/2} \left(\, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\cot ^2(a+b x)\right)-1\right)}{3 b c (c \sec (a+b x))^{3/2}}","\frac{d^2 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{d^2 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{\sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{d^2 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{2 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{2 d (d \csc (a+b x))^{3/2}}{3 b c (c \sec (a+b x))^{3/2}}",1,"(2*d*(d*Csc[a + b*x])^(3/2)*(-1 + Hypergeometric2F1[3/4, 1, 7/4, -Cot[a + b*x]^2]))/(3*b*c*(c*Sec[a + b*x])^(3/2))","C",1
274,1,80,94,0.6951893,"\int \frac{(d \csc (a+b x))^{3/2}}{(c \sec (a+b x))^{5/2}} \, dx","Integrate[(d*Csc[a + b*x])^(3/2)/(c*Sec[a + b*x])^(5/2),x]","-\frac{d^3 \sqrt{c \sec (a+b x)} \left(3 \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)+2 \cot ^2(a+b x)\right)}{b c^3 (d \csc (a+b x))^{3/2}}","-\frac{3 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{2 d \sqrt{d \csc (a+b x)}}{b c (c \sec (a+b x))^{3/2}}",1,"-((d^3*(2*Cot[a + b*x]^2 + 3*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]])/(b*c^3*(d*Csc[a + b*x])^(3/2)))","C",1
275,1,70,322,0.2264113,"\int \frac{\sqrt{d \csc (a+b x)}}{(c \sec (a+b x))^{5/2}} \, dx","Integrate[Sqrt[d*Csc[a + b*x]]/(c*Sec[a + b*x])^(5/2),x]","-\frac{\cot (a+b x) \sqrt{d \csc (a+b x)} \left(2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\cot ^2(a+b x)\right)+\cos (2 (a+b x))-1\right)}{4 b c^2 \sqrt{c \sec (a+b x)}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{4 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}-\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{8 \sqrt{2} b c^2 \sqrt{c \sec (a+b x)}}+\frac{d}{2 b c (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}",1,"-1/4*(Cot[a + b*x]*Sqrt[d*Csc[a + b*x]]*(-1 + Cos[2*(a + b*x)] + 2*Hypergeometric2F1[3/4, 1, 7/4, -Cot[a + b*x]^2]))/(b*c^2*Sqrt[c*Sec[a + b*x]])","C",1
276,1,79,95,0.3607973,"\int \frac{1}{\sqrt{d \csc (a+b x)} (c \sec (a+b x))^{5/2}} \, dx","Integrate[1/(Sqrt[d*Csc[a + b*x]]*(c*Sec[a + b*x])^(5/2)),x]","\frac{d \sqrt{c \sec (a+b x)} \left(3 \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)+\cos (2 (a+b x))+1\right)}{6 b c^3 (d \csc (a+b x))^{3/2}}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b c^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}+\frac{d}{3 b c (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}",1,"(d*(1 + Cos[2*(a + b*x)] + 3*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]])/(6*b*c^3*(d*Csc[a + b*x])^(3/2))","C",1
277,1,81,371,0.373361,"\int \frac{1}{(d \csc (a+b x))^{3/2} (c \sec (a+b x))^{5/2}} \, dx","Integrate[1/((d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(5/2)),x]","-\frac{\csc ^3(a+b x) \left(2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\cot ^2(a+b x)\right)+\cos (2 (a+b x))-\cos (4 (a+b x))\right)}{32 b c (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}","-\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}+\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{32 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}-\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}+\frac{3 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{64 \sqrt{2} b c^2 d^2 \sqrt{c \sec (a+b x)}}-\frac{c}{4 b d (c \sec (a+b x))^{7/2} \sqrt{d \csc (a+b x)}}+\frac{1}{16 b c d (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}",1,"-1/32*(Csc[a + b*x]^3*(Cos[2*(a + b*x)] - Cos[4*(a + b*x)] + 2*Hypergeometric2F1[3/4, 1, 7/4, -Cot[a + b*x]^2]))/(b*c*(d*Csc[a + b*x])^(3/2)*(c*Sec[a + b*x])^(3/2))","C",1
278,1,90,135,0.6522528,"\int \frac{1}{(d \csc (a+b x))^{5/2} (c \sec (a+b x))^{5/2}} \, dx","Integrate[1/((d*Csc[a + b*x])^(5/2)*(c*Sec[a + b*x])^(5/2)),x]","\frac{\sqrt{c \sec (a+b x)} \left(3 \sqrt[4]{-\cot ^2(a+b x)} \, _2F_1\left(-\frac{1}{2},\frac{1}{4};\frac{1}{2};\csc ^2(a+b x)\right)-2 \cos ^2(a+b x) \cos (2 (a+b x))\right)}{20 b c^3 d (d \csc (a+b x))^{3/2}}","\frac{3 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{20 b c^2 d^2 \sqrt{\sin (2 a+2 b x)} \sqrt{c \sec (a+b x)} \sqrt{d \csc (a+b x)}}-\frac{c}{5 b d (c \sec (a+b x))^{7/2} (d \csc (a+b x))^{3/2}}+\frac{1}{10 b c d (c \sec (a+b x))^{3/2} (d \csc (a+b x))^{3/2}}",1,"((-2*Cos[a + b*x]^2*Cos[2*(a + b*x)] + 3*(-Cot[a + b*x]^2)^(1/4)*Hypergeometric2F1[-1/2, 1/4, 1/2, Csc[a + b*x]^2])*Sqrt[c*Sec[a + b*x]])/(20*b*c^3*d*(d*Csc[a + b*x])^(3/2))","C",1
279,1,95,406,0.4026095,"\int \frac{1}{(d \csc (a+b x))^{7/2} (c \sec (a+b x))^{5/2}} \, dx","Integrate[1/((d*Csc[a + b*x])^(7/2)*(c*Sec[a + b*x])^(5/2)),x]","-\frac{\cot (a+b x) \sqrt{d \csc (a+b x)} \left(10 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};-\cot ^2(a+b x)\right)+3 \cos (2 (a+b x))-9 \cos (4 (a+b x))+2 \cos (6 (a+b x))+4\right)}{384 b c^2 d^4 \sqrt{c \sec (a+b x)}}","-\frac{5 \tan ^{-1}\left(1-\sqrt{2} \sqrt{\tan (a+b x)}\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{128 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}+\frac{5 \tan ^{-1}\left(\sqrt{2} \sqrt{\tan (a+b x)}+1\right) \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)}}{128 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}-\frac{5 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)-\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{256 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}+\frac{5 \sqrt{\tan (a+b x)} \sqrt{d \csc (a+b x)} \log \left(\tan (a+b x)+\sqrt{2} \sqrt{\tan (a+b x)}+1\right)}{256 \sqrt{2} b c^2 d^4 \sqrt{c \sec (a+b x)}}-\frac{5 c}{48 b d^3 (c \sec (a+b x))^{7/2} \sqrt{d \csc (a+b x)}}+\frac{5}{192 b c d^3 (c \sec (a+b x))^{3/2} \sqrt{d \csc (a+b x)}}-\frac{c}{6 b d (c \sec (a+b x))^{7/2} (d \csc (a+b x))^{5/2}}",1,"-1/384*(Cot[a + b*x]*Sqrt[d*Csc[a + b*x]]*(4 + 3*Cos[2*(a + b*x)] - 9*Cos[4*(a + b*x)] + 2*Cos[6*(a + b*x)] + 10*Hypergeometric2F1[3/4, 1, 7/4, -Cot[a + b*x]^2]))/(b*c^2*d^4*Sqrt[c*Sec[a + b*x]])","C",1
280,1,278,81,2.2758316,"\int \csc ^n(e+f x) \sec ^m(e+f x) \, dx","Integrate[Csc[e + f*x]^n*Sec[e + f*x]^m,x]","-\frac{(n-3) \sec ^m(e+f x) \csc ^{n-1}(e+f x) F_1\left(\frac{1}{2}-\frac{n}{2};m,-m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left((n-3) F_1\left(\frac{1}{2}-\frac{n}{2};m,-m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-2 \tan ^2\left(\frac{1}{2} (e+f x)\right) \left((m+n-1) F_1\left(\frac{3}{2}-\frac{n}{2};m,-m-n+2;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+m F_1\left(\frac{3}{2}-\frac{n}{2};m+1,-m-n+1;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)\right)}","\frac{\cos ^2(e+f x)^{\frac{m+1}{2}} \sec ^{m+1}(e+f x) \csc ^{n-1}(e+f x) \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"-(((-3 + n)*AppellF1[1/2 - n/2, m, 1 - m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Csc[e + f*x]^(-1 + n)*Sec[e + f*x]^m)/(f*(-1 + n)*((-3 + n)*AppellF1[1/2 - n/2, m, 1 - m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] - 2*((-1 + m + n)*AppellF1[3/2 - n/2, m, 2 - m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + m*AppellF1[3/2 - n/2, 1 + m, 1 - m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Tan[(e + f*x)/2]^2)))","C",0
281,1,280,86,0.5899034,"\int \csc ^n(e+f x) (a \sec (e+f x))^m \, dx","Integrate[Csc[e + f*x]^n*(a*Sec[e + f*x])^m,x]","-\frac{(n-3) \csc ^{n-1}(e+f x) (a \sec (e+f x))^m F_1\left(\frac{1}{2}-\frac{n}{2};m,-m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left((n-3) F_1\left(\frac{1}{2}-\frac{n}{2};m,-m-n+1;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-2 \tan ^2\left(\frac{1}{2} (e+f x)\right) \left((m+n-1) F_1\left(\frac{3}{2}-\frac{n}{2};m,-m-n+2;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+m F_1\left(\frac{3}{2}-\frac{n}{2};m+1,-m-n+1;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)\right)}","\frac{\cos ^2(e+f x)^{\frac{m+1}{2}} \csc ^{n-1}(e+f x) (a \sec (e+f x))^{m+1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{a f (1-n)}",1,"-(((-3 + n)*AppellF1[1/2 - n/2, m, 1 - m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Csc[e + f*x]^(-1 + n)*(a*Sec[e + f*x])^m)/(f*(-1 + n)*((-3 + n)*AppellF1[1/2 - n/2, m, 1 - m - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] - 2*((-1 + m + n)*AppellF1[3/2 - n/2, m, 2 - m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + m*AppellF1[3/2 - n/2, 1 + m, 1 - m - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Tan[(e + f*x)/2]^2)))","C",0
282,1,281,84,0.3230966,"\int (b \csc (e+f x))^n \sec ^m(e+f x) \, dx","Integrate[(b*Csc[e + f*x])^n*Sec[e + f*x]^m,x]","-\frac{b (n-3) \sec ^m(e+f x) (b \csc (e+f x))^{n-1} F_1\left(\frac{1-n}{2};m,-m-n+1;\frac{3-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left((n-3) F_1\left(\frac{1-n}{2};m,-m-n+1;\frac{3-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-2 \tan ^2\left(\frac{1}{2} (e+f x)\right) \left((m+n-1) F_1\left(\frac{3-n}{2};m,-m-n+2;\frac{5-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+m F_1\left(\frac{3-n}{2};m+1,-m-n+1;\frac{5-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)\right)}","\frac{b \cos ^2(e+f x)^{\frac{m+1}{2}} \sec ^{m+1}(e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"-((b*(-3 + n)*AppellF1[(1 - n)/2, m, 1 - m - n, (3 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*(b*Csc[e + f*x])^(-1 + n)*Sec[e + f*x]^m)/(f*(-1 + n)*((-3 + n)*AppellF1[(1 - n)/2, m, 1 - m - n, (3 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] - 2*((-1 + m + n)*AppellF1[(3 - n)/2, m, 2 - m - n, (5 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + m*AppellF1[(3 - n)/2, 1 + m, 1 - m - n, (5 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Tan[(e + f*x)/2]^2)))","C",0
283,1,283,89,0.1855154,"\int (b \csc (e+f x))^n (a \sec (e+f x))^m \, dx","Integrate[(b*Csc[e + f*x])^n*(a*Sec[e + f*x])^m,x]","-\frac{b (n-3) (a \sec (e+f x))^m (b \csc (e+f x))^{n-1} F_1\left(\frac{1-n}{2};m,-m-n+1;\frac{3-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)}{f (n-1) \left((n-3) F_1\left(\frac{1-n}{2};m,-m-n+1;\frac{3-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-2 \tan ^2\left(\frac{1}{2} (e+f x)\right) \left((m+n-1) F_1\left(\frac{3-n}{2};m,-m-n+2;\frac{5-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+m F_1\left(\frac{3-n}{2};m+1,-m-n+1;\frac{5-n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)\right)}","\frac{b \cos ^2(e+f x)^{\frac{m+1}{2}} (a \sec (e+f x))^{m+1} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{m+1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{a f (1-n)}",1,"-((b*(-3 + n)*AppellF1[(1 - n)/2, m, 1 - m - n, (3 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*(b*Csc[e + f*x])^(-1 + n)*(a*Sec[e + f*x])^m)/(f*(-1 + n)*((-3 + n)*AppellF1[(1 - n)/2, m, 1 - m - n, (3 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] - 2*((-1 + m + n)*AppellF1[(3 - n)/2, m, 2 - m - n, (5 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2] + m*AppellF1[(3 - n)/2, 1 + m, 1 - m - n, (5 - n)/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2])*Tan[(e + f*x)/2]^2)))","C",0
284,1,51,48,0.0404278,"\int (b \csc (e+f x))^n \sec ^5(e+f x) \, dx","Integrate[(b*Csc[e + f*x])^n*Sec[e + f*x]^5,x]","-\frac{b (b \csc (e+f x))^{n-1} \, _2F_1\left(3,\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (n-1)}","\frac{(b \csc (e+f x))^{n+5} \, _2F_1\left(3,\frac{n+5}{2};\frac{n+7}{2};\csc ^2(e+f x)\right)}{b^5 f (n+5)}",1,"-((b*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[3, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(-1 + n)))","A",1
285,1,51,49,0.0381265,"\int (b \csc (e+f x))^n \sec ^3(e+f x) \, dx","Integrate[(b*Csc[e + f*x])^n*Sec[e + f*x]^3,x]","-\frac{b (b \csc (e+f x))^{n-1} \, _2F_1\left(2,\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (n-1)}","-\frac{(b \csc (e+f x))^{n+3} \, _2F_1\left(2,\frac{n+3}{2};\frac{n+5}{2};\csc ^2(e+f x)\right)}{b^3 f (n+3)}",1,"-((b*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[2, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(-1 + n)))","A",1
286,1,51,48,0.0339626,"\int (b \csc (e+f x))^n \sec (e+f x) \, dx","Integrate[(b*Csc[e + f*x])^n*Sec[e + f*x],x]","-\frac{b (b \csc (e+f x))^{n-1} \, _2F_1\left(1,\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (n-1)}","\frac{(b \csc (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\csc ^2(e+f x)\right)}{b f (n+1)}",1,"-((b*(b*Csc[e + f*x])^(-1 + n)*Hypergeometric2F1[1, (1 - n)/2, (3 - n)/2, Sin[e + f*x]^2])/(f*(-1 + n)))","A",1
287,1,23,24,0.023052,"\int \cos (e+f x) (b \csc (e+f x))^n \, dx","Integrate[Cos[e + f*x]*(b*Csc[e + f*x])^n,x]","-\frac{b (b \csc (e+f x))^{n-1}}{f (n-1)}","\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}",1,"-((b*(b*Csc[e + f*x])^(-1 + n))/(f*(-1 + n)))","A",1
288,1,45,52,0.1372494,"\int \cos ^3(e+f x) (b \csc (e+f x))^n \, dx","Integrate[Cos[e + f*x]^3*(b*Csc[e + f*x])^n,x]","-\frac{b ((n-1) \cos (2 (e+f x))+n-5) (b \csc (e+f x))^{n-1}}{2 f (n-3) (n-1)}","\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}-\frac{b^3 (b \csc (e+f x))^{n-3}}{f (3-n)}",1,"-1/2*(b*(-5 + n + (-1 + n)*Cos[2*(e + f*x)])*(b*Csc[e + f*x])^(-1 + n))/(f*(-3 + n)*(-1 + n))","A",1
289,1,81,78,0.5622813,"\int \cos ^5(e+f x) (b \csc (e+f x))^n \, dx","Integrate[Cos[e + f*x]^5*(b*Csc[e + f*x])^n,x]","-\frac{\sin ^5(e+f x) \left(\left(n^2-8 n+15\right) \csc ^4(e+f x)-2 \left(n^2-6 n+5\right) \csc ^2(e+f x)+n^2-4 n+3\right) (b \csc (e+f x))^n}{f (n-5) (n-3) (n-1)}","\frac{b^5 (b \csc (e+f x))^{n-5}}{f (5-n)}-\frac{2 b^3 (b \csc (e+f x))^{n-3}}{f (3-n)}+\frac{b (b \csc (e+f x))^{n-1}}{f (1-n)}",1,"-(((b*Csc[e + f*x])^n*(3 - 4*n + n^2 - 2*(5 - 6*n + n^2)*Csc[e + f*x]^2 + (15 - 8*n + n^2)*Csc[e + f*x]^4)*Sin[e + f*x]^5)/(f*(-5 + n)*(-3 + n)*(-1 + n)))","A",1
290,1,77,72,0.6107909,"\int (b \csc (e+f x))^n \sec ^6(e+f x) \, dx","Integrate[(b*Csc[e + f*x])^n*Sec[e + f*x]^6,x]","\frac{\tan (e+f x) \sec ^2(e+f x)^{-n/2} (b \csc (e+f x))^n \, _2F_1\left(-\frac{n}{2}-2,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2(e+f x)\right)}{f (1-n)}","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{7}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"((b*Csc[e + f*x])^n*Hypergeometric2F1[-2 - n/2, 1/2 - n/2, 3/2 - n/2, -Tan[e + f*x]^2]*Tan[e + f*x])/(f*(1 - n)*(Sec[e + f*x]^2)^(n/2))","A",1
291,1,77,72,0.5292563,"\int (b \csc (e+f x))^n \sec ^4(e+f x) \, dx","Integrate[(b*Csc[e + f*x])^n*Sec[e + f*x]^4,x]","\frac{\tan (e+f x) \sec ^2(e+f x)^{-n/2} (b \csc (e+f x))^n \, _2F_1\left(-\frac{n}{2}-1,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2(e+f x)\right)}{f (1-n)}","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{5}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"((b*Csc[e + f*x])^n*Hypergeometric2F1[-1 - n/2, 1/2 - n/2, 3/2 - n/2, -Tan[e + f*x]^2]*Tan[e + f*x])/(f*(1 - n)*(Sec[e + f*x]^2)^(n/2))","A",1
292,1,75,72,0.468308,"\int (b \csc (e+f x))^n \sec ^2(e+f x) \, dx","Integrate[(b*Csc[e + f*x])^n*Sec[e + f*x]^2,x]","\frac{\tan (e+f x) \sec ^2(e+f x)^{-n/2} (b \csc (e+f x))^n \, _2F_1\left(\frac{1}{2}-\frac{n}{2},-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2(e+f x)\right)}{f (1-n)}","\frac{b \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n)}",1,"((b*Csc[e + f*x])^n*Hypergeometric2F1[1/2 - n/2, -1/2*n, 3/2 - n/2, -Tan[e + f*x]^2]*Tan[e + f*x])/(f*(1 - n)*(Sec[e + f*x]^2)^(n/2))","A",1
293,1,65,72,0.1067246,"\int (b \csc (e+f x))^n \, dx","Integrate[(b*Csc[e + f*x])^n,x]","-\frac{\sin (e+f x) \cos (e+f x) \sin ^2(e+f x)^{\frac{n-1}{2}} (b \csc (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{3}{2};\cos ^2(e+f x)\right)}{f}","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}",1,"-((Cos[e + f*x]*(b*Csc[e + f*x])^n*Hypergeometric2F1[1/2, (1 + n)/2, 3/2, Cos[e + f*x]^2]*Sin[e + f*x]*(Sin[e + f*x]^2)^((-1 + n)/2))/f)","A",1
294,1,165,72,0.4775173,"\int \cos ^2(e+f x) (b \csc (e+f x))^n \, dx","Integrate[Cos[e + f*x]^2*(b*Csc[e + f*x])^n,x]","-\frac{2 \tan \left(\frac{1}{2} (e+f x)\right) \sec ^2\left(\frac{1}{2} (e+f x)\right)^{-n} (b \csc (e+f x))^n \left(\, _2F_1\left(1-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-4 \, _2F_1\left(2-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+4 \, _2F_1\left(3-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)}{f (n-1)}","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}",1,"(-2*(b*Csc[e + f*x])^n*(Hypergeometric2F1[1 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2] - 4*Hypergeometric2F1[2 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2] + 4*Hypergeometric2F1[3 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2])*Tan[(e + f*x)/2])/(f*(-1 + n)*(Sec[(e + f*x)/2]^2)^n)","B",1
295,1,246,72,0.6223291,"\int \cos ^4(e+f x) (b \csc (e+f x))^n \, dx","Integrate[Cos[e + f*x]^4*(b*Csc[e + f*x])^n,x]","-\frac{2 \tan \left(\frac{1}{2} (e+f x)\right) \sec ^2\left(\frac{1}{2} (e+f x)\right)^{-n} (b \csc (e+f x))^n \left(\, _2F_1\left(1-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-8 \left(\, _2F_1\left(2-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-3 \, _2F_1\left(3-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+4 \, _2F_1\left(4-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-2 \, _2F_1\left(5-n,\frac{1}{2}-\frac{n}{2};\frac{3}{2}-\frac{n}{2};-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)\right)}{f (n-1)}","\frac{b \cos (e+f x) (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{f (1-n) \sqrt{\cos ^2(e+f x)}}",1,"(-2*(b*Csc[e + f*x])^n*(Hypergeometric2F1[1 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2] - 8*(Hypergeometric2F1[2 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2] - 3*Hypergeometric2F1[3 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2] + 4*Hypergeometric2F1[4 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2] - 2*Hypergeometric2F1[5 - n, 1/2 - n/2, 3/2 - n/2, -Tan[(e + f*x)/2]^2]))*Tan[(e + f*x)/2])/(f*(-1 + n)*(Sec[(e + f*x)/2]^2)^n)","B",1
296,1,92,81,1.8881825,"\int (b \csc (e+f x))^n (c \sec (e+f x))^{3/2} \, dx","Integrate[(b*Csc[e + f*x])^n*(c*Sec[e + f*x])^(3/2),x]","\frac{2 \cot (e+f x) (c \sec (e+f x))^{3/2} \left(-\tan ^2(e+f x)\right)^{\frac{n+1}{2}} (b \csc (e+f x))^n \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+3);\frac{1}{4} (2 n+7);\sec ^2(e+f x)\right)}{f (2 n+3)}","\frac{b \cos ^2(e+f x)^{5/4} (c \sec (e+f x))^{5/2} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{5}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}",1,"(2*Cot[e + f*x]*(b*Csc[e + f*x])^n*Hypergeometric2F1[(1 + n)/2, (3 + 2*n)/4, (7 + 2*n)/4, Sec[e + f*x]^2]*(c*Sec[e + f*x])^(3/2)*(-Tan[e + f*x]^2)^((1 + n)/2))/(f*(3 + 2*n))","A",1
297,1,90,81,1.7177454,"\int (b \csc (e+f x))^n \sqrt{c \sec (e+f x)} \, dx","Integrate[(b*Csc[e + f*x])^n*Sqrt[c*Sec[e + f*x]],x]","\frac{2 \cot (e+f x) \sqrt{c \sec (e+f x)} \left(-\tan ^2(e+f x)\right)^{\frac{n+1}{2}} (b \csc (e+f x))^n \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n+1);\frac{1}{4} (2 n+5);\sec ^2(e+f x)\right)}{2 f n+f}","\frac{b \cos ^2(e+f x)^{3/4} (c \sec (e+f x))^{3/2} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{3}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}",1,"(2*Cot[e + f*x]*(b*Csc[e + f*x])^n*Hypergeometric2F1[(1 + n)/2, (1 + 2*n)/4, (5 + 2*n)/4, Sec[e + f*x]^2]*Sqrt[c*Sec[e + f*x]]*(-Tan[e + f*x]^2)^((1 + n)/2))/(f + 2*f*n)","A",1
298,1,326,81,3.1832575,"\int \frac{(b \csc (e+f x))^n}{\sqrt{c \sec (e+f x)}} \, dx","Integrate[(b*Csc[e + f*x])^n/Sqrt[c*Sec[e + f*x]],x]","-\frac{4 (n-3) \sin \left(\frac{1}{2} (e+f x)\right) \cos ^3\left(\frac{1}{2} (e+f x)\right) F_1\left(\frac{1}{2}-\frac{n}{2};-\frac{1}{2},\frac{3}{2}-n;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right) (b \csc (e+f x))^n}{f (n-1) \sqrt{c \sec (e+f x)} \left(2 (3-2 n) \sin ^2\left(\frac{1}{2} (e+f x)\right) F_1\left(\frac{3}{2}-\frac{n}{2};-\frac{1}{2},\frac{5}{2}-n;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)+2 (n-3) \cos ^2\left(\frac{1}{2} (e+f x)\right) F_1\left(\frac{1}{2}-\frac{n}{2};-\frac{1}{2},\frac{3}{2}-n;\frac{3}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)-(\cos (e+f x)-1) F_1\left(\frac{3}{2}-\frac{n}{2};\frac{1}{2},\frac{3}{2}-n;\frac{5}{2}-\frac{n}{2};\tan ^2\left(\frac{1}{2} (e+f x)\right),-\tan ^2\left(\frac{1}{2} (e+f x)\right)\right)\right)}","\frac{b \sqrt[4]{\cos ^2(e+f x)} \sqrt{c \sec (e+f x)} (b \csc (e+f x))^{n-1} \, _2F_1\left(\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n)}",1,"(-4*(-3 + n)*AppellF1[1/2 - n/2, -1/2, 3/2 - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^3*(b*Csc[e + f*x])^n*Sin[(e + f*x)/2])/(f*(-1 + n)*Sqrt[c*Sec[e + f*x]]*(2*(-3 + n)*AppellF1[1/2 - n/2, -1/2, 3/2 - n, 3/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Cos[(e + f*x)/2]^2 - AppellF1[3/2 - n/2, 1/2, 3/2 - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*(-1 + Cos[e + f*x]) + 2*(3 - 2*n)*AppellF1[3/2 - n/2, -1/2, 5/2 - n, 5/2 - n/2, Tan[(e + f*x)/2]^2, -Tan[(e + f*x)/2]^2]*Sin[(e + f*x)/2]^2))","C",0
299,1,115,81,1.0202146,"\int \frac{(b \csc (e+f x))^n}{(c \sec (e+f x))^{3/2}} \, dx","Integrate[(b*Csc[e + f*x])^n/(c*Sec[e + f*x])^(3/2),x]","-\frac{2 \cos (2 (e+f x)) \cot (e+f x) \sqrt{c \sec (e+f x)} \left(-\tan ^2(e+f x)\right)^{\frac{n+1}{2}} (b \csc (e+f x))^n \, _2F_1\left(\frac{n+1}{2},\frac{1}{4} (2 n-3);\frac{1}{4} (2 n+1);\sec ^2(e+f x)\right)}{c^2 f (2 n-3) \left(\sec ^2(e+f x)-2\right)}","\frac{b (b \csc (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(e+f x)\right)}{c f (1-n) \sqrt[4]{\cos ^2(e+f x)} \sqrt{c \sec (e+f x)}}",1,"(-2*Cos[2*(e + f*x)]*Cot[e + f*x]*(b*Csc[e + f*x])^n*Hypergeometric2F1[(1 + n)/2, (-3 + 2*n)/4, (1 + 2*n)/4, Sec[e + f*x]^2]*Sqrt[c*Sec[e + f*x]]*(-Tan[e + f*x]^2)^((1 + n)/2))/(c^2*f*(-3 + 2*n)*(-2 + Sec[e + f*x]^2))","A",1