1,1,11,0,0.0040155,"\int \sin (a+b x) \, dx","Int[Sin[a + b*x],x]","-\frac{\cos (a+b x)}{b}","-\frac{\cos (a+b x)}{b}",1,"-(Cos[a + b*x]/b)","A",1,1,6,0.1667,1,"{2638}"
2,1,25,0,0.008774,"\int \sin ^2(a+b x) \, dx","Int[Sin[a + b*x]^2,x]","\frac{x}{2}-\frac{\sin (a+b x) \cos (a+b x)}{2 b}","\frac{x}{2}-\frac{\sin (a+b x) \cos (a+b x)}{2 b}",1,"x/2 - (Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",2,2,8,0.2500,1,"{2635, 8}"
3,1,27,0,0.010362,"\int \sin ^3(a+b x) \, dx","Int[Sin[a + b*x]^3,x]","\frac{\cos ^3(a+b x)}{3 b}-\frac{\cos (a+b x)}{b}","\frac{\cos ^3(a+b x)}{3 b}-\frac{\cos (a+b x)}{b}",1,"-(Cos[a + b*x]/b) + Cos[a + b*x]^3/(3*b)","A",2,1,8,0.1250,1,"{2633}"
4,1,46,0,0.0197972,"\int \sin ^4(a+b x) \, dx","Int[Sin[a + b*x]^4,x]","-\frac{\sin ^3(a+b x) \cos (a+b x)}{4 b}-\frac{3 \sin (a+b x) \cos (a+b x)}{8 b}+\frac{3 x}{8}","-\frac{\sin ^3(a+b x) \cos (a+b x)}{4 b}-\frac{3 \sin (a+b x) \cos (a+b x)}{8 b}+\frac{3 x}{8}",1,"(3*x)/8 - (3*Cos[a + b*x]*Sin[a + b*x])/(8*b) - (Cos[a + b*x]*Sin[a + b*x]^3)/(4*b)","A",3,2,8,0.2500,1,"{2635, 8}"
5,1,42,0,0.0130112,"\int \sin ^5(a+b x) \, dx","Int[Sin[a + b*x]^5,x]","-\frac{\cos ^5(a+b x)}{5 b}+\frac{2 \cos ^3(a+b x)}{3 b}-\frac{\cos (a+b x)}{b}","-\frac{\cos ^5(a+b x)}{5 b}+\frac{2 \cos ^3(a+b x)}{3 b}-\frac{\cos (a+b x)}{b}",1,"-(Cos[a + b*x]/b) + (2*Cos[a + b*x]^3)/(3*b) - Cos[a + b*x]^5/(5*b)","A",2,1,8,0.1250,1,"{2633}"
6,1,67,0,0.0327676,"\int \sin ^6(a+b x) \, dx","Int[Sin[a + b*x]^6,x]","-\frac{\sin ^5(a+b x) \cos (a+b x)}{6 b}-\frac{5 \sin ^3(a+b x) \cos (a+b x)}{24 b}-\frac{5 \sin (a+b x) \cos (a+b x)}{16 b}+\frac{5 x}{16}","-\frac{\sin ^5(a+b x) \cos (a+b x)}{6 b}-\frac{5 \sin ^3(a+b x) \cos (a+b x)}{24 b}-\frac{5 \sin (a+b x) \cos (a+b x)}{16 b}+\frac{5 x}{16}",1,"(5*x)/16 - (5*Cos[a + b*x]*Sin[a + b*x])/(16*b) - (5*Cos[a + b*x]*Sin[a + b*x]^3)/(24*b) - (Cos[a + b*x]*Sin[a + b*x]^5)/(6*b)","A",4,2,8,0.2500,1,"{2635, 8}"
7,1,54,0,0.0157233,"\int \sin ^7(a+b x) \, dx","Int[Sin[a + b*x]^7,x]","\frac{\cos ^7(a+b x)}{7 b}-\frac{3 \cos ^5(a+b x)}{5 b}+\frac{\cos ^3(a+b x)}{b}-\frac{\cos (a+b x)}{b}","\frac{\cos ^7(a+b x)}{7 b}-\frac{3 \cos ^5(a+b x)}{5 b}+\frac{\cos ^3(a+b x)}{b}-\frac{\cos (a+b x)}{b}",1,"-(Cos[a + b*x]/b) + Cos[a + b*x]^3/b - (3*Cos[a + b*x]^5)/(5*b) + Cos[a + b*x]^7/(7*b)","A",2,1,8,0.1250,1,"{2633}"
8,1,88,0,0.0484121,"\int \sin ^8(a+b x) \, dx","Int[Sin[a + b*x]^8,x]","-\frac{\sin ^7(a+b x) \cos (a+b x)}{8 b}-\frac{7 \sin ^5(a+b x) \cos (a+b x)}{48 b}-\frac{35 \sin ^3(a+b x) \cos (a+b x)}{192 b}-\frac{35 \sin (a+b x) \cos (a+b x)}{128 b}+\frac{35 x}{128}","-\frac{\sin ^7(a+b x) \cos (a+b x)}{8 b}-\frac{7 \sin ^5(a+b x) \cos (a+b x)}{48 b}-\frac{35 \sin ^3(a+b x) \cos (a+b x)}{192 b}-\frac{35 \sin (a+b x) \cos (a+b x)}{128 b}+\frac{35 x}{128}",1,"(35*x)/128 - (35*Cos[a + b*x]*Sin[a + b*x])/(128*b) - (35*Cos[a + b*x]*Sin[a + b*x]^3)/(192*b) - (7*Cos[a + b*x]*Sin[a + b*x]^5)/(48*b) - (Cos[a + b*x]*Sin[a + b*x]^7)/(8*b)","A",5,2,8,0.2500,1,"{2635, 8}"
9,1,60,0,0.026722,"\int \sin ^{\frac{7}{2}}(b x) \, dx","Int[Sin[b*x]^(7/2),x]","-\frac{10 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{21 b}-\frac{2 \sin ^{\frac{5}{2}}(b x) \cos (b x)}{7 b}-\frac{10 \sqrt{\sin (b x)} \cos (b x)}{21 b}","-\frac{10 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{21 b}-\frac{2 \sin ^{\frac{5}{2}}(b x) \cos (b x)}{7 b}-\frac{10 \sqrt{\sin (b x)} \cos (b x)}{21 b}",1,"(-10*EllipticF[Pi/4 - (b*x)/2, 2])/(21*b) - (10*Cos[b*x]*Sqrt[Sin[b*x]])/(21*b) - (2*Cos[b*x]*Sin[b*x]^(5/2))/(7*b)","A",3,2,8,0.2500,1,"{2635, 2641}"
10,1,41,0,0.015399,"\int \sin ^{\frac{5}{2}}(b x) \, dx","Int[Sin[b*x]^(5/2),x]","-\frac{6 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{5 b}-\frac{2 \sin ^{\frac{3}{2}}(b x) \cos (b x)}{5 b}","-\frac{6 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{5 b}-\frac{2 \sin ^{\frac{3}{2}}(b x) \cos (b x)}{5 b}",1,"(-6*EllipticE[Pi/4 - (b*x)/2, 2])/(5*b) - (2*Cos[b*x]*Sin[b*x]^(3/2))/(5*b)","A",2,2,8,0.2500,1,"{2635, 2639}"
11,1,41,0,0.0154634,"\int \sin ^{\frac{3}{2}}(b x) \, dx","Int[Sin[b*x]^(3/2),x]","-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{3 b}-\frac{2 \sqrt{\sin (b x)} \cos (b x)}{3 b}","-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{3 b}-\frac{2 \sqrt{\sin (b x)} \cos (b x)}{3 b}",1,"(-2*EllipticF[Pi/4 - (b*x)/2, 2])/(3*b) - (2*Cos[b*x]*Sqrt[Sin[b*x]])/(3*b)","A",2,2,8,0.2500,1,"{2635, 2641}"
12,1,19,0,0.0076162,"\int \sqrt{\sin (b x)} \, dx","Int[Sqrt[Sin[b*x]],x]","-\frac{2 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{b}","-\frac{2 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{b}",1,"(-2*EllipticE[Pi/4 - (b*x)/2, 2])/b","A",1,1,8,0.1250,1,"{2639}"
13,1,19,0,0.008046,"\int \frac{1}{\sqrt{\sin (b x)}} \, dx","Int[1/Sqrt[Sin[b*x]],x]","-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{b}","-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{b}",1,"(-2*EllipticF[Pi/4 - (b*x)/2, 2])/b","A",1,1,8,0.1250,1,"{2641}"
14,1,37,0,0.0131666,"\int \frac{1}{\sin ^{\frac{3}{2}}(b x)} \, dx","Int[Sin[b*x]^(-3/2),x]","\frac{2 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{b}-\frac{2 \cos (b x)}{b \sqrt{\sin (b x)}}","\frac{2 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{b}-\frac{2 \cos (b x)}{b \sqrt{\sin (b x)}}",1,"(2*EllipticE[Pi/4 - (b*x)/2, 2])/b - (2*Cos[b*x])/(b*Sqrt[Sin[b*x]])","A",2,2,8,0.2500,1,"{2636, 2639}"
15,1,41,0,0.0149834,"\int \frac{1}{\sin ^{\frac{5}{2}}(b x)} \, dx","Int[Sin[b*x]^(-5/2),x]","-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{3 b}-\frac{2 \cos (b x)}{3 b \sin ^{\frac{3}{2}}(b x)}","-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{3 b}-\frac{2 \cos (b x)}{3 b \sin ^{\frac{3}{2}}(b x)}",1,"(-2*EllipticF[Pi/4 - (b*x)/2, 2])/(3*b) - (2*Cos[b*x])/(3*b*Sin[b*x]^(3/2))","A",2,2,8,0.2500,1,"{2636, 2641}"
16,1,60,0,0.0243357,"\int \frac{1}{\sin ^{\frac{7}{2}}(b x)} \, dx","Int[Sin[b*x]^(-7/2),x]","\frac{6 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{5 b}-\frac{2 \cos (b x)}{5 b \sin ^{\frac{5}{2}}(b x)}-\frac{6 \cos (b x)}{5 b \sqrt{\sin (b x)}}","\frac{6 E\left(\left.\frac{\pi }{4}-\frac{b x}{2}\right|2\right)}{5 b}-\frac{2 \cos (b x)}{5 b \sin ^{\frac{5}{2}}(b x)}-\frac{6 \cos (b x)}{5 b \sqrt{\sin (b x)}}",1,"(6*EllipticE[Pi/4 - (b*x)/2, 2])/(5*b) - (2*Cos[b*x])/(5*b*Sin[b*x]^(5/2)) - (6*Cos[b*x])/(5*b*Sqrt[Sin[b*x]])","A",3,2,8,0.2500,1,"{2636, 2639}"
17,1,70,0,0.0287382,"\int \sin ^{\frac{7}{2}}(a+b x) \, dx","Int[Sin[a + b*x]^(7/2),x]","\frac{10 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{21 b}-\frac{2 \sin ^{\frac{5}{2}}(a+b x) \cos (a+b x)}{7 b}-\frac{10 \sqrt{\sin (a+b x)} \cos (a+b x)}{21 b}","\frac{10 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{21 b}-\frac{2 \sin ^{\frac{5}{2}}(a+b x) \cos (a+b x)}{7 b}-\frac{10 \sqrt{\sin (a+b x)} \cos (a+b x)}{21 b}",1,"(10*EllipticF[(a - Pi/2 + b*x)/2, 2])/(21*b) - (10*Cos[a + b*x]*Sqrt[Sin[a + b*x]])/(21*b) - (2*Cos[a + b*x]*Sin[a + b*x]^(5/2))/(7*b)","A",3,2,10,0.2000,1,"{2635, 2641}"
18,1,47,0,0.0169634,"\int \sin ^{\frac{5}{2}}(a+b x) \, dx","Int[Sin[a + b*x]^(5/2),x]","\frac{6 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}-\frac{2 \sin ^{\frac{3}{2}}(a+b x) \cos (a+b x)}{5 b}","\frac{6 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}-\frac{2 \sin ^{\frac{3}{2}}(a+b x) \cos (a+b x)}{5 b}",1,"(6*EllipticE[(a - Pi/2 + b*x)/2, 2])/(5*b) - (2*Cos[a + b*x]*Sin[a + b*x]^(3/2))/(5*b)","A",2,2,10,0.2000,1,"{2635, 2639}"
19,1,47,0,0.0164747,"\int \sin ^{\frac{3}{2}}(a+b x) \, dx","Int[Sin[a + b*x]^(3/2),x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \sqrt{\sin (a+b x)} \cos (a+b x)}{3 b}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \sqrt{\sin (a+b x)} \cos (a+b x)}{3 b}",1,"(2*EllipticF[(a - Pi/2 + b*x)/2, 2])/(3*b) - (2*Cos[a + b*x]*Sqrt[Sin[a + b*x]])/(3*b)","A",2,2,10,0.2000,1,"{2635, 2641}"
20,1,21,0,0.0077866,"\int \sqrt{\sin (a+b x)} \, dx","Int[Sqrt[Sin[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}","\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(2*EllipticE[(a - Pi/2 + b*x)/2, 2])/b","A",1,1,10,0.1000,1,"{2639}"
21,1,21,0,0.0077145,"\int \frac{1}{\sqrt{\sin (a+b x)}} \, dx","Int[1/Sqrt[Sin[a + b*x]],x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(2*EllipticF[(a - Pi/2 + b*x)/2, 2])/b","A",1,1,10,0.1000,1,"{2641}"
22,1,43,0,0.0146858,"\int \frac{1}{\sin ^{\frac{3}{2}}(a+b x)} \, dx","Int[Sin[a + b*x]^(-3/2),x]","-\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}-\frac{2 \cos (a+b x)}{b \sqrt{\sin (a+b x)}}","-\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}-\frac{2 \cos (a+b x)}{b \sqrt{\sin (a+b x)}}",1,"(-2*EllipticE[(a - Pi/2 + b*x)/2, 2])/b - (2*Cos[a + b*x])/(b*Sqrt[Sin[a + b*x]])","A",2,2,10,0.2000,1,"{2636, 2639}"
23,1,47,0,0.0163912,"\int \frac{1}{\sin ^{\frac{5}{2}}(a+b x)} \, dx","Int[Sin[a + b*x]^(-5/2),x]","\frac{2 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \cos (a+b x)}{3 b \sin ^{\frac{3}{2}}(a+b x)}","\frac{2 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \cos (a+b x)}{3 b \sin ^{\frac{3}{2}}(a+b x)}",1,"(2*EllipticF[(a - Pi/2 + b*x)/2, 2])/(3*b) - (2*Cos[a + b*x])/(3*b*Sin[a + b*x]^(3/2))","A",2,2,10,0.2000,1,"{2636, 2641}"
24,1,70,0,0.0268507,"\int \frac{1}{\sin ^{\frac{7}{2}}(a+b x)} \, dx","Int[Sin[a + b*x]^(-7/2),x]","-\frac{6 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}-\frac{2 \cos (a+b x)}{5 b \sin ^{\frac{5}{2}}(a+b x)}-\frac{6 \cos (a+b x)}{5 b \sqrt{\sin (a+b x)}}","-\frac{6 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}-\frac{2 \cos (a+b x)}{5 b \sin ^{\frac{5}{2}}(a+b x)}-\frac{6 \cos (a+b x)}{5 b \sqrt{\sin (a+b x)}}",1,"(-6*EllipticE[(a - Pi/2 + b*x)/2, 2])/(5*b) - (2*Cos[a + b*x])/(5*b*Sin[a + b*x]^(5/2)) - (6*Cos[a + b*x])/(5*b*Sqrt[Sin[a + b*x]])","A",3,2,10,0.2000,1,"{2636, 2639}"
25,1,103,0,0.0523121,"\int (c \sin (a+b x))^{7/2} \, dx","Int[(c*Sin[a + b*x])^(7/2),x]","-\frac{10 c^3 \cos (a+b x) \sqrt{c \sin (a+b x)}}{21 b}+\frac{10 c^4 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{21 b \sqrt{c \sin (a+b x)}}-\frac{2 c \cos (a+b x) (c \sin (a+b x))^{5/2}}{7 b}","-\frac{10 c^3 \cos (a+b x) \sqrt{c \sin (a+b x)}}{21 b}+\frac{10 c^4 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{21 b \sqrt{c \sin (a+b x)}}-\frac{2 c \cos (a+b x) (c \sin (a+b x))^{5/2}}{7 b}",1,"(10*c^4*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(21*b*Sqrt[c*Sin[a + b*x]]) - (10*c^3*Cos[a + b*x]*Sqrt[c*Sin[a + b*x]])/(21*b) - (2*c*Cos[a + b*x]*(c*Sin[a + b*x])^(5/2))/(7*b)","A",4,3,12,0.2500,1,"{2635, 2642, 2641}"
26,1,75,0,0.0316081,"\int (c \sin (a+b x))^{5/2} \, dx","Int[(c*Sin[a + b*x])^(5/2),x]","\frac{6 c^2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{5 b \sqrt{\sin (a+b x)}}-\frac{2 c \cos (a+b x) (c \sin (a+b x))^{3/2}}{5 b}","\frac{6 c^2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{5 b \sqrt{\sin (a+b x)}}-\frac{2 c \cos (a+b x) (c \sin (a+b x))^{3/2}}{5 b}",1,"(6*c^2*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[c*Sin[a + b*x]])/(5*b*Sqrt[Sin[a + b*x]]) - (2*c*Cos[a + b*x]*(c*Sin[a + b*x])^(3/2))/(5*b)","A",3,3,12,0.2500,1,"{2635, 2640, 2639}"
27,1,75,0,0.0326279,"\int (c \sin (a+b x))^{3/2} \, dx","Int[(c*Sin[a + b*x])^(3/2),x]","\frac{2 c^2 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b \sqrt{c \sin (a+b x)}}-\frac{2 c \cos (a+b x) \sqrt{c \sin (a+b x)}}{3 b}","\frac{2 c^2 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b \sqrt{c \sin (a+b x)}}-\frac{2 c \cos (a+b x) \sqrt{c \sin (a+b x)}}{3 b}",1,"(2*c^2*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b*Sqrt[c*Sin[a + b*x]]) - (2*c*Cos[a + b*x]*Sqrt[c*Sin[a + b*x]])/(3*b)","A",3,3,12,0.2500,1,"{2635, 2642, 2641}"
28,1,43,0,0.0183664,"\int \sqrt{c \sin (a+b x)} \, dx","Int[Sqrt[c*Sin[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{b \sqrt{\sin (a+b x)}}","\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{b \sqrt{\sin (a+b x)}}",1,"(2*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[c*Sin[a + b*x]])/(b*Sqrt[Sin[a + b*x]])","A",2,2,12,0.1667,1,"{2640, 2639}"
29,1,43,0,0.0179524,"\int \frac{1}{\sqrt{c \sin (a+b x)}} \, dx","Int[1/Sqrt[c*Sin[a + b*x]],x]","\frac{2 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{c \sin (a+b x)}}","\frac{2 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{c \sin (a+b x)}}",1,"(2*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(b*Sqrt[c*Sin[a + b*x]])","A",2,2,12,0.1667,1,"{2642, 2641}"
30,1,73,0,0.0323439,"\int \frac{1}{(c \sin (a+b x))^{3/2}} \, dx","Int[(c*Sin[a + b*x])^(-3/2),x]","-\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{b c^2 \sqrt{\sin (a+b x)}}-\frac{2 \cos (a+b x)}{b c \sqrt{c \sin (a+b x)}}","-\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{b c^2 \sqrt{\sin (a+b x)}}-\frac{2 \cos (a+b x)}{b c \sqrt{c \sin (a+b x)}}",1,"(-2*Cos[a + b*x])/(b*c*Sqrt[c*Sin[a + b*x]]) - (2*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[c*Sin[a + b*x]])/(b*c^2*Sqrt[Sin[a + b*x]])","A",3,3,12,0.2500,1,"{2636, 2640, 2639}"
31,1,77,0,0.0325813,"\int \frac{1}{(c \sin (a+b x))^{5/2}} \, dx","Int[(c*Sin[a + b*x])^(-5/2),x]","\frac{2 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b c^2 \sqrt{c \sin (a+b x)}}-\frac{2 \cos (a+b x)}{3 b c (c \sin (a+b x))^{3/2}}","\frac{2 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b c^2 \sqrt{c \sin (a+b x)}}-\frac{2 \cos (a+b x)}{3 b c (c \sin (a+b x))^{3/2}}",1,"(-2*Cos[a + b*x])/(3*b*c*(c*Sin[a + b*x])^(3/2)) + (2*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b*c^2*Sqrt[c*Sin[a + b*x]])","A",3,3,12,0.2500,1,"{2636, 2642, 2641}"
32,1,105,0,0.0510645,"\int \frac{1}{(c \sin (a+b x))^{7/2}} \, dx","Int[(c*Sin[a + b*x])^(-7/2),x]","-\frac{6 \cos (a+b x)}{5 b c^3 \sqrt{c \sin (a+b x)}}-\frac{6 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{5 b c^4 \sqrt{\sin (a+b x)}}-\frac{2 \cos (a+b x)}{5 b c (c \sin (a+b x))^{5/2}}","-\frac{6 \cos (a+b x)}{5 b c^3 \sqrt{c \sin (a+b x)}}-\frac{6 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \sin (a+b x)}}{5 b c^4 \sqrt{\sin (a+b x)}}-\frac{2 \cos (a+b x)}{5 b c (c \sin (a+b x))^{5/2}}",1,"(-2*Cos[a + b*x])/(5*b*c*(c*Sin[a + b*x])^(5/2)) - (6*Cos[a + b*x])/(5*b*c^3*Sqrt[c*Sin[a + b*x]]) - (6*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[c*Sin[a + b*x]])/(5*b*c^4*Sqrt[Sin[a + b*x]])","A",4,3,12,0.2500,1,"{2636, 2640, 2639}"
33,1,58,0,0.0143208,"\int (c \sin (a+b x))^{4/3} \, dx","Int[(c*Sin[a + b*x])^(4/3),x]","\frac{3 \cos (a+b x) (c \sin (a+b x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sin ^2(a+b x)\right)}{7 b c \sqrt{\cos ^2(a+b x)}}","\frac{3 \cos (a+b x) (c \sin (a+b x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sin ^2(a+b x)\right)}{7 b c \sqrt{\cos ^2(a+b x)}}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(7/3))/(7*b*c*Sqrt[Cos[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
34,1,58,0,0.0138778,"\int (c \sin (a+b x))^{2/3} \, dx","Int[(c*Sin[a + b*x])^(2/3),x]","\frac{3 \cos (a+b x) (c \sin (a+b x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\sin ^2(a+b x)\right)}{5 b c \sqrt{\cos ^2(a+b x)}}","\frac{3 \cos (a+b x) (c \sin (a+b x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\sin ^2(a+b x)\right)}{5 b c \sqrt{\cos ^2(a+b x)}}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(5/3))/(5*b*c*Sqrt[Cos[a + b*x]^2])","A",1,1,12,0.08333,1,"{2643}"
35,1,58,0,0.0135465,"\int \sqrt[3]{c \sin (a+b x)} \, dx","Int[(c*Sin[a + b*x])^(1/3),x]","\frac{3 \cos (a+b x) (c \sin (a+b x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(a+b x)\right)}{4 b c \sqrt{\cos ^2(a+b x)}}","\frac{3 \left(1-i \sqrt{3}\right) \sqrt{3-i \sqrt{3}} \sqrt[3]{c} \sec (a+b x) \sqrt{1-\frac{(c \sin (a+b x))^{2/3}}{c^{2/3}}} \sqrt{\frac{2 (c \sin (a+b x))^{2/3}}{\left(3-i \sqrt{3}\right) c^{2/3}}+\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt{\frac{2 (c \sin (a+b x))^{2/3}}{\left(3+i \sqrt{3}\right) c^{2/3}}+\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{1-\frac{(c \sin (a+b x))^{2/3}}{c^{2/3}}}}{\sqrt{3-i \sqrt{3}}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{2 \sqrt{2} b}-\frac{3 \sqrt{\frac{3}{2} \left(3-i \sqrt{3}\right)} \sqrt[3]{c} \sec (a+b x) \sqrt{1-\frac{(c \sin (a+b x))^{2/3}}{c^{2/3}}} \sqrt{\frac{2 (c \sin (a+b x))^{2/3}}{\left(3-i \sqrt{3}\right) c^{2/3}}+\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt{\frac{2 (c \sin (a+b x))^{2/3}}{\left(3+i \sqrt{3}\right) c^{2/3}}+\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} E\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{1-\frac{(c \sin (a+b x))^{2/3}}{c^{2/3}}}}{\sqrt{3+i \sqrt{3}}}\right)|\frac{3 i-\sqrt{3}}{3 i+\sqrt{3}}\right)}{b}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(4/3))/(4*b*c*Sqrt[Cos[a + b*x]^2])","C",1,1,12,0.08333,1,"{2643}"
36,1,58,0,0.0165006,"\int \frac{1}{\sqrt[3]{c \sin (a+b x)}} \, dx","Int[(c*Sin[a + b*x])^(-1/3),x]","\frac{3 \cos (a+b x) (c \sin (a+b x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sin ^2(a+b x)\right)}{2 b c \sqrt{\cos ^2(a+b x)}}","-\frac{3 \sqrt{3-i \sqrt{3}} \sec (a+b x) \sqrt{1-\frac{(c \sin (a+b x))^{2/3}}{c^{2/3}}} \sqrt{\frac{2 (c \sin (a+b x))^{2/3}}{\left(3-i \sqrt{3}\right) c^{2/3}}+\frac{\sqrt{3}+i}{\sqrt{3}+3 i}} \sqrt{\frac{2 (c \sin (a+b x))^{2/3}}{\left(3+i \sqrt{3}\right) c^{2/3}}+\frac{-\sqrt{3}+i}{-\sqrt{3}+3 i}} F\left(\sin ^{-1}\left(\frac{\sqrt{2} \sqrt{1-\frac{(c \sin (a+b x))^{2/3}}{c^{2/3}}}}{\sqrt{3-i \sqrt{3}}}\right)|\frac{3 i+\sqrt{3}}{3 i-\sqrt{3}}\right)}{\sqrt{2} b \sqrt[3]{c}}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(2/3))/(2*b*c*Sqrt[Cos[a + b*x]^2])","C",1,1,12,0.08333,1,"{2643}"
37,1,56,0,0.0155328,"\int \frac{1}{(c \sin (a+b x))^{2/3}} \, dx","Int[(c*Sin[a + b*x])^(-2/3),x]","\frac{3 \cos (a+b x) \sqrt[3]{c \sin (a+b x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sin ^2(a+b x)\right)}{b c \sqrt{\cos ^2(a+b x)}}","\frac{3^{3/4} \sec (a+b x) \sqrt[3]{c \sin (a+b x)} \left(c^{2/3}-(c \sin (a+b x))^{2/3}\right) \sqrt{\frac{c^{4/3} \left(\frac{(c \sin (a+b x))^{4/3}}{c^{4/3}}+\frac{(c \sin (a+b x))^{2/3}}{c^{2/3}}+1\right)}{\left(c^{2/3}-\left(1+\sqrt{3}\right) (c \sin (a+b x))^{2/3}\right)^2}} F\left(\cos ^{-1}\left(\frac{c^{2/3}-\left(1-\sqrt{3}\right) (c \sin (a+b x))^{2/3}}{c^{2/3}-\left(1+\sqrt{3}\right) (c \sin (a+b x))^{2/3}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 b c^{5/3} \sqrt{-\frac{(c \sin (a+b x))^{2/3} \left(c^{2/3}-(c \sin (a+b x))^{2/3}\right)}{\left(c^{2/3}-\left(1+\sqrt{3}\right) (c \sin (a+b x))^{2/3}\right)^2}}}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1/3))/(b*c*Sqrt[Cos[a + b*x]^2])","C",1,1,12,0.08333,1,"{2643}"
38,1,56,0,0.0167059,"\int \frac{1}{(c \sin (a+b x))^{4/3}} \, dx","Int[(c*Sin[a + b*x])^(-4/3),x]","-\frac{3 \cos (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sin ^2(a+b x)\right)}{b c \sqrt{\cos ^2(a+b x)} \sqrt[3]{c \sin (a+b x)}}","-\frac{3 \cos (a+b x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sin ^2(a+b x)\right)}{b c \sqrt{\cos ^2(a+b x)} \sqrt[3]{c \sin (a+b x)}}",1,"(-3*Cos[a + b*x]*Hypergeometric2F1[-1/6, 1/2, 5/6, Sin[a + b*x]^2])/(b*c*Sqrt[Cos[a + b*x]^2]*(c*Sin[a + b*x])^(1/3))","A",1,1,12,0.08333,1,"{2643}"
39,1,63,0,0.0159425,"\int \sin ^n(a+b x) \, dx","Int[Sin[a + b*x]^n,x]","\frac{\cos (a+b x) \sin ^{n+1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b (n+1) \sqrt{\cos ^2(a+b x)}}","\frac{\cos (a+b x) \sin ^{n+1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b (n+1) \sqrt{\cos ^2(a+b x)}}",1,"(Cos[a + b*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[a + b*x]^2]*Sin[a + b*x]^(1 + n))/(b*(1 + n)*Sqrt[Cos[a + b*x]^2])","A",1,1,8,0.1250,1,"{2643}"
40,1,68,0,0.0179258,"\int (c \sin (a+b x))^n \, dx","Int[(c*Sin[a + b*x])^n,x]","\frac{\cos (a+b x) (c \sin (a+b x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b c (n+1) \sqrt{\cos ^2(a+b x)}}","\frac{\cos (a+b x) (c \sin (a+b x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(a+b x)\right)}{b c (n+1) \sqrt{\cos ^2(a+b x)}}",1,"(Cos[a + b*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + n))/(b*c*(1 + n)*Sqrt[Cos[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
41,1,81,0,0.0297226,"\int (a \sin (e+f x))^m (b \sin (e+f x))^n \, dx","Int[(a*Sin[e + f*x])^m*(b*Sin[e + f*x])^n,x]","\frac{\cos (e+f x) (a \sin (e+f x))^{m+1} (b \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\sin ^2(e+f x)\right)}{a f (m+n+1) \sqrt{\cos ^2(e+f x)}}","\frac{\cos (e+f x) (a \sin (e+f x))^{m+1} (b \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m+n+1);\frac{1}{2} (m+n+3);\sin ^2(e+f x)\right)}{a f (m+n+1) \sqrt{\cos ^2(e+f x)}}",1,"(Cos[e + f*x]*Hypergeometric2F1[1/2, (1 + m + n)/2, (3 + m + n)/2, Sin[e + f*x]^2]*(a*Sin[e + f*x])^(1 + m)*(b*Sin[e + f*x])^n)/(a*f*(1 + m + n)*Sqrt[Cos[e + f*x]^2])","A",2,2,21,0.09524,1,"{20, 2643}"
42,1,15,0,0.0193339,"\int \cos ^3(a+b x) \sin (a+b x) \, dx","Int[Cos[a + b*x]^3*Sin[a + b*x],x]","-\frac{\cos ^4(a+b x)}{4 b}","-\frac{\cos ^4(a+b x)}{4 b}",1,"-Cos[a + b*x]^4/(4*b)","A",2,2,15,0.1333,1,"{2565, 30}"
43,1,15,0,0.0206154,"\int \cos ^2(a+b x) \sin (a+b x) \, dx","Int[Cos[a + b*x]^2*Sin[a + b*x],x]","-\frac{\cos ^3(a+b x)}{3 b}","-\frac{\cos ^3(a+b x)}{3 b}",1,"-Cos[a + b*x]^3/(3*b)","A",2,2,15,0.1333,1,"{2565, 30}"
44,1,15,0,0.0108554,"\int \cos (a+b x) \sin (a+b x) \, dx","Int[Cos[a + b*x]*Sin[a + b*x],x]","\frac{\sin ^2(a+b x)}{2 b}","\frac{\sin ^2(a+b x)}{2 b}",1,"Sin[a + b*x]^2/(2*b)","A",2,2,13,0.1538,1,"{2564, 30}"
45,1,12,0,0.0044883,"\int \tan (a+b x) \, dx","Int[Tan[a + b*x],x]","-\frac{\log (\cos (a+b x))}{b}","-\frac{\log (\cos (a+b x))}{b}",1,"-(Log[Cos[a + b*x]]/b)","A",1,1,6,0.1667,1,"{3475}"
46,1,10,0,0.0107023,"\int \sec (a+b x) \tan (a+b x) \, dx","Int[Sec[a + b*x]*Tan[a + b*x],x]","\frac{\sec (a+b x)}{b}","\frac{\sec (a+b x)}{b}",1,"Sec[a + b*x]/b","A",2,2,13,0.1538,1,"{2606, 8}"
47,1,15,0,0.0194794,"\int \sec ^2(a+b x) \tan (a+b x) \, dx","Int[Sec[a + b*x]^2*Tan[a + b*x],x]","\frac{\sec ^2(a+b x)}{2 b}","\frac{\sec ^2(a+b x)}{2 b}",1,"Sec[a + b*x]^2/(2*b)","A",2,2,15,0.1333,1,"{2606, 30}"
48,1,15,0,0.018593,"\int \sec ^3(a+b x) \tan (a+b x) \, dx","Int[Sec[a + b*x]^3*Tan[a + b*x],x]","\frac{\sec ^3(a+b x)}{3 b}","\frac{\sec ^3(a+b x)}{3 b}",1,"Sec[a + b*x]^3/(3*b)","A",2,2,15,0.1333,1,"{2606, 30}"
49,1,61,0,0.0430188,"\int \cos ^7(a+b x) \sin ^2(a+b x) \, dx","Int[Cos[a + b*x]^7*Sin[a + b*x]^2,x]","-\frac{\sin ^9(a+b x)}{9 b}+\frac{3 \sin ^7(a+b x)}{7 b}-\frac{3 \sin ^5(a+b x)}{5 b}+\frac{\sin ^3(a+b x)}{3 b}","-\frac{\sin ^9(a+b x)}{9 b}+\frac{3 \sin ^7(a+b x)}{7 b}-\frac{3 \sin ^5(a+b x)}{5 b}+\frac{\sin ^3(a+b x)}{3 b}",1,"Sin[a + b*x]^3/(3*b) - (3*Sin[a + b*x]^5)/(5*b) + (3*Sin[a + b*x]^7)/(7*b) - Sin[a + b*x]^9/(9*b)","A",3,2,17,0.1176,1,"{2564, 270}"
50,1,46,0,0.0382698,"\int \cos ^5(a+b x) \sin ^2(a+b x) \, dx","Int[Cos[a + b*x]^5*Sin[a + b*x]^2,x]","\frac{\sin ^7(a+b x)}{7 b}-\frac{2 \sin ^5(a+b x)}{5 b}+\frac{\sin ^3(a+b x)}{3 b}","\frac{\sin ^7(a+b x)}{7 b}-\frac{2 \sin ^5(a+b x)}{5 b}+\frac{\sin ^3(a+b x)}{3 b}",1,"Sin[a + b*x]^3/(3*b) - (2*Sin[a + b*x]^5)/(5*b) + Sin[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2564, 270}"
51,1,31,0,0.0348122,"\int \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[Cos[a + b*x]^3*Sin[a + b*x]^2,x]","\frac{\sin ^3(a+b x)}{3 b}-\frac{\sin ^5(a+b x)}{5 b}","\frac{\sin ^3(a+b x)}{3 b}-\frac{\sin ^5(a+b x)}{5 b}",1,"Sin[a + b*x]^3/(3*b) - Sin[a + b*x]^5/(5*b)","A",3,2,17,0.1176,1,"{2564, 14}"
52,1,15,0,0.0183016,"\int \cos (a+b x) \sin ^2(a+b x) \, dx","Int[Cos[a + b*x]*Sin[a + b*x]^2,x]","\frac{\sin ^3(a+b x)}{3 b}","\frac{\sin ^3(a+b x)}{3 b}",1,"Sin[a + b*x]^3/(3*b)","A",2,2,15,0.1333,1,"{2564, 30}"
53,1,14,0,0.0081899,"\int \tan ^2(a+b x) \, dx","Int[Tan[a + b*x]^2,x]","\frac{\tan (a+b x)}{b}-x","\frac{\tan (a+b x)}{b}-x",1,"-x + Tan[a + b*x]/b","A",2,2,8,0.2500,1,"{3473, 8}"
54,1,15,0,0.0295692,"\int \sec ^2(a+b x) \tan ^2(a+b x) \, dx","Int[Sec[a + b*x]^2*Tan[a + b*x]^2,x]","\frac{\tan ^3(a+b x)}{3 b}","\frac{\tan ^3(a+b x)}{3 b}",1,"Tan[a + b*x]^3/(3*b)","A",2,2,17,0.1176,1,"{2607, 30}"
55,1,31,0,0.0340102,"\int \sec ^4(a+b x) \tan ^2(a+b x) \, dx","Int[Sec[a + b*x]^4*Tan[a + b*x]^2,x]","\frac{\tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{3 b}","\frac{\tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{3 b}",1,"Tan[a + b*x]^3/(3*b) + Tan[a + b*x]^5/(5*b)","A",3,2,17,0.1176,1,"{2607, 14}"
56,1,46,0,0.038507,"\int \sec ^6(a+b x) \tan ^2(a+b x) \, dx","Int[Sec[a + b*x]^6*Tan[a + b*x]^2,x]","\frac{\tan ^7(a+b x)}{7 b}+\frac{2 \tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{3 b}","\frac{\tan ^7(a+b x)}{7 b}+\frac{2 \tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{3 b}",1,"Tan[a + b*x]^3/(3*b) + (2*Tan[a + b*x]^5)/(5*b) + Tan[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2607, 270}"
57,1,61,0,0.039758,"\int \sec ^8(a+b x) \tan ^2(a+b x) \, dx","Int[Sec[a + b*x]^8*Tan[a + b*x]^2,x]","\frac{\tan ^9(a+b x)}{9 b}+\frac{3 \tan ^7(a+b x)}{7 b}+\frac{3 \tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{3 b}","\frac{\tan ^9(a+b x)}{9 b}+\frac{3 \tan ^7(a+b x)}{7 b}+\frac{3 \tan ^5(a+b x)}{5 b}+\frac{\tan ^3(a+b x)}{3 b}",1,"Tan[a + b*x]^3/(3*b) + (3*Tan[a + b*x]^5)/(5*b) + (3*Tan[a + b*x]^7)/(7*b) + Tan[a + b*x]^9/(9*b)","A",3,2,17,0.1176,1,"{2607, 270}"
58,1,88,0,0.0658742,"\int \cos ^6(a+b x) \sin ^2(a+b x) \, dx","Int[Cos[a + b*x]^6*Sin[a + b*x]^2,x]","-\frac{\sin (a+b x) \cos ^7(a+b x)}{8 b}+\frac{\sin (a+b x) \cos ^5(a+b x)}{48 b}+\frac{5 \sin (a+b x) \cos ^3(a+b x)}{192 b}+\frac{5 \sin (a+b x) \cos (a+b x)}{128 b}+\frac{5 x}{128}","-\frac{\sin (a+b x) \cos ^7(a+b x)}{8 b}+\frac{\sin (a+b x) \cos ^5(a+b x)}{48 b}+\frac{5 \sin (a+b x) \cos ^3(a+b x)}{192 b}+\frac{5 \sin (a+b x) \cos (a+b x)}{128 b}+\frac{5 x}{128}",1,"(5*x)/128 + (5*Cos[a + b*x]*Sin[a + b*x])/(128*b) + (5*Cos[a + b*x]^3*Sin[a + b*x])/(192*b) + (Cos[a + b*x]^5*Sin[a + b*x])/(48*b) - (Cos[a + b*x]^7*Sin[a + b*x])/(8*b)","A",5,3,17,0.1765,1,"{2568, 2635, 8}"
59,1,67,0,0.051307,"\int \cos ^4(a+b x) \sin ^2(a+b x) \, dx","Int[Cos[a + b*x]^4*Sin[a + b*x]^2,x]","-\frac{\sin (a+b x) \cos ^5(a+b x)}{6 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{24 b}+\frac{\sin (a+b x) \cos (a+b x)}{16 b}+\frac{x}{16}","-\frac{\sin (a+b x) \cos ^5(a+b x)}{6 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{24 b}+\frac{\sin (a+b x) \cos (a+b x)}{16 b}+\frac{x}{16}",1,"x/16 + (Cos[a + b*x]*Sin[a + b*x])/(16*b) + (Cos[a + b*x]^3*Sin[a + b*x])/(24*b) - (Cos[a + b*x]^5*Sin[a + b*x])/(6*b)","A",4,3,17,0.1765,1,"{2568, 2635, 8}"
60,1,46,0,0.0396221,"\int \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[Cos[a + b*x]^2*Sin[a + b*x]^2,x]","-\frac{\sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{\sin (a+b x) \cos (a+b x)}{8 b}+\frac{x}{8}","-\frac{\sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{\sin (a+b x) \cos (a+b x)}{8 b}+\frac{x}{8}",1,"x/8 + (Cos[a + b*x]*Sin[a + b*x])/(8*b) - (Cos[a + b*x]^3*Sin[a + b*x])/(4*b)","A",3,3,17,0.1765,1,"{2568, 2635, 8}"
61,1,25,0,0.0092417,"\int \sin ^2(a+b x) \, dx","Int[Sin[a + b*x]^2,x]","\frac{x}{2}-\frac{\sin (a+b x) \cos (a+b x)}{2 b}","\frac{x}{2}-\frac{\sin (a+b x) \cos (a+b x)}{2 b}",1,"x/2 - (Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",2,2,8,0.2500,1,"{2635, 8}"
62,1,23,0,0.0147116,"\int \sin (a+b x) \tan (a+b x) \, dx","Int[Sin[a + b*x]*Tan[a + b*x],x]","\frac{\tanh ^{-1}(\sin (a+b x))}{b}-\frac{\sin (a+b x)}{b}","\frac{\tanh ^{-1}(\sin (a+b x))}{b}-\frac{\sin (a+b x)}{b}",1,"ArcTanh[Sin[a + b*x]]/b - Sin[a + b*x]/b","A",3,3,13,0.2308,1,"{2592, 321, 206}"
63,1,34,0,0.0230989,"\int \sec (a+b x) \tan ^2(a+b x) \, dx","Int[Sec[a + b*x]*Tan[a + b*x]^2,x]","\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}-\frac{\tanh ^{-1}(\sin (a+b x))}{2 b}",1,"-ArcTanh[Sin[a + b*x]]/(2*b) + (Sec[a + b*x]*Tan[a + b*x])/(2*b)","A",2,2,15,0.1333,1,"{2611, 3770}"
64,1,55,0,0.0448754,"\int \sec ^3(a+b x) \tan ^2(a+b x) \, dx","Int[Sec[a + b*x]^3*Tan[a + b*x]^2,x]","-\frac{\tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\tan (a+b x) \sec ^3(a+b x)}{4 b}-\frac{\tan (a+b x) \sec (a+b x)}{8 b}","-\frac{\tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\tan (a+b x) \sec ^3(a+b x)}{4 b}-\frac{\tan (a+b x) \sec (a+b x)}{8 b}",1,"-ArcTanh[Sin[a + b*x]]/(8*b) - (Sec[a + b*x]*Tan[a + b*x])/(8*b) + (Sec[a + b*x]^3*Tan[a + b*x])/(4*b)","A",3,3,17,0.1765,1,"{2611, 3768, 3770}"
65,1,76,0,0.0594764,"\int \sec ^5(a+b x) \tan ^2(a+b x) \, dx","Int[Sec[a + b*x]^5*Tan[a + b*x]^2,x]","-\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan (a+b x) \sec ^5(a+b x)}{6 b}-\frac{\tan (a+b x) \sec ^3(a+b x)}{24 b}-\frac{\tan (a+b x) \sec (a+b x)}{16 b}","-\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan (a+b x) \sec ^5(a+b x)}{6 b}-\frac{\tan (a+b x) \sec ^3(a+b x)}{24 b}-\frac{\tan (a+b x) \sec (a+b x)}{16 b}",1,"-ArcTanh[Sin[a + b*x]]/(16*b) - (Sec[a + b*x]*Tan[a + b*x])/(16*b) - (Sec[a + b*x]^3*Tan[a + b*x])/(24*b) + (Sec[a + b*x]^5*Tan[a + b*x])/(6*b)","A",4,3,17,0.1765,1,"{2611, 3768, 3770}"
66,1,31,0,0.0334502,"\int \cos ^5(a+b x) \sin ^3(a+b x) \, dx","Int[Cos[a + b*x]^5*Sin[a + b*x]^3,x]","\frac{\cos ^8(a+b x)}{8 b}-\frac{\cos ^6(a+b x)}{6 b}","\frac{\cos ^8(a+b x)}{8 b}-\frac{\cos ^6(a+b x)}{6 b}",1,"-Cos[a + b*x]^6/(6*b) + Cos[a + b*x]^8/(8*b)","A",3,2,17,0.1176,1,"{2565, 14}"
67,1,31,0,0.034393,"\int \cos ^4(a+b x) \sin ^3(a+b x) \, dx","Int[Cos[a + b*x]^4*Sin[a + b*x]^3,x]","\frac{\cos ^7(a+b x)}{7 b}-\frac{\cos ^5(a+b x)}{5 b}","\frac{\cos ^7(a+b x)}{7 b}-\frac{\cos ^5(a+b x)}{5 b}",1,"-Cos[a + b*x]^5/(5*b) + Cos[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2565, 14}"
68,1,31,0,0.0333805,"\int \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{\sin ^4(a+b x)}{4 b}-\frac{\sin ^6(a+b x)}{6 b}","\frac{\sin ^4(a+b x)}{4 b}-\frac{\sin ^6(a+b x)}{6 b}",1,"Sin[a + b*x]^4/(4*b) - Sin[a + b*x]^6/(6*b)","A",3,2,17,0.1176,1,"{2564, 14}"
69,1,31,0,0.0323095,"\int \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[Cos[a + b*x]^2*Sin[a + b*x]^3,x]","\frac{\cos ^5(a+b x)}{5 b}-\frac{\cos ^3(a+b x)}{3 b}","\frac{\cos ^5(a+b x)}{5 b}-\frac{\cos ^3(a+b x)}{3 b}",1,"-Cos[a + b*x]^3/(3*b) + Cos[a + b*x]^5/(5*b)","A",3,2,17,0.1176,1,"{2565, 14}"
70,1,15,0,0.0176114,"\int \cos (a+b x) \sin ^3(a+b x) \, dx","Int[Cos[a + b*x]*Sin[a + b*x]^3,x]","\frac{\sin ^4(a+b x)}{4 b}","\frac{\sin ^4(a+b x)}{4 b}",1,"Sin[a + b*x]^4/(4*b)","A",2,2,15,0.1333,1,"{2564, 30}"
71,1,28,0,0.0206091,"\int \sin ^2(a+b x) \tan (a+b x) \, dx","Int[Sin[a + b*x]^2*Tan[a + b*x],x]","\frac{\cos ^2(a+b x)}{2 b}-\frac{\log (\cos (a+b x))}{b}","\frac{\cos ^2(a+b x)}{2 b}-\frac{\log (\cos (a+b x))}{b}",1,"Cos[a + b*x]^2/(2*b) - Log[Cos[a + b*x]]/b","A",3,2,15,0.1333,1,"{2590, 14}"
72,1,21,0,0.0209529,"\int \sin (a+b x) \tan ^2(a+b x) \, dx","Int[Sin[a + b*x]*Tan[a + b*x]^2,x]","\frac{\cos (a+b x)}{b}+\frac{\sec (a+b x)}{b}","\frac{\cos (a+b x)}{b}+\frac{\sec (a+b x)}{b}",1,"Cos[a + b*x]/b + Sec[a + b*x]/b","A",3,2,15,0.1333,1,"{2590, 14}"
73,1,27,0,0.0111813,"\int \tan ^3(a+b x) \, dx","Int[Tan[a + b*x]^3,x]","\frac{\tan ^2(a+b x)}{2 b}+\frac{\log (\cos (a+b x))}{b}","\frac{\tan ^2(a+b x)}{2 b}+\frac{\log (\cos (a+b x))}{b}",1,"Log[Cos[a + b*x]]/b + Tan[a + b*x]^2/(2*b)","A",2,2,8,0.2500,1,"{3473, 3475}"
74,1,27,0,0.0200087,"\int \sec (a+b x) \tan ^3(a+b x) \, dx","Int[Sec[a + b*x]*Tan[a + b*x]^3,x]","\frac{\sec ^3(a+b x)}{3 b}-\frac{\sec (a+b x)}{b}","\frac{\sec ^3(a+b x)}{3 b}-\frac{\sec (a+b x)}{b}",1,"-(Sec[a + b*x]/b) + Sec[a + b*x]^3/(3*b)","A",2,1,15,0.06667,1,"{2606}"
75,1,15,0,0.0278485,"\int \sec ^2(a+b x) \tan ^3(a+b x) \, dx","Int[Sec[a + b*x]^2*Tan[a + b*x]^3,x]","\frac{\tan ^4(a+b x)}{4 b}","\frac{\tan ^4(a+b x)}{4 b}",1,"Tan[a + b*x]^4/(4*b)","A",2,2,17,0.1176,1,"{2607, 30}"
76,1,31,0,0.032495,"\int \sec ^3(a+b x) \tan ^3(a+b x) \, dx","Int[Sec[a + b*x]^3*Tan[a + b*x]^3,x]","\frac{\sec ^5(a+b x)}{5 b}-\frac{\sec ^3(a+b x)}{3 b}","\frac{\sec ^5(a+b x)}{5 b}-\frac{\sec ^3(a+b x)}{3 b}",1,"-Sec[a + b*x]^3/(3*b) + Sec[a + b*x]^5/(5*b)","A",3,2,17,0.1176,1,"{2606, 14}"
77,1,31,0,0.0325137,"\int \sec ^4(a+b x) \tan ^3(a+b x) \, dx","Int[Sec[a + b*x]^4*Tan[a + b*x]^3,x]","\frac{\sec ^6(a+b x)}{6 b}-\frac{\sec ^4(a+b x)}{4 b}","\frac{\sec ^6(a+b x)}{6 b}-\frac{\sec ^4(a+b x)}{4 b}",1,"-Sec[a + b*x]^4/(4*b) + Sec[a + b*x]^6/(6*b)","A",3,2,17,0.1176,1,"{2606, 14}"
78,1,31,0,0.0321572,"\int \sec ^5(a+b x) \tan ^3(a+b x) \, dx","Int[Sec[a + b*x]^5*Tan[a + b*x]^3,x]","\frac{\sec ^7(a+b x)}{7 b}-\frac{\sec ^5(a+b x)}{5 b}","\frac{\sec ^7(a+b x)}{7 b}-\frac{\sec ^5(a+b x)}{5 b}",1,"-Sec[a + b*x]^5/(5*b) + Sec[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2606, 14}"
79,1,31,0,0.0321571,"\int \sec ^6(a+b x) \tan ^3(a+b x) \, dx","Int[Sec[a + b*x]^6*Tan[a + b*x]^3,x]","\frac{\sec ^8(a+b x)}{8 b}-\frac{\sec ^6(a+b x)}{6 b}","\frac{\sec ^8(a+b x)}{8 b}-\frac{\sec ^6(a+b x)}{6 b}",1,"-Sec[a + b*x]^6/(6*b) + Sec[a + b*x]^8/(8*b)","A",3,2,17,0.1176,1,"{2606, 14}"
80,1,61,0,0.039662,"\int \cos ^7(a+b x) \sin ^4(a+b x) \, dx","Int[Cos[a + b*x]^7*Sin[a + b*x]^4,x]","-\frac{\sin ^{11}(a+b x)}{11 b}+\frac{\sin ^9(a+b x)}{3 b}-\frac{3 \sin ^7(a+b x)}{7 b}+\frac{\sin ^5(a+b x)}{5 b}","-\frac{\sin ^{11}(a+b x)}{11 b}+\frac{\sin ^9(a+b x)}{3 b}-\frac{3 \sin ^7(a+b x)}{7 b}+\frac{\sin ^5(a+b x)}{5 b}",1,"Sin[a + b*x]^5/(5*b) - (3*Sin[a + b*x]^7)/(7*b) + Sin[a + b*x]^9/(3*b) - Sin[a + b*x]^11/(11*b)","A",3,2,17,0.1176,1,"{2564, 270}"
81,1,46,0,0.0356168,"\int \cos ^5(a+b x) \sin ^4(a+b x) \, dx","Int[Cos[a + b*x]^5*Sin[a + b*x]^4,x]","\frac{\sin ^9(a+b x)}{9 b}-\frac{2 \sin ^7(a+b x)}{7 b}+\frac{\sin ^5(a+b x)}{5 b}","\frac{\sin ^9(a+b x)}{9 b}-\frac{2 \sin ^7(a+b x)}{7 b}+\frac{\sin ^5(a+b x)}{5 b}",1,"Sin[a + b*x]^5/(5*b) - (2*Sin[a + b*x]^7)/(7*b) + Sin[a + b*x]^9/(9*b)","A",3,2,17,0.1176,1,"{2564, 270}"
82,1,31,0,0.0324848,"\int \cos ^3(a+b x) \sin ^4(a+b x) \, dx","Int[Cos[a + b*x]^3*Sin[a + b*x]^4,x]","\frac{\sin ^5(a+b x)}{5 b}-\frac{\sin ^7(a+b x)}{7 b}","\frac{\sin ^5(a+b x)}{5 b}-\frac{\sin ^7(a+b x)}{7 b}",1,"Sin[a + b*x]^5/(5*b) - Sin[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2564, 14}"
83,1,15,0,0.0176357,"\int \cos (a+b x) \sin ^4(a+b x) \, dx","Int[Cos[a + b*x]*Sin[a + b*x]^4,x]","\frac{\sin ^5(a+b x)}{5 b}","\frac{\sin ^5(a+b x)}{5 b}",1,"Sin[a + b*x]^5/(5*b)","A",2,2,15,0.1333,1,"{2564, 30}"
84,1,40,0,0.0387557,"\int \sin ^2(a+b x) \tan ^2(a+b x) \, dx","Int[Sin[a + b*x]^2*Tan[a + b*x]^2,x]","\frac{3 \tan (a+b x)}{2 b}-\frac{\sin ^2(a+b x) \tan (a+b x)}{2 b}-\frac{3 x}{2}","\frac{3 \tan (a+b x)}{2 b}-\frac{\sin ^2(a+b x) \tan (a+b x)}{2 b}-\frac{3 x}{2}",1,"(-3*x)/2 + (3*Tan[a + b*x])/(2*b) - (Sin[a + b*x]^2*Tan[a + b*x])/(2*b)","A",4,4,17,0.2353,1,"{2591, 288, 321, 203}"
85,1,28,0,0.0160507,"\int \tan ^4(a+b x) \, dx","Int[Tan[a + b*x]^4,x]","\frac{\tan ^3(a+b x)}{3 b}-\frac{\tan (a+b x)}{b}+x","\frac{\tan ^3(a+b x)}{3 b}-\frac{\tan (a+b x)}{b}+x",1,"x - Tan[a + b*x]/b + Tan[a + b*x]^3/(3*b)","A",3,2,8,0.2500,1,"{3473, 8}"
86,1,15,0,0.0276559,"\int \sec ^2(a+b x) \tan ^4(a+b x) \, dx","Int[Sec[a + b*x]^2*Tan[a + b*x]^4,x]","\frac{\tan ^5(a+b x)}{5 b}","\frac{\tan ^5(a+b x)}{5 b}",1,"Tan[a + b*x]^5/(5*b)","A",2,2,17,0.1176,1,"{2607, 30}"
87,1,31,0,0.0320576,"\int \sec ^4(a+b x) \tan ^4(a+b x) \, dx","Int[Sec[a + b*x]^4*Tan[a + b*x]^4,x]","\frac{\tan ^7(a+b x)}{7 b}+\frac{\tan ^5(a+b x)}{5 b}","\frac{\tan ^7(a+b x)}{7 b}+\frac{\tan ^5(a+b x)}{5 b}",1,"Tan[a + b*x]^5/(5*b) + Tan[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2607, 14}"
88,1,46,0,0.0357062,"\int \sec ^6(a+b x) \tan ^4(a+b x) \, dx","Int[Sec[a + b*x]^6*Tan[a + b*x]^4,x]","\frac{\tan ^9(a+b x)}{9 b}+\frac{2 \tan ^7(a+b x)}{7 b}+\frac{\tan ^5(a+b x)}{5 b}","\frac{\tan ^9(a+b x)}{9 b}+\frac{2 \tan ^7(a+b x)}{7 b}+\frac{\tan ^5(a+b x)}{5 b}",1,"Tan[a + b*x]^5/(5*b) + (2*Tan[a + b*x]^7)/(7*b) + Tan[a + b*x]^9/(9*b)","A",3,2,17,0.1176,1,"{2607, 270}"
89,1,111,0,0.096975,"\int \cos ^6(a+b x) \sin ^4(a+b x) \, dx","Int[Cos[a + b*x]^6*Sin[a + b*x]^4,x]","-\frac{\sin ^3(a+b x) \cos ^7(a+b x)}{10 b}-\frac{3 \sin (a+b x) \cos ^7(a+b x)}{80 b}+\frac{\sin (a+b x) \cos ^5(a+b x)}{160 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{128 b}+\frac{3 \sin (a+b x) \cos (a+b x)}{256 b}+\frac{3 x}{256}","-\frac{\sin ^3(a+b x) \cos ^7(a+b x)}{10 b}-\frac{3 \sin (a+b x) \cos ^7(a+b x)}{80 b}+\frac{\sin (a+b x) \cos ^5(a+b x)}{160 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{128 b}+\frac{3 \sin (a+b x) \cos (a+b x)}{256 b}+\frac{3 x}{256}",1,"(3*x)/256 + (3*Cos[a + b*x]*Sin[a + b*x])/(256*b) + (Cos[a + b*x]^3*Sin[a + b*x])/(128*b) + (Cos[a + b*x]^5*Sin[a + b*x])/(160*b) - (3*Cos[a + b*x]^7*Sin[a + b*x])/(80*b) - (Cos[a + b*x]^7*Sin[a + b*x]^3)/(10*b)","A",6,3,17,0.1765,1,"{2568, 2635, 8}"
90,1,90,0,0.0832022,"\int \cos ^4(a+b x) \sin ^4(a+b x) \, dx","Int[Cos[a + b*x]^4*Sin[a + b*x]^4,x]","-\frac{\sin ^3(a+b x) \cos ^5(a+b x)}{8 b}-\frac{\sin (a+b x) \cos ^5(a+b x)}{16 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{64 b}+\frac{3 \sin (a+b x) \cos (a+b x)}{128 b}+\frac{3 x}{128}","-\frac{\sin ^3(a+b x) \cos ^5(a+b x)}{8 b}-\frac{\sin (a+b x) \cos ^5(a+b x)}{16 b}+\frac{\sin (a+b x) \cos ^3(a+b x)}{64 b}+\frac{3 \sin (a+b x) \cos (a+b x)}{128 b}+\frac{3 x}{128}",1,"(3*x)/128 + (3*Cos[a + b*x]*Sin[a + b*x])/(128*b) + (Cos[a + b*x]^3*Sin[a + b*x])/(64*b) - (Cos[a + b*x]^5*Sin[a + b*x])/(16*b) - (Cos[a + b*x]^5*Sin[a + b*x]^3)/(8*b)","A",5,3,17,0.1765,1,"{2568, 2635, 8}"
91,1,69,0,0.0683697,"\int \cos ^2(a+b x) \sin ^4(a+b x) \, dx","Int[Cos[a + b*x]^2*Sin[a + b*x]^4,x]","-\frac{\sin ^3(a+b x) \cos ^3(a+b x)}{6 b}-\frac{\sin (a+b x) \cos ^3(a+b x)}{8 b}+\frac{\sin (a+b x) \cos (a+b x)}{16 b}+\frac{x}{16}","-\frac{\sin ^3(a+b x) \cos ^3(a+b x)}{6 b}-\frac{\sin (a+b x) \cos ^3(a+b x)}{8 b}+\frac{\sin (a+b x) \cos (a+b x)}{16 b}+\frac{x}{16}",1,"x/16 + (Cos[a + b*x]*Sin[a + b*x])/(16*b) - (Cos[a + b*x]^3*Sin[a + b*x])/(8*b) - (Cos[a + b*x]^3*Sin[a + b*x]^3)/(6*b)","A",4,3,17,0.1765,1,"{2568, 2635, 8}"
92,1,46,0,0.0199329,"\int \sin ^4(a+b x) \, dx","Int[Sin[a + b*x]^4,x]","-\frac{\sin ^3(a+b x) \cos (a+b x)}{4 b}-\frac{3 \sin (a+b x) \cos (a+b x)}{8 b}+\frac{3 x}{8}","-\frac{\sin ^3(a+b x) \cos (a+b x)}{4 b}-\frac{3 \sin (a+b x) \cos (a+b x)}{8 b}+\frac{3 x}{8}",1,"(3*x)/8 - (3*Cos[a + b*x]*Sin[a + b*x])/(8*b) - (Cos[a + b*x]*Sin[a + b*x]^3)/(4*b)","A",3,2,8,0.2500,1,"{2635, 8}"
93,1,38,0,0.0266243,"\int \sin ^3(a+b x) \tan (a+b x) \, dx","Int[Sin[a + b*x]^3*Tan[a + b*x],x]","-\frac{\sin ^3(a+b x)}{3 b}-\frac{\sin (a+b x)}{b}+\frac{\tanh ^{-1}(\sin (a+b x))}{b}","-\frac{\sin ^3(a+b x)}{3 b}-\frac{\sin (a+b x)}{b}+\frac{\tanh ^{-1}(\sin (a+b x))}{b}",1,"ArcTanh[Sin[a + b*x]]/b - Sin[a + b*x]/b - Sin[a + b*x]^3/(3*b)","A",4,3,15,0.2000,1,"{2592, 302, 206}"
94,1,49,0,0.0292958,"\int \sin (a+b x) \tan ^3(a+b x) \, dx","Int[Sin[a + b*x]*Tan[a + b*x]^3,x]","\frac{3 \sin (a+b x)}{2 b}+\frac{\sin (a+b x) \tan ^2(a+b x)}{2 b}-\frac{3 \tanh ^{-1}(\sin (a+b x))}{2 b}","\frac{3 \sin (a+b x)}{2 b}+\frac{\sin (a+b x) \tan ^2(a+b x)}{2 b}-\frac{3 \tanh ^{-1}(\sin (a+b x))}{2 b}",1,"(-3*ArcTanh[Sin[a + b*x]])/(2*b) + (3*Sin[a + b*x])/(2*b) + (Sin[a + b*x]*Tan[a + b*x]^2)/(2*b)","A",4,4,15,0.2667,1,"{2592, 288, 321, 206}"
95,1,55,0,0.0423837,"\int \sec (a+b x) \tan ^4(a+b x) \, dx","Int[Sec[a + b*x]*Tan[a + b*x]^4,x]","\frac{3 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\tan ^3(a+b x) \sec (a+b x)}{4 b}-\frac{3 \tan (a+b x) \sec (a+b x)}{8 b}","\frac{3 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\tan ^3(a+b x) \sec (a+b x)}{4 b}-\frac{3 \tan (a+b x) \sec (a+b x)}{8 b}",1,"(3*ArcTanh[Sin[a + b*x]])/(8*b) - (3*Sec[a + b*x]*Tan[a + b*x])/(8*b) + (Sec[a + b*x]*Tan[a + b*x]^3)/(4*b)","A",3,2,15,0.1333,1,"{2611, 3770}"
96,1,78,0,0.074756,"\int \sec ^3(a+b x) \tan ^4(a+b x) \, dx","Int[Sec[a + b*x]^3*Tan[a + b*x]^4,x]","\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan ^3(a+b x) \sec ^3(a+b x)}{6 b}-\frac{\tan (a+b x) \sec ^3(a+b x)}{8 b}+\frac{\tan (a+b x) \sec (a+b x)}{16 b}","\frac{\tanh ^{-1}(\sin (a+b x))}{16 b}+\frac{\tan ^3(a+b x) \sec ^3(a+b x)}{6 b}-\frac{\tan (a+b x) \sec ^3(a+b x)}{8 b}+\frac{\tan (a+b x) \sec (a+b x)}{16 b}",1,"ArcTanh[Sin[a + b*x]]/(16*b) + (Sec[a + b*x]*Tan[a + b*x])/(16*b) - (Sec[a + b*x]^3*Tan[a + b*x])/(8*b) + (Sec[a + b*x]^3*Tan[a + b*x]^3)/(6*b)","A",4,3,17,0.1765,1,"{2611, 3768, 3770}"
97,1,99,0,0.0893559,"\int \sec ^5(a+b x) \tan ^4(a+b x) \, dx","Int[Sec[a + b*x]^5*Tan[a + b*x]^4,x]","\frac{3 \tanh ^{-1}(\sin (a+b x))}{128 b}+\frac{\tan ^3(a+b x) \sec ^5(a+b x)}{8 b}-\frac{\tan (a+b x) \sec ^5(a+b x)}{16 b}+\frac{\tan (a+b x) \sec ^3(a+b x)}{64 b}+\frac{3 \tan (a+b x) \sec (a+b x)}{128 b}","\frac{3 \tanh ^{-1}(\sin (a+b x))}{128 b}+\frac{\tan ^3(a+b x) \sec ^5(a+b x)}{8 b}-\frac{\tan (a+b x) \sec ^5(a+b x)}{16 b}+\frac{\tan (a+b x) \sec ^3(a+b x)}{64 b}+\frac{3 \tan (a+b x) \sec (a+b x)}{128 b}",1,"(3*ArcTanh[Sin[a + b*x]])/(128*b) + (3*Sec[a + b*x]*Tan[a + b*x])/(128*b) + (Sec[a + b*x]^3*Tan[a + b*x])/(64*b) - (Sec[a + b*x]^5*Tan[a + b*x])/(16*b) + (Sec[a + b*x]^5*Tan[a + b*x]^3)/(8*b)","A",5,3,17,0.1765,1,"{2611, 3768, 3770}"
98,1,46,0,0.0410329,"\int \cos ^7(a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]^7*Sin[a + b*x]^5,x]","-\frac{\cos ^{12}(a+b x)}{12 b}+\frac{\cos ^{10}(a+b x)}{5 b}-\frac{\cos ^8(a+b x)}{8 b}","-\frac{\cos ^{12}(a+b x)}{12 b}+\frac{\cos ^{10}(a+b x)}{5 b}-\frac{\cos ^8(a+b x)}{8 b}",1,"-Cos[a + b*x]^8/(8*b) + Cos[a + b*x]^10/(5*b) - Cos[a + b*x]^12/(12*b)","A",4,3,17,0.1765,1,"{2565, 266, 43}"
99,1,46,0,0.0356549,"\int \cos ^6(a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]^6*Sin[a + b*x]^5,x]","-\frac{\cos ^{11}(a+b x)}{11 b}+\frac{2 \cos ^9(a+b x)}{9 b}-\frac{\cos ^7(a+b x)}{7 b}","-\frac{\cos ^{11}(a+b x)}{11 b}+\frac{2 \cos ^9(a+b x)}{9 b}-\frac{\cos ^7(a+b x)}{7 b}",1,"-Cos[a + b*x]^7/(7*b) + (2*Cos[a + b*x]^9)/(9*b) - Cos[a + b*x]^11/(11*b)","A",3,2,17,0.1176,1,"{2565, 270}"
100,1,46,0,0.0402625,"\int \cos ^5(a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]^5*Sin[a + b*x]^5,x]","\frac{\sin ^{10}(a+b x)}{10 b}-\frac{\sin ^8(a+b x)}{4 b}+\frac{\sin ^6(a+b x)}{6 b}","\frac{\sin ^{10}(a+b x)}{10 b}-\frac{\sin ^8(a+b x)}{4 b}+\frac{\sin ^6(a+b x)}{6 b}",1,"Sin[a + b*x]^6/(6*b) - Sin[a + b*x]^8/(4*b) + Sin[a + b*x]^10/(10*b)","A",4,3,17,0.1765,1,"{2564, 266, 43}"
101,1,46,0,0.0364733,"\int \cos ^4(a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]^4*Sin[a + b*x]^5,x]","-\frac{\cos ^9(a+b x)}{9 b}+\frac{2 \cos ^7(a+b x)}{7 b}-\frac{\cos ^5(a+b x)}{5 b}","-\frac{\cos ^9(a+b x)}{9 b}+\frac{2 \cos ^7(a+b x)}{7 b}-\frac{\cos ^5(a+b x)}{5 b}",1,"-Cos[a + b*x]^5/(5*b) + (2*Cos[a + b*x]^7)/(7*b) - Cos[a + b*x]^9/(9*b)","A",3,2,17,0.1176,1,"{2565, 270}"
102,1,31,0,0.0323852,"\int \cos ^3(a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]^3*Sin[a + b*x]^5,x]","\frac{\sin ^6(a+b x)}{6 b}-\frac{\sin ^8(a+b x)}{8 b}","\frac{\sin ^6(a+b x)}{6 b}-\frac{\sin ^8(a+b x)}{8 b}",1,"Sin[a + b*x]^6/(6*b) - Sin[a + b*x]^8/(8*b)","A",3,2,17,0.1176,1,"{2564, 14}"
103,1,46,0,0.0354446,"\int \cos ^2(a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]^2*Sin[a + b*x]^5,x]","-\frac{\cos ^7(a+b x)}{7 b}+\frac{2 \cos ^5(a+b x)}{5 b}-\frac{\cos ^3(a+b x)}{3 b}","-\frac{\cos ^7(a+b x)}{7 b}+\frac{2 \cos ^5(a+b x)}{5 b}-\frac{\cos ^3(a+b x)}{3 b}",1,"-Cos[a + b*x]^3/(3*b) + (2*Cos[a + b*x]^5)/(5*b) - Cos[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2565, 270}"
104,1,15,0,0.0173331,"\int \cos (a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]*Sin[a + b*x]^5,x]","\frac{\sin ^6(a+b x)}{6 b}","\frac{\sin ^6(a+b x)}{6 b}",1,"Sin[a + b*x]^6/(6*b)","A",2,2,15,0.1333,1,"{2564, 30}"
105,1,40,0,0.0256355,"\int \sin ^4(a+b x) \tan (a+b x) \, dx","Int[Sin[a + b*x]^4*Tan[a + b*x],x]","-\frac{\cos ^4(a+b x)}{4 b}+\frac{\cos ^2(a+b x)}{b}-\frac{\log (\cos (a+b x))}{b}","-\frac{\cos ^4(a+b x)}{4 b}+\frac{\cos ^2(a+b x)}{b}-\frac{\log (\cos (a+b x))}{b}",1,"Cos[a + b*x]^2/b - Cos[a + b*x]^4/(4*b) - Log[Cos[a + b*x]]/b","A",4,3,15,0.2000,1,"{2590, 266, 43}"
106,1,37,0,0.0342953,"\int \sin ^3(a+b x) \tan ^2(a+b x) \, dx","Int[Sin[a + b*x]^3*Tan[a + b*x]^2,x]","-\frac{\cos ^3(a+b x)}{3 b}+\frac{2 \cos (a+b x)}{b}+\frac{\sec (a+b x)}{b}","-\frac{\cos ^3(a+b x)}{3 b}+\frac{2 \cos (a+b x)}{b}+\frac{\sec (a+b x)}{b}",1,"(2*Cos[a + b*x])/b - Cos[a + b*x]^3/(3*b) + Sec[a + b*x]/b","A",3,2,17,0.1176,1,"{2590, 270}"
107,1,43,0,0.0379609,"\int \sin ^2(a+b x) \tan ^3(a+b x) \, dx","Int[Sin[a + b*x]^2*Tan[a + b*x]^3,x]","-\frac{\cos ^2(a+b x)}{2 b}+\frac{\sec ^2(a+b x)}{2 b}+\frac{2 \log (\cos (a+b x))}{b}","-\frac{\cos ^2(a+b x)}{2 b}+\frac{\sec ^2(a+b x)}{2 b}+\frac{2 \log (\cos (a+b x))}{b}",1,"-Cos[a + b*x]^2/(2*b) + (2*Log[Cos[a + b*x]])/b + Sec[a + b*x]^2/(2*b)","A",4,3,17,0.1765,1,"{2590, 266, 43}"
108,1,38,0,0.0252488,"\int \sin (a+b x) \tan ^4(a+b x) \, dx","Int[Sin[a + b*x]*Tan[a + b*x]^4,x]","-\frac{\cos (a+b x)}{b}+\frac{\sec ^3(a+b x)}{3 b}-\frac{2 \sec (a+b x)}{b}","-\frac{\cos (a+b x)}{b}+\frac{\sec ^3(a+b x)}{3 b}-\frac{2 \sec (a+b x)}{b}",1,"-(Cos[a + b*x]/b) - (2*Sec[a + b*x])/b + Sec[a + b*x]^3/(3*b)","A",3,2,15,0.1333,1,"{2590, 270}"
109,1,43,0,0.0210946,"\int \tan ^5(a+b x) \, dx","Int[Tan[a + b*x]^5,x]","\frac{\tan ^4(a+b x)}{4 b}-\frac{\tan ^2(a+b x)}{2 b}-\frac{\log (\cos (a+b x))}{b}","\frac{\tan ^4(a+b x)}{4 b}-\frac{\tan ^2(a+b x)}{2 b}-\frac{\log (\cos (a+b x))}{b}",1,"-(Log[Cos[a + b*x]]/b) - Tan[a + b*x]^2/(2*b) + Tan[a + b*x]^4/(4*b)","A",3,2,8,0.2500,1,"{3473, 3475}"
110,1,41,0,0.023039,"\int \sec (a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]*Tan[a + b*x]^5,x]","\frac{\sec ^5(a+b x)}{5 b}-\frac{2 \sec ^3(a+b x)}{3 b}+\frac{\sec (a+b x)}{b}","\frac{\sec ^5(a+b x)}{5 b}-\frac{2 \sec ^3(a+b x)}{3 b}+\frac{\sec (a+b x)}{b}",1,"Sec[a + b*x]/b - (2*Sec[a + b*x]^3)/(3*b) + Sec[a + b*x]^5/(5*b)","A",3,2,15,0.1333,1,"{2606, 194}"
111,1,15,0,0.026738,"\int \sec ^2(a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]^2*Tan[a + b*x]^5,x]","\frac{\tan ^6(a+b x)}{6 b}","\frac{\tan ^6(a+b x)}{6 b}",1,"Tan[a + b*x]^6/(6*b)","A",2,2,17,0.1176,1,"{2607, 30}"
112,1,46,0,0.0358386,"\int \sec ^3(a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]^3*Tan[a + b*x]^5,x]","\frac{\sec ^7(a+b x)}{7 b}-\frac{2 \sec ^5(a+b x)}{5 b}+\frac{\sec ^3(a+b x)}{3 b}","\frac{\sec ^7(a+b x)}{7 b}-\frac{2 \sec ^5(a+b x)}{5 b}+\frac{\sec ^3(a+b x)}{3 b}",1,"Sec[a + b*x]^3/(3*b) - (2*Sec[a + b*x]^5)/(5*b) + Sec[a + b*x]^7/(7*b)","A",3,2,17,0.1176,1,"{2606, 270}"
113,1,31,0,0.0311392,"\int \sec ^4(a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]^4*Tan[a + b*x]^5,x]","\frac{\tan ^8(a+b x)}{8 b}+\frac{\tan ^6(a+b x)}{6 b}","\frac{\tan ^8(a+b x)}{8 b}+\frac{\tan ^6(a+b x)}{6 b}",1,"Tan[a + b*x]^6/(6*b) + Tan[a + b*x]^8/(8*b)","A",3,2,17,0.1176,1,"{2607, 14}"
114,1,46,0,0.0350931,"\int \sec ^5(a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]^5*Tan[a + b*x]^5,x]","\frac{\sec ^9(a+b x)}{9 b}-\frac{2 \sec ^7(a+b x)}{7 b}+\frac{\sec ^5(a+b x)}{5 b}","\frac{\sec ^9(a+b x)}{9 b}-\frac{2 \sec ^7(a+b x)}{7 b}+\frac{\sec ^5(a+b x)}{5 b}",1,"Sec[a + b*x]^5/(5*b) - (2*Sec[a + b*x]^7)/(7*b) + Sec[a + b*x]^9/(9*b)","A",3,2,17,0.1176,1,"{2606, 270}"
115,1,46,0,0.0391812,"\int \sec ^6(a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]^6*Tan[a + b*x]^5,x]","\frac{\sec ^{10}(a+b x)}{10 b}-\frac{\sec ^8(a+b x)}{4 b}+\frac{\sec ^6(a+b x)}{6 b}","\frac{\sec ^{10}(a+b x)}{10 b}-\frac{\sec ^8(a+b x)}{4 b}+\frac{\sec ^6(a+b x)}{6 b}",1,"Sec[a + b*x]^6/(6*b) - Sec[a + b*x]^8/(4*b) + Sec[a + b*x]^10/(10*b)","A",4,3,17,0.1765,1,"{2606, 266, 43}"
116,1,46,0,0.0345757,"\int \sec ^7(a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]^7*Tan[a + b*x]^5,x]","\frac{\sec ^{11}(a+b x)}{11 b}-\frac{2 \sec ^9(a+b x)}{9 b}+\frac{\sec ^7(a+b x)}{7 b}","\frac{\sec ^{11}(a+b x)}{11 b}-\frac{2 \sec ^9(a+b x)}{9 b}+\frac{\sec ^7(a+b x)}{7 b}",1,"Sec[a + b*x]^7/(7*b) - (2*Sec[a + b*x]^9)/(9*b) + Sec[a + b*x]^11/(11*b)","A",3,2,17,0.1176,1,"{2606, 270}"
117,1,46,0,0.0402263,"\int \sec ^8(a+b x) \tan ^5(a+b x) \, dx","Int[Sec[a + b*x]^8*Tan[a + b*x]^5,x]","\frac{\sec ^{12}(a+b x)}{12 b}-\frac{\sec ^{10}(a+b x)}{5 b}+\frac{\sec ^8(a+b x)}{8 b}","\frac{\sec ^{12}(a+b x)}{12 b}-\frac{\sec ^{10}(a+b x)}{5 b}+\frac{\sec ^8(a+b x)}{8 b}",1,"Sec[a + b*x]^8/(8*b) - Sec[a + b*x]^10/(5*b) + Sec[a + b*x]^12/(12*b)","A",4,3,17,0.1765,1,"{2606, 266, 43}"
118,1,66,0,0.0469644,"\int \sin ^3(a+b x) \tan ^3(a+b x) \, dx","Int[Sin[a + b*x]^3*Tan[a + b*x]^3,x]","\frac{5 \sin ^3(a+b x)}{6 b}+\frac{5 \sin (a+b x)}{2 b}+\frac{\sin ^3(a+b x) \tan ^2(a+b x)}{2 b}-\frac{5 \tanh ^{-1}(\sin (a+b x))}{2 b}","\frac{5 \sin ^3(a+b x)}{6 b}+\frac{5 \sin (a+b x)}{2 b}+\frac{\sin ^3(a+b x) \tan ^2(a+b x)}{2 b}-\frac{5 \tanh ^{-1}(\sin (a+b x))}{2 b}",1,"(-5*ArcTanh[Sin[a + b*x]])/(2*b) + (5*Sin[a + b*x])/(2*b) + (5*Sin[a + b*x]^3)/(6*b) + (Sin[a + b*x]^3*Tan[a + b*x]^2)/(2*b)","A",5,4,17,0.2353,1,"{2592, 288, 302, 206}"
119,1,50,0,0.0279641,"\int \sin (a+b x) \tan ^6(a+b x) \, dx","Int[Sin[a + b*x]*Tan[a + b*x]^6,x]","\frac{\cos (a+b x)}{b}+\frac{\sec ^5(a+b x)}{5 b}-\frac{\sec ^3(a+b x)}{b}+\frac{3 \sec (a+b x)}{b}","\frac{\cos (a+b x)}{b}+\frac{\sec ^5(a+b x)}{5 b}-\frac{\sec ^3(a+b x)}{b}+\frac{3 \sec (a+b x)}{b}",1,"Cos[a + b*x]/b + (3*Sec[a + b*x])/b - Sec[a + b*x]^3/b + Sec[a + b*x]^5/(5*b)","A",3,2,15,0.1333,1,"{2590, 270}"
120,1,53,0,0.029208,"\int \cos ^5(a+b x) \cot (a+b x) \, dx","Int[Cos[a + b*x]^5*Cot[a + b*x],x]","\frac{\cos ^5(a+b x)}{5 b}+\frac{\cos ^3(a+b x)}{3 b}+\frac{\cos (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}","\frac{\cos ^5(a+b x)}{5 b}+\frac{\cos ^3(a+b x)}{3 b}+\frac{\cos (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(ArcTanh[Cos[a + b*x]]/b) + Cos[a + b*x]/b + Cos[a + b*x]^3/(3*b) + Cos[a + b*x]^5/(5*b)","A",4,3,15,0.2000,1,"{2592, 302, 206}"
121,1,40,0,0.0273101,"\int \cos ^4(a+b x) \cot (a+b x) \, dx","Int[Cos[a + b*x]^4*Cot[a + b*x],x]","\frac{\sin ^4(a+b x)}{4 b}-\frac{\sin ^2(a+b x)}{b}+\frac{\log (\sin (a+b x))}{b}","\frac{\sin ^4(a+b x)}{4 b}-\frac{\sin ^2(a+b x)}{b}+\frac{\log (\sin (a+b x))}{b}",1,"Log[Sin[a + b*x]]/b - Sin[a + b*x]^2/b + Sin[a + b*x]^4/(4*b)","A",4,3,15,0.2000,1,"{2590, 266, 43}"
122,1,38,0,0.025659,"\int \cos ^3(a+b x) \cot (a+b x) \, dx","Int[Cos[a + b*x]^3*Cot[a + b*x],x]","\frac{\cos ^3(a+b x)}{3 b}+\frac{\cos (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}","\frac{\cos ^3(a+b x)}{3 b}+\frac{\cos (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(ArcTanh[Cos[a + b*x]]/b) + Cos[a + b*x]/b + Cos[a + b*x]^3/(3*b)","A",4,3,15,0.2000,1,"{2592, 302, 206}"
123,1,27,0,0.0211221,"\int \cos ^2(a+b x) \cot (a+b x) \, dx","Int[Cos[a + b*x]^2*Cot[a + b*x],x]","\frac{\log (\sin (a+b x))}{b}-\frac{\sin ^2(a+b x)}{2 b}","\frac{\log (\sin (a+b x))}{b}-\frac{\sin ^2(a+b x)}{2 b}",1,"Log[Sin[a + b*x]]/b - Sin[a + b*x]^2/(2*b)","A",3,2,15,0.1333,1,"{2590, 14}"
124,1,23,0,0.0147569,"\int \cos (a+b x) \cot (a+b x) \, dx","Int[Cos[a + b*x]*Cot[a + b*x],x]","\frac{\cos (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}","\frac{\cos (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(ArcTanh[Cos[a + b*x]]/b) + Cos[a + b*x]/b","A",3,3,13,0.2308,1,"{2592, 321, 206}"
125,1,11,0,0.0040922,"\int \cot (a+b x) \, dx","Int[Cot[a + b*x],x]","\frac{\log (\sin (a+b x))}{b}","\frac{\log (\sin (a+b x))}{b}",1,"Log[Sin[a + b*x]]/b","A",1,1,6,0.1667,1,"{3475}"
126,1,11,0,0.0099491,"\int \csc (a+b x) \sec (a+b x) \, dx","Int[Csc[a + b*x]*Sec[a + b*x],x]","\frac{\log (\tan (a+b x))}{b}","\frac{\log (\tan (a+b x))}{b}",1,"Log[Tan[a + b*x]]/b","A",2,2,13,0.1538,1,"{2620, 29}"
127,1,23,0,0.0216238,"\int \csc (a+b x) \sec ^2(a+b x) \, dx","Int[Csc[a + b*x]*Sec[a + b*x]^2,x]","\frac{\sec (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}","\frac{\sec (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(ArcTanh[Cos[a + b*x]]/b) + Sec[a + b*x]/b","A",3,3,15,0.2000,1,"{2622, 321, 207}"
128,1,27,0,0.0202023,"\int \csc (a+b x) \sec ^3(a+b x) \, dx","Int[Csc[a + b*x]*Sec[a + b*x]^3,x]","\frac{\tan ^2(a+b x)}{2 b}+\frac{\log (\tan (a+b x))}{b}","\frac{\tan ^2(a+b x)}{2 b}+\frac{\log (\tan (a+b x))}{b}",1,"Log[Tan[a + b*x]]/b + Tan[a + b*x]^2/(2*b)","A",3,2,15,0.1333,1,"{2620, 14}"
129,1,38,0,0.0256347,"\int \csc (a+b x) \sec ^4(a+b x) \, dx","Int[Csc[a + b*x]*Sec[a + b*x]^4,x]","\frac{\sec ^3(a+b x)}{3 b}+\frac{\sec (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}","\frac{\sec ^3(a+b x)}{3 b}+\frac{\sec (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(ArcTanh[Cos[a + b*x]]/b) + Sec[a + b*x]/b + Sec[a + b*x]^3/(3*b)","A",4,3,15,0.2000,1,"{2622, 302, 207}"
130,1,39,0,0.0262298,"\int \csc (a+b x) \sec ^5(a+b x) \, dx","Int[Csc[a + b*x]*Sec[a + b*x]^5,x]","\frac{\tan ^4(a+b x)}{4 b}+\frac{\tan ^2(a+b x)}{b}+\frac{\log (\tan (a+b x))}{b}","\frac{\tan ^4(a+b x)}{4 b}+\frac{\tan ^2(a+b x)}{b}+\frac{\log (\tan (a+b x))}{b}",1,"Log[Tan[a + b*x]]/b + Tan[a + b*x]^2/b + Tan[a + b*x]^4/(4*b)","A",4,3,15,0.2000,1,"{2620, 266, 43}"
131,1,53,0,0.0279177,"\int \csc (a+b x) \sec ^6(a+b x) \, dx","Int[Csc[a + b*x]*Sec[a + b*x]^6,x]","\frac{\sec ^5(a+b x)}{5 b}+\frac{\sec ^3(a+b x)}{3 b}+\frac{\sec (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}","\frac{\sec ^5(a+b x)}{5 b}+\frac{\sec ^3(a+b x)}{3 b}+\frac{\sec (a+b x)}{b}-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(ArcTanh[Cos[a + b*x]]/b) + Sec[a + b*x]/b + Sec[a + b*x]^3/(3*b) + Sec[a + b*x]^5/(5*b)","A",4,3,15,0.2000,1,"{2622, 302, 207}"
132,1,57,0,0.0312009,"\int \csc (a+b x) \sec ^7(a+b x) \, dx","Int[Csc[a + b*x]*Sec[a + b*x]^7,x]","\frac{\tan ^6(a+b x)}{6 b}+\frac{3 \tan ^4(a+b x)}{4 b}+\frac{3 \tan ^2(a+b x)}{2 b}+\frac{\log (\tan (a+b x))}{b}","\frac{\tan ^6(a+b x)}{6 b}+\frac{3 \tan ^4(a+b x)}{4 b}+\frac{3 \tan ^2(a+b x)}{2 b}+\frac{\log (\tan (a+b x))}{b}",1,"Log[Tan[a + b*x]]/b + (3*Tan[a + b*x]^2)/(2*b) + (3*Tan[a + b*x]^4)/(4*b) + Tan[a + b*x]^6/(6*b)","A",4,3,15,0.2000,1,"{2620, 266, 43}"
133,1,50,0,0.038405,"\int \cos ^5(a+b x) \cot ^2(a+b x) \, dx","Int[Cos[a + b*x]^5*Cot[a + b*x]^2,x]","-\frac{\sin ^5(a+b x)}{5 b}+\frac{\sin ^3(a+b x)}{b}-\frac{3 \sin (a+b x)}{b}-\frac{\csc (a+b x)}{b}","-\frac{\sin ^5(a+b x)}{5 b}+\frac{\sin ^3(a+b x)}{b}-\frac{3 \sin (a+b x)}{b}-\frac{\csc (a+b x)}{b}",1,"-(Csc[a + b*x]/b) - (3*Sin[a + b*x])/b + Sin[a + b*x]^3/b - Sin[a + b*x]^5/(5*b)","A",3,2,17,0.1176,1,"{2590, 270}"
134,1,61,0,0.0455062,"\int \cos ^4(a+b x) \cot ^2(a+b x) \, dx","Int[Cos[a + b*x]^4*Cot[a + b*x]^2,x]","-\frac{15 \cot (a+b x)}{8 b}+\frac{\cos ^4(a+b x) \cot (a+b x)}{4 b}+\frac{5 \cos ^2(a+b x) \cot (a+b x)}{8 b}-\frac{15 x}{8}","-\frac{15 \cot (a+b x)}{8 b}+\frac{\cos ^4(a+b x) \cot (a+b x)}{4 b}+\frac{5 \cos ^2(a+b x) \cot (a+b x)}{8 b}-\frac{15 x}{8}",1,"(-15*x)/8 - (15*Cot[a + b*x])/(8*b) + (5*Cos[a + b*x]^2*Cot[a + b*x])/(8*b) + (Cos[a + b*x]^4*Cot[a + b*x])/(4*b)","A",5,4,17,0.2353,1,"{2591, 288, 321, 203}"
135,1,38,0,0.0344497,"\int \cos ^3(a+b x) \cot ^2(a+b x) \, dx","Int[Cos[a + b*x]^3*Cot[a + b*x]^2,x]","\frac{\sin ^3(a+b x)}{3 b}-\frac{2 \sin (a+b x)}{b}-\frac{\csc (a+b x)}{b}","\frac{\sin ^3(a+b x)}{3 b}-\frac{2 \sin (a+b x)}{b}-\frac{\csc (a+b x)}{b}",1,"-(Csc[a + b*x]/b) - (2*Sin[a + b*x])/b + Sin[a + b*x]^3/(3*b)","A",3,2,17,0.1176,1,"{2590, 270}"
136,1,40,0,0.0367128,"\int \cos ^2(a+b x) \cot ^2(a+b x) \, dx","Int[Cos[a + b*x]^2*Cot[a + b*x]^2,x]","-\frac{3 \cot (a+b x)}{2 b}+\frac{\cos ^2(a+b x) \cot (a+b x)}{2 b}-\frac{3 x}{2}","-\frac{3 \cot (a+b x)}{2 b}+\frac{\cos ^2(a+b x) \cot (a+b x)}{2 b}-\frac{3 x}{2}",1,"(-3*x)/2 - (3*Cot[a + b*x])/(2*b) + (Cos[a + b*x]^2*Cot[a + b*x])/(2*b)","A",4,4,17,0.2353,1,"{2591, 288, 321, 203}"
137,1,23,0,0.0203114,"\int \cos (a+b x) \cot ^2(a+b x) \, dx","Int[Cos[a + b*x]*Cot[a + b*x]^2,x]","-\frac{\sin (a+b x)}{b}-\frac{\csc (a+b x)}{b}","-\frac{\sin (a+b x)}{b}-\frac{\csc (a+b x)}{b}",1,"-(Csc[a + b*x]/b) - Sin[a + b*x]/b","A",3,2,15,0.1333,1,"{2590, 14}"
138,1,15,0,0.0078847,"\int \cot ^2(a+b x) \, dx","Int[Cot[a + b*x]^2,x]","-\frac{\cot (a+b x)}{b}-x","-\frac{\cot (a+b x)}{b}-x",1,"-x - Cot[a + b*x]/b","A",2,2,8,0.2500,1,"{3473, 8}"
139,1,11,0,0.0093198,"\int \cot (a+b x) \csc (a+b x) \, dx","Int[Cot[a + b*x]*Csc[a + b*x],x]","-\frac{\csc (a+b x)}{b}","-\frac{\csc (a+b x)}{b}",1,"-(Csc[a + b*x]/b)","A",2,2,13,0.1538,1,"{2606, 8}"
140,1,23,0,0.0217056,"\int \csc ^2(a+b x) \sec (a+b x) \, dx","Int[Csc[a + b*x]^2*Sec[a + b*x],x]","\frac{\tanh ^{-1}(\sin (a+b x))}{b}-\frac{\csc (a+b x)}{b}","\frac{\tanh ^{-1}(\sin (a+b x))}{b}-\frac{\csc (a+b x)}{b}",1,"ArcTanh[Sin[a + b*x]]/b - Csc[a + b*x]/b","A",3,3,15,0.2000,1,"{2621, 321, 207}"
141,1,22,0,0.0303198,"\int \csc ^2(a+b x) \sec ^2(a+b x) \, dx","Int[Csc[a + b*x]^2*Sec[a + b*x]^2,x]","\frac{\tan (a+b x)}{b}-\frac{\cot (a+b x)}{b}","\frac{\tan (a+b x)}{b}-\frac{\cot (a+b x)}{b}",1,"-(Cot[a + b*x]/b) + Tan[a + b*x]/b","A",3,2,17,0.1176,1,"{2620, 14}"
142,1,49,0,0.0431818,"\int \csc ^2(a+b x) \sec ^3(a+b x) \, dx","Int[Csc[a + b*x]^2*Sec[a + b*x]^3,x]","-\frac{3 \csc (a+b x)}{2 b}+\frac{3 \tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\csc (a+b x) \sec ^2(a+b x)}{2 b}","-\frac{3 \csc (a+b x)}{2 b}+\frac{3 \tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\csc (a+b x) \sec ^2(a+b x)}{2 b}",1,"(3*ArcTanh[Sin[a + b*x]])/(2*b) - (3*Csc[a + b*x])/(2*b) + (Csc[a + b*x]*Sec[a + b*x]^2)/(2*b)","A",4,4,17,0.2353,1,"{2621, 288, 321, 207}"
143,1,38,0,0.0367211,"\int \csc ^2(a+b x) \sec ^4(a+b x) \, dx","Int[Csc[a + b*x]^2*Sec[a + b*x]^4,x]","\frac{\tan ^3(a+b x)}{3 b}+\frac{2 \tan (a+b x)}{b}-\frac{\cot (a+b x)}{b}","\frac{\tan ^3(a+b x)}{3 b}+\frac{2 \tan (a+b x)}{b}-\frac{\cot (a+b x)}{b}",1,"-(Cot[a + b*x]/b) + (2*Tan[a + b*x])/b + Tan[a + b*x]^3/(3*b)","A",3,2,17,0.1176,1,"{2620, 270}"
144,1,70,0,0.0467545,"\int \csc ^2(a+b x) \sec ^5(a+b x) \, dx","Int[Csc[a + b*x]^2*Sec[a + b*x]^5,x]","-\frac{15 \csc (a+b x)}{8 b}+\frac{15 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\csc (a+b x) \sec ^4(a+b x)}{4 b}+\frac{5 \csc (a+b x) \sec ^2(a+b x)}{8 b}","-\frac{15 \csc (a+b x)}{8 b}+\frac{15 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\csc (a+b x) \sec ^4(a+b x)}{4 b}+\frac{5 \csc (a+b x) \sec ^2(a+b x)}{8 b}",1,"(15*ArcTanh[Sin[a + b*x]])/(8*b) - (15*Csc[a + b*x])/(8*b) + (5*Csc[a + b*x]*Sec[a + b*x]^2)/(8*b) + (Csc[a + b*x]*Sec[a + b*x]^4)/(4*b)","A",5,4,17,0.2353,1,"{2621, 288, 321, 207}"
145,1,58,0,0.04388,"\int \cos ^4(a+b x) \cot ^3(a+b x) \, dx","Int[Cos[a + b*x]^4*Cot[a + b*x]^3,x]","-\frac{\sin ^4(a+b x)}{4 b}+\frac{3 \sin ^2(a+b x)}{2 b}-\frac{\csc ^2(a+b x)}{2 b}-\frac{3 \log (\sin (a+b x))}{b}","-\frac{\sin ^4(a+b x)}{4 b}+\frac{3 \sin ^2(a+b x)}{2 b}-\frac{\csc ^2(a+b x)}{2 b}-\frac{3 \log (\sin (a+b x))}{b}",1,"-Csc[a + b*x]^2/(2*b) - (3*Log[Sin[a + b*x]])/b + (3*Sin[a + b*x]^2)/(2*b) - Sin[a + b*x]^4/(4*b)","A",4,3,17,0.1765,1,"{2590, 266, 43}"
146,1,66,0,0.0449874,"\int \cos ^3(a+b x) \cot ^3(a+b x) \, dx","Int[Cos[a + b*x]^3*Cot[a + b*x]^3,x]","-\frac{5 \cos ^3(a+b x)}{6 b}-\frac{5 \cos (a+b x)}{2 b}-\frac{\cos ^3(a+b x) \cot ^2(a+b x)}{2 b}+\frac{5 \tanh ^{-1}(\cos (a+b x))}{2 b}","-\frac{5 \cos ^3(a+b x)}{6 b}-\frac{5 \cos (a+b x)}{2 b}-\frac{\cos ^3(a+b x) \cot ^2(a+b x)}{2 b}+\frac{5 \tanh ^{-1}(\cos (a+b x))}{2 b}",1,"(5*ArcTanh[Cos[a + b*x]])/(2*b) - (5*Cos[a + b*x])/(2*b) - (5*Cos[a + b*x]^3)/(6*b) - (Cos[a + b*x]^3*Cot[a + b*x]^2)/(2*b)","A",5,4,17,0.2353,1,"{2592, 288, 302, 206}"
147,1,43,0,0.0388649,"\int \cos ^2(a+b x) \cot ^3(a+b x) \, dx","Int[Cos[a + b*x]^2*Cot[a + b*x]^3,x]","\frac{\sin ^2(a+b x)}{2 b}-\frac{\csc ^2(a+b x)}{2 b}-\frac{2 \log (\sin (a+b x))}{b}","\frac{\sin ^2(a+b x)}{2 b}-\frac{\csc ^2(a+b x)}{2 b}-\frac{2 \log (\sin (a+b x))}{b}",1,"-Csc[a + b*x]^2/(2*b) - (2*Log[Sin[a + b*x]])/b + Sin[a + b*x]^2/(2*b)","A",4,3,17,0.1765,1,"{2590, 266, 43}"
148,1,49,0,0.0292992,"\int \cos (a+b x) \cot ^3(a+b x) \, dx","Int[Cos[a + b*x]*Cot[a + b*x]^3,x]","-\frac{3 \cos (a+b x)}{2 b}-\frac{\cos (a+b x) \cot ^2(a+b x)}{2 b}+\frac{3 \tanh ^{-1}(\cos (a+b x))}{2 b}","-\frac{3 \cos (a+b x)}{2 b}-\frac{\cos (a+b x) \cot ^2(a+b x)}{2 b}+\frac{3 \tanh ^{-1}(\cos (a+b x))}{2 b}",1,"(3*ArcTanh[Cos[a + b*x]])/(2*b) - (3*Cos[a + b*x])/(2*b) - (Cos[a + b*x]*Cot[a + b*x]^2)/(2*b)","A",4,4,15,0.2667,1,"{2592, 288, 321, 206}"
149,1,28,0,0.0129672,"\int \cot ^3(a+b x) \, dx","Int[Cot[a + b*x]^3,x]","-\frac{\cot ^2(a+b x)}{2 b}-\frac{\log (\sin (a+b x))}{b}","-\frac{\cot ^2(a+b x)}{2 b}-\frac{\log (\sin (a+b x))}{b}",1,"-Cot[a + b*x]^2/(2*b) - Log[Sin[a + b*x]]/b","A",2,2,8,0.2500,1,"{3473, 3475}"
150,1,34,0,0.0226236,"\int \cot ^2(a+b x) \csc (a+b x) \, dx","Int[Cot[a + b*x]^2*Csc[a + b*x],x]","\frac{\tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{\cot (a+b x) \csc (a+b x)}{2 b}","\frac{\tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{\cot (a+b x) \csc (a+b x)}{2 b}",1,"ArcTanh[Cos[a + b*x]]/(2*b) - (Cot[a + b*x]*Csc[a + b*x])/(2*b)","A",2,2,15,0.1333,1,"{2611, 3770}"
151,1,15,0,0.0178605,"\int \cot (a+b x) \csc ^2(a+b x) \, dx","Int[Cot[a + b*x]*Csc[a + b*x]^2,x]","-\frac{\csc ^2(a+b x)}{2 b}","-\frac{\csc ^2(a+b x)}{2 b}",1,"-Csc[a + b*x]^2/(2*b)","A",2,2,15,0.1333,1,"{2606, 30}"
152,1,27,0,0.0218528,"\int \csc ^3(a+b x) \sec (a+b x) \, dx","Int[Csc[a + b*x]^3*Sec[a + b*x],x]","\frac{\log (\tan (a+b x))}{b}-\frac{\cot ^2(a+b x)}{2 b}","\frac{\log (\tan (a+b x))}{b}-\frac{\cot ^2(a+b x)}{2 b}",1,"-Cot[a + b*x]^2/(2*b) + Log[Tan[a + b*x]]/b","A",3,2,15,0.1333,1,"{2620, 14}"
153,1,49,0,0.0429918,"\int \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\frac{3 \sec (a+b x)}{2 b}-\frac{3 \tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{\csc ^2(a+b x) \sec (a+b x)}{2 b}","\frac{3 \sec (a+b x)}{2 b}-\frac{3 \tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{\csc ^2(a+b x) \sec (a+b x)}{2 b}",1,"(-3*ArcTanh[Cos[a + b*x]])/(2*b) + (3*Sec[a + b*x])/(2*b) - (Csc[a + b*x]^2*Sec[a + b*x])/(2*b)","A",4,4,17,0.2353,1,"{2622, 288, 321, 207}"
154,1,43,0,0.0381614,"\int \csc ^3(a+b x) \sec ^3(a+b x) \, dx","Int[Csc[a + b*x]^3*Sec[a + b*x]^3,x]","\frac{\tan ^2(a+b x)}{2 b}-\frac{\cot ^2(a+b x)}{2 b}+\frac{2 \log (\tan (a+b x))}{b}","\frac{\tan ^2(a+b x)}{2 b}-\frac{\cot ^2(a+b x)}{2 b}+\frac{2 \log (\tan (a+b x))}{b}",1,"-Cot[a + b*x]^2/(2*b) + (2*Log[Tan[a + b*x]])/b + Tan[a + b*x]^2/(2*b)","A",4,3,17,0.1765,1,"{2620, 266, 43}"
155,1,66,0,0.0427421,"\int \csc ^3(a+b x) \sec ^4(a+b x) \, dx","Int[Csc[a + b*x]^3*Sec[a + b*x]^4,x]","\frac{5 \sec ^3(a+b x)}{6 b}+\frac{5 \sec (a+b x)}{2 b}-\frac{5 \tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{\csc ^2(a+b x) \sec ^3(a+b x)}{2 b}","\frac{5 \sec ^3(a+b x)}{6 b}+\frac{5 \sec (a+b x)}{2 b}-\frac{5 \tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{\csc ^2(a+b x) \sec ^3(a+b x)}{2 b}",1,"(-5*ArcTanh[Cos[a + b*x]])/(2*b) + (5*Sec[a + b*x])/(2*b) + (5*Sec[a + b*x]^3)/(6*b) - (Csc[a + b*x]^2*Sec[a + b*x]^3)/(2*b)","A",5,4,17,0.2353,1,"{2622, 288, 302, 207}"
156,1,58,0,0.0431127,"\int \csc ^3(a+b x) \sec ^5(a+b x) \, dx","Int[Csc[a + b*x]^3*Sec[a + b*x]^5,x]","\frac{\tan ^4(a+b x)}{4 b}+\frac{3 \tan ^2(a+b x)}{2 b}-\frac{\cot ^2(a+b x)}{2 b}+\frac{3 \log (\tan (a+b x))}{b}","\frac{\tan ^4(a+b x)}{4 b}+\frac{3 \tan ^2(a+b x)}{2 b}-\frac{\cot ^2(a+b x)}{2 b}+\frac{3 \log (\tan (a+b x))}{b}",1,"-Cot[a + b*x]^2/(2*b) + (3*Log[Tan[a + b*x]])/b + (3*Tan[a + b*x]^2)/(2*b) + Tan[a + b*x]^4/(4*b)","A",4,3,17,0.1765,1,"{2620, 266, 43}"
157,1,68,0,0.0440119,"\int \cos ^5(a+b x) \cot ^4(a+b x) \, dx","Int[Cos[a + b*x]^5*Cot[a + b*x]^4,x]","\frac{\sin ^5(a+b x)}{5 b}-\frac{4 \sin ^3(a+b x)}{3 b}+\frac{6 \sin (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}+\frac{4 \csc (a+b x)}{b}","\frac{\sin ^5(a+b x)}{5 b}-\frac{4 \sin ^3(a+b x)}{3 b}+\frac{6 \sin (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}+\frac{4 \csc (a+b x)}{b}",1,"(4*Csc[a + b*x])/b - Csc[a + b*x]^3/(3*b) + (6*Sin[a + b*x])/b - (4*Sin[a + b*x]^3)/(3*b) + Sin[a + b*x]^5/(5*b)","A",3,2,17,0.1176,1,"{2590, 270}"
158,1,80,0,0.0484905,"\int \cos ^4(a+b x) \cot ^4(a+b x) \, dx","Int[Cos[a + b*x]^4*Cot[a + b*x]^4,x]","-\frac{35 \cot ^3(a+b x)}{24 b}+\frac{35 \cot (a+b x)}{8 b}+\frac{\cos ^4(a+b x) \cot ^3(a+b x)}{4 b}+\frac{7 \cos ^2(a+b x) \cot ^3(a+b x)}{8 b}+\frac{35 x}{8}","-\frac{35 \cot ^3(a+b x)}{24 b}+\frac{35 \cot (a+b x)}{8 b}+\frac{\cos ^4(a+b x) \cot ^3(a+b x)}{4 b}+\frac{7 \cos ^2(a+b x) \cot ^3(a+b x)}{8 b}+\frac{35 x}{8}",1,"(35*x)/8 + (35*Cot[a + b*x])/(8*b) - (35*Cot[a + b*x]^3)/(24*b) + (7*Cos[a + b*x]^2*Cot[a + b*x]^3)/(8*b) + (Cos[a + b*x]^4*Cot[a + b*x]^3)/(4*b)","A",6,4,17,0.2353,1,"{2591, 288, 302, 203}"
159,1,53,0,0.0402648,"\int \cos ^3(a+b x) \cot ^4(a+b x) \, dx","Int[Cos[a + b*x]^3*Cot[a + b*x]^4,x]","-\frac{\sin ^3(a+b x)}{3 b}+\frac{3 \sin (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}+\frac{3 \csc (a+b x)}{b}","-\frac{\sin ^3(a+b x)}{3 b}+\frac{3 \sin (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}+\frac{3 \csc (a+b x)}{b}",1,"(3*Csc[a + b*x])/b - Csc[a + b*x]^3/(3*b) + (3*Sin[a + b*x])/b - Sin[a + b*x]^3/(3*b)","A",3,2,17,0.1176,1,"{2590, 270}"
160,1,57,0,0.0410902,"\int \cos ^2(a+b x) \cot ^4(a+b x) \, dx","Int[Cos[a + b*x]^2*Cot[a + b*x]^4,x]","-\frac{5 \cot ^3(a+b x)}{6 b}+\frac{5 \cot (a+b x)}{2 b}+\frac{\cos ^2(a+b x) \cot ^3(a+b x)}{2 b}+\frac{5 x}{2}","-\frac{5 \cot ^3(a+b x)}{6 b}+\frac{5 \cot (a+b x)}{2 b}+\frac{\cos ^2(a+b x) \cot ^3(a+b x)}{2 b}+\frac{5 x}{2}",1,"(5*x)/2 + (5*Cot[a + b*x])/(2*b) - (5*Cot[a + b*x]^3)/(6*b) + (Cos[a + b*x]^2*Cot[a + b*x]^3)/(2*b)","A",5,4,17,0.2353,1,"{2591, 288, 302, 203}"
161,1,37,0,0.0254015,"\int \cos (a+b x) \cot ^4(a+b x) \, dx","Int[Cos[a + b*x]*Cot[a + b*x]^4,x]","\frac{\sin (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}+\frac{2 \csc (a+b x)}{b}","\frac{\sin (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}+\frac{2 \csc (a+b x)}{b}",1,"(2*Csc[a + b*x])/b - Csc[a + b*x]^3/(3*b) + Sin[a + b*x]/b","A",3,2,15,0.1333,1,"{2590, 270}"
162,1,27,0,0.0165922,"\int \cot ^4(a+b x) \, dx","Int[Cot[a + b*x]^4,x]","-\frac{\cot ^3(a+b x)}{3 b}+\frac{\cot (a+b x)}{b}+x","-\frac{\cot ^3(a+b x)}{3 b}+\frac{\cot (a+b x)}{b}+x",1,"x + Cot[a + b*x]/b - Cot[a + b*x]^3/(3*b)","A",3,2,8,0.2500,1,"{3473, 8}"
163,1,26,0,0.0209366,"\int \cot ^3(a+b x) \csc (a+b x) \, dx","Int[Cot[a + b*x]^3*Csc[a + b*x],x]","\frac{\csc (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}","\frac{\csc (a+b x)}{b}-\frac{\csc ^3(a+b x)}{3 b}",1,"Csc[a + b*x]/b - Csc[a + b*x]^3/(3*b)","A",2,1,15,0.06667,1,"{2606}"
164,1,15,0,0.029278,"\int \cot ^2(a+b x) \csc ^2(a+b x) \, dx","Int[Cot[a + b*x]^2*Csc[a + b*x]^2,x]","-\frac{\cot ^3(a+b x)}{3 b}","-\frac{\cot ^3(a+b x)}{3 b}",1,"-Cot[a + b*x]^3/(3*b)","A",2,2,17,0.1176,1,"{2607, 30}"
165,1,15,0,0.0184351,"\int \cot (a+b x) \csc ^3(a+b x) \, dx","Int[Cot[a + b*x]*Csc[a + b*x]^3,x]","-\frac{\csc ^3(a+b x)}{3 b}","-\frac{\csc ^3(a+b x)}{3 b}",1,"-Csc[a + b*x]^3/(3*b)","A",2,2,15,0.1333,1,"{2606, 30}"
166,1,38,0,0.0258361,"\int \csc ^4(a+b x) \sec (a+b x) \, dx","Int[Csc[a + b*x]^4*Sec[a + b*x],x]","-\frac{\csc ^3(a+b x)}{3 b}-\frac{\csc (a+b x)}{b}+\frac{\tanh ^{-1}(\sin (a+b x))}{b}","-\frac{\csc ^3(a+b x)}{3 b}-\frac{\csc (a+b x)}{b}+\frac{\tanh ^{-1}(\sin (a+b x))}{b}",1,"ArcTanh[Sin[a + b*x]]/b - Csc[a + b*x]/b - Csc[a + b*x]^3/(3*b)","A",4,3,15,0.2000,1,"{2621, 302, 207}"
167,1,37,0,0.0351279,"\int \csc ^4(a+b x) \sec ^2(a+b x) \, dx","Int[Csc[a + b*x]^4*Sec[a + b*x]^2,x]","\frac{\tan (a+b x)}{b}-\frac{\cot ^3(a+b x)}{3 b}-\frac{2 \cot (a+b x)}{b}","\frac{\tan (a+b x)}{b}-\frac{\cot ^3(a+b x)}{3 b}-\frac{2 \cot (a+b x)}{b}",1,"(-2*Cot[a + b*x])/b - Cot[a + b*x]^3/(3*b) + Tan[a + b*x]/b","A",3,2,17,0.1176,1,"{2620, 270}"
168,1,66,0,0.042476,"\int \csc ^4(a+b x) \sec ^3(a+b x) \, dx","Int[Csc[a + b*x]^4*Sec[a + b*x]^3,x]","-\frac{5 \csc ^3(a+b x)}{6 b}-\frac{5 \csc (a+b x)}{2 b}+\frac{5 \tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{2 b}","-\frac{5 \csc ^3(a+b x)}{6 b}-\frac{5 \csc (a+b x)}{2 b}+\frac{5 \tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{2 b}",1,"(5*ArcTanh[Sin[a + b*x]])/(2*b) - (5*Csc[a + b*x])/(2*b) - (5*Csc[a + b*x]^3)/(6*b) + (Csc[a + b*x]^3*Sec[a + b*x]^2)/(2*b)","A",5,4,17,0.2353,1,"{2621, 288, 302, 207}"
169,1,53,0,0.0383726,"\int \csc ^4(a+b x) \sec ^4(a+b x) \, dx","Int[Csc[a + b*x]^4*Sec[a + b*x]^4,x]","\frac{\tan ^3(a+b x)}{3 b}+\frac{3 \tan (a+b x)}{b}-\frac{\cot ^3(a+b x)}{3 b}-\frac{3 \cot (a+b x)}{b}","\frac{\tan ^3(a+b x)}{3 b}+\frac{3 \tan (a+b x)}{b}-\frac{\cot ^3(a+b x)}{3 b}-\frac{3 \cot (a+b x)}{b}",1,"(-3*Cot[a + b*x])/b - Cot[a + b*x]^3/(3*b) + (3*Tan[a + b*x])/b + Tan[a + b*x]^3/(3*b)","A",3,2,17,0.1176,1,"{2620, 270}"
170,1,89,0,0.0493638,"\int \csc ^4(a+b x) \sec ^5(a+b x) \, dx","Int[Csc[a + b*x]^4*Sec[a + b*x]^5,x]","-\frac{35 \csc ^3(a+b x)}{24 b}-\frac{35 \csc (a+b x)}{8 b}+\frac{35 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\csc ^3(a+b x) \sec ^4(a+b x)}{4 b}+\frac{7 \csc ^3(a+b x) \sec ^2(a+b x)}{8 b}","-\frac{35 \csc ^3(a+b x)}{24 b}-\frac{35 \csc (a+b x)}{8 b}+\frac{35 \tanh ^{-1}(\sin (a+b x))}{8 b}+\frac{\csc ^3(a+b x) \sec ^4(a+b x)}{4 b}+\frac{7 \csc ^3(a+b x) \sec ^2(a+b x)}{8 b}",1,"(35*ArcTanh[Sin[a + b*x]])/(8*b) - (35*Csc[a + b*x])/(8*b) - (35*Csc[a + b*x]^3)/(24*b) + (7*Csc[a + b*x]^3*Sec[a + b*x]^2)/(8*b) + (Csc[a + b*x]^3*Sec[a + b*x]^4)/(4*b)","A",6,4,17,0.2353,1,"{2621, 288, 302, 207}"
171,1,69,0,0.0475192,"\int \cos ^4(a+b x) \cot ^5(a+b x) \, dx","Int[Cos[a + b*x]^4*Cot[a + b*x]^5,x]","\frac{\sin ^4(a+b x)}{4 b}-\frac{2 \sin ^2(a+b x)}{b}-\frac{\csc ^4(a+b x)}{4 b}+\frac{2 \csc ^2(a+b x)}{b}+\frac{6 \log (\sin (a+b x))}{b}","\frac{\sin ^4(a+b x)}{4 b}-\frac{2 \sin ^2(a+b x)}{b}-\frac{\csc ^4(a+b x)}{4 b}+\frac{2 \csc ^2(a+b x)}{b}+\frac{6 \log (\sin (a+b x))}{b}",1,"(2*Csc[a + b*x]^2)/b - Csc[a + b*x]^4/(4*b) + (6*Log[Sin[a + b*x]])/b - (2*Sin[a + b*x]^2)/b + Sin[a + b*x]^4/(4*b)","A",4,3,17,0.1765,1,"{2590, 266, 43}"
172,1,89,0,0.0501559,"\int \cos ^3(a+b x) \cot ^5(a+b x) \, dx","Int[Cos[a + b*x]^3*Cot[a + b*x]^5,x]","\frac{35 \cos ^3(a+b x)}{24 b}+\frac{35 \cos (a+b x)}{8 b}-\frac{\cos ^3(a+b x) \cot ^4(a+b x)}{4 b}+\frac{7 \cos ^3(a+b x) \cot ^2(a+b x)}{8 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{8 b}","\frac{35 \cos ^3(a+b x)}{24 b}+\frac{35 \cos (a+b x)}{8 b}-\frac{\cos ^3(a+b x) \cot ^4(a+b x)}{4 b}+\frac{7 \cos ^3(a+b x) \cot ^2(a+b x)}{8 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{8 b}",1,"(-35*ArcTanh[Cos[a + b*x]])/(8*b) + (35*Cos[a + b*x])/(8*b) + (35*Cos[a + b*x]^3)/(24*b) + (7*Cos[a + b*x]^3*Cot[a + b*x]^2)/(8*b) - (Cos[a + b*x]^3*Cot[a + b*x]^4)/(4*b)","A",6,4,17,0.2353,1,"{2592, 288, 302, 206}"
173,1,58,0,0.0426495,"\int \cos ^2(a+b x) \cot ^5(a+b x) \, dx","Int[Cos[a + b*x]^2*Cot[a + b*x]^5,x]","-\frac{\sin ^2(a+b x)}{2 b}-\frac{\csc ^4(a+b x)}{4 b}+\frac{3 \csc ^2(a+b x)}{2 b}+\frac{3 \log (\sin (a+b x))}{b}","-\frac{\sin ^2(a+b x)}{2 b}-\frac{\csc ^4(a+b x)}{4 b}+\frac{3 \csc ^2(a+b x)}{2 b}+\frac{3 \log (\sin (a+b x))}{b}",1,"(3*Csc[a + b*x]^2)/(2*b) - Csc[a + b*x]^4/(4*b) + (3*Log[Sin[a + b*x]])/b - Sin[a + b*x]^2/(2*b)","A",4,3,17,0.1765,1,"{2590, 266, 43}"
174,1,70,0,0.0361286,"\int \cos (a+b x) \cot ^5(a+b x) \, dx","Int[Cos[a + b*x]*Cot[a + b*x]^5,x]","\frac{15 \cos (a+b x)}{8 b}-\frac{\cos (a+b x) \cot ^4(a+b x)}{4 b}+\frac{5 \cos (a+b x) \cot ^2(a+b x)}{8 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{8 b}","\frac{15 \cos (a+b x)}{8 b}-\frac{\cos (a+b x) \cot ^4(a+b x)}{4 b}+\frac{5 \cos (a+b x) \cot ^2(a+b x)}{8 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{8 b}",1,"(-15*ArcTanh[Cos[a + b*x]])/(8*b) + (15*Cos[a + b*x])/(8*b) + (5*Cos[a + b*x]*Cot[a + b*x]^2)/(8*b) - (Cos[a + b*x]*Cot[a + b*x]^4)/(4*b)","A",5,4,15,0.2667,1,"{2592, 288, 321, 206}"
175,1,42,0,0.0210047,"\int \cot ^5(a+b x) \, dx","Int[Cot[a + b*x]^5,x]","-\frac{\cot ^4(a+b x)}{4 b}+\frac{\cot ^2(a+b x)}{2 b}+\frac{\log (\sin (a+b x))}{b}","-\frac{\cot ^4(a+b x)}{4 b}+\frac{\cot ^2(a+b x)}{2 b}+\frac{\log (\sin (a+b x))}{b}",1,"Cot[a + b*x]^2/(2*b) - Cot[a + b*x]^4/(4*b) + Log[Sin[a + b*x]]/b","A",3,2,8,0.2500,1,"{3473, 3475}"
176,1,55,0,0.0421048,"\int \cot ^4(a+b x) \csc (a+b x) \, dx","Int[Cot[a + b*x]^4*Csc[a + b*x],x]","-\frac{3 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\cot ^3(a+b x) \csc (a+b x)}{4 b}+\frac{3 \cot (a+b x) \csc (a+b x)}{8 b}","-\frac{3 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\cot ^3(a+b x) \csc (a+b x)}{4 b}+\frac{3 \cot (a+b x) \csc (a+b x)}{8 b}",1,"(-3*ArcTanh[Cos[a + b*x]])/(8*b) + (3*Cot[a + b*x]*Csc[a + b*x])/(8*b) - (Cot[a + b*x]^3*Csc[a + b*x])/(4*b)","A",3,2,15,0.1333,1,"{2611, 3770}"
177,1,15,0,0.0276831,"\int \cot ^3(a+b x) \csc ^2(a+b x) \, dx","Int[Cot[a + b*x]^3*Csc[a + b*x]^2,x]","-\frac{\cot ^4(a+b x)}{4 b}","-\frac{\cot ^4(a+b x)}{4 b}",1,"-Cot[a + b*x]^4/(4*b)","A",2,2,17,0.1176,1,"{2607, 30}"
178,1,55,0,0.0451343,"\int \cot ^2(a+b x) \csc ^3(a+b x) \, dx","Int[Cot[a + b*x]^2*Csc[a + b*x]^3,x]","\frac{\tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\cot (a+b x) \csc ^3(a+b x)}{4 b}+\frac{\cot (a+b x) \csc (a+b x)}{8 b}","\frac{\tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\cot (a+b x) \csc ^3(a+b x)}{4 b}+\frac{\cot (a+b x) \csc (a+b x)}{8 b}",1,"ArcTanh[Cos[a + b*x]]/(8*b) + (Cot[a + b*x]*Csc[a + b*x])/(8*b) - (Cot[a + b*x]*Csc[a + b*x]^3)/(4*b)","A",3,3,17,0.1765,1,"{2611, 3768, 3770}"
179,1,15,0,0.0183253,"\int \cot (a+b x) \csc ^4(a+b x) \, dx","Int[Cot[a + b*x]*Csc[a + b*x]^4,x]","-\frac{\csc ^4(a+b x)}{4 b}","-\frac{\csc ^4(a+b x)}{4 b}",1,"-Csc[a + b*x]^4/(4*b)","A",2,2,15,0.1333,1,"{2606, 30}"
180,1,40,0,0.0271886,"\int \csc ^5(a+b x) \sec (a+b x) \, dx","Int[Csc[a + b*x]^5*Sec[a + b*x],x]","-\frac{\cot ^4(a+b x)}{4 b}-\frac{\cot ^2(a+b x)}{b}+\frac{\log (\tan (a+b x))}{b}","-\frac{\cot ^4(a+b x)}{4 b}-\frac{\cot ^2(a+b x)}{b}+\frac{\log (\tan (a+b x))}{b}",1,"-(Cot[a + b*x]^2/b) - Cot[a + b*x]^4/(4*b) + Log[Tan[a + b*x]]/b","A",4,3,15,0.2000,1,"{2620, 266, 43}"
181,1,70,0,0.0428248,"\int \csc ^5(a+b x) \sec ^2(a+b x) \, dx","Int[Csc[a + b*x]^5*Sec[a + b*x]^2,x]","\frac{15 \sec (a+b x)}{8 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\csc ^4(a+b x) \sec (a+b x)}{4 b}-\frac{5 \csc ^2(a+b x) \sec (a+b x)}{8 b}","\frac{15 \sec (a+b x)}{8 b}-\frac{15 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\csc ^4(a+b x) \sec (a+b x)}{4 b}-\frac{5 \csc ^2(a+b x) \sec (a+b x)}{8 b}",1,"(-15*ArcTanh[Cos[a + b*x]])/(8*b) + (15*Sec[a + b*x])/(8*b) - (5*Csc[a + b*x]^2*Sec[a + b*x])/(8*b) - (Csc[a + b*x]^4*Sec[a + b*x])/(4*b)","A",5,4,17,0.2353,1,"{2622, 288, 321, 207}"
182,1,58,0,0.0398449,"\int \csc ^5(a+b x) \sec ^3(a+b x) \, dx","Int[Csc[a + b*x]^5*Sec[a + b*x]^3,x]","\frac{\tan ^2(a+b x)}{2 b}-\frac{\cot ^4(a+b x)}{4 b}-\frac{3 \cot ^2(a+b x)}{2 b}+\frac{3 \log (\tan (a+b x))}{b}","\frac{\tan ^2(a+b x)}{2 b}-\frac{\cot ^4(a+b x)}{4 b}-\frac{3 \cot ^2(a+b x)}{2 b}+\frac{3 \log (\tan (a+b x))}{b}",1,"(-3*Cot[a + b*x]^2)/(2*b) - Cot[a + b*x]^4/(4*b) + (3*Log[Tan[a + b*x]])/b + Tan[a + b*x]^2/(2*b)","A",4,3,17,0.1765,1,"{2620, 266, 43}"
183,1,89,0,0.0462182,"\int \csc ^5(a+b x) \sec ^4(a+b x) \, dx","Int[Csc[a + b*x]^5*Sec[a + b*x]^4,x]","\frac{35 \sec ^3(a+b x)}{24 b}+\frac{35 \sec (a+b x)}{8 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\csc ^4(a+b x) \sec ^3(a+b x)}{4 b}-\frac{7 \csc ^2(a+b x) \sec ^3(a+b x)}{8 b}","\frac{35 \sec ^3(a+b x)}{24 b}+\frac{35 \sec (a+b x)}{8 b}-\frac{35 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\csc ^4(a+b x) \sec ^3(a+b x)}{4 b}-\frac{7 \csc ^2(a+b x) \sec ^3(a+b x)}{8 b}",1,"(-35*ArcTanh[Cos[a + b*x]])/(8*b) + (35*Sec[a + b*x])/(8*b) + (35*Sec[a + b*x]^3)/(24*b) - (7*Csc[a + b*x]^2*Sec[a + b*x]^3)/(8*b) - (Csc[a + b*x]^4*Sec[a + b*x]^3)/(4*b)","A",6,4,17,0.2353,1,"{2622, 288, 302, 207}"
184,1,69,0,0.0459103,"\int \csc ^5(a+b x) \sec ^5(a+b x) \, dx","Int[Csc[a + b*x]^5*Sec[a + b*x]^5,x]","\frac{\tan ^4(a+b x)}{4 b}+\frac{2 \tan ^2(a+b x)}{b}-\frac{\cot ^4(a+b x)}{4 b}-\frac{2 \cot ^2(a+b x)}{b}+\frac{6 \log (\tan (a+b x))}{b}","\frac{\tan ^4(a+b x)}{4 b}+\frac{2 \tan ^2(a+b x)}{b}-\frac{\cot ^4(a+b x)}{4 b}-\frac{2 \cot ^2(a+b x)}{b}+\frac{6 \log (\tan (a+b x))}{b}",1,"(-2*Cot[a + b*x]^2)/b - Cot[a + b*x]^4/(4*b) + (6*Log[Tan[a + b*x]])/b + (2*Tan[a + b*x]^2)/b + Tan[a + b*x]^4/(4*b)","A",4,3,17,0.1765,1,"{2620, 266, 43}"
185,1,17,0,0.025849,"\int \cot ^2(x) \csc ^4(x) \, dx","Int[Cot[x]^2*Csc[x]^4,x]","-\frac{1}{5} \cot ^5(x)-\frac{\cot ^3(x)}{3}","-\frac{1}{5} \cot ^5(x)-\frac{\cot ^3(x)}{3}",1,"-Cot[x]^3/3 - Cot[x]^5/5","A",3,2,9,0.2222,1,"{2607, 14}"
186,1,17,0,0.0260525,"\int \cot ^3(x) \csc ^4(x) \, dx","Int[Cot[x]^3*Csc[x]^4,x]","\frac{\csc ^4(x)}{4}-\frac{\csc ^6(x)}{6}","\frac{\csc ^4(x)}{4}-\frac{\csc ^6(x)}{6}",1,"Csc[x]^4/4 - Csc[x]^6/6","A",3,2,9,0.2222,1,"{2606, 14}"
187,1,22,0,0.0252584,"\int (d \cos (a+b x))^{3/2} \sin (a+b x) \, dx","Int[(d*Cos[a + b*x])^(3/2)*Sin[a + b*x],x]","-\frac{2 (d \cos (a+b x))^{5/2}}{5 b d}","-\frac{2 (d \cos (a+b x))^{5/2}}{5 b d}",1,"(-2*(d*Cos[a + b*x])^(5/2))/(5*b*d)","A",2,2,19,0.1053,1,"{2565, 30}"
188,1,22,0,0.0217415,"\int \sqrt{d \cos (a+b x)} \sin (a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Sin[a + b*x],x]","-\frac{2 (d \cos (a+b x))^{3/2}}{3 b d}","-\frac{2 (d \cos (a+b x))^{3/2}}{3 b d}",1,"(-2*(d*Cos[a + b*x])^(3/2))/(3*b*d)","A",2,2,19,0.1053,1,"{2565, 30}"
189,1,20,0,0.0232669,"\int \frac{\sin (a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Sin[a + b*x]/Sqrt[d*Cos[a + b*x]],x]","-\frac{2 \sqrt{d \cos (a+b x)}}{b d}","-\frac{2 \sqrt{d \cos (a+b x)}}{b d}",1,"(-2*Sqrt[d*Cos[a + b*x]])/(b*d)","A",2,2,19,0.1053,1,"{2565, 30}"
190,1,20,0,0.0258174,"\int \frac{\sin (a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]/(d*Cos[a + b*x])^(3/2),x]","\frac{2}{b d \sqrt{d \cos (a+b x)}}","\frac{2}{b d \sqrt{d \cos (a+b x)}}",1,"2/(b*d*Sqrt[d*Cos[a + b*x]])","A",2,2,19,0.1053,1,"{2565, 30}"
191,1,22,0,0.0268243,"\int \frac{\sin (a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]/(d*Cos[a + b*x])^(5/2),x]","\frac{2}{3 b d (d \cos (a+b x))^{3/2}}","\frac{2}{3 b d (d \cos (a+b x))^{3/2}}",1,"2/(3*b*d*(d*Cos[a + b*x])^(3/2))","A",2,2,19,0.1053,1,"{2565, 30}"
192,1,22,0,0.0263088,"\int \frac{\sin (a+b x)}{(d \cos (a+b x))^{7/2}} \, dx","Int[Sin[a + b*x]/(d*Cos[a + b*x])^(7/2),x]","\frac{2}{5 b d (d \cos (a+b x))^{5/2}}","\frac{2}{5 b d (d \cos (a+b x))^{5/2}}",1,"2/(5*b*d*(d*Cos[a + b*x])^(5/2))","A",2,2,19,0.1053,1,"{2565, 30}"
193,1,22,0,0.0270828,"\int \frac{\sin (a+b x)}{(d \cos (a+b x))^{9/2}} \, dx","Int[Sin[a + b*x]/(d*Cos[a + b*x])^(9/2),x]","\frac{2}{7 b d (d \cos (a+b x))^{7/2}}","\frac{2}{7 b d (d \cos (a+b x))^{7/2}}",1,"2/(7*b*d*(d*Cos[a + b*x])^(7/2))","A",2,2,19,0.1053,1,"{2565, 30}"
194,1,126,0,0.1009931,"\int (d \cos (a+b x))^{9/2} \sin ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(9/2)*Sin[a + b*x]^2,x]","\frac{28 d^3 \sin (a+b x) (d \cos (a+b x))^{3/2}}{585 b}+\frac{28 d^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{195 b \sqrt{\cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{11/2}}{13 b d}+\frac{4 d \sin (a+b x) (d \cos (a+b x))^{7/2}}{117 b}","\frac{28 d^3 \sin (a+b x) (d \cos (a+b x))^{3/2}}{585 b}+\frac{28 d^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{195 b \sqrt{\cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{11/2}}{13 b d}+\frac{4 d \sin (a+b x) (d \cos (a+b x))^{7/2}}{117 b}",1,"(28*d^4*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(195*b*Sqrt[Cos[a + b*x]]) + (28*d^3*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(585*b) + (4*d*(d*Cos[a + b*x])^(7/2)*Sin[a + b*x])/(117*b) - (2*(d*Cos[a + b*x])^(11/2)*Sin[a + b*x])/(13*b*d)","A",5,4,21,0.1905,1,"{2568, 2635, 2640, 2639}"
195,1,126,0,0.0977436,"\int (d \cos (a+b x))^{7/2} \sin ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(7/2)*Sin[a + b*x]^2,x]","\frac{20 d^3 \sin (a+b x) \sqrt{d \cos (a+b x)}}{231 b}+\frac{20 d^4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{231 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{9/2}}{11 b d}+\frac{4 d \sin (a+b x) (d \cos (a+b x))^{5/2}}{77 b}","\frac{20 d^3 \sin (a+b x) \sqrt{d \cos (a+b x)}}{231 b}+\frac{20 d^4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{231 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{9/2}}{11 b d}+\frac{4 d \sin (a+b x) (d \cos (a+b x))^{5/2}}{77 b}",1,"(20*d^4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(231*b*Sqrt[d*Cos[a + b*x]]) + (20*d^3*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(231*b) + (4*d*(d*Cos[a + b*x])^(5/2)*Sin[a + b*x])/(77*b) - (2*(d*Cos[a + b*x])^(9/2)*Sin[a + b*x])/(11*b*d)","A",5,4,21,0.1905,1,"{2568, 2635, 2642, 2641}"
196,1,98,0,0.0782281,"\int (d \cos (a+b x))^{5/2} \sin ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(5/2)*Sin[a + b*x]^2,x]","\frac{4 d^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{15 b \sqrt{\cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{7/2}}{9 b d}+\frac{4 d \sin (a+b x) (d \cos (a+b x))^{3/2}}{45 b}","\frac{4 d^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{15 b \sqrt{\cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{7/2}}{9 b d}+\frac{4 d \sin (a+b x) (d \cos (a+b x))^{3/2}}{45 b}",1,"(4*d^2*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(15*b*Sqrt[Cos[a + b*x]]) + (4*d*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(45*b) - (2*(d*Cos[a + b*x])^(7/2)*Sin[a + b*x])/(9*b*d)","A",4,4,21,0.1905,1,"{2568, 2635, 2640, 2639}"
197,1,98,0,0.0788385,"\int (d \cos (a+b x))^{3/2} \sin ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(3/2)*Sin[a + b*x]^2,x]","\frac{4 d^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{5/2}}{7 b d}+\frac{4 d \sin (a+b x) \sqrt{d \cos (a+b x)}}{21 b}","\frac{4 d^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{5/2}}{7 b d}+\frac{4 d \sin (a+b x) \sqrt{d \cos (a+b x)}}{21 b}",1,"(4*d^2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(21*b*Sqrt[d*Cos[a + b*x]]) + (4*d*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(21*b) - (2*(d*Cos[a + b*x])^(5/2)*Sin[a + b*x])/(7*b*d)","A",4,4,21,0.1905,1,"{2568, 2635, 2642, 2641}"
198,1,69,0,0.0562589,"\int \sqrt{d \cos (a+b x)} \sin ^2(a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Sin[a + b*x]^2,x]","\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b \sqrt{\cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{3/2}}{5 b d}","\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b \sqrt{\cos (a+b x)}}-\frac{2 \sin (a+b x) (d \cos (a+b x))^{3/2}}{5 b d}",1,"(4*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*Sqrt[Cos[a + b*x]]) - (2*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(5*b*d)","A",3,3,21,0.1429,1,"{2568, 2640, 2639}"
199,1,69,0,0.0578891,"\int \frac{\sin ^2(a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Sin[a + b*x]^2/Sqrt[d*Cos[a + b*x]],x]","\frac{4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin (a+b x) \sqrt{d \cos (a+b x)}}{3 b d}","\frac{4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin (a+b x) \sqrt{d \cos (a+b x)}}{3 b d}",1,"(4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(3*b*Sqrt[d*Cos[a + b*x]]) - (2*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(3*b*d)","A",3,3,21,0.1429,1,"{2568, 2642, 2641}"
200,1,68,0,0.0637746,"\int \frac{\sin ^2(a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]^2/(d*Cos[a + b*x])^(3/2),x]","\frac{2 \sin (a+b x)}{b d \sqrt{d \cos (a+b x)}}-\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\cos (a+b x)}}","\frac{2 \sin (a+b x)}{b d \sqrt{d \cos (a+b x)}}-\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\cos (a+b x)}}",1,"(-4*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(b*d^2*Sqrt[Cos[a + b*x]]) + (2*Sin[a + b*x])/(b*d*Sqrt[d*Cos[a + b*x]])","A",3,3,21,0.1429,1,"{2566, 2640, 2639}"
201,1,72,0,0.0644769,"\int \frac{\sin ^2(a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^2/(d*Cos[a + b*x])^(5/2),x]","\frac{2 \sin (a+b x)}{3 b d (d \cos (a+b x))^{3/2}}-\frac{4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b d^2 \sqrt{d \cos (a+b x)}}","\frac{2 \sin (a+b x)}{3 b d (d \cos (a+b x))^{3/2}}-\frac{4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b d^2 \sqrt{d \cos (a+b x)}}",1,"(-4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(3*b*d^2*Sqrt[d*Cos[a + b*x]]) + (2*Sin[a + b*x])/(3*b*d*(d*Cos[a + b*x])^(3/2))","A",3,3,21,0.1429,1,"{2566, 2642, 2641}"
202,1,100,0,0.0817502,"\int \frac{\sin ^2(a+b x)}{(d \cos (a+b x))^{7/2}} \, dx","Int[Sin[a + b*x]^2/(d*Cos[a + b*x])^(7/2),x]","-\frac{4 \sin (a+b x)}{5 b d^3 \sqrt{d \cos (a+b x)}}+\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\cos (a+b x)}}+\frac{2 \sin (a+b x)}{5 b d (d \cos (a+b x))^{5/2}}","-\frac{4 \sin (a+b x)}{5 b d^3 \sqrt{d \cos (a+b x)}}+\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\cos (a+b x)}}+\frac{2 \sin (a+b x)}{5 b d (d \cos (a+b x))^{5/2}}",1,"(4*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*d^4*Sqrt[Cos[a + b*x]]) + (2*Sin[a + b*x])/(5*b*d*(d*Cos[a + b*x])^(5/2)) - (4*Sin[a + b*x])/(5*b*d^3*Sqrt[d*Cos[a + b*x]])","A",4,4,21,0.1905,1,"{2566, 2636, 2640, 2639}"
203,1,100,0,0.0819411,"\int \frac{\sin ^2(a+b x)}{(d \cos (a+b x))^{9/2}} \, dx","Int[Sin[a + b*x]^2/(d*Cos[a + b*x])^(9/2),x]","-\frac{4 \sin (a+b x)}{21 b d^3 (d \cos (a+b x))^{3/2}}-\frac{4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b d^4 \sqrt{d \cos (a+b x)}}+\frac{2 \sin (a+b x)}{7 b d (d \cos (a+b x))^{7/2}}","-\frac{4 \sin (a+b x)}{21 b d^3 (d \cos (a+b x))^{3/2}}-\frac{4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{21 b d^4 \sqrt{d \cos (a+b x)}}+\frac{2 \sin (a+b x)}{7 b d (d \cos (a+b x))^{7/2}}",1,"(-4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(21*b*d^4*Sqrt[d*Cos[a + b*x]]) + (2*Sin[a + b*x])/(7*b*d*(d*Cos[a + b*x])^(7/2)) - (4*Sin[a + b*x])/(21*b*d^3*(d*Cos[a + b*x])^(3/2))","A",4,4,21,0.1905,1,"{2566, 2636, 2642, 2641}"
204,1,45,0,0.0421826,"\int \sqrt{d \cos (a+b x)} \sin ^3(a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Sin[a + b*x]^3,x]","\frac{2 (d \cos (a+b x))^{7/2}}{7 b d^3}-\frac{2 (d \cos (a+b x))^{3/2}}{3 b d}","\frac{2 (d \cos (a+b x))^{7/2}}{7 b d^3}-\frac{2 (d \cos (a+b x))^{3/2}}{3 b d}",1,"(-2*(d*Cos[a + b*x])^(3/2))/(3*b*d) + (2*(d*Cos[a + b*x])^(7/2))/(7*b*d^3)","A",3,2,21,0.09524,1,"{2565, 14}"
205,1,43,0,0.0462557,"\int \frac{\sin ^3(a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Sin[a + b*x]^3/Sqrt[d*Cos[a + b*x]],x]","\frac{2 (d \cos (a+b x))^{5/2}}{5 b d^3}-\frac{2 \sqrt{d \cos (a+b x)}}{b d}","\frac{2 (d \cos (a+b x))^{5/2}}{5 b d^3}-\frac{2 \sqrt{d \cos (a+b x)}}{b d}",1,"(-2*Sqrt[d*Cos[a + b*x]])/(b*d) + (2*(d*Cos[a + b*x])^(5/2))/(5*b*d^3)","A",3,2,21,0.09524,1,"{2565, 14}"
206,1,43,0,0.0513659,"\int \frac{\sin ^3(a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]^3/(d*Cos[a + b*x])^(3/2),x]","\frac{2 (d \cos (a+b x))^{3/2}}{3 b d^3}+\frac{2}{b d \sqrt{d \cos (a+b x)}}","\frac{2 (d \cos (a+b x))^{3/2}}{3 b d^3}+\frac{2}{b d \sqrt{d \cos (a+b x)}}",1,"2/(b*d*Sqrt[d*Cos[a + b*x]]) + (2*(d*Cos[a + b*x])^(3/2))/(3*b*d^3)","A",3,2,21,0.09524,1,"{2565, 14}"
207,1,43,0,0.0517832,"\int \frac{\sin ^3(a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^3/(d*Cos[a + b*x])^(5/2),x]","\frac{2 \sqrt{d \cos (a+b x)}}{b d^3}+\frac{2}{3 b d (d \cos (a+b x))^{3/2}}","\frac{2 \sqrt{d \cos (a+b x)}}{b d^3}+\frac{2}{3 b d (d \cos (a+b x))^{3/2}}",1,"2/(3*b*d*(d*Cos[a + b*x])^(3/2)) + (2*Sqrt[d*Cos[a + b*x]])/(b*d^3)","A",3,2,21,0.09524,1,"{2565, 14}"
208,1,43,0,0.0508097,"\int \frac{\sin ^3(a+b x)}{(d \cos (a+b x))^{7/2}} \, dx","Int[Sin[a + b*x]^3/(d*Cos[a + b*x])^(7/2),x]","\frac{2}{5 b d (d \cos (a+b x))^{5/2}}-\frac{2}{b d^3 \sqrt{d \cos (a+b x)}}","\frac{2}{5 b d (d \cos (a+b x))^{5/2}}-\frac{2}{b d^3 \sqrt{d \cos (a+b x)}}",1,"2/(5*b*d*(d*Cos[a + b*x])^(5/2)) - 2/(b*d^3*Sqrt[d*Cos[a + b*x]])","A",3,2,21,0.09524,1,"{2565, 14}"
209,1,45,0,0.0502524,"\int \frac{\sin ^3(a+b x)}{(d \cos (a+b x))^{9/2}} \, dx","Int[Sin[a + b*x]^3/(d*Cos[a + b*x])^(9/2),x]","\frac{2}{7 b d (d \cos (a+b x))^{7/2}}-\frac{2}{3 b d^3 (d \cos (a+b x))^{3/2}}","\frac{2}{7 b d (d \cos (a+b x))^{7/2}}-\frac{2}{3 b d^3 (d \cos (a+b x))^{3/2}}",1,"2/(7*b*d*(d*Cos[a + b*x])^(7/2)) - 2/(3*b*d^3*(d*Cos[a + b*x])^(3/2))","A",3,2,21,0.09524,1,"{2565, 14}"
210,1,45,0,0.0513467,"\int \frac{\sin ^3(a+b x)}{(d \cos (a+b x))^{11/2}} \, dx","Int[Sin[a + b*x]^3/(d*Cos[a + b*x])^(11/2),x]","\frac{2}{9 b d (d \cos (a+b x))^{9/2}}-\frac{2}{5 b d^3 (d \cos (a+b x))^{5/2}}","\frac{2}{9 b d (d \cos (a+b x))^{9/2}}-\frac{2}{5 b d^3 (d \cos (a+b x))^{5/2}}",1,"2/(9*b*d*(d*Cos[a + b*x])^(9/2)) - 2/(5*b*d^3*(d*Cos[a + b*x])^(5/2))","A",3,2,21,0.09524,1,"{2565, 14}"
211,1,156,0,0.1490107,"\int (d \cos (a+b x))^{9/2} \sin ^4(a+b x) \, dx","Int[(d*Cos[a + b*x])^(9/2)*Sin[a + b*x]^4,x]","\frac{56 d^3 \sin (a+b x) (d \cos (a+b x))^{3/2}}{3315 b}+\frac{56 d^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{1105 b \sqrt{\cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{11/2}}{17 b d}-\frac{12 \sin (a+b x) (d \cos (a+b x))^{11/2}}{221 b d}+\frac{8 d \sin (a+b x) (d \cos (a+b x))^{7/2}}{663 b}","\frac{56 d^3 \sin (a+b x) (d \cos (a+b x))^{3/2}}{3315 b}+\frac{56 d^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{1105 b \sqrt{\cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{11/2}}{17 b d}-\frac{12 \sin (a+b x) (d \cos (a+b x))^{11/2}}{221 b d}+\frac{8 d \sin (a+b x) (d \cos (a+b x))^{7/2}}{663 b}",1,"(56*d^4*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(1105*b*Sqrt[Cos[a + b*x]]) + (56*d^3*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(3315*b) + (8*d*(d*Cos[a + b*x])^(7/2)*Sin[a + b*x])/(663*b) - (12*(d*Cos[a + b*x])^(11/2)*Sin[a + b*x])/(221*b*d) - (2*(d*Cos[a + b*x])^(11/2)*Sin[a + b*x]^3)/(17*b*d)","A",6,4,21,0.1905,1,"{2568, 2635, 2640, 2639}"
212,1,156,0,0.1474771,"\int (d \cos (a+b x))^{7/2} \sin ^4(a+b x) \, dx","Int[(d*Cos[a + b*x])^(7/2)*Sin[a + b*x]^4,x]","\frac{8 d^3 \sin (a+b x) \sqrt{d \cos (a+b x)}}{231 b}+\frac{8 d^4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{231 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{9/2}}{15 b d}-\frac{4 \sin (a+b x) (d \cos (a+b x))^{9/2}}{55 b d}+\frac{8 d \sin (a+b x) (d \cos (a+b x))^{5/2}}{385 b}","\frac{8 d^3 \sin (a+b x) \sqrt{d \cos (a+b x)}}{231 b}+\frac{8 d^4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{231 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{9/2}}{15 b d}-\frac{4 \sin (a+b x) (d \cos (a+b x))^{9/2}}{55 b d}+\frac{8 d \sin (a+b x) (d \cos (a+b x))^{5/2}}{385 b}",1,"(8*d^4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(231*b*Sqrt[d*Cos[a + b*x]]) + (8*d^3*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(231*b) + (8*d*(d*Cos[a + b*x])^(5/2)*Sin[a + b*x])/(385*b) - (4*(d*Cos[a + b*x])^(9/2)*Sin[a + b*x])/(55*b*d) - (2*(d*Cos[a + b*x])^(9/2)*Sin[a + b*x]^3)/(15*b*d)","A",6,4,21,0.1905,1,"{2568, 2635, 2642, 2641}"
213,1,128,0,0.1257501,"\int (d \cos (a+b x))^{5/2} \sin ^4(a+b x) \, dx","Int[(d*Cos[a + b*x])^(5/2)*Sin[a + b*x]^4,x]","\frac{8 d^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{65 b \sqrt{\cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{7/2}}{13 b d}-\frac{4 \sin (a+b x) (d \cos (a+b x))^{7/2}}{39 b d}+\frac{8 d \sin (a+b x) (d \cos (a+b x))^{3/2}}{195 b}","\frac{8 d^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{65 b \sqrt{\cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{7/2}}{13 b d}-\frac{4 \sin (a+b x) (d \cos (a+b x))^{7/2}}{39 b d}+\frac{8 d \sin (a+b x) (d \cos (a+b x))^{3/2}}{195 b}",1,"(8*d^2*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(65*b*Sqrt[Cos[a + b*x]]) + (8*d*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(195*b) - (4*(d*Cos[a + b*x])^(7/2)*Sin[a + b*x])/(39*b*d) - (2*(d*Cos[a + b*x])^(7/2)*Sin[a + b*x]^3)/(13*b*d)","A",5,4,21,0.1905,1,"{2568, 2635, 2640, 2639}"
214,1,128,0,0.1331334,"\int (d \cos (a+b x))^{3/2} \sin ^4(a+b x) \, dx","Int[(d*Cos[a + b*x])^(3/2)*Sin[a + b*x]^4,x]","\frac{8 d^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{77 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{5/2}}{11 b d}-\frac{12 \sin (a+b x) (d \cos (a+b x))^{5/2}}{77 b d}+\frac{8 d \sin (a+b x) \sqrt{d \cos (a+b x)}}{77 b}","\frac{8 d^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{77 b \sqrt{d \cos (a+b x)}}-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{5/2}}{11 b d}-\frac{12 \sin (a+b x) (d \cos (a+b x))^{5/2}}{77 b d}+\frac{8 d \sin (a+b x) \sqrt{d \cos (a+b x)}}{77 b}",1,"(8*d^2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(77*b*Sqrt[d*Cos[a + b*x]]) + (8*d*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(77*b) - (12*(d*Cos[a + b*x])^(5/2)*Sin[a + b*x])/(77*b*d) - (2*(d*Cos[a + b*x])^(5/2)*Sin[a + b*x]^3)/(11*b*d)","A",5,4,21,0.1905,1,"{2568, 2635, 2642, 2641}"
215,1,99,0,0.0964384,"\int \sqrt{d \cos (a+b x)} \sin ^4(a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Sin[a + b*x]^4,x]","-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{3/2}}{9 b d}-\frac{4 \sin (a+b x) (d \cos (a+b x))^{3/2}}{15 b d}+\frac{8 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{15 b \sqrt{\cos (a+b x)}}","-\frac{2 \sin ^3(a+b x) (d \cos (a+b x))^{3/2}}{9 b d}-\frac{4 \sin (a+b x) (d \cos (a+b x))^{3/2}}{15 b d}+\frac{8 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{15 b \sqrt{\cos (a+b x)}}",1,"(8*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(15*b*Sqrt[Cos[a + b*x]]) - (4*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(15*b*d) - (2*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x]^3)/(9*b*d)","A",4,3,21,0.1429,1,"{2568, 2640, 2639}"
216,1,99,0,0.0981128,"\int \frac{\sin ^4(a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Sin[a + b*x]^4/Sqrt[d*Cos[a + b*x]],x]","-\frac{2 \sin ^3(a+b x) \sqrt{d \cos (a+b x)}}{7 b d}-\frac{4 \sin (a+b x) \sqrt{d \cos (a+b x)}}{7 b d}+\frac{8 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{7 b \sqrt{d \cos (a+b x)}}","-\frac{2 \sin ^3(a+b x) \sqrt{d \cos (a+b x)}}{7 b d}-\frac{4 \sin (a+b x) \sqrt{d \cos (a+b x)}}{7 b d}+\frac{8 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{7 b \sqrt{d \cos (a+b x)}}",1,"(8*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(7*b*Sqrt[d*Cos[a + b*x]]) - (4*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(7*b*d) - (2*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x]^3)/(7*b*d)","A",4,3,21,0.1429,1,"{2568, 2642, 2641}"
217,1,100,0,0.1045857,"\int \frac{\sin ^4(a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Sin[a + b*x]^4/(d*Cos[a + b*x])^(3/2),x]","\frac{12 \sin (a+b x) (d \cos (a+b x))^{3/2}}{5 b d^3}-\frac{24 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^2 \sqrt{\cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{b d \sqrt{d \cos (a+b x)}}","\frac{12 \sin (a+b x) (d \cos (a+b x))^{3/2}}{5 b d^3}-\frac{24 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^2 \sqrt{\cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{b d \sqrt{d \cos (a+b x)}}",1,"(-24*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*d^2*Sqrt[Cos[a + b*x]]) + (12*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(5*b*d^3) + (2*Sin[a + b*x]^3)/(b*d*Sqrt[d*Cos[a + b*x]])","A",4,4,21,0.1905,1,"{2566, 2568, 2640, 2639}"
218,1,102,0,0.1056196,"\int \frac{\sin ^4(a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Sin[a + b*x]^4/(d*Cos[a + b*x])^(5/2),x]","\frac{4 \sin (a+b x) \sqrt{d \cos (a+b x)}}{3 b d^3}-\frac{8 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b d^2 \sqrt{d \cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{3 b d (d \cos (a+b x))^{3/2}}","\frac{4 \sin (a+b x) \sqrt{d \cos (a+b x)}}{3 b d^3}-\frac{8 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b d^2 \sqrt{d \cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{3 b d (d \cos (a+b x))^{3/2}}",1,"(-8*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(3*b*d^2*Sqrt[d*Cos[a + b*x]]) + (4*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(3*b*d^3) + (2*Sin[a + b*x]^3)/(3*b*d*(d*Cos[a + b*x])^(3/2))","A",4,4,21,0.1905,1,"{2566, 2568, 2642, 2641}"
219,1,102,0,0.1134201,"\int \frac{\sin ^4(a+b x)}{(d \cos (a+b x))^{7/2}} \, dx","Int[Sin[a + b*x]^4/(d*Cos[a + b*x])^(7/2),x]","-\frac{12 \sin (a+b x)}{5 b d^3 \sqrt{d \cos (a+b x)}}+\frac{24 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{5 b d (d \cos (a+b x))^{5/2}}","-\frac{12 \sin (a+b x)}{5 b d^3 \sqrt{d \cos (a+b x)}}+\frac{24 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{5 b d (d \cos (a+b x))^{5/2}}",1,"(24*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*d^4*Sqrt[Cos[a + b*x]]) - (12*Sin[a + b*x])/(5*b*d^3*Sqrt[d*Cos[a + b*x]]) + (2*Sin[a + b*x]^3)/(5*b*d*(d*Cos[a + b*x])^(5/2))","A",4,3,21,0.1429,1,"{2566, 2640, 2639}"
220,1,102,0,0.1114948,"\int \frac{\sin ^4(a+b x)}{(d \cos (a+b x))^{9/2}} \, dx","Int[Sin[a + b*x]^4/(d*Cos[a + b*x])^(9/2),x]","-\frac{4 \sin (a+b x)}{7 b d^3 (d \cos (a+b x))^{3/2}}+\frac{8 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{7 b d^4 \sqrt{d \cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{7 b d (d \cos (a+b x))^{7/2}}","-\frac{4 \sin (a+b x)}{7 b d^3 (d \cos (a+b x))^{3/2}}+\frac{8 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{7 b d^4 \sqrt{d \cos (a+b x)}}+\frac{2 \sin ^3(a+b x)}{7 b d (d \cos (a+b x))^{7/2}}",1,"(8*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(7*b*d^4*Sqrt[d*Cos[a + b*x]]) - (4*Sin[a + b*x])/(7*b*d^3*(d*Cos[a + b*x])^(3/2)) + (2*Sin[a + b*x]^3)/(7*b*d*(d*Cos[a + b*x])^(7/2))","A",4,3,21,0.1429,1,"{2566, 2642, 2641}"
221,1,52,0,0.035061,"\int \cos ^{\frac{3}{2}}(a+b x) \sin ^5(a+b x) \, dx","Int[Cos[a + b*x]^(3/2)*Sin[a + b*x]^5,x]","-\frac{2 \cos ^{\frac{13}{2}}(a+b x)}{13 b}+\frac{4 \cos ^{\frac{9}{2}}(a+b x)}{9 b}-\frac{2 \cos ^{\frac{5}{2}}(a+b x)}{5 b}","-\frac{2 \cos ^{\frac{13}{2}}(a+b x)}{13 b}+\frac{4 \cos ^{\frac{9}{2}}(a+b x)}{9 b}-\frac{2 \cos ^{\frac{5}{2}}(a+b x)}{5 b}",1,"(-2*Cos[a + b*x]^(5/2))/(5*b) + (4*Cos[a + b*x]^(9/2))/(9*b) - (2*Cos[a + b*x]^(13/2))/(13*b)","A",3,2,19,0.1053,1,"{2565, 270}"
222,1,100,0,0.0769487,"\int (d \cos (a+b x))^{9/2} \csc (a+b x) \, dx","Int[(d*Cos[a + b*x])^(9/2)*Csc[a + b*x],x]","\frac{2 d^3 (d \cos (a+b x))^{3/2}}{3 b}+\frac{d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d (d \cos (a+b x))^{7/2}}{7 b}","\frac{2 d^3 (d \cos (a+b x))^{3/2}}{3 b}+\frac{d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d (d \cos (a+b x))^{7/2}}{7 b}",1,"(d^(9/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b - (d^(9/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b + (2*d^3*(d*Cos[a + b*x])^(3/2))/(3*b) + (2*d*(d*Cos[a + b*x])^(7/2))/(7*b)","A",7,6,19,0.3158,1,"{2565, 321, 329, 298, 203, 206}"
223,1,99,0,0.0710352,"\int (d \cos (a+b x))^{7/2} \csc (a+b x) \, dx","Int[(d*Cos[a + b*x])^(7/2)*Csc[a + b*x],x]","\frac{2 d^3 \sqrt{d \cos (a+b x)}}{b}-\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d (d \cos (a+b x))^{5/2}}{5 b}","\frac{2 d^3 \sqrt{d \cos (a+b x)}}{b}-\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d (d \cos (a+b x))^{5/2}}{5 b}",1,"-((d^(7/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b) - (d^(7/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b + (2*d^3*Sqrt[d*Cos[a + b*x]])/b + (2*d*(d*Cos[a + b*x])^(5/2))/(5*b)","A",7,6,19,0.3158,1,"{2565, 321, 329, 212, 206, 203}"
224,1,78,0,0.0649495,"\int (d \cos (a+b x))^{5/2} \csc (a+b x) \, dx","Int[(d*Cos[a + b*x])^(5/2)*Csc[a + b*x],x]","\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d (d \cos (a+b x))^{3/2}}{3 b}","\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d (d \cos (a+b x))^{3/2}}{3 b}",1,"(d^(5/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b - (d^(5/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b + (2*d*(d*Cos[a + b*x])^(3/2))/(3*b)","A",6,6,19,0.3158,1,"{2565, 321, 329, 298, 203, 206}"
225,1,77,0,0.0625691,"\int (d \cos (a+b x))^{3/2} \csc (a+b x) \, dx","Int[(d*Cos[a + b*x])^(3/2)*Csc[a + b*x],x]","-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d \sqrt{d \cos (a+b x)}}{b}","-\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}+\frac{2 d \sqrt{d \cos (a+b x)}}{b}",1,"-((d^(3/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b) - (d^(3/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b + (2*d*Sqrt[d*Cos[a + b*x]])/b","A",6,6,19,0.3158,1,"{2565, 321, 329, 212, 206, 203}"
226,1,58,0,0.0511264,"\int \sqrt{d \cos (a+b x)} \csc (a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Csc[a + b*x],x]","\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}","\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b}",1,"(Sqrt[d]*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b - (Sqrt[d]*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/b","A",5,5,19,0.2632,1,"{2565, 329, 298, 203, 206}"
227,1,59,0,0.0510998,"\int \frac{\csc (a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Csc[a + b*x]/Sqrt[d*Cos[a + b*x]],x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b \sqrt{d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b \sqrt{d}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b \sqrt{d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b \sqrt{d}}",1,"-(ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*Sqrt[d])) - ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*Sqrt[d])","A",5,5,19,0.2632,1,"{2565, 329, 212, 206, 203}"
228,1,78,0,0.0666221,"\int \frac{\csc (a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]/(d*Cos[a + b*x])^(3/2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{3/2}}+\frac{2}{b d \sqrt{d \cos (a+b x)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{3/2}}+\frac{2}{b d \sqrt{d \cos (a+b x)}}",1,"ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(3/2)) - ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(3/2)) + 2/(b*d*Sqrt[d*Cos[a + b*x]])","A",6,6,19,0.3158,1,"{2565, 325, 329, 298, 203, 206}"
229,1,81,0,0.0642343,"\int \frac{\csc (a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]/(d*Cos[a + b*x])^(5/2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{5/2}}+\frac{2}{3 b d (d \cos (a+b x))^{3/2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{5/2}}+\frac{2}{3 b d (d \cos (a+b x))^{3/2}}",1,"-(ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(5/2))) - ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(5/2)) + 2/(3*b*d*(d*Cos[a + b*x])^(3/2))","A",6,6,19,0.3158,1,"{2565, 325, 329, 212, 206, 203}"
230,1,100,0,0.0778657,"\int \frac{\csc (a+b x)}{(d \cos (a+b x))^{7/2}} \, dx","Int[Csc[a + b*x]/(d*Cos[a + b*x])^(7/2),x]","\frac{2}{b d^3 \sqrt{d \cos (a+b x)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{7/2}}+\frac{2}{5 b d (d \cos (a+b x))^{5/2}}","\frac{2}{b d^3 \sqrt{d \cos (a+b x)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{7/2}}+\frac{2}{5 b d (d \cos (a+b x))^{5/2}}",1,"ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(7/2)) - ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(7/2)) + 2/(5*b*d*(d*Cos[a + b*x])^(5/2)) + 2/(b*d^3*Sqrt[d*Cos[a + b*x]])","A",7,6,19,0.3158,1,"{2565, 325, 329, 298, 203, 206}"
231,1,103,0,0.0752345,"\int \frac{\csc (a+b x)}{(d \cos (a+b x))^{9/2}} \, dx","Int[Csc[a + b*x]/(d*Cos[a + b*x])^(9/2),x]","\frac{2}{3 b d^3 (d \cos (a+b x))^{3/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{9/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{9/2}}+\frac{2}{7 b d (d \cos (a+b x))^{7/2}}","\frac{2}{3 b d^3 (d \cos (a+b x))^{3/2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{9/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{b d^{9/2}}+\frac{2}{7 b d (d \cos (a+b x))^{7/2}}",1,"-(ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(9/2))) - ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]]/(b*d^(9/2)) + 2/(7*b*d*(d*Cos[a + b*x])^(7/2)) + 2/(3*b*d^3*(d*Cos[a + b*x])^(3/2))","A",7,6,19,0.3158,1,"{2565, 325, 329, 212, 206, 203}"
232,1,124,0,0.1012527,"\int (d \cos (a+b x))^{11/2} \csc ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(11/2)*Csc[a + b*x]^2,x]","-\frac{15 d^5 \sin (a+b x) \sqrt{d \cos (a+b x)}}{7 b}-\frac{9 d^3 \sin (a+b x) (d \cos (a+b x))^{5/2}}{7 b}-\frac{15 d^6 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{7 b \sqrt{d \cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{9/2}}{b}","-\frac{15 d^5 \sin (a+b x) \sqrt{d \cos (a+b x)}}{7 b}-\frac{9 d^3 \sin (a+b x) (d \cos (a+b x))^{5/2}}{7 b}-\frac{15 d^6 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{7 b \sqrt{d \cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{9/2}}{b}",1,"-((d*(d*Cos[a + b*x])^(9/2)*Csc[a + b*x])/b) - (15*d^6*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(7*b*Sqrt[d*Cos[a + b*x]]) - (15*d^5*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(7*b) - (9*d^3*(d*Cos[a + b*x])^(5/2)*Sin[a + b*x])/(7*b)","A",5,4,21,0.1905,1,"{2567, 2635, 2642, 2641}"
233,1,96,0,0.0824111,"\int (d \cos (a+b x))^{9/2} \csc ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(9/2)*Csc[a + b*x]^2,x]","-\frac{7 d^3 \sin (a+b x) (d \cos (a+b x))^{3/2}}{5 b}-\frac{21 d^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b \sqrt{\cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{7/2}}{b}","-\frac{7 d^3 \sin (a+b x) (d \cos (a+b x))^{3/2}}{5 b}-\frac{21 d^4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b \sqrt{\cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{7/2}}{b}",1,"-((d*(d*Cos[a + b*x])^(7/2)*Csc[a + b*x])/b) - (21*d^4*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*Sqrt[Cos[a + b*x]]) - (7*d^3*(d*Cos[a + b*x])^(3/2)*Sin[a + b*x])/(5*b)","A",4,4,21,0.1905,1,"{2567, 2635, 2640, 2639}"
234,1,96,0,0.0814523,"\int (d \cos (a+b x))^{7/2} \csc ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(7/2)*Csc[a + b*x]^2,x]","-\frac{5 d^3 \sin (a+b x) \sqrt{d \cos (a+b x)}}{3 b}-\frac{5 d^4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b \sqrt{d \cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{5/2}}{b}","-\frac{5 d^3 \sin (a+b x) \sqrt{d \cos (a+b x)}}{3 b}-\frac{5 d^4 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b \sqrt{d \cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{5/2}}{b}",1,"-((d*(d*Cos[a + b*x])^(5/2)*Csc[a + b*x])/b) - (5*d^4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(3*b*Sqrt[d*Cos[a + b*x]]) - (5*d^3*Sqrt[d*Cos[a + b*x]]*Sin[a + b*x])/(3*b)","A",4,4,21,0.1905,1,"{2567, 2635, 2642, 2641}"
235,1,66,0,0.0627215,"\int (d \cos (a+b x))^{5/2} \csc ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(5/2)*Csc[a + b*x]^2,x]","-\frac{3 d^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b \sqrt{\cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{3/2}}{b}","-\frac{3 d^2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b \sqrt{\cos (a+b x)}}-\frac{d \csc (a+b x) (d \cos (a+b x))^{3/2}}{b}",1,"-((d*(d*Cos[a + b*x])^(3/2)*Csc[a + b*x])/b) - (3*d^2*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(b*Sqrt[Cos[a + b*x]])","A",3,3,21,0.1429,1,"{2567, 2640, 2639}"
236,1,66,0,0.0637282,"\int (d \cos (a+b x))^{3/2} \csc ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^(3/2)*Csc[a + b*x]^2,x]","-\frac{d^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{d \cos (a+b x)}}-\frac{d \csc (a+b x) \sqrt{d \cos (a+b x)}}{b}","-\frac{d^2 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{d \cos (a+b x)}}-\frac{d \csc (a+b x) \sqrt{d \cos (a+b x)}}{b}",1,"-((d*Sqrt[d*Cos[a + b*x]]*Csc[a + b*x])/b) - (d^2*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(b*Sqrt[d*Cos[a + b*x]])","A",3,3,21,0.1429,1,"{2567, 2642, 2641}"
237,1,65,0,0.0572064,"\int \sqrt{d \cos (a+b x)} \csc ^2(a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^2,x]","-\frac{\csc (a+b x) (d \cos (a+b x))^{3/2}}{b d}-\frac{E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b \sqrt{\cos (a+b x)}}","-\frac{\csc (a+b x) (d \cos (a+b x))^{3/2}}{b d}-\frac{E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b \sqrt{\cos (a+b x)}}",1,"-(((d*Cos[a + b*x])^(3/2)*Csc[a + b*x])/(b*d)) - (Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(b*Sqrt[Cos[a + b*x]])","A",3,3,21,0.1429,1,"{2570, 2640, 2639}"
238,1,64,0,0.0578789,"\int \frac{\csc ^2(a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Csc[a + b*x]^2/Sqrt[d*Cos[a + b*x]],x]","\frac{\sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{d \cos (a+b x)}}-\frac{\csc (a+b x) \sqrt{d \cos (a+b x)}}{b d}","\frac{\sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b \sqrt{d \cos (a+b x)}}-\frac{\csc (a+b x) \sqrt{d \cos (a+b x)}}{b d}",1,"-((Sqrt[d*Cos[a + b*x]]*Csc[a + b*x])/(b*d)) + (Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(b*Sqrt[d*Cos[a + b*x]])","A",3,3,21,0.1429,1,"{2570, 2642, 2641}"
239,1,94,0,0.0804821,"\int \frac{\csc ^2(a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]^2/(d*Cos[a + b*x])^(3/2),x]","-\frac{3 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\cos (a+b x)}}+\frac{3 \sin (a+b x)}{b d \sqrt{d \cos (a+b x)}}-\frac{\csc (a+b x)}{b d \sqrt{d \cos (a+b x)}}","-\frac{3 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\cos (a+b x)}}+\frac{3 \sin (a+b x)}{b d \sqrt{d \cos (a+b x)}}-\frac{\csc (a+b x)}{b d \sqrt{d \cos (a+b x)}}",1,"-(Csc[a + b*x]/(b*d*Sqrt[d*Cos[a + b*x]])) - (3*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(b*d^2*Sqrt[Cos[a + b*x]]) + (3*Sin[a + b*x])/(b*d*Sqrt[d*Cos[a + b*x]])","A",4,4,21,0.1905,1,"{2570, 2636, 2640, 2639}"
240,1,98,0,0.0829941,"\int \frac{\csc ^2(a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]^2/(d*Cos[a + b*x])^(5/2),x]","\frac{5 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b d^2 \sqrt{d \cos (a+b x)}}+\frac{5 \sin (a+b x)}{3 b d (d \cos (a+b x))^{3/2}}-\frac{\csc (a+b x)}{b d (d \cos (a+b x))^{3/2}}","\frac{5 \sqrt{\cos (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b d^2 \sqrt{d \cos (a+b x)}}+\frac{5 \sin (a+b x)}{3 b d (d \cos (a+b x))^{3/2}}-\frac{\csc (a+b x)}{b d (d \cos (a+b x))^{3/2}}",1,"-(Csc[a + b*x]/(b*d*(d*Cos[a + b*x])^(3/2))) + (5*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2])/(3*b*d^2*Sqrt[d*Cos[a + b*x]]) + (5*Sin[a + b*x])/(3*b*d*(d*Cos[a + b*x])^(3/2))","A",4,4,21,0.1905,1,"{2570, 2636, 2642, 2641}"
241,1,126,0,0.1022051,"\int \frac{\csc ^2(a+b x)}{(d \cos (a+b x))^{7/2}} \, dx","Int[Csc[a + b*x]^2/(d*Cos[a + b*x])^(7/2),x]","\frac{21 \sin (a+b x)}{5 b d^3 \sqrt{d \cos (a+b x)}}-\frac{21 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\cos (a+b x)}}+\frac{7 \sin (a+b x)}{5 b d (d \cos (a+b x))^{5/2}}-\frac{\csc (a+b x)}{b d (d \cos (a+b x))^{5/2}}","\frac{21 \sin (a+b x)}{5 b d^3 \sqrt{d \cos (a+b x)}}-\frac{21 E\left(\left.\frac{1}{2} (a+b x)\right|2\right) \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\cos (a+b x)}}+\frac{7 \sin (a+b x)}{5 b d (d \cos (a+b x))^{5/2}}-\frac{\csc (a+b x)}{b d (d \cos (a+b x))^{5/2}}",1,"-(Csc[a + b*x]/(b*d*(d*Cos[a + b*x])^(5/2))) - (21*Sqrt[d*Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2])/(5*b*d^4*Sqrt[Cos[a + b*x]]) + (7*Sin[a + b*x])/(5*b*d*(d*Cos[a + b*x])^(5/2)) + (21*Sin[a + b*x])/(5*b*d^3*Sqrt[d*Cos[a + b*x]])","A",5,4,21,0.1905,1,"{2570, 2636, 2640, 2639}"
242,1,135,0,0.0894689,"\int (d \cos (a+b x))^{11/2} \csc ^3(a+b x) \, dx","Int[(d*Cos[a + b*x])^(11/2)*Csc[a + b*x]^3,x]","-\frac{9 d^5 \sqrt{d \cos (a+b x)}}{2 b}-\frac{9 d^3 (d \cos (a+b x))^{5/2}}{10 b}+\frac{9 d^{11/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{9 d^{11/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{9/2}}{2 b}","-\frac{9 d^5 \sqrt{d \cos (a+b x)}}{2 b}-\frac{9 d^3 (d \cos (a+b x))^{5/2}}{10 b}+\frac{9 d^{11/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{9 d^{11/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{9/2}}{2 b}",1,"(9*d^(11/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) + (9*d^(11/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) - (9*d^5*Sqrt[d*Cos[a + b*x]])/(2*b) - (9*d^3*(d*Cos[a + b*x])^(5/2))/(10*b) - (d*(d*Cos[a + b*x])^(9/2)*Csc[a + b*x]^2)/(2*b)","A",8,7,21,0.3333,1,"{2565, 288, 321, 329, 212, 206, 203}"
243,1,113,0,0.081668,"\int (d \cos (a+b x))^{9/2} \csc ^3(a+b x) \, dx","Int[(d*Cos[a + b*x])^(9/2)*Csc[a + b*x]^3,x]","-\frac{7 d^3 (d \cos (a+b x))^{3/2}}{6 b}-\frac{7 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{7 d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{7/2}}{2 b}","-\frac{7 d^3 (d \cos (a+b x))^{3/2}}{6 b}-\frac{7 d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{7 d^{9/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{7/2}}{2 b}",1,"(-7*d^(9/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) + (7*d^(9/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) - (7*d^3*(d*Cos[a + b*x])^(3/2))/(6*b) - (d*(d*Cos[a + b*x])^(7/2)*Csc[a + b*x]^2)/(2*b)","A",7,7,21,0.3333,1,"{2565, 288, 321, 329, 298, 203, 206}"
244,1,113,0,0.0801313,"\int (d \cos (a+b x))^{7/2} \csc ^3(a+b x) \, dx","Int[(d*Cos[a + b*x])^(7/2)*Csc[a + b*x]^3,x]","-\frac{5 d^3 \sqrt{d \cos (a+b x)}}{2 b}+\frac{5 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{5 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{5/2}}{2 b}","-\frac{5 d^3 \sqrt{d \cos (a+b x)}}{2 b}+\frac{5 d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{5 d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{5/2}}{2 b}",1,"(5*d^(7/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) + (5*d^(7/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) - (5*d^3*Sqrt[d*Cos[a + b*x]])/(2*b) - (d*(d*Cos[a + b*x])^(5/2)*Csc[a + b*x]^2)/(2*b)","A",7,7,21,0.3333,1,"{2565, 288, 321, 329, 212, 206, 203}"
245,1,91,0,0.0734711,"\int (d \cos (a+b x))^{5/2} \csc ^3(a+b x) \, dx","Int[(d*Cos[a + b*x])^(5/2)*Csc[a + b*x]^3,x]","-\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{3 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{3/2}}{2 b}","-\frac{3 d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{3 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) (d \cos (a+b x))^{3/2}}{2 b}",1,"(-3*d^(5/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) + (3*d^(5/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) - (d*(d*Cos[a + b*x])^(3/2)*Csc[a + b*x]^2)/(2*b)","A",6,6,21,0.2857,1,"{2565, 288, 329, 298, 203, 206}"
246,1,91,0,0.0705803,"\int (d \cos (a+b x))^{3/2} \csc ^3(a+b x) \, dx","Int[(d*Cos[a + b*x])^(3/2)*Csc[a + b*x]^3,x]","\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) \sqrt{d \cos (a+b x)}}{2 b}","\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{d \csc ^2(a+b x) \sqrt{d \cos (a+b x)}}{2 b}",1,"(d^(3/2)*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) + (d^(3/2)*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) - (d*Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^2)/(2*b)","A",6,6,21,0.2857,1,"{2565, 288, 329, 212, 206, 203}"
247,1,93,0,0.065534,"\int \sqrt{d \cos (a+b x)} \csc ^3(a+b x) \, dx","Int[Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^3,x]","\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{\csc ^2(a+b x) (d \cos (a+b x))^{3/2}}{2 b d}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}","\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}-\frac{\csc ^2(a+b x) (d \cos (a+b x))^{3/2}}{2 b d}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b}",1,"(Sqrt[d]*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) - (Sqrt[d]*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b) - ((d*Cos[a + b*x])^(3/2)*Csc[a + b*x]^2)/(2*b*d)","A",6,6,21,0.2857,1,"{2565, 290, 329, 298, 203, 206}"
248,1,93,0,0.0654275,"\int \frac{\csc ^3(a+b x)}{\sqrt{d \cos (a+b x)}} \, dx","Int[Csc[a + b*x]^3/Sqrt[d*Cos[a + b*x]],x]","-\frac{3 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b \sqrt{d}}-\frac{\csc ^2(a+b x) \sqrt{d \cos (a+b x)}}{2 b d}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b \sqrt{d}}","-\frac{3 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b \sqrt{d}}-\frac{\csc ^2(a+b x) \sqrt{d \cos (a+b x)}}{2 b d}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b \sqrt{d}}",1,"(-3*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*Sqrt[d]) - (3*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*Sqrt[d]) - (Sqrt[d*Cos[a + b*x]]*Csc[a + b*x]^2)/(2*b*d)","A",6,6,21,0.2857,1,"{2565, 290, 329, 212, 206, 203}"
249,1,115,0,0.0825338,"\int \frac{\csc ^3(a+b x)}{(d \cos (a+b x))^{3/2}} \, dx","Int[Csc[a + b*x]^3/(d*Cos[a + b*x])^(3/2),x]","\frac{5 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{3/2}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{3/2}}+\frac{5}{2 b d \sqrt{d \cos (a+b x)}}-\frac{\csc ^2(a+b x)}{2 b d \sqrt{d \cos (a+b x)}}","\frac{5 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{3/2}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{3/2}}+\frac{5}{2 b d \sqrt{d \cos (a+b x)}}-\frac{\csc ^2(a+b x)}{2 b d \sqrt{d \cos (a+b x)}}",1,"(5*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*d^(3/2)) - (5*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*d^(3/2)) + 5/(2*b*d*Sqrt[d*Cos[a + b*x]]) - Csc[a + b*x]^2/(2*b*d*Sqrt[d*Cos[a + b*x]])","A",7,7,21,0.3333,1,"{2565, 290, 325, 329, 298, 203, 206}"
250,1,115,0,0.0833959,"\int \frac{\csc ^3(a+b x)}{(d \cos (a+b x))^{5/2}} \, dx","Int[Csc[a + b*x]^3/(d*Cos[a + b*x])^(5/2),x]","-\frac{7 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{5/2}}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{5/2}}+\frac{7}{6 b d (d \cos (a+b x))^{3/2}}-\frac{\csc ^2(a+b x)}{2 b d (d \cos (a+b x))^{3/2}}","-\frac{7 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{5/2}}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{5/2}}+\frac{7}{6 b d (d \cos (a+b x))^{3/2}}-\frac{\csc ^2(a+b x)}{2 b d (d \cos (a+b x))^{3/2}}",1,"(-7*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*d^(5/2)) - (7*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*d^(5/2)) + 7/(6*b*d*(d*Cos[a + b*x])^(3/2)) - Csc[a + b*x]^2/(2*b*d*(d*Cos[a + b*x])^(3/2))","A",7,7,21,0.3333,1,"{2565, 290, 325, 329, 212, 206, 203}"
251,1,137,0,0.0921429,"\int \frac{\csc ^3(a+b x)}{(d \cos (a+b x))^{7/2}} \, dx","Int[Csc[a + b*x]^3/(d*Cos[a + b*x])^(7/2),x]","\frac{9}{2 b d^3 \sqrt{d \cos (a+b x)}}+\frac{9 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{7/2}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{7/2}}+\frac{9}{10 b d (d \cos (a+b x))^{5/2}}-\frac{\csc ^2(a+b x)}{2 b d (d \cos (a+b x))^{5/2}}","\frac{9}{2 b d^3 \sqrt{d \cos (a+b x)}}+\frac{9 \tan ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{7/2}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt{d \cos (a+b x)}}{\sqrt{d}}\right)}{4 b d^{7/2}}+\frac{9}{10 b d (d \cos (a+b x))^{5/2}}-\frac{\csc ^2(a+b x)}{2 b d (d \cos (a+b x))^{5/2}}",1,"(9*ArcTan[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*d^(7/2)) - (9*ArcTanh[Sqrt[d*Cos[a + b*x]]/Sqrt[d]])/(4*b*d^(7/2)) + 9/(10*b*d*(d*Cos[a + b*x])^(5/2)) + 9/(2*b*d^3*Sqrt[d*Cos[a + b*x]]) - Csc[a + b*x]^2/(2*b*d*(d*Cos[a + b*x])^(5/2))","A",8,7,21,0.3333,1,"{2565, 290, 325, 329, 298, 203, 206}"
252,1,22,0,0.0222108,"\int \sqrt[5]{d \cos (a+b x)} \sin (a+b x) \, dx","Int[(d*Cos[a + b*x])^(1/5)*Sin[a + b*x],x]","-\frac{5 (d \cos (a+b x))^{6/5}}{6 b d}","-\frac{5 (d \cos (a+b x))^{6/5}}{6 b d}",1,"(-5*(d*Cos[a + b*x])^(6/5))/(6*b*d)","A",2,2,19,0.1053,1,"{2565, 30}"
253,1,21,0,0.0240266,"\int \cos ^3(x) \sqrt{\sin (x)} \, dx","Int[Cos[x]^3*Sqrt[Sin[x]],x]","\frac{2}{3} \sin ^{\frac{3}{2}}(x)-\frac{2}{7} \sin ^{\frac{7}{2}}(x)","\frac{2}{3} \sin ^{\frac{3}{2}}(x)-\frac{2}{7} \sin ^{\frac{7}{2}}(x)",1,"(2*Sin[x]^(3/2))/3 - (2*Sin[x]^(7/2))/7","A",3,2,11,0.1818,1,"{2564, 14}"
254,1,21,0,0.0243724,"\int \cos ^3(x) \sin ^{\frac{3}{2}}(x) \, dx","Int[Cos[x]^3*Sin[x]^(3/2),x]","\frac{2}{5} \sin ^{\frac{5}{2}}(x)-\frac{2}{9} \sin ^{\frac{9}{2}}(x)","\frac{2}{5} \sin ^{\frac{5}{2}}(x)-\frac{2}{9} \sin ^{\frac{9}{2}}(x)",1,"(2*Sin[x]^(5/2))/5 - (2*Sin[x]^(9/2))/9","A",3,2,11,0.1818,1,"{2564, 14}"
255,1,21,0,0.0249217,"\int \cos ^3(x) \sin ^{\frac{5}{2}}(x) \, dx","Int[Cos[x]^3*Sin[x]^(5/2),x]","\frac{2}{7} \sin ^{\frac{7}{2}}(x)-\frac{2}{11} \sin ^{\frac{11}{2}}(x)","\frac{2}{7} \sin ^{\frac{7}{2}}(x)-\frac{2}{11} \sin ^{\frac{11}{2}}(x)",1,"(2*Sin[x]^(7/2))/7 - (2*Sin[x]^(11/2))/11","A",3,2,11,0.1818,1,"{2564, 14}"
256,1,19,0,0.0232385,"\int \frac{\cos ^3(x)}{\sqrt{\sin (x)}} \, dx","Int[Cos[x]^3/Sqrt[Sin[x]],x]","2 \sqrt{\sin (x)}-\frac{2}{5} \sin ^{\frac{5}{2}}(x)","2 \sqrt{\sin (x)}-\frac{2}{5} \sin ^{\frac{5}{2}}(x)",1,"2*Sqrt[Sin[x]] - (2*Sin[x]^(5/2))/5","A",3,2,11,0.1818,1,"{2564, 14}"
257,1,132,0,0.1596006,"\int (d \cos (a+b x))^{9/2} \sqrt{c \sin (a+b x)} \, dx","Int[(d*Cos[a + b*x])^(9/2)*Sqrt[c*Sin[a + b*x]],x]","\frac{7 d^3 (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{30 b c}+\frac{7 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{20 b \sqrt{\sin (2 a+2 b x)}}+\frac{d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{7/2}}{5 b c}","\frac{7 d^3 (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{30 b c}+\frac{7 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{20 b \sqrt{\sin (2 a+2 b x)}}+\frac{d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{7/2}}{5 b c}",1,"(7*d^3*(d*Cos[a + b*x])^(3/2)*(c*Sin[a + b*x])^(3/2))/(30*b*c) + (d*(d*Cos[a + b*x])^(7/2)*(c*Sin[a + b*x])^(3/2))/(5*b*c) + (7*d^4*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(20*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,3,25,0.1200,1,"{2569, 2572, 2639}"
258,1,95,0,0.1031532,"\int (d \cos (a+b x))^{5/2} \sqrt{c \sin (a+b x)} \, dx","Int[(d*Cos[a + b*x])^(5/2)*Sqrt[c*Sin[a + b*x]],x]","\frac{d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{2 b \sqrt{\sin (2 a+2 b x)}}+\frac{d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{3 b c}","\frac{d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{2 b \sqrt{\sin (2 a+2 b x)}}+\frac{d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{3 b c}",1,"(d*(d*Cos[a + b*x])^(3/2)*(c*Sin[a + b*x])^(3/2))/(3*b*c) + (d^2*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(2*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,25,0.1200,1,"{2569, 2572, 2639}"
259,1,53,0,0.0489386,"\int \sqrt{d \cos (a+b x)} \sqrt{c \sin (a+b x)} \, dx","Int[Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]],x]","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b \sqrt{\sin (2 a+2 b x)}}","\frac{E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b \sqrt{\sin (2 a+2 b x)}}",1,"(Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(b*Sqrt[Sin[2*a + 2*b*x]])","A",2,2,25,0.08000,1,"{2572, 2639}"
260,1,93,0,0.1067542,"\int \frac{\sqrt{c \sin (a+b x)}}{(d \cos (a+b x))^{3/2}} \, dx","Int[Sqrt[c*Sin[a + b*x]]/(d*Cos[a + b*x])^(3/2),x]","\frac{2 (c \sin (a+b x))^{3/2}}{b c d \sqrt{d \cos (a+b x)}}-\frac{2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}","\frac{2 (c \sin (a+b x))^{3/2}}{b c d \sqrt{d \cos (a+b x)}}-\frac{2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}",1,"(2*(c*Sin[a + b*x])^(3/2))/(b*c*d*Sqrt[d*Cos[a + b*x]]) - (2*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(b*d^2*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,25,0.1200,1,"{2571, 2572, 2639}"
261,1,134,0,0.1628206,"\int \frac{\sqrt{c \sin (a+b x)}}{(d \cos (a+b x))^{7/2}} \, dx","Int[Sqrt[c*Sin[a + b*x]]/(d*Cos[a + b*x])^(7/2),x]","\frac{4 (c \sin (a+b x))^{3/2}}{5 b c d^3 \sqrt{d \cos (a+b x)}}-\frac{4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\sin (2 a+2 b x)}}+\frac{2 (c \sin (a+b x))^{3/2}}{5 b c d (d \cos (a+b x))^{5/2}}","\frac{4 (c \sin (a+b x))^{3/2}}{5 b c d^3 \sqrt{d \cos (a+b x)}}-\frac{4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\sin (2 a+2 b x)}}+\frac{2 (c \sin (a+b x))^{3/2}}{5 b c d (d \cos (a+b x))^{5/2}}",1,"(2*(c*Sin[a + b*x])^(3/2))/(5*b*c*d*(d*Cos[a + b*x])^(5/2)) + (4*(c*Sin[a + b*x])^(3/2))/(5*b*c*d^3*Sqrt[d*Cos[a + b*x]]) - (4*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(5*b*d^4*Sqrt[Sin[2*a + 2*b*x]])","A",4,3,25,0.1200,1,"{2571, 2572, 2639}"
262,1,320,0,0.2951609,"\int (d \cos (a+b x))^{3/2} \sqrt{c \sin (a+b x)} \, dx","Int[(d*Cos[a + b*x])^(3/2)*Sqrt[c*Sin[a + b*x]],x]","-\frac{\sqrt{c} d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{4 \sqrt{2} b}+\frac{\sqrt{c} d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{4 \sqrt{2} b}+\frac{\sqrt{c} d^{3/2} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b}-\frac{\sqrt{c} d^{3/2} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b}+\frac{d (c \sin (a+b x))^{3/2} \sqrt{d \cos (a+b x)}}{2 b c}","-\frac{\sqrt{c} d^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{4 \sqrt{2} b}+\frac{\sqrt{c} d^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{4 \sqrt{2} b}+\frac{\sqrt{c} d^{3/2} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b}-\frac{\sqrt{c} d^{3/2} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b}+\frac{d (c \sin (a+b x))^{3/2} \sqrt{d \cos (a+b x)}}{2 b c}",1,"-(Sqrt[c]*d^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(4*Sqrt[2]*b) + (Sqrt[c]*d^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(4*Sqrt[2]*b) + (Sqrt[c]*d^(3/2)*Log[Sqrt[c] - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(8*Sqrt[2]*b) - (Sqrt[c]*d^(3/2)*Log[Sqrt[c] + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(8*Sqrt[2]*b) + (d*Sqrt[d*Cos[a + b*x]]*(c*Sin[a + b*x])^(3/2))/(2*b*c)","A",11,8,25,0.3200,1,"{2569, 2574, 297, 1162, 617, 204, 1165, 628}"
263,1,280,0,0.1886747,"\int \frac{\sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}} \, dx","Int[Sqrt[c*Sin[a + b*x]]/Sqrt[d*Cos[a + b*x]],x]","-\frac{\sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{\sqrt{2} b \sqrt{d}}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{\sqrt{2} b \sqrt{d}}+\frac{\sqrt{c} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{d}}-\frac{\sqrt{c} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{d}}","-\frac{\sqrt{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{\sqrt{2} b \sqrt{d}}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{\sqrt{2} b \sqrt{d}}+\frac{\sqrt{c} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{d}}-\frac{\sqrt{c} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b \sqrt{d}}",1,"-((Sqrt[c]*ArcTan[1 - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(Sqrt[2]*b*Sqrt[d])) + (Sqrt[c]*ArcTan[1 + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(Sqrt[2]*b*Sqrt[d]) + (Sqrt[c]*Log[Sqrt[c] - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(2*Sqrt[2]*b*Sqrt[d]) - (Sqrt[c]*Log[Sqrt[c] + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(2*Sqrt[2]*b*Sqrt[d])","A",10,7,25,0.2800,1,"{2574, 297, 1162, 617, 204, 1165, 628}"
264,1,37,0,0.0529633,"\int \frac{\sqrt{c \sin (a+b x)}}{(d \cos (a+b x))^{5/2}} \, dx","Int[Sqrt[c*Sin[a + b*x]]/(d*Cos[a + b*x])^(5/2),x]","\frac{2 (c \sin (a+b x))^{3/2}}{3 b c d (d \cos (a+b x))^{3/2}}","\frac{2 (c \sin (a+b x))^{3/2}}{3 b c d (d \cos (a+b x))^{3/2}}",1,"(2*(c*Sin[a + b*x])^(3/2))/(3*b*c*d*(d*Cos[a + b*x])^(3/2))","A",1,1,25,0.04000,1,"{2563}"
265,1,75,0,0.1125308,"\int \frac{\sqrt{c \sin (a+b x)}}{(d \cos (a+b x))^{9/2}} \, dx","Int[Sqrt[c*Sin[a + b*x]]/(d*Cos[a + b*x])^(9/2),x]","\frac{8 (c \sin (a+b x))^{3/2}}{21 b c d^3 (d \cos (a+b x))^{3/2}}+\frac{2 (c \sin (a+b x))^{3/2}}{7 b c d (d \cos (a+b x))^{7/2}}","\frac{8 (c \sin (a+b x))^{3/2}}{21 b c d^3 (d \cos (a+b x))^{3/2}}+\frac{2 (c \sin (a+b x))^{3/2}}{7 b c d (d \cos (a+b x))^{7/2}}",1,"(2*(c*Sin[a + b*x])^(3/2))/(7*b*c*d*(d*Cos[a + b*x])^(7/2)) + (8*(c*Sin[a + b*x])^(3/2))/(21*b*c*d^3*(d*Cos[a + b*x])^(3/2))","A",2,2,25,0.08000,1,"{2571, 2563}"
266,1,112,0,0.1711863,"\int \frac{\sqrt{c \sin (a+b x)}}{(d \cos (a+b x))^{13/2}} \, dx","Int[Sqrt[c*Sin[a + b*x]]/(d*Cos[a + b*x])^(13/2),x]","\frac{64 (c \sin (a+b x))^{3/2}}{231 b c d^5 (d \cos (a+b x))^{3/2}}+\frac{16 (c \sin (a+b x))^{3/2}}{77 b c d^3 (d \cos (a+b x))^{7/2}}+\frac{2 (c \sin (a+b x))^{3/2}}{11 b c d (d \cos (a+b x))^{11/2}}","\frac{64 (c \sin (a+b x))^{3/2}}{231 b c d^5 (d \cos (a+b x))^{3/2}}+\frac{16 (c \sin (a+b x))^{3/2}}{77 b c d^3 (d \cos (a+b x))^{7/2}}+\frac{2 (c \sin (a+b x))^{3/2}}{11 b c d (d \cos (a+b x))^{11/2}}",1,"(2*(c*Sin[a + b*x])^(3/2))/(11*b*c*d*(d*Cos[a + b*x])^(11/2)) + (16*(c*Sin[a + b*x])^(3/2))/(77*b*c*d^3*(d*Cos[a + b*x])^(7/2)) + (64*(c*Sin[a + b*x])^(3/2))/(231*b*c*d^5*(d*Cos[a + b*x])^(3/2))","A",3,2,25,0.08000,1,"{2571, 2563}"
267,1,131,0,0.1789027,"\int (d \cos (a+b x))^{3/2} (c \sin (a+b x))^{3/2} \, dx","Int[(d*Cos[a + b*x])^(3/2)*(c*Sin[a + b*x])^(3/2),x]","\frac{c^2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{12 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}-\frac{c \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{5/2}}{3 b d}+\frac{c d \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{6 b}","\frac{c^2 d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{12 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}-\frac{c \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{5/2}}{3 b d}+\frac{c d \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{6 b}",1,"(c*d*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])/(6*b) - (c*(d*Cos[a + b*x])^(5/2)*Sqrt[c*Sin[a + b*x]])/(3*b*d) + (c^2*d^2*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(12*b*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",4,4,25,0.1600,1,"{2568, 2569, 2573, 2641}"
268,1,93,0,0.1166278,"\int \frac{(c \sin (a+b x))^{3/2}}{\sqrt{d \cos (a+b x)}} \, dx","Int[(c*Sin[a + b*x])^(3/2)/Sqrt[d*Cos[a + b*x]],x]","\frac{c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}-\frac{c \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b d}","\frac{c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}-\frac{c \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b d}",1,"-((c*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])/(b*d)) + (c^2*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(2*b*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",3,3,25,0.1200,1,"{2568, 2573, 2641}"
269,1,98,0,0.1226788,"\int \frac{(c \sin (a+b x))^{3/2}}{(d \cos (a+b x))^{5/2}} \, dx","Int[(c*Sin[a + b*x])^(3/2)/(d*Cos[a + b*x])^(5/2),x]","\frac{2 c \sqrt{c \sin (a+b x)}}{3 b d (d \cos (a+b x))^{3/2}}-\frac{c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b d^2 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}","\frac{2 c \sqrt{c \sin (a+b x)}}{3 b d (d \cos (a+b x))^{3/2}}-\frac{c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b d^2 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}",1,"(2*c*Sqrt[c*Sin[a + b*x]])/(3*b*d*(d*Cos[a + b*x])^(3/2)) - (c^2*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(3*b*d^2*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",3,3,25,0.1200,1,"{2566, 2573, 2641}"
270,1,133,0,0.1861471,"\int \frac{(c \sin (a+b x))^{3/2}}{(d \cos (a+b x))^{9/2}} \, dx","Int[(c*Sin[a + b*x])^(3/2)/(d*Cos[a + b*x])^(9/2),x]","-\frac{2 c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{21 b d^4 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}-\frac{2 c \sqrt{c \sin (a+b x)}}{21 b d^3 (d \cos (a+b x))^{3/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{7 b d (d \cos (a+b x))^{7/2}}","-\frac{2 c^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{21 b d^4 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}-\frac{2 c \sqrt{c \sin (a+b x)}}{21 b d^3 (d \cos (a+b x))^{3/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{7 b d (d \cos (a+b x))^{7/2}}",1,"(2*c*Sqrt[c*Sin[a + b*x]])/(7*b*d*(d*Cos[a + b*x])^(7/2)) - (2*c*Sqrt[c*Sin[a + b*x]])/(21*b*d^3*(d*Cos[a + b*x])^(3/2)) - (2*c^2*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(21*b*d^4*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",4,4,25,0.1600,1,"{2566, 2571, 2573, 2641}"
271,1,320,0,0.280711,"\int \sqrt{d \cos (a+b x)} (c \sin (a+b x))^{3/2} \, dx","Int[Sqrt[d*Cos[a + b*x]]*(c*Sin[a + b*x])^(3/2),x]","\frac{c^{3/2} \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}\right)}{4 \sqrt{2} b}-\frac{c^{3/2} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}+1\right)}{4 \sqrt{2} b}-\frac{c^{3/2} \sqrt{d} \log \left(-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{c^{3/2} \sqrt{d} \log \left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{c \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{3/2}}{2 b d}","\frac{c^{3/2} \sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}\right)}{4 \sqrt{2} b}-\frac{c^{3/2} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}+1\right)}{4 \sqrt{2} b}-\frac{c^{3/2} \sqrt{d} \log \left(-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{8 \sqrt{2} b}+\frac{c^{3/2} \sqrt{d} \log \left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{8 \sqrt{2} b}-\frac{c \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{3/2}}{2 b d}",1,"(c^(3/2)*Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/(Sqrt[d]*Sqrt[c*Sin[a + b*x]])])/(4*Sqrt[2]*b) - (c^(3/2)*Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/(Sqrt[d]*Sqrt[c*Sin[a + b*x]])])/(4*Sqrt[2]*b) - (c^(3/2)*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[a + b*x] - (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/Sqrt[c*Sin[a + b*x]]])/(8*Sqrt[2]*b) + (c^(3/2)*Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[a + b*x] + (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/Sqrt[c*Sin[a + b*x]]])/(8*Sqrt[2]*b) - (c*(d*Cos[a + b*x])^(3/2)*Sqrt[c*Sin[a + b*x]])/(2*b*d)","A",11,8,25,0.3200,1,"{2568, 2575, 297, 1162, 617, 204, 1165, 628}"
272,1,313,0,0.275586,"\int \frac{(c \sin (a+b x))^{3/2}}{(d \cos (a+b x))^{3/2}} \, dx","Int[(c*Sin[a + b*x])^(3/2)/(d*Cos[a + b*x])^(3/2),x]","-\frac{c^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}\right)}{\sqrt{2} b d^{3/2}}+\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}+1\right)}{\sqrt{2} b d^{3/2}}+\frac{c^{3/2} \log \left(-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}-\frac{c^{3/2} \log \left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{b d \sqrt{d \cos (a+b x)}}","-\frac{c^{3/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}\right)}{\sqrt{2} b d^{3/2}}+\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}+1\right)}{\sqrt{2} b d^{3/2}}+\frac{c^{3/2} \log \left(-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}-\frac{c^{3/2} \log \left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b d^{3/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{b d \sqrt{d \cos (a+b x)}}",1,"-((c^(3/2)*ArcTan[1 - (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/(Sqrt[d]*Sqrt[c*Sin[a + b*x]])])/(Sqrt[2]*b*d^(3/2))) + (c^(3/2)*ArcTan[1 + (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/(Sqrt[d]*Sqrt[c*Sin[a + b*x]])])/(Sqrt[2]*b*d^(3/2)) + (c^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[a + b*x] - (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/Sqrt[c*Sin[a + b*x]]])/(2*Sqrt[2]*b*d^(3/2)) - (c^(3/2)*Log[Sqrt[d] + Sqrt[d]*Cot[a + b*x] + (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/Sqrt[c*Sin[a + b*x]]])/(2*Sqrt[2]*b*d^(3/2)) + (2*c*Sqrt[c*Sin[a + b*x]])/(b*d*Sqrt[d*Cos[a + b*x]])","A",11,8,25,0.3200,1,"{2566, 2575, 297, 1162, 617, 204, 1165, 628}"
273,1,37,0,0.0597498,"\int \frac{(c \sin (a+b x))^{3/2}}{(d \cos (a+b x))^{7/2}} \, dx","Int[(c*Sin[a + b*x])^(3/2)/(d*Cos[a + b*x])^(7/2),x]","\frac{2 (c \sin (a+b x))^{5/2}}{5 b c d (d \cos (a+b x))^{5/2}}","\frac{2 (c \sin (a+b x))^{5/2}}{5 b c d (d \cos (a+b x))^{5/2}}",1,"(2*(c*Sin[a + b*x])^(5/2))/(5*b*c*d*(d*Cos[a + b*x])^(5/2))","A",1,1,25,0.04000,1,"{2563}"
274,1,106,0,0.1841895,"\int \frac{(c \sin (a+b x))^{3/2}}{(d \cos (a+b x))^{11/2}} \, dx","Int[(c*Sin[a + b*x])^(3/2)/(d*Cos[a + b*x])^(11/2),x]","-\frac{8 c \sqrt{c \sin (a+b x)}}{45 b d^5 \sqrt{d \cos (a+b x)}}-\frac{2 c \sqrt{c \sin (a+b x)}}{45 b d^3 (d \cos (a+b x))^{5/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{9 b d (d \cos (a+b x))^{9/2}}","-\frac{8 c \sqrt{c \sin (a+b x)}}{45 b d^5 \sqrt{d \cos (a+b x)}}-\frac{2 c \sqrt{c \sin (a+b x)}}{45 b d^3 (d \cos (a+b x))^{5/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{9 b d (d \cos (a+b x))^{9/2}}",1,"(2*c*Sqrt[c*Sin[a + b*x]])/(9*b*d*(d*Cos[a + b*x])^(9/2)) - (2*c*Sqrt[c*Sin[a + b*x]])/(45*b*d^3*(d*Cos[a + b*x])^(5/2)) - (8*c*Sqrt[c*Sin[a + b*x]])/(45*b*d^5*Sqrt[d*Cos[a + b*x]])","A",3,3,25,0.1200,1,"{2566, 2571, 2563}"
275,1,141,0,0.2402821,"\int \frac{(c \sin (a+b x))^{3/2}}{(d \cos (a+b x))^{15/2}} \, dx","Int[(c*Sin[a + b*x])^(3/2)/(d*Cos[a + b*x])^(15/2),x]","-\frac{64 c \sqrt{c \sin (a+b x)}}{585 b d^7 \sqrt{d \cos (a+b x)}}-\frac{16 c \sqrt{c \sin (a+b x)}}{585 b d^5 (d \cos (a+b x))^{5/2}}-\frac{2 c \sqrt{c \sin (a+b x)}}{117 b d^3 (d \cos (a+b x))^{9/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{13 b d (d \cos (a+b x))^{13/2}}","-\frac{64 c \sqrt{c \sin (a+b x)}}{585 b d^7 \sqrt{d \cos (a+b x)}}-\frac{16 c \sqrt{c \sin (a+b x)}}{585 b d^5 (d \cos (a+b x))^{5/2}}-\frac{2 c \sqrt{c \sin (a+b x)}}{117 b d^3 (d \cos (a+b x))^{9/2}}+\frac{2 c \sqrt{c \sin (a+b x)}}{13 b d (d \cos (a+b x))^{13/2}}",1,"(2*c*Sqrt[c*Sin[a + b*x]])/(13*b*d*(d*Cos[a + b*x])^(13/2)) - (2*c*Sqrt[c*Sin[a + b*x]])/(117*b*d^3*(d*Cos[a + b*x])^(9/2)) - (16*c*Sqrt[c*Sin[a + b*x]])/(585*b*d^5*(d*Cos[a + b*x])^(5/2)) - (64*c*Sqrt[c*Sin[a + b*x]])/(585*b*d^7*Sqrt[d*Cos[a + b*x]])","A",4,3,25,0.1200,1,"{2566, 2571, 2563}"
276,1,166,0,0.2354134,"\int (d \cos (a+b x))^{9/2} (c \sin (a+b x))^{5/2} \, dx","Int[(d*Cos[a + b*x])^(9/2)*(c*Sin[a + b*x])^(5/2),x]","\frac{3 c^2 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{40 b \sqrt{\sin (2 a+2 b x)}}+\frac{c d^3 (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{20 b}-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{11/2}}{7 b d}+\frac{3 c d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{7/2}}{70 b}","\frac{3 c^2 d^4 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{40 b \sqrt{\sin (2 a+2 b x)}}+\frac{c d^3 (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{20 b}-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{11/2}}{7 b d}+\frac{3 c d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{7/2}}{70 b}",1,"(c*d^3*(d*Cos[a + b*x])^(3/2)*(c*Sin[a + b*x])^(3/2))/(20*b) + (3*c*d*(d*Cos[a + b*x])^(7/2)*(c*Sin[a + b*x])^(3/2))/(70*b) - (c*(d*Cos[a + b*x])^(11/2)*(c*Sin[a + b*x])^(3/2))/(7*b*d) + (3*c^2*d^4*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(40*b*Sqrt[Sin[2*a + 2*b*x]])","A",5,4,25,0.1600,1,"{2568, 2569, 2572, 2639}"
277,1,131,0,0.1757556,"\int (d \cos (a+b x))^{5/2} (c \sin (a+b x))^{5/2} \, dx","Int[(d*Cos[a + b*x])^(5/2)*(c*Sin[a + b*x])^(5/2),x]","\frac{3 c^2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{20 b \sqrt{\sin (2 a+2 b x)}}-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{7/2}}{5 b d}+\frac{c d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{10 b}","\frac{3 c^2 d^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{20 b \sqrt{\sin (2 a+2 b x)}}-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{7/2}}{5 b d}+\frac{c d (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{10 b}",1,"(c*d*(d*Cos[a + b*x])^(3/2)*(c*Sin[a + b*x])^(3/2))/(10*b) - (c*(d*Cos[a + b*x])^(7/2)*(c*Sin[a + b*x])^(3/2))/(5*b*d) + (3*c^2*d^2*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(20*b*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2568, 2569, 2572, 2639}"
278,1,95,0,0.1084008,"\int \sqrt{d \cos (a+b x)} (c \sin (a+b x))^{5/2} \, dx","Int[Sqrt[d*Cos[a + b*x]]*(c*Sin[a + b*x])^(5/2),x]","\frac{c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{2 b \sqrt{\sin (2 a+2 b x)}}-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{3 b d}","\frac{c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{2 b \sqrt{\sin (2 a+2 b x)}}-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{3/2}}{3 b d}",1,"-(c*(d*Cos[a + b*x])^(3/2)*(c*Sin[a + b*x])^(3/2))/(3*b*d) + (c^2*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(2*b*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,25,0.1200,1,"{2568, 2572, 2639}"
279,1,94,0,0.1202295,"\int \frac{(c \sin (a+b x))^{5/2}}{(d \cos (a+b x))^{3/2}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/(d*Cos[a + b*x])^(3/2),x]","\frac{2 c (c \sin (a+b x))^{3/2}}{b d \sqrt{d \cos (a+b x)}}-\frac{3 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}","\frac{2 c (c \sin (a+b x))^{3/2}}{b d \sqrt{d \cos (a+b x)}}-\frac{3 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b d^2 \sqrt{\sin (2 a+2 b x)}}",1,"(2*c*(c*Sin[a + b*x])^(3/2))/(b*d*Sqrt[d*Cos[a + b*x]]) - (3*c^2*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(b*d^2*Sqrt[Sin[2*a + 2*b*x]])","A",3,3,25,0.1200,1,"{2566, 2572, 2639}"
280,1,133,0,0.1739488,"\int \frac{(c \sin (a+b x))^{5/2}}{(d \cos (a+b x))^{7/2}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/(d*Cos[a + b*x])^(7/2),x]","\frac{6 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\sin (2 a+2 b x)}}-\frac{6 c (c \sin (a+b x))^{3/2}}{5 b d^3 \sqrt{d \cos (a+b x)}}+\frac{2 c (c \sin (a+b x))^{3/2}}{5 b d (d \cos (a+b x))^{5/2}}","\frac{6 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{5 b d^4 \sqrt{\sin (2 a+2 b x)}}-\frac{6 c (c \sin (a+b x))^{3/2}}{5 b d^3 \sqrt{d \cos (a+b x)}}+\frac{2 c (c \sin (a+b x))^{3/2}}{5 b d (d \cos (a+b x))^{5/2}}",1,"(2*c*(c*Sin[a + b*x])^(3/2))/(5*b*d*(d*Cos[a + b*x])^(5/2)) - (6*c*(c*Sin[a + b*x])^(3/2))/(5*b*d^3*Sqrt[d*Cos[a + b*x]]) + (6*c^2*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(5*b*d^4*Sqrt[Sin[2*a + 2*b*x]])","A",4,4,25,0.1600,1,"{2566, 2571, 2572, 2639}"
281,1,168,0,0.2396534,"\int \frac{(c \sin (a+b x))^{5/2}}{(d \cos (a+b x))^{11/2}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/(d*Cos[a + b*x])^(11/2),x]","\frac{4 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{15 b d^6 \sqrt{\sin (2 a+2 b x)}}-\frac{4 c (c \sin (a+b x))^{3/2}}{15 b d^5 \sqrt{d \cos (a+b x)}}-\frac{2 c (c \sin (a+b x))^{3/2}}{15 b d^3 (d \cos (a+b x))^{5/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{9 b d (d \cos (a+b x))^{9/2}}","\frac{4 c^2 E\left(\left.a+b x-\frac{\pi }{4}\right|2\right) \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{15 b d^6 \sqrt{\sin (2 a+2 b x)}}-\frac{4 c (c \sin (a+b x))^{3/2}}{15 b d^5 \sqrt{d \cos (a+b x)}}-\frac{2 c (c \sin (a+b x))^{3/2}}{15 b d^3 (d \cos (a+b x))^{5/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{9 b d (d \cos (a+b x))^{9/2}}",1,"(2*c*(c*Sin[a + b*x])^(3/2))/(9*b*d*(d*Cos[a + b*x])^(9/2)) - (2*c*(c*Sin[a + b*x])^(3/2))/(15*b*d^3*(d*Cos[a + b*x])^(5/2)) - (4*c*(c*Sin[a + b*x])^(3/2))/(15*b*d^5*Sqrt[d*Cos[a + b*x]]) + (4*c^2*Sqrt[d*Cos[a + b*x]]*EllipticE[a - Pi/4 + b*x, 2]*Sqrt[c*Sin[a + b*x]])/(15*b*d^6*Sqrt[Sin[2*a + 2*b*x]])","A",5,4,25,0.1600,1,"{2566, 2571, 2572, 2639}"
282,1,320,0,0.2575081,"\int \frac{(c \sin (a+b x))^{5/2}}{\sqrt{d \cos (a+b x)}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/Sqrt[d*Cos[a + b*x]],x]","-\frac{3 c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{4 \sqrt{2} b \sqrt{d}}+\frac{3 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{4 \sqrt{2} b \sqrt{d}}+\frac{3 c^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b \sqrt{d}}-\frac{3 c^{5/2} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b \sqrt{d}}-\frac{c (c \sin (a+b x))^{3/2} \sqrt{d \cos (a+b x)}}{2 b d}","-\frac{3 c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{4 \sqrt{2} b \sqrt{d}}+\frac{3 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{4 \sqrt{2} b \sqrt{d}}+\frac{3 c^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b \sqrt{d}}-\frac{3 c^{5/2} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{8 \sqrt{2} b \sqrt{d}}-\frac{c (c \sin (a+b x))^{3/2} \sqrt{d \cos (a+b x)}}{2 b d}",1,"(-3*c^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(4*Sqrt[2]*b*Sqrt[d]) + (3*c^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(4*Sqrt[2]*b*Sqrt[d]) + (3*c^(5/2)*Log[Sqrt[c] - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(8*Sqrt[2]*b*Sqrt[d]) - (3*c^(5/2)*Log[Sqrt[c] + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(8*Sqrt[2]*b*Sqrt[d]) - (c*Sqrt[d*Cos[a + b*x]]*(c*Sin[a + b*x])^(3/2))/(2*b*d)","A",11,8,25,0.3200,1,"{2568, 2574, 297, 1162, 617, 204, 1165, 628}"
283,1,315,0,0.2657003,"\int \frac{(c \sin (a+b x))^{5/2}}{(d \cos (a+b x))^{5/2}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/(d*Cos[a + b*x])^(5/2),x]","\frac{c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{\sqrt{2} b d^{5/2}}-\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{\sqrt{2} b d^{5/2}}-\frac{c^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b d^{5/2}}+\frac{c^{5/2} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b d^{5/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{3 b d (d \cos (a+b x))^{3/2}}","\frac{c^{5/2} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}\right)}{\sqrt{2} b d^{5/2}}-\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{c} \sqrt{d \cos (a+b x)}}+1\right)}{\sqrt{2} b d^{5/2}}-\frac{c^{5/2} \log \left(-\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b d^{5/2}}+\frac{c^{5/2} \log \left(\frac{\sqrt{2} \sqrt{d} \sqrt{c \sin (a+b x)}}{\sqrt{d \cos (a+b x)}}+\sqrt{c} \tan (a+b x)+\sqrt{c}\right)}{2 \sqrt{2} b d^{5/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{3 b d (d \cos (a+b x))^{3/2}}",1,"(c^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(Sqrt[2]*b*d^(5/2)) - (c^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/(Sqrt[c]*Sqrt[d*Cos[a + b*x]])])/(Sqrt[2]*b*d^(5/2)) - (c^(5/2)*Log[Sqrt[c] - (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(2*Sqrt[2]*b*d^(5/2)) + (c^(5/2)*Log[Sqrt[c] + (Sqrt[2]*Sqrt[d]*Sqrt[c*Sin[a + b*x]])/Sqrt[d*Cos[a + b*x]] + Sqrt[c]*Tan[a + b*x]])/(2*Sqrt[2]*b*d^(5/2)) + (2*c*(c*Sin[a + b*x])^(3/2))/(3*b*d*(d*Cos[a + b*x])^(3/2))","A",11,8,25,0.3200,1,"{2566, 2574, 297, 1162, 617, 204, 1165, 628}"
284,1,37,0,0.059941,"\int \frac{(c \sin (a+b x))^{5/2}}{(d \cos (a+b x))^{9/2}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/(d*Cos[a + b*x])^(9/2),x]","\frac{2 (c \sin (a+b x))^{7/2}}{7 b c d (d \cos (a+b x))^{7/2}}","\frac{2 (c \sin (a+b x))^{7/2}}{7 b c d (d \cos (a+b x))^{7/2}}",1,"(2*(c*Sin[a + b*x])^(7/2))/(7*b*c*d*(d*Cos[a + b*x])^(7/2))","A",1,1,25,0.04000,1,"{2563}"
285,1,106,0,0.1749371,"\int \frac{(c \sin (a+b x))^{5/2}}{(d \cos (a+b x))^{13/2}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/(d*Cos[a + b*x])^(13/2),x]","-\frac{8 c (c \sin (a+b x))^{3/2}}{77 b d^5 (d \cos (a+b x))^{3/2}}-\frac{6 c (c \sin (a+b x))^{3/2}}{77 b d^3 (d \cos (a+b x))^{7/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{11 b d (d \cos (a+b x))^{11/2}}","-\frac{8 c (c \sin (a+b x))^{3/2}}{77 b d^5 (d \cos (a+b x))^{3/2}}-\frac{6 c (c \sin (a+b x))^{3/2}}{77 b d^3 (d \cos (a+b x))^{7/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{11 b d (d \cos (a+b x))^{11/2}}",1,"(2*c*(c*Sin[a + b*x])^(3/2))/(11*b*d*(d*Cos[a + b*x])^(11/2)) - (6*c*(c*Sin[a + b*x])^(3/2))/(77*b*d^3*(d*Cos[a + b*x])^(7/2)) - (8*c*(c*Sin[a + b*x])^(3/2))/(77*b*d^5*(d*Cos[a + b*x])^(3/2))","A",3,3,25,0.1200,1,"{2566, 2571, 2563}"
286,1,141,0,0.2348116,"\int \frac{(c \sin (a+b x))^{5/2}}{(d \cos (a+b x))^{17/2}} \, dx","Int[(c*Sin[a + b*x])^(5/2)/(d*Cos[a + b*x])^(17/2),x]","-\frac{64 c (c \sin (a+b x))^{3/2}}{1155 b d^7 (d \cos (a+b x))^{3/2}}-\frac{16 c (c \sin (a+b x))^{3/2}}{385 b d^5 (d \cos (a+b x))^{7/2}}-\frac{2 c (c \sin (a+b x))^{3/2}}{55 b d^3 (d \cos (a+b x))^{11/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{15 b d (d \cos (a+b x))^{15/2}}","-\frac{64 c (c \sin (a+b x))^{3/2}}{1155 b d^7 (d \cos (a+b x))^{3/2}}-\frac{16 c (c \sin (a+b x))^{3/2}}{385 b d^5 (d \cos (a+b x))^{7/2}}-\frac{2 c (c \sin (a+b x))^{3/2}}{55 b d^3 (d \cos (a+b x))^{11/2}}+\frac{2 c (c \sin (a+b x))^{3/2}}{15 b d (d \cos (a+b x))^{15/2}}",1,"(2*c*(c*Sin[a + b*x])^(3/2))/(15*b*d*(d*Cos[a + b*x])^(15/2)) - (2*c*(c*Sin[a + b*x])^(3/2))/(55*b*d^3*(d*Cos[a + b*x])^(11/2)) - (16*c*(c*Sin[a + b*x])^(3/2))/(385*b*d^5*(d*Cos[a + b*x])^(7/2)) - (64*c*(c*Sin[a + b*x])^(3/2))/(1155*b*d^7*(d*Cos[a + b*x])^(3/2))","A",4,3,25,0.1200,1,"{2566, 2571, 2563}"
287,1,226,0,0.1493616,"\int \frac{\sin ^{\frac{7}{2}}(a+b x)}{\cos ^{\frac{7}{2}}(a+b x)} \, dx","Int[Sin[a + b*x]^(7/2)/Cos[a + b*x]^(7/2),x]","\frac{2 \sin ^{\frac{5}{2}}(a+b x)}{5 b \cos ^{\frac{5}{2}}(a+b x)}-\frac{2 \sqrt{\sin (a+b x)}}{b \sqrt{\cos (a+b x)}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{\sqrt{2} b}-\frac{\log \left(\cot (a+b x)-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}+\frac{\log \left(\cot (a+b x)+\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}","\frac{2 \sin ^{\frac{5}{2}}(a+b x)}{5 b \cos ^{\frac{5}{2}}(a+b x)}-\frac{2 \sqrt{\sin (a+b x)}}{b \sqrt{\cos (a+b x)}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{\sqrt{2} b}-\frac{\log \left(\cot (a+b x)-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}+\frac{\log \left(\cot (a+b x)+\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(Sqrt[2]*b) - ArcTan[1 + (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(Sqrt[2]*b) - Log[1 + Cot[a + b*x] - (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(2*Sqrt[2]*b) + Log[1 + Cot[a + b*x] + (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(2*Sqrt[2]*b) - (2*Sqrt[Sin[a + b*x]])/(b*Sqrt[Cos[a + b*x]]) + (2*Sin[a + b*x]^(5/2))/(5*b*Cos[a + b*x]^(5/2))","A",12,8,21,0.3810,1,"{2566, 2575, 297, 1162, 617, 204, 1165, 628}"
288,1,16,0,0.0226398,"\int \frac{\sin ^{\frac{3}{2}}(x)}{\cos ^{\frac{7}{2}}(x)} \, dx","Int[Sin[x]^(3/2)/Cos[x]^(7/2),x]","\frac{2 \sin ^{\frac{5}{2}}(x)}{5 \cos ^{\frac{5}{2}}(x)}","\frac{2 \sin ^{\frac{5}{2}}(x)}{5 \cos ^{\frac{5}{2}}(x)}",1,"(2*Sin[x]^(5/2))/(5*Cos[x]^(5/2))","A",1,1,13,0.07692,1,"{2563}"
289,1,122,0,0.0816404,"\int \frac{\sqrt{\sin (x)}}{\sqrt{\cos (x)}} \, dx","Int[Sqrt[Sin[x]]/Sqrt[Cos[x]],x]","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{\sqrt{2}}+\frac{\log \left(\tan (x)-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\tan (x)+\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{2 \sqrt{2}}","-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{\sqrt{2}}+\frac{\log \left(\tan (x)-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{2 \sqrt{2}}-\frac{\log \left(\tan (x)+\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{2 \sqrt{2}}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]]]/Sqrt[2]) + ArcTan[1 + (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]]]/Sqrt[2] + Log[1 - (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]] + Tan[x]]/(2*Sqrt[2]) - Log[1 + (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]] + Tan[x]]/(2*Sqrt[2])","A",10,7,13,0.5385,1,"{2574, 297, 1162, 617, 204, 1165, 628}"
290,1,143,0,0.1137513,"\int \frac{\sin ^{\frac{5}{2}}(x)}{\sqrt{\cos (x)}} \, dx","Int[Sin[x]^(5/2)/Sqrt[Cos[x]],x]","-\frac{1}{2} \sin ^{\frac{3}{2}}(x) \sqrt{\cos (x)}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{4 \sqrt{2}}+\frac{3 \log \left(\tan (x)-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{8 \sqrt{2}}-\frac{3 \log \left(\tan (x)+\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{8 \sqrt{2}}","-\frac{1}{2} \sin ^{\frac{3}{2}}(x) \sqrt{\cos (x)}-\frac{3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}\right)}{4 \sqrt{2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{4 \sqrt{2}}+\frac{3 \log \left(\tan (x)-\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{8 \sqrt{2}}-\frac{3 \log \left(\tan (x)+\frac{\sqrt{2} \sqrt{\sin (x)}}{\sqrt{\cos (x)}}+1\right)}{8 \sqrt{2}}",1,"(-3*ArcTan[1 - (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]]])/(4*Sqrt[2]) + (3*ArcTan[1 + (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]]])/(4*Sqrt[2]) + (3*Log[1 - (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]] + Tan[x]])/(8*Sqrt[2]) - (3*Log[1 + (Sqrt[2]*Sqrt[Sin[x]])/Sqrt[Cos[x]] + Tan[x]])/(8*Sqrt[2]) - (Sqrt[Cos[x]]*Sin[x]^(3/2))/2","A",11,8,13,0.6154,1,"{2568, 2574, 297, 1162, 617, 204, 1165, 628}"
291,1,132,0,0.1780042,"\int \frac{(d \cos (a+b x))^{7/2}}{\sqrt{c \sin (a+b x)}} \, dx","Int[(d*Cos[a + b*x])^(7/2)/Sqrt[c*Sin[a + b*x]],x]","\frac{5 d^3 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{6 b c}+\frac{5 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{12 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{d \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{5/2}}{3 b c}","\frac{5 d^3 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{6 b c}+\frac{5 d^4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{12 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{d \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{5/2}}{3 b c}",1,"(5*d^3*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])/(6*b*c) + (d*(d*Cos[a + b*x])^(5/2)*Sqrt[c*Sin[a + b*x]])/(3*b*c) + (5*d^4*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(12*b*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",4,3,25,0.1200,1,"{2569, 2573, 2641}"
292,1,92,0,0.1128952,"\int \frac{(d \cos (a+b x))^{3/2}}{\sqrt{c \sin (a+b x)}} \, dx","Int[(d*Cos[a + b*x])^(3/2)/Sqrt[c*Sin[a + b*x]],x]","\frac{d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{d \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b c}","\frac{d^2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{2 b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{d \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}{b c}",1,"(d*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])/(b*c) + (d^2*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(2*b*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",3,3,25,0.1200,1,"{2569, 2573, 2641}"
293,1,53,0,0.0554808,"\int \frac{1}{\sqrt{d \cos (a+b x)} \sqrt{c \sin (a+b x)}} \, dx","Int[1/(Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]]),x]","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}","\frac{\sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{b \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}",1,"(EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(b*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",2,2,25,0.08000,1,"{2573, 2641}"
294,1,97,0,0.1137116,"\int \frac{1}{(d \cos (a+b x))^{5/2} \sqrt{c \sin (a+b x)}} \, dx","Int[1/((d*Cos[a + b*x])^(5/2)*Sqrt[c*Sin[a + b*x]]),x]","\frac{2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b d^2 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{2 \sqrt{c \sin (a+b x)}}{3 b c d (d \cos (a+b x))^{3/2}}","\frac{2 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{3 b d^2 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{2 \sqrt{c \sin (a+b x)}}{3 b c d (d \cos (a+b x))^{3/2}}",1,"(2*Sqrt[c*Sin[a + b*x]])/(3*b*c*d*(d*Cos[a + b*x])^(3/2)) + (2*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(3*b*d^2*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",3,3,25,0.1200,1,"{2571, 2573, 2641}"
295,1,134,0,0.1722689,"\int \frac{1}{(d \cos (a+b x))^{9/2} \sqrt{c \sin (a+b x)}} \, dx","Int[1/((d*Cos[a + b*x])^(9/2)*Sqrt[c*Sin[a + b*x]]),x]","\frac{4 \sqrt{c \sin (a+b x)}}{7 b c d^3 (d \cos (a+b x))^{3/2}}+\frac{4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{7 b d^4 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{2 \sqrt{c \sin (a+b x)}}{7 b c d (d \cos (a+b x))^{7/2}}","\frac{4 \sqrt{c \sin (a+b x)}}{7 b c d^3 (d \cos (a+b x))^{3/2}}+\frac{4 \sqrt{\sin (2 a+2 b x)} F\left(\left.a+b x-\frac{\pi }{4}\right|2\right)}{7 b d^4 \sqrt{c \sin (a+b x)} \sqrt{d \cos (a+b x)}}+\frac{2 \sqrt{c \sin (a+b x)}}{7 b c d (d \cos (a+b x))^{7/2}}",1,"(2*Sqrt[c*Sin[a + b*x]])/(7*b*c*d*(d*Cos[a + b*x])^(7/2)) + (4*Sqrt[c*Sin[a + b*x]])/(7*b*c*d^3*(d*Cos[a + b*x])^(3/2)) + (4*EllipticF[a - Pi/4 + b*x, 2]*Sqrt[Sin[2*a + 2*b*x]])/(7*b*d^4*Sqrt[d*Cos[a + b*x]]*Sqrt[c*Sin[a + b*x]])","A",4,3,25,0.1200,1,"{2571, 2573, 2641}"
296,1,280,0,0.1767862,"\int \frac{\sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}} \, dx","Int[Sqrt[d*Cos[a + b*x]]/Sqrt[c*Sin[a + b*x]],x]","\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}\right)}{\sqrt{2} b \sqrt{c}}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}+1\right)}{\sqrt{2} b \sqrt{c}}-\frac{\sqrt{d} \log \left(-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b \sqrt{c}}+\frac{\sqrt{d} \log \left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b \sqrt{c}}","\frac{\sqrt{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}\right)}{\sqrt{2} b \sqrt{c}}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{d} \sqrt{c \sin (a+b x)}}+1\right)}{\sqrt{2} b \sqrt{c}}-\frac{\sqrt{d} \log \left(-\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b \sqrt{c}}+\frac{\sqrt{d} \log \left(\frac{\sqrt{2} \sqrt{c} \sqrt{d \cos (a+b x)}}{\sqrt{c \sin (a+b x)}}+\sqrt{d} \cot (a+b x)+\sqrt{d}\right)}{2 \sqrt{2} b \sqrt{c}}",1,"(Sqrt[d]*ArcTan[1 - (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/(Sqrt[d]*Sqrt[c*Sin[a + b*x]])])/(Sqrt[2]*b*Sqrt[c]) - (Sqrt[d]*ArcTan[1 + (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/(Sqrt[d]*Sqrt[c*Sin[a + b*x]])])/(Sqrt[2]*b*Sqrt[c]) - (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[a + b*x] - (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/Sqrt[c*Sin[a + b*x]]])/(2*Sqrt[2]*b*Sqrt[c]) + (Sqrt[d]*Log[Sqrt[d] + Sqrt[d]*Cot[a + b*x] + (Sqrt[2]*Sqrt[c]*Sqrt[d*Cos[a + b*x]])/Sqrt[c*Sin[a + b*x]]])/(2*Sqrt[2]*b*Sqrt[c])","A",10,7,25,0.2800,1,"{2575, 297, 1162, 617, 204, 1165, 628}"
297,1,35,0,0.0539481,"\int \frac{1}{(d \cos (a+b x))^{3/2} \sqrt{c \sin (a+b x)}} \, dx","Int[1/((d*Cos[a + b*x])^(3/2)*Sqrt[c*Sin[a + b*x]]),x]","\frac{2 \sqrt{c \sin (a+b x)}}{b c d \sqrt{d \cos (a+b x)}}","\frac{2 \sqrt{c \sin (a+b x)}}{b c d \sqrt{d \cos (a+b x)}}",1,"(2*Sqrt[c*Sin[a + b*x]])/(b*c*d*Sqrt[d*Cos[a + b*x]])","A",1,1,25,0.04000,1,"{2563}"
298,1,75,0,0.1112301,"\int \frac{1}{(d \cos (a+b x))^{7/2} \sqrt{c \sin (a+b x)}} \, dx","Int[1/((d*Cos[a + b*x])^(7/2)*Sqrt[c*Sin[a + b*x]]),x]","\frac{8 \sqrt{c \sin (a+b x)}}{5 b c d^3 \sqrt{d \cos (a+b x)}}+\frac{2 \sqrt{c \sin (a+b x)}}{5 b c d (d \cos (a+b x))^{5/2}}","\frac{8 \sqrt{c \sin (a+b x)}}{5 b c d^3 \sqrt{d \cos (a+b x)}}+\frac{2 \sqrt{c \sin (a+b x)}}{5 b c d (d \cos (a+b x))^{5/2}}",1,"(2*Sqrt[c*Sin[a + b*x]])/(5*b*c*d*(d*Cos[a + b*x])^(5/2)) + (8*Sqrt[c*Sin[a + b*x]])/(5*b*c*d^3*Sqrt[d*Cos[a + b*x]])","A",2,2,25,0.08000,1,"{2571, 2563}"
299,1,112,0,0.1687541,"\int \frac{1}{(d \cos (a+b x))^{11/2} \sqrt{c \sin (a+b x)}} \, dx","Int[1/((d*Cos[a + b*x])^(11/2)*Sqrt[c*Sin[a + b*x]]),x]","\frac{64 \sqrt{c \sin (a+b x)}}{45 b c d^5 \sqrt{d \cos (a+b x)}}+\frac{16 \sqrt{c \sin (a+b x)}}{45 b c d^3 (d \cos (a+b x))^{5/2}}+\frac{2 \sqrt{c \sin (a+b x)}}{9 b c d (d \cos (a+b x))^{9/2}}","\frac{64 \sqrt{c \sin (a+b x)}}{45 b c d^5 \sqrt{d \cos (a+b x)}}+\frac{16 \sqrt{c \sin (a+b x)}}{45 b c d^3 (d \cos (a+b x))^{5/2}}+\frac{2 \sqrt{c \sin (a+b x)}}{9 b c d (d \cos (a+b x))^{9/2}}",1,"(2*Sqrt[c*Sin[a + b*x]])/(9*b*c*d*(d*Cos[a + b*x])^(9/2)) + (16*Sqrt[c*Sin[a + b*x]])/(45*b*c*d^3*(d*Cos[a + b*x])^(5/2)) + (64*Sqrt[c*Sin[a + b*x]])/(45*b*c*d^5*Sqrt[d*Cos[a + b*x]])","A",3,2,25,0.08000,1,"{2571, 2563}"
300,1,174,0,0.0889395,"\int \frac{\sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}} \, dx","Int[Sqrt[Cos[a + b*x]]/Sqrt[Sin[a + b*x]],x]","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{\sqrt{2} b}-\frac{\log \left(\cot (a+b x)-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}+\frac{\log \left(\cot (a+b x)+\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}","\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{\sqrt{2} b}-\frac{\log \left(\cot (a+b x)-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}+\frac{\log \left(\cot (a+b x)+\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(Sqrt[2]*b) - ArcTan[1 + (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(Sqrt[2]*b) - Log[1 + Cot[a + b*x] - (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(2*Sqrt[2]*b) + Log[1 + Cot[a + b*x] + (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(2*Sqrt[2]*b)","A",10,7,21,0.3333,1,"{2575, 297, 1162, 617, 204, 1165, 628}"
301,1,199,0,0.1138404,"\int \frac{\cos ^{\frac{3}{2}}(a+b x)}{\sin ^{\frac{3}{2}}(a+b x)} \, dx","Int[Cos[a + b*x]^(3/2)/Sin[a + b*x]^(3/2),x]","-\frac{2 \sqrt{\cos (a+b x)}}{b \sqrt{\sin (a+b x)}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{\sqrt{2} b}-\frac{\log \left(\tan (a+b x)-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}+\frac{\log \left(\tan (a+b x)+\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}","-\frac{2 \sqrt{\cos (a+b x)}}{b \sqrt{\sin (a+b x)}}+\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}\right)}{\sqrt{2} b}-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{\sqrt{2} b}-\frac{\log \left(\tan (a+b x)-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}+\frac{\log \left(\tan (a+b x)+\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}",1,"ArcTan[1 - (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]]]/(Sqrt[2]*b) - ArcTan[1 + (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]]]/(Sqrt[2]*b) - Log[1 - (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]] + Tan[a + b*x]]/(2*Sqrt[2]*b) + Log[1 + (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]] + Tan[a + b*x]]/(2*Sqrt[2]*b) - (2*Sqrt[Cos[a + b*x]])/(b*Sqrt[Sin[a + b*x]])","A",11,8,21,0.3810,1,"{2567, 2574, 297, 1162, 617, 204, 1165, 628}"
302,1,201,0,0.1152621,"\int \frac{\cos ^{\frac{5}{2}}(a+b x)}{\sin ^{\frac{5}{2}}(a+b x)} \, dx","Int[Cos[a + b*x]^(5/2)/Sin[a + b*x]^(5/2),x]","-\frac{2 \cos ^{\frac{3}{2}}(a+b x)}{3 b \sin ^{\frac{3}{2}}(a+b x)}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}\right)}{\sqrt{2} b}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{\sqrt{2} b}+\frac{\log \left(\cot (a+b x)-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}-\frac{\log \left(\cot (a+b x)+\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}","-\frac{2 \cos ^{\frac{3}{2}}(a+b x)}{3 b \sin ^{\frac{3}{2}}(a+b x)}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}\right)}{\sqrt{2} b}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{\sqrt{2} b}+\frac{\log \left(\cot (a+b x)-\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}-\frac{\log \left(\cot (a+b x)+\frac{\sqrt{2} \sqrt{\cos (a+b x)}}{\sqrt{\sin (a+b x)}}+1\right)}{2 \sqrt{2} b}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(Sqrt[2]*b)) + ArcTan[1 + (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(Sqrt[2]*b) + Log[1 + Cot[a + b*x] - (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(2*Sqrt[2]*b) - Log[1 + Cot[a + b*x] + (Sqrt[2]*Sqrt[Cos[a + b*x]])/Sqrt[Sin[a + b*x]]]/(2*Sqrt[2]*b) - (2*Cos[a + b*x]^(3/2))/(3*b*Sin[a + b*x]^(3/2))","A",11,8,21,0.3810,1,"{2567, 2575, 297, 1162, 617, 204, 1165, 628}"
303,1,226,0,0.1389943,"\int \frac{\cos ^{\frac{7}{2}}(a+b x)}{\sin ^{\frac{7}{2}}(a+b x)} \, dx","Int[Cos[a + b*x]^(7/2)/Sin[a + b*x]^(7/2),x]","-\frac{2 \cos ^{\frac{5}{2}}(a+b x)}{5 b \sin ^{\frac{5}{2}}(a+b x)}+\frac{2 \sqrt{\cos (a+b x)}}{b \sqrt{\sin (a+b x)}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}\right)}{\sqrt{2} b}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{\sqrt{2} b}+\frac{\log \left(\tan (a+b x)-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}-\frac{\log \left(\tan (a+b x)+\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}","-\frac{2 \cos ^{\frac{5}{2}}(a+b x)}{5 b \sin ^{\frac{5}{2}}(a+b x)}+\frac{2 \sqrt{\cos (a+b x)}}{b \sqrt{\sin (a+b x)}}-\frac{\tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}\right)}{\sqrt{2} b}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{\sqrt{2} b}+\frac{\log \left(\tan (a+b x)-\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}-\frac{\log \left(\tan (a+b x)+\frac{\sqrt{2} \sqrt{\sin (a+b x)}}{\sqrt{\cos (a+b x)}}+1\right)}{2 \sqrt{2} b}",1,"-(ArcTan[1 - (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]]]/(Sqrt[2]*b)) + ArcTan[1 + (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]]]/(Sqrt[2]*b) + Log[1 - (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]] + Tan[a + b*x]]/(2*Sqrt[2]*b) - Log[1 + (Sqrt[2]*Sqrt[Sin[a + b*x]])/Sqrt[Cos[a + b*x]] + Tan[a + b*x]]/(2*Sqrt[2]*b) - (2*Cos[a + b*x]^(5/2))/(5*b*Sin[a + b*x]^(5/2)) + (2*Sqrt[Cos[a + b*x]])/(b*Sqrt[Sin[a + b*x]])","A",12,8,21,0.3810,1,"{2567, 2574, 297, 1162, 617, 204, 1165, 628}"
304,1,58,0,0.0393083,"\int \cos ^4(e+f x) \sqrt[3]{b \sin (e+f x)} \, dx","Int[Cos[e + f*x]^4*(b*Sin[e + f*x])^(1/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(-\frac{3}{2},\frac{2}{3};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(-\frac{3}{2},\frac{2}{3};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[-3/2, 2/3, 5/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(4/3))/(4*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,21,0.04762,1,"{2577}"
305,1,58,0,0.0382235,"\int \cos ^2(e+f x) \sqrt[3]{b \sin (e+f x)} \, dx","Int[Cos[e + f*x]^2*(b*Sin[e + f*x])^(1/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(-\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[-1/2, 2/3, 5/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(4/3))/(4*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,21,0.04762,1,"{2577}"
306,1,58,0,0.01495,"\int \sqrt[3]{b \sin (e+f x)} \, dx","Int[(b*Sin[e + f*x])^(1/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(4/3))/(4*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,12,0.08333,1,"{2643}"
307,1,58,0,0.0376715,"\int \sec ^2(e+f x) \sqrt[3]{b \sin (e+f x)} \, dx","Int[Sec[e + f*x]^2*(b*Sin[e + f*x])^(1/3),x]","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f}","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{3}{2};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f}",1,"(3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[2/3, 3/2, 5/3, Sin[e + f*x]^2]*Sec[e + f*x]*(b*Sin[e + f*x])^(4/3))/(4*b*f)","A",1,1,21,0.04762,1,"{2577}"
308,1,58,0,0.0378301,"\int \sec ^4(e+f x) \sqrt[3]{b \sin (e+f x)} \, dx","Int[Sec[e + f*x]^4*(b*Sin[e + f*x])^(1/3),x]","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{5}{2};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f}","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{4/3} \, _2F_1\left(\frac{2}{3},\frac{5}{2};\frac{5}{3};\sin ^2(e+f x)\right)}{4 b f}",1,"(3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[2/3, 5/2, 5/3, Sin[e + f*x]^2]*Sec[e + f*x]*(b*Sin[e + f*x])^(4/3))/(4*b*f)","A",1,1,21,0.04762,1,"{2577}"
309,1,58,0,0.0433625,"\int \cos ^4(e+f x) (b \sin (e+f x))^{5/3} \, dx","Int[Cos[e + f*x]^4*(b*Sin[e + f*x])^(5/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(-\frac{3}{2},\frac{4}{3};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(-\frac{3}{2},\frac{4}{3};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[-3/2, 4/3, 7/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(8/3))/(8*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,21,0.04762,1,"{2577}"
310,1,58,0,0.0450176,"\int \cos ^2(e+f x) (b \sin (e+f x))^{5/3} \, dx","Int[Cos[e + f*x]^2*(b*Sin[e + f*x])^(5/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(-\frac{1}{2},\frac{4}{3};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(-\frac{1}{2},\frac{4}{3};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[-1/2, 4/3, 7/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(8/3))/(8*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,21,0.04762,1,"{2577}"
311,1,58,0,0.0141124,"\int (b \sin (e+f x))^{5/3} \, dx","Int[(b*Sin[e + f*x])^(5/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(\frac{1}{2},\frac{4}{3};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[1/2, 4/3, 7/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(8/3))/(8*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,12,0.08333,1,"{2643}"
312,1,58,0,0.0440728,"\int \sec ^2(e+f x) (b \sin (e+f x))^{5/3} \, dx","Int[Sec[e + f*x]^2*(b*Sin[e + f*x])^(5/3),x]","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(\frac{4}{3},\frac{3}{2};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f}","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(\frac{4}{3},\frac{3}{2};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f}",1,"(3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[4/3, 3/2, 7/3, Sin[e + f*x]^2]*Sec[e + f*x]*(b*Sin[e + f*x])^(8/3))/(8*b*f)","A",1,1,21,0.04762,1,"{2577}"
313,1,58,0,0.0444031,"\int \sec ^4(e+f x) (b \sin (e+f x))^{5/3} \, dx","Int[Sec[e + f*x]^4*(b*Sin[e + f*x])^(5/3),x]","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(\frac{4}{3},\frac{5}{2};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f}","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{8/3} \, _2F_1\left(\frac{4}{3},\frac{5}{2};\frac{7}{3};\sin ^2(e+f x)\right)}{8 b f}",1,"(3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[4/3, 5/2, 7/3, Sin[e + f*x]^2]*Sec[e + f*x]*(b*Sin[e + f*x])^(8/3))/(8*b*f)","A",1,1,21,0.04762,1,"{2577}"
314,1,58,0,0.0436346,"\int \frac{\cos ^4(e+f x)}{\sqrt[3]{b \sin (e+f x)}} \, dx","Int[Cos[e + f*x]^4/(b*Sin[e + f*x])^(1/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(-\frac{3}{2},\frac{1}{3};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(-\frac{3}{2},\frac{1}{3};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[-3/2, 1/3, 4/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(2/3))/(2*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,21,0.04762,1,"{2577}"
315,1,58,0,0.0392388,"\int \frac{\cos ^2(e+f x)}{\sqrt[3]{b \sin (e+f x)}} \, dx","Int[Cos[e + f*x]^2/(b*Sin[e + f*x])^(1/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(-\frac{1}{2},\frac{1}{3};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[-1/2, 1/3, 4/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(2/3))/(2*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,21,0.04762,1,"{2577}"
316,1,58,0,0.0146014,"\int \frac{1}{\sqrt[3]{b \sin (e+f x)}} \, dx","Int[(b*Sin[e + f*x])^(-1/3),x]","\frac{3 \cos (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)}}","\frac{3 \cos (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)}}",1,"(3*Cos[e + f*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sin[e + f*x]^2]*(b*Sin[e + f*x])^(2/3))/(2*b*f*Sqrt[Cos[e + f*x]^2])","A",1,1,12,0.08333,1,"{2643}"
317,1,58,0,0.0397975,"\int \frac{\sec ^2(e+f x)}{\sqrt[3]{b \sin (e+f x)}} \, dx","Int[Sec[e + f*x]^2/(b*Sin[e + f*x])^(1/3),x]","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{3}{2};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f}","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{3}{2};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f}",1,"(3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[1/3, 3/2, 4/3, Sin[e + f*x]^2]*Sec[e + f*x]*(b*Sin[e + f*x])^(2/3))/(2*b*f)","A",1,1,21,0.04762,1,"{2577}"
318,1,58,0,0.0385146,"\int \frac{\sec ^4(e+f x)}{\sqrt[3]{b \sin (e+f x)}} \, dx","Int[Sec[e + f*x]^4/(b*Sin[e + f*x])^(1/3),x]","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{5}{2};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f}","\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) (b \sin (e+f x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{5}{2};\frac{4}{3};\sin ^2(e+f x)\right)}{2 b f}",1,"(3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[1/3, 5/2, 4/3, Sin[e + f*x]^2]*Sec[e + f*x]*(b*Sin[e + f*x])^(2/3))/(2*b*f)","A",1,1,21,0.04762,1,"{2577}"
319,1,58,0,0.0462221,"\int \frac{\cos ^4(e+f x)}{(b \sin (e+f x))^{5/3}} \, dx","Int[Cos[e + f*x]^4/(b*Sin[e + f*x])^(5/3),x]","-\frac{3 \cos (e+f x) \, _2F_1\left(-\frac{3}{2},-\frac{1}{3};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)} (b \sin (e+f x))^{2/3}}","-\frac{3 \cos (e+f x) \, _2F_1\left(-\frac{3}{2},-\frac{1}{3};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)} (b \sin (e+f x))^{2/3}}",1,"(-3*Cos[e + f*x]*Hypergeometric2F1[-3/2, -1/3, 2/3, Sin[e + f*x]^2])/(2*b*f*Sqrt[Cos[e + f*x]^2]*(b*Sin[e + f*x])^(2/3))","A",1,1,21,0.04762,1,"{2577}"
320,1,58,0,0.0456165,"\int \frac{\cos ^2(e+f x)}{(b \sin (e+f x))^{5/3}} \, dx","Int[Cos[e + f*x]^2/(b*Sin[e + f*x])^(5/3),x]","-\frac{3 \cos (e+f x) \, _2F_1\left(-\frac{1}{2},-\frac{1}{3};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)} (b \sin (e+f x))^{2/3}}","-\frac{3 \cos (e+f x) \, _2F_1\left(-\frac{1}{2},-\frac{1}{3};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)} (b \sin (e+f x))^{2/3}}",1,"(-3*Cos[e + f*x]*Hypergeometric2F1[-1/2, -1/3, 2/3, Sin[e + f*x]^2])/(2*b*f*Sqrt[Cos[e + f*x]^2]*(b*Sin[e + f*x])^(2/3))","A",1,1,21,0.04762,1,"{2577}"
321,1,58,0,0.0144688,"\int \frac{1}{(b \sin (e+f x))^{5/3}} \, dx","Int[(b*Sin[e + f*x])^(-5/3),x]","-\frac{3 \cos (e+f x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)} (b \sin (e+f x))^{2/3}}","-\frac{3 \cos (e+f x) \, _2F_1\left(-\frac{1}{3},\frac{1}{2};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f \sqrt{\cos ^2(e+f x)} (b \sin (e+f x))^{2/3}}",1,"(-3*Cos[e + f*x]*Hypergeometric2F1[-1/3, 1/2, 2/3, Sin[e + f*x]^2])/(2*b*f*Sqrt[Cos[e + f*x]^2]*(b*Sin[e + f*x])^(2/3))","A",1,1,12,0.08333,1,"{2643}"
322,1,58,0,0.0455026,"\int \frac{\sec ^2(e+f x)}{(b \sin (e+f x))^{5/3}} \, dx","Int[Sec[e + f*x]^2/(b*Sin[e + f*x])^(5/3),x]","-\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) \, _2F_1\left(-\frac{1}{3},\frac{3}{2};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f (b \sin (e+f x))^{2/3}}","-\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) \, _2F_1\left(-\frac{1}{3},\frac{3}{2};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f (b \sin (e+f x))^{2/3}}",1,"(-3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[-1/3, 3/2, 2/3, Sin[e + f*x]^2]*Sec[e + f*x])/(2*b*f*(b*Sin[e + f*x])^(2/3))","A",1,1,21,0.04762,1,"{2577}"
323,1,58,0,0.0464785,"\int \frac{\sec ^4(e+f x)}{(b \sin (e+f x))^{5/3}} \, dx","Int[Sec[e + f*x]^4/(b*Sin[e + f*x])^(5/3),x]","-\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) \, _2F_1\left(-\frac{1}{3},\frac{5}{2};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f (b \sin (e+f x))^{2/3}}","-\frac{3 \sqrt{\cos ^2(e+f x)} \sec (e+f x) \, _2F_1\left(-\frac{1}{3},\frac{5}{2};\frac{2}{3};\sin ^2(e+f x)\right)}{2 b f (b \sin (e+f x))^{2/3}}",1,"(-3*Sqrt[Cos[e + f*x]^2]*Hypergeometric2F1[-1/3, 5/2, 2/3, Sin[e + f*x]^2]*Sec[e + f*x])/(2*b*f*(b*Sin[e + f*x])^(2/3))","A",1,1,21,0.04762,1,"{2577}"
324,1,128,0,0.1512702,"\int \frac{\sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}} \, dx","Int[Sin[a + b*x]^(1/3)/Cos[a + b*x]^(1/3),x]","-\frac{\log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}+\frac{\log \left(\frac{\sin ^{\frac{4}{3}}(a+b x)}{\cos ^{\frac{4}{3}}(a+b x)}-\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}","-\frac{\log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}+\frac{\log \left(\frac{\sin ^{\frac{4}{3}}(a+b x)}{\cos ^{\frac{4}{3}}(a+b x)}-\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}",1,"-(Sqrt[3]*ArcTan[(1 - (2*Sin[a + b*x]^(2/3))/Cos[a + b*x]^(2/3))/Sqrt[3]])/(2*b) - Log[1 + Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3)]/(2*b) + Log[1 - Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3) + Sin[a + b*x]^(4/3)/Cos[a + b*x]^(4/3)]/(4*b)","A",8,8,21,0.3810,1,"{2574, 275, 292, 31, 634, 618, 204, 628}"
325,1,224,0,0.3294615,"\int \frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)} \, dx","Int[Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3),x]","\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}-\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+\sqrt{3}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{b}","\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}-\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+\sqrt{3}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{b}",1,"-ArcTan[Sqrt[3] - (2*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3)]/(2*b) + ArcTan[Sqrt[3] + (2*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3)]/(2*b) + ArcTan[Sin[a + b*x]^(1/3)/Cos[a + b*x]^(1/3)]/b + (Sqrt[3]*Log[1 - (Sqrt[3]*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3) + Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3)])/(4*b) - (Sqrt[3]*Log[1 + (Sqrt[3]*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3) + Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3)])/(4*b)","A",11,7,21,0.3333,1,"{2574, 295, 634, 618, 204, 628, 203}"
326,1,249,0,0.3478168,"\int \frac{\sin ^{\frac{4}{3}}(a+b x)}{\cos ^{\frac{4}{3}}(a+b x)} \, dx","Int[Sin[a + b*x]^(4/3)/Cos[a + b*x]^(4/3),x]","\frac{3 \sqrt[3]{\sin (a+b x)}}{b \sqrt[3]{\cos (a+b x)}}+\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}-\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+\sqrt{3}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{b}","\frac{3 \sqrt[3]{\sin (a+b x)}}{b \sqrt[3]{\cos (a+b x)}}+\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}-\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}-\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+\sqrt{3}\right)}{2 b}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{b}",1,"-ArcTan[Sqrt[3] - (2*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)]/(2*b) + ArcTan[Sqrt[3] + (2*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)]/(2*b) + ArcTan[Cos[a + b*x]^(1/3)/Sin[a + b*x]^(1/3)]/b + (Sqrt[3]*Log[1 + Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3) - (Sqrt[3]*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)])/(4*b) - (Sqrt[3]*Log[1 + Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3) + (Sqrt[3]*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)])/(4*b) + (3*Sin[a + b*x]^(1/3))/(b*Cos[a + b*x]^(1/3))","A",12,8,21,0.3810,1,"{2566, 2575, 295, 634, 618, 204, 628, 203}"
327,1,155,0,0.1746708,"\int \frac{\sin ^{\frac{5}{3}}(a+b x)}{\cos ^{\frac{5}{3}}(a+b x)} \, dx","Int[Sin[a + b*x]^(5/3)/Cos[a + b*x]^(5/3),x]","\frac{3 \sin ^{\frac{2}{3}}(a+b x)}{2 b \cos ^{\frac{2}{3}}(a+b x)}+\frac{\log \left(\frac{\cos ^{\frac{4}{3}}(a+b x)}{\sin ^{\frac{4}{3}}(a+b x)}-\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}","\frac{3 \sin ^{\frac{2}{3}}(a+b x)}{2 b \cos ^{\frac{2}{3}}(a+b x)}+\frac{\log \left(\frac{\cos ^{\frac{4}{3}}(a+b x)}{\sin ^{\frac{4}{3}}(a+b x)}-\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}",1,"-(Sqrt[3]*ArcTan[(1 - (2*Cos[a + b*x]^(2/3))/Sin[a + b*x]^(2/3))/Sqrt[3]])/(2*b) + Log[1 + Cos[a + b*x]^(4/3)/Sin[a + b*x]^(4/3) - Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3)]/(4*b) - Log[1 + Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3)]/(2*b) + (3*Sin[a + b*x]^(2/3))/(2*b*Cos[a + b*x]^(2/3))","A",9,9,21,0.4286,1,"{2566, 2575, 275, 292, 31, 634, 618, 204, 628}"
328,1,155,0,0.1101214,"\int \frac{\sin ^{\frac{7}{3}}(a+b x)}{\cos ^{\frac{7}{3}}(a+b x)} \, dx","Int[Sin[a + b*x]^(7/3)/Cos[a + b*x]^(7/3),x]","\frac{3 \sin ^{\frac{4}{3}}(a+b x)}{4 b \cos ^{\frac{4}{3}}(a+b x)}+\frac{\log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\log \left(\frac{\sin ^{\frac{4}{3}}(a+b x)}{\cos ^{\frac{4}{3}}(a+b x)}-\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}","\frac{3 \sin ^{\frac{4}{3}}(a+b x)}{4 b \cos ^{\frac{4}{3}}(a+b x)}+\frac{\log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\log \left(\frac{\sin ^{\frac{4}{3}}(a+b x)}{\cos ^{\frac{4}{3}}(a+b x)}-\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}",1,"(Sqrt[3]*ArcTan[(1 - (2*Sin[a + b*x]^(2/3))/Cos[a + b*x]^(2/3))/Sqrt[3]])/(2*b) + Log[1 + Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3)]/(2*b) - Log[1 - Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3) + Sin[a + b*x]^(4/3)/Cos[a + b*x]^(4/3)]/(4*b) + (3*Sin[a + b*x]^(4/3))/(4*b*Cos[a + b*x]^(4/3))","A",9,9,21,0.4286,1,"{2566, 2574, 275, 292, 31, 634, 618, 204, 628}"
329,1,128,0,0.0822267,"\int \frac{\sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}} \, dx","Int[Cos[a + b*x]^(1/3)/Sin[a + b*x]^(1/3),x]","-\frac{\log \left(\frac{\cos ^{\frac{4}{3}}(a+b x)}{\sin ^{\frac{4}{3}}(a+b x)}-\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}+\frac{\log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}","-\frac{\log \left(\frac{\cos ^{\frac{4}{3}}(a+b x)}{\sin ^{\frac{4}{3}}(a+b x)}-\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}+\frac{\log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}",1,"(Sqrt[3]*ArcTan[(1 - (2*Cos[a + b*x]^(2/3))/Sin[a + b*x]^(2/3))/Sqrt[3]])/(2*b) - Log[1 + Cos[a + b*x]^(4/3)/Sin[a + b*x]^(4/3) - Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3)]/(4*b) + Log[1 + Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3)]/(2*b)","A",8,8,21,0.3810,1,"{2575, 275, 292, 31, 634, 618, 204, 628}"
330,1,225,0,0.3002669,"\int \frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)} \, dx","Int[Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3),x]","-\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+\sqrt{3}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{b}","-\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+1\right)}{4 b}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}+\sqrt{3}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\cos (a+b x)}}{\sqrt[3]{\sin (a+b x)}}\right)}{b}",1,"ArcTan[Sqrt[3] - (2*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)]/(2*b) - ArcTan[Sqrt[3] + (2*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)]/(2*b) - ArcTan[Cos[a + b*x]^(1/3)/Sin[a + b*x]^(1/3)]/b - (Sqrt[3]*Log[1 + Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3) - (Sqrt[3]*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)])/(4*b) + (Sqrt[3]*Log[1 + Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3) + (Sqrt[3]*Cos[a + b*x]^(1/3))/Sin[a + b*x]^(1/3)])/(4*b)","A",11,7,21,0.3333,1,"{2575, 295, 634, 618, 204, 628, 203}"
331,1,250,0,0.3258249,"\int \frac{\cos ^{\frac{4}{3}}(a+b x)}{\sin ^{\frac{4}{3}}(a+b x)} \, dx","Int[Cos[a + b*x]^(4/3)/Sin[a + b*x]^(4/3),x]","-\frac{3 \sqrt[3]{\cos (a+b x)}}{b \sqrt[3]{\sin (a+b x)}}-\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+\sqrt{3}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{b}","-\frac{3 \sqrt[3]{\cos (a+b x)}}{b \sqrt[3]{\sin (a+b x)}}-\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}-\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}+\frac{\sqrt{3} \log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+\frac{\sqrt{3} \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+1\right)}{4 b}+\frac{\tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}+\sqrt{3}\right)}{2 b}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{\sin (a+b x)}}{\sqrt[3]{\cos (a+b x)}}\right)}{b}",1,"ArcTan[Sqrt[3] - (2*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3)]/(2*b) - ArcTan[Sqrt[3] + (2*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3)]/(2*b) - ArcTan[Sin[a + b*x]^(1/3)/Cos[a + b*x]^(1/3)]/b - (Sqrt[3]*Log[1 - (Sqrt[3]*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3) + Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3)])/(4*b) + (Sqrt[3]*Log[1 + (Sqrt[3]*Sin[a + b*x]^(1/3))/Cos[a + b*x]^(1/3) + Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3)])/(4*b) - (3*Cos[a + b*x]^(1/3))/(b*Sin[a + b*x]^(1/3))","A",12,8,21,0.3810,1,"{2567, 2574, 295, 634, 618, 204, 628, 203}"
332,1,155,0,0.1111313,"\int \frac{\cos ^{\frac{5}{3}}(a+b x)}{\sin ^{\frac{5}{3}}(a+b x)} \, dx","Int[Cos[a + b*x]^(5/3)/Sin[a + b*x]^(5/3),x]","-\frac{3 \cos ^{\frac{2}{3}}(a+b x)}{2 b \sin ^{\frac{2}{3}}(a+b x)}+\frac{\log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\log \left(\frac{\sin ^{\frac{4}{3}}(a+b x)}{\cos ^{\frac{4}{3}}(a+b x)}-\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}","-\frac{3 \cos ^{\frac{2}{3}}(a+b x)}{2 b \sin ^{\frac{2}{3}}(a+b x)}+\frac{\log \left(\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\log \left(\frac{\sin ^{\frac{4}{3}}(a+b x)}{\cos ^{\frac{4}{3}}(a+b x)}-\frac{\sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sin ^{\frac{2}{3}}(a+b x)}{\cos ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}",1,"(Sqrt[3]*ArcTan[(1 - (2*Sin[a + b*x]^(2/3))/Cos[a + b*x]^(2/3))/Sqrt[3]])/(2*b) + Log[1 + Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3)]/(2*b) - Log[1 - Sin[a + b*x]^(2/3)/Cos[a + b*x]^(2/3) + Sin[a + b*x]^(4/3)/Cos[a + b*x]^(4/3)]/(4*b) - (3*Cos[a + b*x]^(2/3))/(2*b*Sin[a + b*x]^(2/3))","A",9,9,21,0.4286,1,"{2567, 2574, 275, 292, 31, 634, 618, 204, 628}"
333,1,155,0,0.13426,"\int \frac{\cos ^{\frac{7}{3}}(a+b x)}{\sin ^{\frac{7}{3}}(a+b x)} \, dx","Int[Cos[a + b*x]^(7/3)/Sin[a + b*x]^(7/3),x]","-\frac{3 \cos ^{\frac{4}{3}}(a+b x)}{4 b \sin ^{\frac{4}{3}}(a+b x)}+\frac{\log \left(\frac{\cos ^{\frac{4}{3}}(a+b x)}{\sin ^{\frac{4}{3}}(a+b x)}-\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}","-\frac{3 \cos ^{\frac{4}{3}}(a+b x)}{4 b \sin ^{\frac{4}{3}}(a+b x)}+\frac{\log \left(\frac{\cos ^{\frac{4}{3}}(a+b x)}{\sin ^{\frac{4}{3}}(a+b x)}-\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{4 b}-\frac{\log \left(\frac{\cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}+1\right)}{2 b}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \cos ^{\frac{2}{3}}(a+b x)}{\sin ^{\frac{2}{3}}(a+b x)}}{\sqrt{3}}\right)}{2 b}",1,"-(Sqrt[3]*ArcTan[(1 - (2*Cos[a + b*x]^(2/3))/Sin[a + b*x]^(2/3))/Sqrt[3]])/(2*b) + Log[1 + Cos[a + b*x]^(4/3)/Sin[a + b*x]^(4/3) - Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3)]/(4*b) - Log[1 + Cos[a + b*x]^(2/3)/Sin[a + b*x]^(2/3)]/(2*b) - (3*Cos[a + b*x]^(4/3))/(4*b*Sin[a + b*x]^(4/3))","A",9,9,21,0.4286,1,"{2567, 2575, 275, 292, 31, 634, 618, 204, 628}"
334,1,16,0,0.0220673,"\int \frac{\cos ^{\frac{2}{3}}(x)}{\sin ^{\frac{8}{3}}(x)} \, dx","Int[Cos[x]^(2/3)/Sin[x]^(8/3),x]","-\frac{3 \cos ^{\frac{5}{3}}(x)}{5 \sin ^{\frac{5}{3}}(x)}","-\frac{3 \cos ^{\frac{5}{3}}(x)}{5 \sin ^{\frac{5}{3}}(x)}",1,"(-3*Cos[x]^(5/3))/(5*Sin[x]^(5/3))","A",1,1,13,0.07692,1,"{2563}"
335,1,16,0,0.0231872,"\int \frac{\sin ^{\frac{2}{3}}(x)}{\cos ^{\frac{8}{3}}(x)} \, dx","Int[Sin[x]^(2/3)/Cos[x]^(8/3),x]","\frac{3 \sin ^{\frac{5}{3}}(x)}{5 \cos ^{\frac{5}{3}}(x)}","\frac{3 \sin ^{\frac{5}{3}}(x)}{5 \cos ^{\frac{5}{3}}(x)}",1,"(3*Sin[x]^(5/3))/(5*Cos[x]^(5/3))","A",1,1,13,0.07692,1,"{2563}"
336,1,80,0,0.0419246,"\int \cos ^n(e+f x) \sin ^m(e+f x) \, dx","Int[Cos[e + f*x]^n*Sin[e + f*x]^m,x]","-\frac{\sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} \cos ^{n+1}(e+f x) \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{f (n+1)}","-\frac{\sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} \cos ^{n+1}(e+f x) \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{f (n+1)}",1,"-((Cos[e + f*x]^(1 + n)*Hypergeometric2F1[(1 - m)/2, (1 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*Sin[e + f*x]^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(f*(1 + n)))","A",1,1,17,0.05882,1,"{2576}"
337,1,85,0,0.0445437,"\int (d \cos (e+f x))^n \sin ^m(e+f x) \, dx","Int[(d*Cos[e + f*x])^n*Sin[e + f*x]^m,x]","-\frac{\sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} (d \cos (e+f x))^{n+1} \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}","-\frac{\sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} (d \cos (e+f x))^{n+1} \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}",1,"-(((d*Cos[e + f*x])^(1 + n)*Hypergeometric2F1[(1 - m)/2, (1 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*Sin[e + f*x]^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(d*f*(1 + n)))","A",1,1,19,0.05263,1,"{2576}"
338,1,83,0,0.0432349,"\int \cos ^n(e+f x) (b \sin (e+f x))^m \, dx","Int[Cos[e + f*x]^n*(b*Sin[e + f*x])^m,x]","-\frac{b \sin ^2(e+f x)^{\frac{1-m}{2}} \cos ^{n+1}(e+f x) (b \sin (e+f x))^{m-1} \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{f (n+1)}","-\frac{b \sin ^2(e+f x)^{\frac{1-m}{2}} \cos ^{n+1}(e+f x) (b \sin (e+f x))^{m-1} \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{f (n+1)}",1,"-((b*Cos[e + f*x]^(1 + n)*Hypergeometric2F1[(1 - m)/2, (1 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*(b*Sin[e + f*x])^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(f*(1 + n)))","A",1,1,19,0.05263,1,"{2576}"
339,1,88,0,0.0480973,"\int (d \cos (e+f x))^n (b \sin (e+f x))^m \, dx","Int[(d*Cos[e + f*x])^n*(b*Sin[e + f*x])^m,x]","-\frac{b \sin ^2(e+f x)^{\frac{1-m}{2}} (b \sin (e+f x))^{m-1} (d \cos (e+f x))^{n+1} \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}","-\frac{b \sin ^2(e+f x)^{\frac{1-m}{2}} (b \sin (e+f x))^{m-1} (d \cos (e+f x))^{n+1} \, _2F_1\left(\frac{1-m}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(e+f x)\right)}{d f (n+1)}",1,"-((b*(d*Cos[e + f*x])^(1 + n)*Hypergeometric2F1[(1 - m)/2, (1 + n)/2, (3 + n)/2, Cos[e + f*x]^2]*(b*Sin[e + f*x])^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(d*f*(1 + n)))","A",1,1,21,0.04762,1,"{2576}"
340,1,74,0,0.0697001,"\int \cos ^5(a+b x) (c \sin (a+b x))^m \, dx","Int[Cos[a + b*x]^5*(c*Sin[a + b*x])^m,x]","-\frac{2 (c \sin (a+b x))^{m+3}}{b c^3 (m+3)}+\frac{(c \sin (a+b x))^{m+5}}{b c^5 (m+5)}+\frac{(c \sin (a+b x))^{m+1}}{b c (m+1)}","-\frac{2 (c \sin (a+b x))^{m+3}}{b c^3 (m+3)}+\frac{(c \sin (a+b x))^{m+5}}{b c^5 (m+5)}+\frac{(c \sin (a+b x))^{m+1}}{b c (m+1)}",1,"(c*Sin[a + b*x])^(1 + m)/(b*c*(1 + m)) - (2*(c*Sin[a + b*x])^(3 + m))/(b*c^3*(3 + m)) + (c*Sin[a + b*x])^(5 + m)/(b*c^5*(5 + m))","A",3,2,19,0.1053,1,"{2564, 270}"
341,1,50,0,0.0506607,"\int \cos ^3(a+b x) (c \sin (a+b x))^m \, dx","Int[Cos[a + b*x]^3*(c*Sin[a + b*x])^m,x]","\frac{(c \sin (a+b x))^{m+1}}{b c (m+1)}-\frac{(c \sin (a+b x))^{m+3}}{b c^3 (m+3)}","\frac{(c \sin (a+b x))^{m+1}}{b c (m+1)}-\frac{(c \sin (a+b x))^{m+3}}{b c^3 (m+3)}",1,"(c*Sin[a + b*x])^(1 + m)/(b*c*(1 + m)) - (c*Sin[a + b*x])^(3 + m)/(b*c^3*(3 + m))","A",3,2,19,0.1053,1,"{2564, 14}"
342,1,24,0,0.0248876,"\int \cos (a+b x) (c \sin (a+b x))^m \, dx","Int[Cos[a + b*x]*(c*Sin[a + b*x])^m,x]","\frac{(c \sin (a+b x))^{m+1}}{b c (m+1)}","\frac{(c \sin (a+b x))^{m+1}}{b c (m+1)}",1,"(c*Sin[a + b*x])^(1 + m)/(b*c*(1 + m))","A",2,2,17,0.1176,1,"{2564, 30}"
343,1,48,0,0.0411817,"\int \sec (a+b x) (c \sin (a+b x))^m \, dx","Int[Sec[a + b*x]*(c*Sin[a + b*x])^m,x]","\frac{(c \sin (a+b x))^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}","\frac{(c \sin (a+b x))^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}",1,"(Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m))","A",2,2,17,0.1176,1,"{2564, 364}"
344,1,48,0,0.046838,"\int \sec ^3(a+b x) (c \sin (a+b x))^m \, dx","Int[Sec[a + b*x]^3*(c*Sin[a + b*x])^m,x]","\frac{(c \sin (a+b x))^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}","\frac{(c \sin (a+b x))^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}",1,"(Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m))","A",2,2,19,0.1053,1,"{2564, 364}"
345,1,68,0,0.0409665,"\int \cos ^4(a+b x) (c \sin (a+b x))^m \, dx","Int[Cos[a + b*x]^4*(c*Sin[a + b*x])^m,x]","\frac{\cos (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{\cos ^2(a+b x)}}","\frac{\cos (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{\cos ^2(a+b x)}}",1,"(Cos[a + b*x]*Hypergeometric2F1[-3/2, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m)*Sqrt[Cos[a + b*x]^2])","A",1,1,19,0.05263,1,"{2577}"
346,1,68,0,0.0406509,"\int \cos ^2(a+b x) (c \sin (a+b x))^m \, dx","Int[Cos[a + b*x]^2*(c*Sin[a + b*x])^m,x]","\frac{\cos (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{\cos ^2(a+b x)}}","\frac{\cos (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{\cos ^2(a+b x)}}",1,"(Cos[a + b*x]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m)*Sqrt[Cos[a + b*x]^2])","A",1,1,19,0.05263,1,"{2577}"
347,1,68,0,0.0146984,"\int (c \sin (a+b x))^m \, dx","Int[(c*Sin[a + b*x])^m,x]","\frac{\cos (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{\cos ^2(a+b x)}}","\frac{\cos (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{\cos ^2(a+b x)}}",1,"(Cos[a + b*x]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m)*Sqrt[Cos[a + b*x]^2])","A",1,1,10,0.1000,1,"{2643}"
348,1,68,0,0.0401584,"\int \sec ^2(a+b x) (c \sin (a+b x))^m \, dx","Int[Sec[a + b*x]^2*(c*Sin[a + b*x])^m,x]","\frac{\sqrt{\cos ^2(a+b x)} \sec (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}","\frac{\sqrt{\cos ^2(a+b x)} \sec (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}",1,"(Sqrt[Cos[a + b*x]^2]*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*Sec[a + b*x]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m))","A",1,1,19,0.05263,1,"{2577}"
349,1,68,0,0.0399385,"\int \sec ^4(a+b x) (c \sin (a+b x))^m \, dx","Int[Sec[a + b*x]^4*(c*Sin[a + b*x])^m,x]","\frac{\sqrt{\cos ^2(a+b x)} \sec (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}","\frac{\sqrt{\cos ^2(a+b x)} \sec (a+b x) (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}",1,"(Sqrt[Cos[a + b*x]^2]*Hypergeometric2F1[5/2, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*Sec[a + b*x]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m))","A",1,1,19,0.05263,1,"{2577}"
350,1,75,0,0.0546918,"\int (d \cos (a+b x))^{3/2} (c \sin (a+b x))^m \, dx","Int[(d*Cos[a + b*x])^(3/2)*(c*Sin[a + b*x])^m,x]","\frac{d \sqrt{d \cos (a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt[4]{\cos ^2(a+b x)}}","\frac{d \sqrt{d \cos (a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt[4]{\cos ^2(a+b x)}}",1,"(d*Sqrt[d*Cos[a + b*x]]*Hypergeometric2F1[-1/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m)*(Cos[a + b*x]^2)^(1/4))","A",1,1,23,0.04348,1,"{2577}"
351,1,75,0,0.0475906,"\int \sqrt{d \cos (a+b x)} (c \sin (a+b x))^m \, dx","Int[Sqrt[d*Cos[a + b*x]]*(c*Sin[a + b*x])^m,x]","\frac{d \sqrt[4]{\cos ^2(a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{d \cos (a+b x)}}","\frac{d \sqrt[4]{\cos ^2(a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) \sqrt{d \cos (a+b x)}}",1,"(d*(Cos[a + b*x]^2)^(1/4)*Hypergeometric2F1[1/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m)*Sqrt[d*Cos[a + b*x]])","A",1,1,23,0.04348,1,"{2577}"
352,1,75,0,0.0490397,"\int \frac{(c \sin (a+b x))^m}{\sqrt{d \cos (a+b x)}} \, dx","Int[(c*Sin[a + b*x])^m/Sqrt[d*Cos[a + b*x]],x]","\frac{d \cos ^2(a+b x)^{3/4} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{3}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) (d \cos (a+b x))^{3/2}}","\frac{d \cos ^2(a+b x)^{3/4} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{3}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1) (d \cos (a+b x))^{3/2}}",1,"(d*(Cos[a + b*x]^2)^(3/4)*Hypergeometric2F1[3/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m)*(d*Cos[a + b*x])^(3/2))","A",1,1,23,0.04348,1,"{2577}"
353,1,77,0,0.0578259,"\int \frac{(c \sin (a+b x))^m}{(d \cos (a+b x))^{3/2}} \, dx","Int[(c*Sin[a + b*x])^m/(d*Cos[a + b*x])^(3/2),x]","\frac{\sqrt[4]{\cos ^2(a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{5}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1) \sqrt{d \cos (a+b x)}}","\frac{\sqrt[4]{\cos ^2(a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{5}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1) \sqrt{d \cos (a+b x)}}",1,"((Cos[a + b*x]^2)^(1/4)*Hypergeometric2F1[5/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*d*(1 + m)*Sqrt[d*Cos[a + b*x]])","A",1,1,23,0.04348,1,"{2577}"
354,1,77,0,0.0549027,"\int \frac{(c \sin (a+b x))^m}{(d \cos (a+b x))^{5/2}} \, dx","Int[(c*Sin[a + b*x])^m/(d*Cos[a + b*x])^(5/2),x]","\frac{\cos ^2(a+b x)^{3/4} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{7}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1) (d \cos (a+b x))^{3/2}}","\frac{\cos ^2(a+b x)^{3/4} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{7}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1) (d \cos (a+b x))^{3/2}}",1,"((Cos[a + b*x]^2)^(3/4)*Hypergeometric2F1[7/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*d*(1 + m)*(d*Cos[a + b*x])^(3/2))","A",1,1,23,0.04348,1,"{2577}"
355,1,76,0,0.0655888,"\int (d \cos (a+b x))^n \sin ^5(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Sin[a + b*x]^5,x]","\frac{2 (d \cos (a+b x))^{n+3}}{b d^3 (n+3)}-\frac{(d \cos (a+b x))^{n+5}}{b d^5 (n+5)}-\frac{(d \cos (a+b x))^{n+1}}{b d (n+1)}","\frac{2 (d \cos (a+b x))^{n+3}}{b d^3 (n+3)}-\frac{(d \cos (a+b x))^{n+5}}{b d^5 (n+5)}-\frac{(d \cos (a+b x))^{n+1}}{b d (n+1)}",1,"-((d*Cos[a + b*x])^(1 + n)/(b*d*(1 + n))) + (2*(d*Cos[a + b*x])^(3 + n))/(b*d^3*(3 + n)) - (d*Cos[a + b*x])^(5 + n)/(b*d^5*(5 + n))","A",3,2,19,0.1053,1,"{2565, 270}"
356,1,50,0,0.0500521,"\int (d \cos (a+b x))^n \sin ^3(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Sin[a + b*x]^3,x]","\frac{(d \cos (a+b x))^{n+3}}{b d^3 (n+3)}-\frac{(d \cos (a+b x))^{n+1}}{b d (n+1)}","\frac{(d \cos (a+b x))^{n+3}}{b d^3 (n+3)}-\frac{(d \cos (a+b x))^{n+1}}{b d (n+1)}",1,"-((d*Cos[a + b*x])^(1 + n)/(b*d*(1 + n))) + (d*Cos[a + b*x])^(3 + n)/(b*d^3*(3 + n))","A",3,2,19,0.1053,1,"{2565, 14}"
357,1,25,0,0.022271,"\int (d \cos (a+b x))^n \sin (a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Sin[a + b*x],x]","-\frac{(d \cos (a+b x))^{n+1}}{b d (n+1)}","-\frac{(d \cos (a+b x))^{n+1}}{b d (n+1)}",1,"-((d*Cos[a + b*x])^(1 + n)/(b*d*(1 + n)))","A",2,2,17,0.1176,1,"{2565, 30}"
358,1,49,0,0.0404455,"\int (d \cos (a+b x))^n \csc (a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Csc[a + b*x],x]","-\frac{(d \cos (a+b x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}","-\frac{(d \cos (a+b x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}",1,"-(((d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2])/(b*d*(1 + n)))","A",2,2,17,0.1176,1,"{2565, 364}"
359,1,49,0,0.046728,"\int (d \cos (a+b x))^n \csc ^3(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Csc[a + b*x]^3,x]","-\frac{(d \cos (a+b x))^{n+1} \, _2F_1\left(2,\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}","-\frac{(d \cos (a+b x))^{n+1} \, _2F_1\left(2,\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}",1,"-(((d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2])/(b*d*(1 + n)))","A",2,2,19,0.1053,1,"{2565, 364}"
360,1,49,0,0.0463348,"\int (d \cos (a+b x))^n \csc ^5(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Csc[a + b*x]^5,x]","-\frac{(d \cos (a+b x))^{n+1} \, _2F_1\left(3,\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}","-\frac{(d \cos (a+b x))^{n+1} \, _2F_1\left(3,\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}",1,"-(((d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[3, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2])/(b*d*(1 + n)))","A",2,2,19,0.1053,1,"{2565, 364}"
361,1,69,0,0.0391226,"\int (d \cos (a+b x))^n \sin ^4(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Sin[a + b*x]^4,x]","-\frac{\sin (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{3}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{\sin ^2(a+b x)}}","-\frac{\sin (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{3}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{\sin ^2(a+b x)}}",1,"-(((d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[-3/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sin[a + b*x])/(b*d*(1 + n)*Sqrt[Sin[a + b*x]^2]))","A",1,1,19,0.05263,1,"{2576}"
362,1,69,0,0.0396596,"\int (d \cos (a+b x))^n \sin ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Sin[a + b*x]^2,x]","-\frac{\sin (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{\sin ^2(a+b x)}}","-\frac{\sin (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{\sin ^2(a+b x)}}",1,"-(((d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[-1/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sin[a + b*x])/(b*d*(1 + n)*Sqrt[Sin[a + b*x]^2]))","A",1,1,19,0.05263,1,"{2576}"
363,1,69,0,0.0154633,"\int (d \cos (a+b x))^n \, dx","Int[(d*Cos[a + b*x])^n,x]","-\frac{\sin (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{\sin ^2(a+b x)}}","-\frac{\sin (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{\sin ^2(a+b x)}}",1,"-(((d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sin[a + b*x])/(b*d*(1 + n)*Sqrt[Sin[a + b*x]^2]))","A",1,1,10,0.1000,1,"{2643}"
364,1,69,0,0.0397905,"\int (d \cos (a+b x))^n \csc ^2(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Csc[a + b*x]^2,x]","-\frac{\sqrt{\sin ^2(a+b x)} \csc (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{3}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}","-\frac{\sqrt{\sin ^2(a+b x)} \csc (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{3}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}",1,"-(((d*Cos[a + b*x])^(1 + n)*Csc[a + b*x]*Hypergeometric2F1[3/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*d*(1 + n)))","A",1,1,19,0.05263,1,"{2576}"
365,1,69,0,0.0380494,"\int (d \cos (a+b x))^n \csc ^4(a+b x) \, dx","Int[(d*Cos[a + b*x])^n*Csc[a + b*x]^4,x]","-\frac{\sqrt{\sin ^2(a+b x)} \csc (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{5}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}","-\frac{\sqrt{\sin ^2(a+b x)} \csc (a+b x) (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{5}{2},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1)}",1,"-(((d*Cos[a + b*x])^(1 + n)*Csc[a + b*x]*Hypergeometric2F1[5/2, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sqrt[Sin[a + b*x]^2])/(b*d*(1 + n)))","A",1,1,19,0.05263,1,"{2576}"
366,1,76,0,0.0534167,"\int (d \cos (a+b x))^n (c \sin (a+b x))^{5/2} \, dx","Int[(d*Cos[a + b*x])^n*(c*Sin[a + b*x])^(5/2),x]","-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{3}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sin ^2(a+b x)^{3/4}}","-\frac{c (c \sin (a+b x))^{3/2} (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{3}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sin ^2(a+b x)^{3/4}}",1,"-((c*(d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[-3/4, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*(c*Sin[a + b*x])^(3/2))/(b*d*(1 + n)*(Sin[a + b*x]^2)^(3/4)))","A",1,1,23,0.04348,1,"{2576}"
367,1,76,0,0.0533769,"\int (d \cos (a+b x))^n (c \sin (a+b x))^{3/2} \, dx","Int[(d*Cos[a + b*x])^n*(c*Sin[a + b*x])^(3/2),x]","-\frac{c \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{1}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt[4]{\sin ^2(a+b x)}}","-\frac{c \sqrt{c \sin (a+b x)} (d \cos (a+b x))^{n+1} \, _2F_1\left(-\frac{1}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt[4]{\sin ^2(a+b x)}}",1,"-((c*(d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[-1/4, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*Sqrt[c*Sin[a + b*x]])/(b*d*(1 + n)*(Sin[a + b*x]^2)^(1/4)))","A",1,1,23,0.04348,1,"{2576}"
368,1,76,0,0.0454629,"\int (d \cos (a+b x))^n \sqrt{c \sin (a+b x)} \, dx","Int[(d*Cos[a + b*x])^n*Sqrt[c*Sin[a + b*x]],x]","-\frac{c \sqrt[4]{\sin ^2(a+b x)} (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{1}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{c \sin (a+b x)}}","-\frac{c \sqrt[4]{\sin ^2(a+b x)} (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{1}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) \sqrt{c \sin (a+b x)}}",1,"-((c*(d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[1/4, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^(1/4))/(b*d*(1 + n)*Sqrt[c*Sin[a + b*x]]))","A",1,1,23,0.04348,1,"{2576}"
369,1,76,0,0.0484558,"\int \frac{(d \cos (a+b x))^n}{\sqrt{c \sin (a+b x)}} \, dx","Int[(d*Cos[a + b*x])^n/Sqrt[c*Sin[a + b*x]],x]","-\frac{c \sin ^2(a+b x)^{3/4} (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{3}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) (c \sin (a+b x))^{3/2}}","-\frac{c \sin ^2(a+b x)^{3/4} (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{3}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b d (n+1) (c \sin (a+b x))^{3/2}}",1,"-((c*(d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[3/4, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^(3/4))/(b*d*(1 + n)*(c*Sin[a + b*x])^(3/2)))","A",1,1,23,0.04348,1,"{2576}"
370,1,78,0,0.0562769,"\int \frac{(d \cos (a+b x))^n}{(c \sin (a+b x))^{3/2}} \, dx","Int[(d*Cos[a + b*x])^n/(c*Sin[a + b*x])^(3/2),x]","-\frac{\sqrt[4]{\sin ^2(a+b x)} (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{5}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b c d (n+1) \sqrt{c \sin (a+b x)}}","-\frac{\sqrt[4]{\sin ^2(a+b x)} (d \cos (a+b x))^{n+1} \, _2F_1\left(\frac{5}{4},\frac{n+1}{2};\frac{n+3}{2};\cos ^2(a+b x)\right)}{b c d (n+1) \sqrt{c \sin (a+b x)}}",1,"-(((d*Cos[a + b*x])^(1 + n)*Hypergeometric2F1[5/4, (1 + n)/2, (3 + n)/2, Cos[a + b*x]^2]*(Sin[a + b*x]^2)^(1/4))/(b*c*d*(1 + n)*Sqrt[c*Sin[a + b*x]]))","A",1,1,23,0.04348,1,"{2576}"
371,1,85,0,0.0592543,"\int \sqrt{b \sec (e+f x)} \sin ^7(e+f x) \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^7,x]","\frac{2 b^7}{13 f (b \sec (e+f x))^{13/2}}-\frac{2 b^5}{3 f (b \sec (e+f x))^{9/2}}+\frac{6 b^3}{5 f (b \sec (e+f x))^{5/2}}-\frac{2 b}{f \sqrt{b \sec (e+f x)}}","\frac{2 b^7}{13 f (b \sec (e+f x))^{13/2}}-\frac{2 b^5}{3 f (b \sec (e+f x))^{9/2}}+\frac{6 b^3}{5 f (b \sec (e+f x))^{5/2}}-\frac{2 b}{f \sqrt{b \sec (e+f x)}}",1,"(2*b^7)/(13*f*(b*Sec[e + f*x])^(13/2)) - (2*b^5)/(3*f*(b*Sec[e + f*x])^(9/2)) + (6*b^3)/(5*f*(b*Sec[e + f*x])^(5/2)) - (2*b)/(f*Sqrt[b*Sec[e + f*x]])","A",3,2,21,0.09524,1,"{2622, 270}"
372,1,63,0,0.0497374,"\int \sqrt{b \sec (e+f x)} \sin ^5(e+f x) \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^5,x]","-\frac{2 b^5}{9 f (b \sec (e+f x))^{9/2}}+\frac{4 b^3}{5 f (b \sec (e+f x))^{5/2}}-\frac{2 b}{f \sqrt{b \sec (e+f x)}}","-\frac{2 b^5}{9 f (b \sec (e+f x))^{9/2}}+\frac{4 b^3}{5 f (b \sec (e+f x))^{5/2}}-\frac{2 b}{f \sqrt{b \sec (e+f x)}}",1,"(-2*b^5)/(9*f*(b*Sec[e + f*x])^(9/2)) + (4*b^3)/(5*f*(b*Sec[e + f*x])^(5/2)) - (2*b)/(f*Sqrt[b*Sec[e + f*x]])","A",3,2,21,0.09524,1,"{2622, 270}"
373,1,41,0,0.0428639,"\int \sqrt{b \sec (e+f x)} \sin ^3(e+f x) \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^3,x]","\frac{2 b^3}{5 f (b \sec (e+f x))^{5/2}}-\frac{2 b}{f \sqrt{b \sec (e+f x)}}","\frac{2 b^3}{5 f (b \sec (e+f x))^{5/2}}-\frac{2 b}{f \sqrt{b \sec (e+f x)}}",1,"(2*b^3)/(5*f*(b*Sec[e + f*x])^(5/2)) - (2*b)/(f*Sqrt[b*Sec[e + f*x]])","A",3,2,21,0.09524,1,"{2622, 14}"
374,1,18,0,0.0296487,"\int \sqrt{b \sec (e+f x)} \sin (e+f x) \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sin[e + f*x],x]","-\frac{2 b}{f \sqrt{b \sec (e+f x)}}","-\frac{2 b}{f \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(f*Sqrt[b*Sec[e + f*x]])","A",2,2,19,0.1053,1,"{2622, 30}"
375,1,58,0,0.0458734,"\int \csc (e+f x) \sqrt{b \sec (e+f x)} \, dx","Int[Csc[e + f*x]*Sqrt[b*Sec[e + f*x]],x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}",1,"(Sqrt[b]*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/f - (Sqrt[b]*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/f","A",5,5,19,0.2632,1,"{2622, 329, 298, 203, 206}"
376,1,93,0,0.0758129,"\int \csc ^3(e+f x) \sqrt{b \sec (e+f x)} \, dx","Int[Csc[e + f*x]^3*Sqrt[b*Sec[e + f*x]],x]","-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{2 b f}+\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}-\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}","-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{2 b f}+\frac{3 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}-\frac{3 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}",1,"(3*Sqrt[b]*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*f) - (3*Sqrt[b]*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*f) - (Cot[e + f*x]^2*(b*Sec[e + f*x])^(3/2))/(2*b*f)","A",6,6,21,0.2857,1,"{2622, 288, 329, 298, 203, 206}"
377,1,123,0,0.0857987,"\int \csc ^5(e+f x) \sqrt{b \sec (e+f x)} \, dx","Int[Csc[e + f*x]^5*Sqrt[b*Sec[e + f*x]],x]","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{7/2}}{4 b^3 f}-\frac{7 \cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{16 b f}+\frac{21 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}-\frac{21 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{7/2}}{4 b^3 f}-\frac{7 \cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{16 b f}+\frac{21 \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}-\frac{21 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}",1,"(21*Sqrt[b]*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*f) - (21*Sqrt[b]*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*f) - (7*Cot[e + f*x]^2*(b*Sec[e + f*x])^(3/2))/(16*b*f) - (Cot[e + f*x]^4*(b*Sec[e + f*x])^(7/2))/(4*b^3*f)","A",7,6,21,0.2857,1,"{2622, 288, 329, 298, 203, 206}"
378,1,123,0,0.1431078,"\int \sqrt{b \sec (e+f x)} \sin ^6(e+f x) \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^6,x]","-\frac{2 b \sin ^5(e+f x)}{11 f \sqrt{b \sec (e+f x)}}-\frac{20 b \sin ^3(e+f x)}{77 f \sqrt{b \sec (e+f x)}}-\frac{40 b \sin (e+f x)}{77 f \sqrt{b \sec (e+f x)}}+\frac{80 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{77 f}","-\frac{2 b \sin ^5(e+f x)}{11 f \sqrt{b \sec (e+f x)}}-\frac{20 b \sin ^3(e+f x)}{77 f \sqrt{b \sec (e+f x)}}-\frac{40 b \sin (e+f x)}{77 f \sqrt{b \sec (e+f x)}}+\frac{80 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{77 f}",1,"(80*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(77*f) - (40*b*Sin[e + f*x])/(77*f*Sqrt[b*Sec[e + f*x]]) - (20*b*Sin[e + f*x]^3)/(77*f*Sqrt[b*Sec[e + f*x]]) - (2*b*Sin[e + f*x]^5)/(11*f*Sqrt[b*Sec[e + f*x]])","A",5,3,21,0.1429,1,"{2627, 3771, 2641}"
379,1,95,0,0.0984107,"\int \sqrt{b \sec (e+f x)} \sin ^4(e+f x) \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^4,x]","-\frac{2 b \sin ^3(e+f x)}{7 f \sqrt{b \sec (e+f x)}}-\frac{4 b \sin (e+f x)}{7 f \sqrt{b \sec (e+f x)}}+\frac{8 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{7 f}","-\frac{2 b \sin ^3(e+f x)}{7 f \sqrt{b \sec (e+f x)}}-\frac{4 b \sin (e+f x)}{7 f \sqrt{b \sec (e+f x)}}+\frac{8 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{7 f}",1,"(8*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(7*f) - (4*b*Sin[e + f*x])/(7*f*Sqrt[b*Sec[e + f*x]]) - (2*b*Sin[e + f*x]^3)/(7*f*Sqrt[b*Sec[e + f*x]])","A",4,3,21,0.1429,1,"{2627, 3771, 2641}"
380,1,67,0,0.0582376,"\int \sqrt{b \sec (e+f x)} \sin ^2(e+f x) \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^2,x]","\frac{4 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}-\frac{2 b \sin (e+f x)}{3 f \sqrt{b \sec (e+f x)}}","\frac{4 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}-\frac{2 b \sin (e+f x)}{3 f \sqrt{b \sec (e+f x)}}",1,"(4*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(3*f) - (2*b*Sin[e + f*x])/(3*f*Sqrt[b*Sec[e + f*x]])","A",3,3,21,0.1429,1,"{2627, 3771, 2641}"
381,1,38,0,0.0207547,"\int \sqrt{b \sec (e+f x)} \, dx","Int[Sqrt[b*Sec[e + f*x]],x]","\frac{2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{f}","\frac{2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{f}",1,"(2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/f","A",2,2,12,0.1667,1,"{3771, 2641}"
382,1,62,0,0.0572937,"\int \csc ^2(e+f x) \sqrt{b \sec (e+f x)} \, dx","Int[Csc[e + f*x]^2*Sqrt[b*Sec[e + f*x]],x]","\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{f}-\frac{b \csc (e+f x)}{f \sqrt{b \sec (e+f x)}}","\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{f}-\frac{b \csc (e+f x)}{f \sqrt{b \sec (e+f x)}}",1,"-((b*Csc[e + f*x])/(f*Sqrt[b*Sec[e + f*x]])) + (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/f","A",3,3,21,0.1429,1,"{2625, 3771, 2641}"
383,1,95,0,0.0956976,"\int \csc ^4(e+f x) \sqrt{b \sec (e+f x)} \, dx","Int[Csc[e + f*x]^4*Sqrt[b*Sec[e + f*x]],x]","-\frac{b \csc ^3(e+f x)}{3 f \sqrt{b \sec (e+f x)}}-\frac{5 b \csc (e+f x)}{6 f \sqrt{b \sec (e+f x)}}+\frac{5 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{6 f}","-\frac{b \csc ^3(e+f x)}{3 f \sqrt{b \sec (e+f x)}}-\frac{5 b \csc (e+f x)}{6 f \sqrt{b \sec (e+f x)}}+\frac{5 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{6 f}",1,"(-5*b*Csc[e + f*x])/(6*f*Sqrt[b*Sec[e + f*x]]) - (b*Csc[e + f*x]^3)/(3*f*Sqrt[b*Sec[e + f*x]]) + (5*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(6*f)","A",4,3,21,0.1429,1,"{2625, 3771, 2641}"
384,1,123,0,0.1378411,"\int \csc ^6(e+f x) \sqrt{b \sec (e+f x)} \, dx","Int[Csc[e + f*x]^6*Sqrt[b*Sec[e + f*x]],x]","-\frac{b \csc ^5(e+f x)}{5 f \sqrt{b \sec (e+f x)}}-\frac{3 b \csc ^3(e+f x)}{10 f \sqrt{b \sec (e+f x)}}-\frac{3 b \csc (e+f x)}{4 f \sqrt{b \sec (e+f x)}}+\frac{3 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{4 f}","-\frac{b \csc ^5(e+f x)}{5 f \sqrt{b \sec (e+f x)}}-\frac{3 b \csc ^3(e+f x)}{10 f \sqrt{b \sec (e+f x)}}-\frac{3 b \csc (e+f x)}{4 f \sqrt{b \sec (e+f x)}}+\frac{3 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{4 f}",1,"(-3*b*Csc[e + f*x])/(4*f*Sqrt[b*Sec[e + f*x]]) - (3*b*Csc[e + f*x]^3)/(10*f*Sqrt[b*Sec[e + f*x]]) - (b*Csc[e + f*x]^5)/(5*f*Sqrt[b*Sec[e + f*x]]) + (3*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(4*f)","A",5,3,21,0.1429,1,"{2625, 3771, 2641}"
385,1,83,0,0.0627426,"\int (b \sec (e+f x))^{3/2} \sin ^7(e+f x) \, dx","Int[(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^7,x]","\frac{2 b^7}{11 f (b \sec (e+f x))^{11/2}}-\frac{6 b^5}{7 f (b \sec (e+f x))^{7/2}}+\frac{2 b^3}{f (b \sec (e+f x))^{3/2}}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}","\frac{2 b^7}{11 f (b \sec (e+f x))^{11/2}}-\frac{6 b^5}{7 f (b \sec (e+f x))^{7/2}}+\frac{2 b^3}{f (b \sec (e+f x))^{3/2}}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}",1,"(2*b^7)/(11*f*(b*Sec[e + f*x])^(11/2)) - (6*b^5)/(7*f*(b*Sec[e + f*x])^(7/2)) + (2*b^3)/(f*(b*Sec[e + f*x])^(3/2)) + (2*b*Sqrt[b*Sec[e + f*x]])/f","A",3,2,21,0.09524,1,"{2622, 270}"
386,1,63,0,0.0560433,"\int (b \sec (e+f x))^{3/2} \sin ^5(e+f x) \, dx","Int[(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^5,x]","-\frac{2 b^5}{7 f (b \sec (e+f x))^{7/2}}+\frac{4 b^3}{3 f (b \sec (e+f x))^{3/2}}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}","-\frac{2 b^5}{7 f (b \sec (e+f x))^{7/2}}+\frac{4 b^3}{3 f (b \sec (e+f x))^{3/2}}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}",1,"(-2*b^5)/(7*f*(b*Sec[e + f*x])^(7/2)) + (4*b^3)/(3*f*(b*Sec[e + f*x])^(3/2)) + (2*b*Sqrt[b*Sec[e + f*x]])/f","A",3,2,21,0.09524,1,"{2622, 270}"
387,1,41,0,0.0501463,"\int (b \sec (e+f x))^{3/2} \sin ^3(e+f x) \, dx","Int[(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^3,x]","\frac{2 b^3}{3 f (b \sec (e+f x))^{3/2}}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}","\frac{2 b^3}{3 f (b \sec (e+f x))^{3/2}}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}",1,"(2*b^3)/(3*f*(b*Sec[e + f*x])^(3/2)) + (2*b*Sqrt[b*Sec[e + f*x]])/f","A",3,2,21,0.09524,1,"{2622, 14}"
388,1,18,0,0.0343327,"\int (b \sec (e+f x))^{3/2} \sin (e+f x) \, dx","Int[(b*Sec[e + f*x])^(3/2)*Sin[e + f*x],x]","\frac{2 b \sqrt{b \sec (e+f x)}}{f}","\frac{2 b \sqrt{b \sec (e+f x)}}{f}",1,"(2*b*Sqrt[b*Sec[e + f*x]])/f","A",2,2,19,0.1053,1,"{2622, 30}"
389,1,77,0,0.0533208,"\int \csc (e+f x) (b \sec (e+f x))^{3/2} \, dx","Int[Csc[e + f*x]*(b*Sec[e + f*x])^(3/2),x]","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}+\frac{2 b \sqrt{b \sec (e+f x)}}{f}",1,"-((b^(3/2)*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/f) - (b^(3/2)*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/f + (2*b*Sqrt[b*Sec[e + f*x]])/f","A",6,6,19,0.3158,1,"{2622, 321, 329, 212, 206, 203}"
390,1,113,0,0.0839355,"\int \csc ^3(e+f x) (b \sec (e+f x))^{3/2} \, dx","Int[Csc[e + f*x]^3*(b*Sec[e + f*x])^(3/2),x]","-\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}-\frac{5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}+\frac{5 b \sqrt{b \sec (e+f x)}}{2 f}-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{5/2}}{2 b f}","-\frac{5 b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}-\frac{5 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}+\frac{5 b \sqrt{b \sec (e+f x)}}{2 f}-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{5/2}}{2 b f}",1,"(-5*b^(3/2)*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*f) - (5*b^(3/2)*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*f) + (5*b*Sqrt[b*Sec[e + f*x]])/(2*f) - (Cot[e + f*x]^2*(b*Sec[e + f*x])^(5/2))/(2*b*f)","A",7,7,21,0.3333,1,"{2622, 288, 321, 329, 212, 206, 203}"
391,1,128,0,0.1485983,"\int (b \sec (e+f x))^{3/2} \sin ^6(e+f x) \, dx","Int[(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^6,x]","\frac{20 b^3 \sin ^3(e+f x)}{9 f (b \sec (e+f x))^{3/2}}+\frac{8 b^3 \sin (e+f x)}{3 f (b \sec (e+f x))^{3/2}}-\frac{16 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{3 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{2 b \sin ^5(e+f x) \sqrt{b \sec (e+f x)}}{f}","\frac{20 b^3 \sin ^3(e+f x)}{9 f (b \sec (e+f x))^{3/2}}+\frac{8 b^3 \sin (e+f x)}{3 f (b \sec (e+f x))^{3/2}}-\frac{16 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{3 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{2 b \sin ^5(e+f x) \sqrt{b \sec (e+f x)}}{f}",1,"(-16*b^2*EllipticE[(e + f*x)/2, 2])/(3*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) + (8*b^3*Sin[e + f*x])/(3*f*(b*Sec[e + f*x])^(3/2)) + (20*b^3*Sin[e + f*x]^3)/(9*f*(b*Sec[e + f*x])^(3/2)) + (2*b*Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^5)/f","A",5,4,21,0.1905,1,"{2624, 2627, 3771, 2639}"
392,1,98,0,0.1076049,"\int (b \sec (e+f x))^{3/2} \sin ^4(e+f x) \, dx","Int[(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^4,x]","\frac{12 b^3 \sin (e+f x)}{5 f (b \sec (e+f x))^{3/2}}-\frac{24 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{2 b \sin ^3(e+f x) \sqrt{b \sec (e+f x)}}{f}","\frac{12 b^3 \sin (e+f x)}{5 f (b \sec (e+f x))^{3/2}}-\frac{24 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{2 b \sin ^3(e+f x) \sqrt{b \sec (e+f x)}}{f}",1,"(-24*b^2*EllipticE[(e + f*x)/2, 2])/(5*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) + (12*b^3*Sin[e + f*x])/(5*f*(b*Sec[e + f*x])^(3/2)) + (2*b*Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^3)/f","A",4,4,21,0.1905,1,"{2624, 2627, 3771, 2639}"
393,1,66,0,0.0657789,"\int (b \sec (e+f x))^{3/2} \sin ^2(e+f x) \, dx","Int[(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^2,x]","\frac{2 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{f}-\frac{4 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","\frac{2 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{f}-\frac{4 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(-4*b^2*EllipticE[(e + f*x)/2, 2])/(f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) + (2*b*Sqrt[b*Sec[e + f*x]]*Sin[e + f*x])/f","A",3,3,21,0.1429,1,"{2624, 3771, 2639}"
394,1,66,0,0.0366553,"\int (b \sec (e+f x))^{3/2} \, dx","Int[(b*Sec[e + f*x])^(3/2),x]","\frac{2 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{f}-\frac{2 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","\frac{2 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{f}-\frac{2 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(-2*b^2*EllipticE[(e + f*x)/2, 2])/(f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) + (2*b*Sqrt[b*Sec[e + f*x]]*Sin[e + f*x])/f","A",3,3,12,0.2500,1,"{3768, 3771, 2639}"
395,1,90,0,0.0823653,"\int \csc ^2(e+f x) (b \sec (e+f x))^{3/2} \, dx","Int[Csc[e + f*x]^2*(b*Sec[e + f*x])^(3/2),x]","-\frac{3 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{b \csc (e+f x) \sqrt{b \sec (e+f x)}}{f}+\frac{3 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{f}","-\frac{3 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{b \csc (e+f x) \sqrt{b \sec (e+f x)}}{f}+\frac{3 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{f}",1,"(-3*b^2*EllipticE[(e + f*x)/2, 2])/(f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (b*Csc[e + f*x]*Sqrt[b*Sec[e + f*x]])/f + (3*b*Sqrt[b*Sec[e + f*x]]*Sin[e + f*x])/f","A",4,4,21,0.1905,1,"{2625, 3768, 3771, 2639}"
396,1,124,0,0.1289829,"\int \csc ^4(e+f x) (b \sec (e+f x))^{3/2} \, dx","Int[Csc[e + f*x]^4*(b*Sec[e + f*x])^(3/2),x]","-\frac{7 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{b \csc ^3(e+f x) \sqrt{b \sec (e+f x)}}{3 f}-\frac{7 b \csc (e+f x) \sqrt{b \sec (e+f x)}}{6 f}+\frac{7 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{2 f}","-\frac{7 b^2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{b \csc ^3(e+f x) \sqrt{b \sec (e+f x)}}{3 f}-\frac{7 b \csc (e+f x) \sqrt{b \sec (e+f x)}}{6 f}+\frac{7 b \sin (e+f x) \sqrt{b \sec (e+f x)}}{2 f}",1,"(-7*b^2*EllipticE[(e + f*x)/2, 2])/(2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (7*b*Csc[e + f*x]*Sqrt[b*Sec[e + f*x]])/(6*f) - (b*Csc[e + f*x]^3*Sqrt[b*Sec[e + f*x]])/(3*f) + (7*b*Sqrt[b*Sec[e + f*x]]*Sin[e + f*x])/(2*f)","A",5,4,21,0.1905,1,"{2625, 3768, 3771, 2639}"
397,1,85,0,0.0623046,"\int (b \sec (e+f x))^{5/2} \sin ^7(e+f x) \, dx","Int[(b*Sec[e + f*x])^(5/2)*Sin[e + f*x]^7,x]","\frac{2 b^7}{9 f (b \sec (e+f x))^{9/2}}-\frac{6 b^5}{5 f (b \sec (e+f x))^{5/2}}+\frac{6 b^3}{f \sqrt{b \sec (e+f x)}}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}","\frac{2 b^7}{9 f (b \sec (e+f x))^{9/2}}-\frac{6 b^5}{5 f (b \sec (e+f x))^{5/2}}+\frac{6 b^3}{f \sqrt{b \sec (e+f x)}}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}",1,"(2*b^7)/(9*f*(b*Sec[e + f*x])^(9/2)) - (6*b^5)/(5*f*(b*Sec[e + f*x])^(5/2)) + (6*b^3)/(f*Sqrt[b*Sec[e + f*x]]) + (2*b*(b*Sec[e + f*x])^(3/2))/(3*f)","A",3,2,21,0.09524,1,"{2622, 270}"
398,1,63,0,0.0557179,"\int (b \sec (e+f x))^{5/2} \sin ^5(e+f x) \, dx","Int[(b*Sec[e + f*x])^(5/2)*Sin[e + f*x]^5,x]","-\frac{2 b^5}{5 f (b \sec (e+f x))^{5/2}}+\frac{4 b^3}{f \sqrt{b \sec (e+f x)}}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}","-\frac{2 b^5}{5 f (b \sec (e+f x))^{5/2}}+\frac{4 b^3}{f \sqrt{b \sec (e+f x)}}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}",1,"(-2*b^5)/(5*f*(b*Sec[e + f*x])^(5/2)) + (4*b^3)/(f*Sqrt[b*Sec[e + f*x]]) + (2*b*(b*Sec[e + f*x])^(3/2))/(3*f)","A",3,2,21,0.09524,1,"{2622, 270}"
399,1,41,0,0.0492443,"\int (b \sec (e+f x))^{5/2} \sin ^3(e+f x) \, dx","Int[(b*Sec[e + f*x])^(5/2)*Sin[e + f*x]^3,x]","\frac{2 b^3}{f \sqrt{b \sec (e+f x)}}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}","\frac{2 b^3}{f \sqrt{b \sec (e+f x)}}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}",1,"(2*b^3)/(f*Sqrt[b*Sec[e + f*x]]) + (2*b*(b*Sec[e + f*x])^(3/2))/(3*f)","A",3,2,21,0.09524,1,"{2622, 14}"
400,1,20,0,0.0357261,"\int (b \sec (e+f x))^{5/2} \sin (e+f x) \, dx","Int[(b*Sec[e + f*x])^(5/2)*Sin[e + f*x],x]","\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}","\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}",1,"(2*b*(b*Sec[e + f*x])^(3/2))/(3*f)","A",2,2,19,0.1053,1,"{2622, 30}"
401,1,78,0,0.0543744,"\int \csc (e+f x) (b \sec (e+f x))^{5/2} \, dx","Int[Csc[e + f*x]*(b*Sec[e + f*x])^(5/2),x]","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{f}+\frac{2 b (b \sec (e+f x))^{3/2}}{3 f}",1,"(b^(5/2)*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/f - (b^(5/2)*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/f + (2*b*(b*Sec[e + f*x])^(3/2))/(3*f)","A",6,6,19,0.3158,1,"{2622, 321, 329, 298, 203, 206}"
402,1,113,0,0.0836008,"\int \csc ^3(e+f x) (b \sec (e+f x))^{5/2} \, dx","Int[Csc[e + f*x]^3*(b*Sec[e + f*x])^(5/2),x]","\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}-\frac{7 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}+\frac{7 b (b \sec (e+f x))^{3/2}}{6 f}-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{7/2}}{2 b f}","\frac{7 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}-\frac{7 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 f}+\frac{7 b (b \sec (e+f x))^{3/2}}{6 f}-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{7/2}}{2 b f}",1,"(7*b^(5/2)*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*f) - (7*b^(5/2)*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*f) + (7*b*(b*Sec[e + f*x])^(3/2))/(6*f) - (Cot[e + f*x]^2*(b*Sec[e + f*x])^(7/2))/(2*b*f)","A",7,7,21,0.3333,1,"{2622, 288, 321, 329, 298, 203, 206}"
403,1,143,0,0.097547,"\int \csc ^5(e+f x) (b \sec (e+f x))^{5/2} \, dx","Int[Csc[e + f*x]^5*(b*Sec[e + f*x])^(5/2),x]","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{11/2}}{4 b^3 f}+\frac{77 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}-\frac{77 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}+\frac{77 b (b \sec (e+f x))^{3/2}}{48 f}-\frac{11 \cot ^2(e+f x) (b \sec (e+f x))^{7/2}}{16 b f}","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{11/2}}{4 b^3 f}+\frac{77 b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}-\frac{77 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 f}+\frac{77 b (b \sec (e+f x))^{3/2}}{48 f}-\frac{11 \cot ^2(e+f x) (b \sec (e+f x))^{7/2}}{16 b f}",1,"(77*b^(5/2)*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*f) - (77*b^(5/2)*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*f) + (77*b*(b*Sec[e + f*x])^(3/2))/(48*f) - (11*Cot[e + f*x]^2*(b*Sec[e + f*x])^(7/2))/(16*b*f) - (Cot[e + f*x]^4*(b*Sec[e + f*x])^(11/2))/(4*b^3*f)","A",8,7,21,0.3333,1,"{2622, 288, 321, 329, 298, 203, 206}"
404,1,130,0,0.1466611,"\int (b \sec (e+f x))^{5/2} \sin ^6(e+f x) \, dx","Int[(b*Sec[e + f*x])^(5/2)*Sin[e + f*x]^6,x]","\frac{20 b^3 \sin ^3(e+f x)}{21 f \sqrt{b \sec (e+f x)}}+\frac{40 b^3 \sin (e+f x)}{21 f \sqrt{b \sec (e+f x)}}-\frac{80 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{21 f}+\frac{2 b \sin ^5(e+f x) (b \sec (e+f x))^{3/2}}{3 f}","\frac{20 b^3 \sin ^3(e+f x)}{21 f \sqrt{b \sec (e+f x)}}+\frac{40 b^3 \sin (e+f x)}{21 f \sqrt{b \sec (e+f x)}}-\frac{80 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{21 f}+\frac{2 b \sin ^5(e+f x) (b \sec (e+f x))^{3/2}}{3 f}",1,"(-80*b^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(21*f) + (40*b^3*Sin[e + f*x])/(21*f*Sqrt[b*Sec[e + f*x]]) + (20*b^3*Sin[e + f*x]^3)/(21*f*Sqrt[b*Sec[e + f*x]]) + (2*b*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^5)/(3*f)","A",5,4,21,0.1905,1,"{2624, 2627, 3771, 2641}"
405,1,100,0,0.1030344,"\int (b \sec (e+f x))^{5/2} \sin ^4(e+f x) \, dx","Int[(b*Sec[e + f*x])^(5/2)*Sin[e + f*x]^4,x]","\frac{4 b^3 \sin (e+f x)}{3 f \sqrt{b \sec (e+f x)}}-\frac{8 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}+\frac{2 b \sin ^3(e+f x) (b \sec (e+f x))^{3/2}}{3 f}","\frac{4 b^3 \sin (e+f x)}{3 f \sqrt{b \sec (e+f x)}}-\frac{8 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}+\frac{2 b \sin ^3(e+f x) (b \sec (e+f x))^{3/2}}{3 f}",1,"(-8*b^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(3*f) + (4*b^3*Sin[e + f*x])/(3*f*Sqrt[b*Sec[e + f*x]]) + (2*b*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^3)/(3*f)","A",4,4,21,0.1905,1,"{2624, 2627, 3771, 2641}"
406,1,70,0,0.0646299,"\int (b \sec (e+f x))^{5/2} \sin ^2(e+f x) \, dx","Int[(b*Sec[e + f*x])^(5/2)*Sin[e + f*x]^2,x]","\frac{2 b \sin (e+f x) (b \sec (e+f x))^{3/2}}{3 f}-\frac{4 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}","\frac{2 b \sin (e+f x) (b \sec (e+f x))^{3/2}}{3 f}-\frac{4 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}",1,"(-4*b^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(3*f) + (2*b*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(3*f)","A",3,3,21,0.1429,1,"{2624, 3771, 2641}"
407,1,70,0,0.034645,"\int (b \sec (e+f x))^{5/2} \, dx","Int[(b*Sec[e + f*x])^(5/2),x]","\frac{2 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}+\frac{2 b \sin (e+f x) (b \sec (e+f x))^{3/2}}{3 f}","\frac{2 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}+\frac{2 b \sin (e+f x) (b \sec (e+f x))^{3/2}}{3 f}",1,"(2*b^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(3*f) + (2*b*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x])/(3*f)","A",3,3,12,0.2500,1,"{3768, 3771, 2641}"
408,1,98,0,0.1022525,"\int \csc ^2(e+f x) (b \sec (e+f x))^{5/2} \, dx","Int[Csc[e + f*x]^2*(b*Sec[e + f*x])^(5/2),x]","-\frac{5 b^3 \csc (e+f x)}{3 f \sqrt{b \sec (e+f x)}}+\frac{5 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}+\frac{2 b \csc (e+f x) (b \sec (e+f x))^{3/2}}{3 f}","-\frac{5 b^3 \csc (e+f x)}{3 f \sqrt{b \sec (e+f x)}}+\frac{5 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 f}+\frac{2 b \csc (e+f x) (b \sec (e+f x))^{3/2}}{3 f}",1,"(-5*b^3*Csc[e + f*x])/(3*f*Sqrt[b*Sec[e + f*x]]) + (5*b^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(3*f) + (2*b*Csc[e + f*x]*(b*Sec[e + f*x])^(3/2))/(3*f)","A",4,4,21,0.1905,1,"{2626, 2625, 3771, 2641}"
409,1,123,0,0.1503226,"\int \csc ^4(e+f x) (b \sec (e+f x))^{5/2} \, dx","Int[Csc[e + f*x]^4*(b*Sec[e + f*x])^(5/2),x]","-\frac{5 b^3 \csc (e+f x)}{2 f \sqrt{b \sec (e+f x)}}+\frac{5 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{2 f}-\frac{b \csc ^3(e+f x) (b \sec (e+f x))^{3/2}}{3 f}+\frac{b \csc (e+f x) (b \sec (e+f x))^{3/2}}{f}","-\frac{5 b^3 \csc (e+f x)}{2 f \sqrt{b \sec (e+f x)}}+\frac{5 b^2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{2 f}-\frac{b \csc ^3(e+f x) (b \sec (e+f x))^{3/2}}{3 f}+\frac{b \csc (e+f x) (b \sec (e+f x))^{3/2}}{f}",1,"(-5*b^3*Csc[e + f*x])/(2*f*Sqrt[b*Sec[e + f*x]]) + (5*b^2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(2*f) + (b*Csc[e + f*x]*(b*Sec[e + f*x])^(3/2))/f - (b*Csc[e + f*x]^3*(b*Sec[e + f*x])^(3/2))/(3*f)","A",5,4,21,0.1905,1,"{2625, 2626, 3771, 2641}"
410,1,87,0,0.0570967,"\int \frac{\sin ^7(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^7/Sqrt[b*Sec[e + f*x]],x]","\frac{2 b^7}{15 f (b \sec (e+f x))^{15/2}}-\frac{6 b^5}{11 f (b \sec (e+f x))^{11/2}}+\frac{6 b^3}{7 f (b \sec (e+f x))^{7/2}}-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}","\frac{2 b^7}{15 f (b \sec (e+f x))^{15/2}}-\frac{6 b^5}{11 f (b \sec (e+f x))^{11/2}}+\frac{6 b^3}{7 f (b \sec (e+f x))^{7/2}}-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}",1,"(2*b^7)/(15*f*(b*Sec[e + f*x])^(15/2)) - (6*b^5)/(11*f*(b*Sec[e + f*x])^(11/2)) + (6*b^3)/(7*f*(b*Sec[e + f*x])^(7/2)) - (2*b)/(3*f*(b*Sec[e + f*x])^(3/2))","A",3,2,21,0.09524,1,"{2622, 270}"
411,1,65,0,0.0496222,"\int \frac{\sin ^5(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^5/Sqrt[b*Sec[e + f*x]],x]","-\frac{2 b^5}{11 f (b \sec (e+f x))^{11/2}}+\frac{4 b^3}{7 f (b \sec (e+f x))^{7/2}}-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}","-\frac{2 b^5}{11 f (b \sec (e+f x))^{11/2}}+\frac{4 b^3}{7 f (b \sec (e+f x))^{7/2}}-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}",1,"(-2*b^5)/(11*f*(b*Sec[e + f*x])^(11/2)) + (4*b^3)/(7*f*(b*Sec[e + f*x])^(7/2)) - (2*b)/(3*f*(b*Sec[e + f*x])^(3/2))","A",3,2,21,0.09524,1,"{2622, 270}"
412,1,43,0,0.0448939,"\int \frac{\sin ^3(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^3/Sqrt[b*Sec[e + f*x]],x]","\frac{2 b^3}{7 f (b \sec (e+f x))^{7/2}}-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}","\frac{2 b^3}{7 f (b \sec (e+f x))^{7/2}}-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}",1,"(2*b^3)/(7*f*(b*Sec[e + f*x])^(7/2)) - (2*b)/(3*f*(b*Sec[e + f*x])^(3/2))","A",3,2,21,0.09524,1,"{2622, 14}"
413,1,20,0,0.0307073,"\int \frac{\sin (e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]/Sqrt[b*Sec[e + f*x]],x]","-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}","-\frac{2 b}{3 f (b \sec (e+f x))^{3/2}}",1,"(-2*b)/(3*f*(b*Sec[e + f*x])^(3/2))","A",2,2,19,0.1053,1,"{2622, 30}"
414,1,59,0,0.0422869,"\int \frac{\csc (e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Csc[e + f*x]/Sqrt[b*Sec[e + f*x]],x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f}",1,"-(ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(Sqrt[b]*f)) - ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(Sqrt[b]*f)","A",5,5,19,0.2632,1,"{2622, 329, 212, 206, 203}"
415,1,93,0,0.0668614,"\int \frac{\csc ^3(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Csc[e + f*x]^3/Sqrt[b*Sec[e + f*x]],x]","-\frac{\cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{2 b f}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f}","-\frac{\cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{2 b f}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 \sqrt{b} f}",1,"-ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(4*Sqrt[b]*f) - ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(4*Sqrt[b]*f) - (Cot[e + f*x]^2*Sqrt[b*Sec[e + f*x]])/(2*b*f)","A",6,6,21,0.2857,1,"{2622, 288, 329, 212, 206, 203}"
416,1,123,0,0.0785193,"\int \frac{\csc ^5(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Csc[e + f*x]^5/Sqrt[b*Sec[e + f*x]],x]","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{5/2}}{4 b^3 f}-\frac{5 \cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{16 b f}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 \sqrt{b} f}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 \sqrt{b} f}","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{5/2}}{4 b^3 f}-\frac{5 \cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{16 b f}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 \sqrt{b} f}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 \sqrt{b} f}",1,"(-5*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*Sqrt[b]*f) - (5*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*Sqrt[b]*f) - (5*Cot[e + f*x]^2*Sqrt[b*Sec[e + f*x]])/(16*b*f) - (Cot[e + f*x]^4*(b*Sec[e + f*x])^(5/2))/(4*b^3*f)","A",7,6,21,0.2857,1,"{2622, 288, 329, 212, 206, 203}"
417,1,123,0,0.1434045,"\int \frac{\sin ^6(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^6/Sqrt[b*Sec[e + f*x]],x]","-\frac{2 b \sin ^5(e+f x)}{13 f (b \sec (e+f x))^{3/2}}-\frac{20 b \sin ^3(e+f x)}{117 f (b \sec (e+f x))^{3/2}}-\frac{8 b \sin (e+f x)}{39 f (b \sec (e+f x))^{3/2}}+\frac{16 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{39 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","-\frac{2 b \sin ^5(e+f x)}{13 f (b \sec (e+f x))^{3/2}}-\frac{20 b \sin ^3(e+f x)}{117 f (b \sec (e+f x))^{3/2}}-\frac{8 b \sin (e+f x)}{39 f (b \sec (e+f x))^{3/2}}+\frac{16 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{39 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(16*EllipticE[(e + f*x)/2, 2])/(39*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (8*b*Sin[e + f*x])/(39*f*(b*Sec[e + f*x])^(3/2)) - (20*b*Sin[e + f*x]^3)/(117*f*(b*Sec[e + f*x])^(3/2)) - (2*b*Sin[e + f*x]^5)/(13*f*(b*Sec[e + f*x])^(3/2))","A",5,3,21,0.1429,1,"{2627, 3771, 2639}"
418,1,95,0,0.0998004,"\int \frac{\sin ^4(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^4/Sqrt[b*Sec[e + f*x]],x]","-\frac{2 b \sin ^3(e+f x)}{9 f (b \sec (e+f x))^{3/2}}-\frac{4 b \sin (e+f x)}{15 f (b \sec (e+f x))^{3/2}}+\frac{8 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{15 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","-\frac{2 b \sin ^3(e+f x)}{9 f (b \sec (e+f x))^{3/2}}-\frac{4 b \sin (e+f x)}{15 f (b \sec (e+f x))^{3/2}}+\frac{8 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{15 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(8*EllipticE[(e + f*x)/2, 2])/(15*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (4*b*Sin[e + f*x])/(15*f*(b*Sec[e + f*x])^(3/2)) - (2*b*Sin[e + f*x]^3)/(9*f*(b*Sec[e + f*x])^(3/2))","A",4,3,21,0.1429,1,"{2627, 3771, 2639}"
419,1,67,0,0.0592002,"\int \frac{\sin ^2(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^2/Sqrt[b*Sec[e + f*x]],x]","\frac{4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{2 b \sin (e+f x)}{5 f (b \sec (e+f x))^{3/2}}","\frac{4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{2 b \sin (e+f x)}{5 f (b \sec (e+f x))^{3/2}}",1,"(4*EllipticE[(e + f*x)/2, 2])/(5*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (2*b*Sin[e + f*x])/(5*f*(b*Sec[e + f*x])^(3/2))","A",3,3,21,0.1429,1,"{2627, 3771, 2639}"
420,1,38,0,0.0200134,"\int \frac{1}{\sqrt{b \sec (e+f x)}} \, dx","Int[1/Sqrt[b*Sec[e + f*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","\frac{2 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(2*EllipticE[(e + f*x)/2, 2])/(f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",2,2,12,0.1667,1,"{3771, 2639}"
421,1,63,0,0.0580531,"\int \frac{\csc ^2(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Csc[e + f*x]^2/Sqrt[b*Sec[e + f*x]],x]","-\frac{b \csc (e+f x)}{f (b \sec (e+f x))^{3/2}}-\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","-\frac{b \csc (e+f x)}{f (b \sec (e+f x))^{3/2}}-\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"-((b*Csc[e + f*x])/(f*(b*Sec[e + f*x])^(3/2))) - EllipticE[(e + f*x)/2, 2]/(f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",3,3,21,0.1429,1,"{2625, 3771, 2639}"
422,1,95,0,0.1010269,"\int \frac{\csc ^4(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Csc[e + f*x]^4/Sqrt[b*Sec[e + f*x]],x]","-\frac{b \csc ^3(e+f x)}{3 f (b \sec (e+f x))^{3/2}}-\frac{b \csc (e+f x)}{2 f (b \sec (e+f x))^{3/2}}-\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","-\frac{b \csc ^3(e+f x)}{3 f (b \sec (e+f x))^{3/2}}-\frac{b \csc (e+f x)}{2 f (b \sec (e+f x))^{3/2}}-\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"-(b*Csc[e + f*x])/(2*f*(b*Sec[e + f*x])^(3/2)) - (b*Csc[e + f*x]^3)/(3*f*(b*Sec[e + f*x])^(3/2)) - EllipticE[(e + f*x)/2, 2]/(2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",4,3,21,0.1429,1,"{2625, 3771, 2639}"
423,1,123,0,0.1434185,"\int \frac{\csc ^6(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Csc[e + f*x]^6/Sqrt[b*Sec[e + f*x]],x]","-\frac{b \csc ^5(e+f x)}{5 f (b \sec (e+f x))^{3/2}}-\frac{7 b \csc ^3(e+f x)}{30 f (b \sec (e+f x))^{3/2}}-\frac{7 b \csc (e+f x)}{20 f (b \sec (e+f x))^{3/2}}-\frac{7 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{20 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}","-\frac{b \csc ^5(e+f x)}{5 f (b \sec (e+f x))^{3/2}}-\frac{7 b \csc ^3(e+f x)}{30 f (b \sec (e+f x))^{3/2}}-\frac{7 b \csc (e+f x)}{20 f (b \sec (e+f x))^{3/2}}-\frac{7 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{20 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(-7*b*Csc[e + f*x])/(20*f*(b*Sec[e + f*x])^(3/2)) - (7*b*Csc[e + f*x]^3)/(30*f*(b*Sec[e + f*x])^(3/2)) - (b*Csc[e + f*x]^5)/(5*f*(b*Sec[e + f*x])^(3/2)) - (7*EllipticE[(e + f*x)/2, 2])/(20*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",5,3,21,0.1429,1,"{2625, 3771, 2639}"
424,1,87,0,0.0632463,"\int \frac{\sin ^7(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]^7/(b*Sec[e + f*x])^(3/2),x]","\frac{2 b^7}{17 f (b \sec (e+f x))^{17/2}}-\frac{6 b^5}{13 f (b \sec (e+f x))^{13/2}}+\frac{2 b^3}{3 f (b \sec (e+f x))^{9/2}}-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}","\frac{2 b^7}{17 f (b \sec (e+f x))^{17/2}}-\frac{6 b^5}{13 f (b \sec (e+f x))^{13/2}}+\frac{2 b^3}{3 f (b \sec (e+f x))^{9/2}}-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}",1,"(2*b^7)/(17*f*(b*Sec[e + f*x])^(17/2)) - (6*b^5)/(13*f*(b*Sec[e + f*x])^(13/2)) + (2*b^3)/(3*f*(b*Sec[e + f*x])^(9/2)) - (2*b)/(5*f*(b*Sec[e + f*x])^(5/2))","A",3,2,21,0.09524,1,"{2622, 270}"
425,1,65,0,0.0581976,"\int \frac{\sin ^5(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]^5/(b*Sec[e + f*x])^(3/2),x]","-\frac{2 b^5}{13 f (b \sec (e+f x))^{13/2}}+\frac{4 b^3}{9 f (b \sec (e+f x))^{9/2}}-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}","-\frac{2 b^5}{13 f (b \sec (e+f x))^{13/2}}+\frac{4 b^3}{9 f (b \sec (e+f x))^{9/2}}-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}",1,"(-2*b^5)/(13*f*(b*Sec[e + f*x])^(13/2)) + (4*b^3)/(9*f*(b*Sec[e + f*x])^(9/2)) - (2*b)/(5*f*(b*Sec[e + f*x])^(5/2))","A",3,2,21,0.09524,1,"{2622, 270}"
426,1,43,0,0.0502984,"\int \frac{\sin ^3(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]^3/(b*Sec[e + f*x])^(3/2),x]","\frac{2 b^3}{9 f (b \sec (e+f x))^{9/2}}-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}","\frac{2 b^3}{9 f (b \sec (e+f x))^{9/2}}-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}",1,"(2*b^3)/(9*f*(b*Sec[e + f*x])^(9/2)) - (2*b)/(5*f*(b*Sec[e + f*x])^(5/2))","A",3,2,21,0.09524,1,"{2622, 14}"
427,1,20,0,0.0361541,"\int \frac{\sin (e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]/(b*Sec[e + f*x])^(3/2),x]","-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}","-\frac{2 b}{5 f (b \sec (e+f x))^{5/2}}",1,"(-2*b)/(5*f*(b*Sec[e + f*x])^(5/2))","A",2,2,19,0.1053,1,"{2622, 30}"
428,1,78,0,0.0543373,"\int \frac{\csc (e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]/(b*Sec[e + f*x])^(3/2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f}+\frac{2}{b f \sqrt{b \sec (e+f x)}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f}+\frac{2}{b f \sqrt{b \sec (e+f x)}}",1,"ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(b^(3/2)*f) - ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(b^(3/2)*f) + 2/(b*f*Sqrt[b*Sec[e + f*x]])","A",6,6,19,0.3158,1,"{2622, 325, 329, 298, 203, 206}"
429,1,93,0,0.0738407,"\int \frac{\csc ^3(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^3/(b*Sec[e + f*x])^(3/2),x]","-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{2 b^3 f}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{3/2} f}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{3/2} f}","-\frac{\cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{2 b^3 f}-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{3/2} f}+\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{3/2} f}",1,"-ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(4*b^(3/2)*f) + ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(4*b^(3/2)*f) - (Cot[e + f*x]^2*(b*Sec[e + f*x])^(3/2))/(2*b^3*f)","A",6,6,21,0.2857,1,"{2622, 290, 329, 298, 203, 206}"
430,1,123,0,0.0858205,"\int \frac{\csc ^5(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^5/(b*Sec[e + f*x])^(3/2),x]","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{3/2}}{4 b^3 f}-\frac{3 \cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{16 b^3 f}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{3/2} f}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{3/2} f}","-\frac{\cot ^4(e+f x) (b \sec (e+f x))^{3/2}}{4 b^3 f}-\frac{3 \cot ^2(e+f x) (b \sec (e+f x))^{3/2}}{16 b^3 f}-\frac{3 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{3/2} f}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{3/2} f}",1,"(-3*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*b^(3/2)*f) + (3*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*b^(3/2)*f) - (3*Cot[e + f*x]^2*(b*Sec[e + f*x])^(3/2))/(16*b^3*f) - (Cot[e + f*x]^4*(b*Sec[e + f*x])^(3/2))/(4*b^3*f)","A",7,7,21,0.3333,1,"{2622, 288, 290, 329, 298, 203, 206}"
431,1,126,0,0.1335043,"\int \frac{\sin ^4(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]^4/(b*Sec[e + f*x])^(3/2),x]","\frac{8 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{77 b^2 f}-\frac{2 b \sin ^3(e+f x)}{11 f (b \sec (e+f x))^{5/2}}+\frac{8 \sin (e+f x)}{77 b f \sqrt{b \sec (e+f x)}}-\frac{12 b \sin (e+f x)}{77 f (b \sec (e+f x))^{5/2}}","\frac{8 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{77 b^2 f}-\frac{2 b \sin ^3(e+f x)}{11 f (b \sec (e+f x))^{5/2}}+\frac{8 \sin (e+f x)}{77 b f \sqrt{b \sec (e+f x)}}-\frac{12 b \sin (e+f x)}{77 f (b \sec (e+f x))^{5/2}}",1,"(8*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(77*b^2*f) - (12*b*Sin[e + f*x])/(77*f*(b*Sec[e + f*x])^(5/2)) + (8*Sin[e + f*x])/(77*b*f*Sqrt[b*Sec[e + f*x]]) - (2*b*Sin[e + f*x]^3)/(11*f*(b*Sec[e + f*x])^(5/2))","A",5,4,21,0.1905,1,"{2627, 3769, 3771, 2641}"
432,1,98,0,0.0821301,"\int \frac{\sin ^2(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]^2/(b*Sec[e + f*x])^(3/2),x]","\frac{4 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{21 b^2 f}+\frac{4 \sin (e+f x)}{21 b f \sqrt{b \sec (e+f x)}}-\frac{2 b \sin (e+f x)}{7 f (b \sec (e+f x))^{5/2}}","\frac{4 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{21 b^2 f}+\frac{4 \sin (e+f x)}{21 b f \sqrt{b \sec (e+f x)}}-\frac{2 b \sin (e+f x)}{7 f (b \sec (e+f x))^{5/2}}",1,"(4*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(21*b^2*f) - (2*b*Sin[e + f*x])/(7*f*(b*Sec[e + f*x])^(5/2)) + (4*Sin[e + f*x])/(21*b*f*Sqrt[b*Sec[e + f*x]])","A",4,4,21,0.1905,1,"{2627, 3769, 3771, 2641}"
433,1,72,0,0.035942,"\int \frac{1}{(b \sec (e+f x))^{3/2}} \, dx","Int[(b*Sec[e + f*x])^(-3/2),x]","\frac{2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 b^2 f}+\frac{2 \sin (e+f x)}{3 b f \sqrt{b \sec (e+f x)}}","\frac{2 \sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{3 b^2 f}+\frac{2 \sin (e+f x)}{3 b f \sqrt{b \sec (e+f x)}}",1,"(2*Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(3*b^2*f) + (2*Sin[e + f*x])/(3*b*f*Sqrt[b*Sec[e + f*x]])","A",3,3,12,0.2500,1,"{3769, 3771, 2641}"
434,1,68,0,0.0655459,"\int \frac{\csc ^2(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^2/(b*Sec[e + f*x])^(3/2),x]","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{b^2 f}-\frac{\csc (e+f x)}{b f \sqrt{b \sec (e+f x)}}","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{b^2 f}-\frac{\csc (e+f x)}{b f \sqrt{b \sec (e+f x)}}",1,"-(Csc[e + f*x]/(b*f*Sqrt[b*Sec[e + f*x]])) - (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(b^2*f)","A",3,3,21,0.1429,1,"{2623, 3771, 2641}"
435,1,102,0,0.1043765,"\int \frac{\csc ^4(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^4/(b*Sec[e + f*x])^(3/2),x]","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{6 b^2 f}-\frac{\csc ^3(e+f x)}{3 b f \sqrt{b \sec (e+f x)}}+\frac{\csc (e+f x)}{6 b f \sqrt{b \sec (e+f x)}}","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{6 b^2 f}-\frac{\csc ^3(e+f x)}{3 b f \sqrt{b \sec (e+f x)}}+\frac{\csc (e+f x)}{6 b f \sqrt{b \sec (e+f x)}}",1,"Csc[e + f*x]/(6*b*f*Sqrt[b*Sec[e + f*x]]) - Csc[e + f*x]^3/(3*b*f*Sqrt[b*Sec[e + f*x]]) - (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(6*b^2*f)","A",4,4,21,0.1905,1,"{2623, 2625, 3771, 2641}"
436,1,132,0,0.1439904,"\int \frac{\csc ^6(e+f x)}{(b \sec (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^6/(b*Sec[e + f*x])^(3/2),x]","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{12 b^2 f}-\frac{\csc ^5(e+f x)}{5 b f \sqrt{b \sec (e+f x)}}+\frac{\csc ^3(e+f x)}{30 b f \sqrt{b \sec (e+f x)}}+\frac{\csc (e+f x)}{12 b f \sqrt{b \sec (e+f x)}}","-\frac{\sqrt{\cos (e+f x)} F\left(\left.\frac{1}{2} (e+f x)\right|2\right) \sqrt{b \sec (e+f x)}}{12 b^2 f}-\frac{\csc ^5(e+f x)}{5 b f \sqrt{b \sec (e+f x)}}+\frac{\csc ^3(e+f x)}{30 b f \sqrt{b \sec (e+f x)}}+\frac{\csc (e+f x)}{12 b f \sqrt{b \sec (e+f x)}}",1,"Csc[e + f*x]/(12*b*f*Sqrt[b*Sec[e + f*x]]) + Csc[e + f*x]^3/(30*b*f*Sqrt[b*Sec[e + f*x]]) - Csc[e + f*x]^5/(5*b*f*Sqrt[b*Sec[e + f*x]]) - (Sqrt[Cos[e + f*x]]*EllipticF[(e + f*x)/2, 2]*Sqrt[b*Sec[e + f*x]])/(12*b^2*f)","A",5,4,21,0.1905,1,"{2623, 2625, 3771, 2641}"
437,1,87,0,0.0630548,"\int \frac{\sin ^7(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Sin[e + f*x]^7/(b*Sec[e + f*x])^(5/2),x]","\frac{2 b^7}{19 f (b \sec (e+f x))^{19/2}}-\frac{2 b^5}{5 f (b \sec (e+f x))^{15/2}}+\frac{6 b^3}{11 f (b \sec (e+f x))^{11/2}}-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}","\frac{2 b^7}{19 f (b \sec (e+f x))^{19/2}}-\frac{2 b^5}{5 f (b \sec (e+f x))^{15/2}}+\frac{6 b^3}{11 f (b \sec (e+f x))^{11/2}}-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}",1,"(2*b^7)/(19*f*(b*Sec[e + f*x])^(19/2)) - (2*b^5)/(5*f*(b*Sec[e + f*x])^(15/2)) + (6*b^3)/(11*f*(b*Sec[e + f*x])^(11/2)) - (2*b)/(7*f*(b*Sec[e + f*x])^(7/2))","A",3,2,21,0.09524,1,"{2622, 270}"
438,1,65,0,0.0585754,"\int \frac{\sin ^5(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Sin[e + f*x]^5/(b*Sec[e + f*x])^(5/2),x]","-\frac{2 b^5}{15 f (b \sec (e+f x))^{15/2}}+\frac{4 b^3}{11 f (b \sec (e+f x))^{11/2}}-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}","-\frac{2 b^5}{15 f (b \sec (e+f x))^{15/2}}+\frac{4 b^3}{11 f (b \sec (e+f x))^{11/2}}-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}",1,"(-2*b^5)/(15*f*(b*Sec[e + f*x])^(15/2)) + (4*b^3)/(11*f*(b*Sec[e + f*x])^(11/2)) - (2*b)/(7*f*(b*Sec[e + f*x])^(7/2))","A",3,2,21,0.09524,1,"{2622, 270}"
439,1,43,0,0.0526156,"\int \frac{\sin ^3(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Sin[e + f*x]^3/(b*Sec[e + f*x])^(5/2),x]","\frac{2 b^3}{11 f (b \sec (e+f x))^{11/2}}-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}","\frac{2 b^3}{11 f (b \sec (e+f x))^{11/2}}-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}",1,"(2*b^3)/(11*f*(b*Sec[e + f*x])^(11/2)) - (2*b)/(7*f*(b*Sec[e + f*x])^(7/2))","A",3,2,21,0.09524,1,"{2622, 14}"
440,1,20,0,0.036703,"\int \frac{\sin (e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Sin[e + f*x]/(b*Sec[e + f*x])^(5/2),x]","-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}","-\frac{2 b}{7 f (b \sec (e+f x))^{7/2}}",1,"(-2*b)/(7*f*(b*Sec[e + f*x])^(7/2))","A",2,2,19,0.1053,1,"{2622, 30}"
441,1,81,0,0.055331,"\int \frac{\csc (e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Csc[e + f*x]/(b*Sec[e + f*x])^(5/2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f}+\frac{2}{3 b f (b \sec (e+f x))^{3/2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{b^{5/2} f}+\frac{2}{3 b f (b \sec (e+f x))^{3/2}}",1,"-(ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(b^(5/2)*f)) - ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]]/(b^(5/2)*f) + 2/(3*b*f*(b*Sec[e + f*x])^(3/2))","A",6,6,19,0.3158,1,"{2622, 325, 329, 212, 206, 203}"
442,1,93,0,0.0728972,"\int \frac{\csc ^3(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Csc[e + f*x]^3/(b*Sec[e + f*x])^(5/2),x]","-\frac{\cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{2 b^3 f}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{5/2} f}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{5/2} f}","-\frac{\cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{2 b^3 f}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{5/2} f}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{4 b^{5/2} f}",1,"(3*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*b^(5/2)*f) + (3*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(4*b^(5/2)*f) - (Cot[e + f*x]^2*Sqrt[b*Sec[e + f*x]])/(2*b^3*f)","A",6,6,21,0.2857,1,"{2622, 290, 329, 212, 206, 203}"
443,1,123,0,0.0840227,"\int \frac{\csc ^5(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Csc[e + f*x]^5/(b*Sec[e + f*x])^(5/2),x]","-\frac{\cot ^4(e+f x) \sqrt{b \sec (e+f x)}}{4 b^3 f}-\frac{\cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{16 b^3 f}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{5/2} f}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{5/2} f}","-\frac{\cot ^4(e+f x) \sqrt{b \sec (e+f x)}}{4 b^3 f}-\frac{\cot ^2(e+f x) \sqrt{b \sec (e+f x)}}{16 b^3 f}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{5/2} f}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{b \sec (e+f x)}}{\sqrt{b}}\right)}{32 b^{5/2} f}",1,"(3*ArcTan[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*b^(5/2)*f) + (3*ArcTanh[Sqrt[b*Sec[e + f*x]]/Sqrt[b]])/(32*b^(5/2)*f) - (Cot[e + f*x]^2*Sqrt[b*Sec[e + f*x]])/(16*b^3*f) - (Cot[e + f*x]^4*Sqrt[b*Sec[e + f*x]])/(4*b^3*f)","A",7,7,21,0.3333,1,"{2622, 288, 290, 329, 212, 206, 203}"
444,1,126,0,0.1319904,"\int \frac{\sin ^4(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Sin[e + f*x]^4/(b*Sec[e + f*x])^(5/2),x]","\frac{8 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{65 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{2 b \sin ^3(e+f x)}{13 f (b \sec (e+f x))^{7/2}}+\frac{8 \sin (e+f x)}{195 b f (b \sec (e+f x))^{3/2}}-\frac{4 b \sin (e+f x)}{39 f (b \sec (e+f x))^{7/2}}","\frac{8 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{65 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{2 b \sin ^3(e+f x)}{13 f (b \sec (e+f x))^{7/2}}+\frac{8 \sin (e+f x)}{195 b f (b \sec (e+f x))^{3/2}}-\frac{4 b \sin (e+f x)}{39 f (b \sec (e+f x))^{7/2}}",1,"(8*EllipticE[(e + f*x)/2, 2])/(65*b^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (4*b*Sin[e + f*x])/(39*f*(b*Sec[e + f*x])^(7/2)) + (8*Sin[e + f*x])/(195*b*f*(b*Sec[e + f*x])^(3/2)) - (2*b*Sin[e + f*x]^3)/(13*f*(b*Sec[e + f*x])^(7/2))","A",5,4,21,0.1905,1,"{2627, 3769, 3771, 2639}"
445,1,98,0,0.0818197,"\int \frac{\sin ^2(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Sin[e + f*x]^2/(b*Sec[e + f*x])^(5/2),x]","\frac{4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{15 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{4 \sin (e+f x)}{45 b f (b \sec (e+f x))^{3/2}}-\frac{2 b \sin (e+f x)}{9 f (b \sec (e+f x))^{7/2}}","\frac{4 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{15 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{4 \sin (e+f x)}{45 b f (b \sec (e+f x))^{3/2}}-\frac{2 b \sin (e+f x)}{9 f (b \sec (e+f x))^{7/2}}",1,"(4*EllipticE[(e + f*x)/2, 2])/(15*b^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (2*b*Sin[e + f*x])/(9*f*(b*Sec[e + f*x])^(7/2)) + (4*Sin[e + f*x])/(45*b*f*(b*Sec[e + f*x])^(3/2))","A",4,4,21,0.1905,1,"{2627, 3769, 3771, 2639}"
446,1,72,0,0.034779,"\int \frac{1}{(b \sec (e+f x))^{5/2}} \, dx","Int[(b*Sec[e + f*x])^(-5/2),x]","\frac{6 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{2 \sin (e+f x)}{5 b f (b \sec (e+f x))^{3/2}}","\frac{6 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{5 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{2 \sin (e+f x)}{5 b f (b \sec (e+f x))^{3/2}}",1,"(6*EllipticE[(e + f*x)/2, 2])/(5*b^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) + (2*Sin[e + f*x])/(5*b*f*(b*Sec[e + f*x])^(3/2))","A",3,3,12,0.2500,1,"{3769, 3771, 2639}"
447,1,68,0,0.0659776,"\int \frac{\csc ^2(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Csc[e + f*x]^2/(b*Sec[e + f*x])^(5/2),x]","-\frac{3 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\csc (e+f x)}{b f (b \sec (e+f x))^{3/2}}","-\frac{3 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\csc (e+f x)}{b f (b \sec (e+f x))^{3/2}}",1,"-(Csc[e + f*x]/(b*f*(b*Sec[e + f*x])^(3/2))) - (3*EllipticE[(e + f*x)/2, 2])/(b^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",3,3,21,0.1429,1,"{2623, 3771, 2639}"
448,1,102,0,0.1081606,"\int \frac{\csc ^4(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Csc[e + f*x]^4/(b*Sec[e + f*x])^(5/2),x]","\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{2 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\csc ^3(e+f x)}{3 b f (b \sec (e+f x))^{3/2}}+\frac{\csc (e+f x)}{2 b f (b \sec (e+f x))^{3/2}}","\frac{E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{2 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\csc ^3(e+f x)}{3 b f (b \sec (e+f x))^{3/2}}+\frac{\csc (e+f x)}{2 b f (b \sec (e+f x))^{3/2}}",1,"Csc[e + f*x]/(2*b*f*(b*Sec[e + f*x])^(3/2)) - Csc[e + f*x]^3/(3*b*f*(b*Sec[e + f*x])^(3/2)) + EllipticE[(e + f*x)/2, 2]/(2*b^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",4,4,21,0.1905,1,"{2623, 2625, 3771, 2639}"
449,1,132,0,0.148684,"\int \frac{\csc ^6(e+f x)}{(b \sec (e+f x))^{5/2}} \, dx","Int[Csc[e + f*x]^6/(b*Sec[e + f*x])^(5/2),x]","\frac{3 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{20 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\csc ^5(e+f x)}{5 b f (b \sec (e+f x))^{3/2}}+\frac{\csc ^3(e+f x)}{10 b f (b \sec (e+f x))^{3/2}}+\frac{3 \csc (e+f x)}{20 b f (b \sec (e+f x))^{3/2}}","\frac{3 E\left(\left.\frac{1}{2} (e+f x)\right|2\right)}{20 b^2 f \sqrt{\cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\csc ^5(e+f x)}{5 b f (b \sec (e+f x))^{3/2}}+\frac{\csc ^3(e+f x)}{10 b f (b \sec (e+f x))^{3/2}}+\frac{3 \csc (e+f x)}{20 b f (b \sec (e+f x))^{3/2}}",1,"(3*Csc[e + f*x])/(20*b*f*(b*Sec[e + f*x])^(3/2)) + Csc[e + f*x]^3/(10*b*f*(b*Sec[e + f*x])^(3/2)) - Csc[e + f*x]^5/(5*b*f*(b*Sec[e + f*x])^(3/2)) + (3*EllipticE[(e + f*x)/2, 2])/(20*b^2*f*Sqrt[Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",5,4,21,0.1905,1,"{2623, 2625, 3771, 2639}"
450,1,449,0,0.4756267,"\int \sqrt{b \sec (e+f x)} (a \sin (e+f x))^{9/2} \, dx","Int[Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(9/2),x]","-\frac{7 a^3 b (a \sin (e+f x))^{3/2}}{16 f \sqrt{b \sec (e+f x)}}-\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{32 \sqrt{2} \sqrt{b} f}+\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{32 \sqrt{2} \sqrt{b} f}+\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} \sqrt{b} f}-\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} \sqrt{b} f}-\frac{a b (a \sin (e+f x))^{7/2}}{4 f \sqrt{b \sec (e+f x)}}","-\frac{7 a^3 b (a \sin (e+f x))^{3/2}}{16 f \sqrt{b \sec (e+f x)}}-\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{32 \sqrt{2} \sqrt{b} f}+\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{32 \sqrt{2} \sqrt{b} f}+\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} \sqrt{b} f}-\frac{21 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} \sqrt{b} f}-\frac{a b (a \sin (e+f x))^{7/2}}{4 f \sqrt{b \sec (e+f x)}}",1,"(-21*a^(9/2)*ArcTan[1 - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(32*Sqrt[2]*Sqrt[b]*f) + (21*a^(9/2)*ArcTan[1 + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(32*Sqrt[2]*Sqrt[b]*f) + (21*a^(9/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(64*Sqrt[2]*Sqrt[b]*f) - (21*a^(9/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(64*Sqrt[2]*Sqrt[b]*f) - (7*a^3*b*(a*Sin[e + f*x])^(3/2))/(16*f*Sqrt[b*Sec[e + f*x]]) - (a*b*(a*Sin[e + f*x])^(7/2))/(4*f*Sqrt[b*Sec[e + f*x]])","A",13,9,25,0.3600,1,"{2583, 2585, 2574, 297, 1162, 617, 204, 1165, 628}"
451,1,414,0,0.3484107,"\int \sqrt{b \sec (e+f x)} (a \sin (e+f x))^{5/2} \, dx","Int[Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(5/2),x]","-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{4 \sqrt{2} \sqrt{b} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{4 \sqrt{2} \sqrt{b} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} \sqrt{b} f}-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} \sqrt{b} f}-\frac{a b (a \sin (e+f x))^{3/2}}{2 f \sqrt{b \sec (e+f x)}}","-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{4 \sqrt{2} \sqrt{b} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{4 \sqrt{2} \sqrt{b} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} \sqrt{b} f}-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} \sqrt{b} f}-\frac{a b (a \sin (e+f x))^{3/2}}{2 f \sqrt{b \sec (e+f x)}}",1,"(-3*a^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(4*Sqrt[2]*Sqrt[b]*f) + (3*a^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(4*Sqrt[2]*Sqrt[b]*f) + (3*a^(5/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(8*Sqrt[2]*Sqrt[b]*f) - (3*a^(5/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(8*Sqrt[2]*Sqrt[b]*f) - (a*b*(a*Sin[e + f*x])^(3/2))/(2*f*Sqrt[b*Sec[e + f*x]])","A",12,9,25,0.3600,1,"{2583, 2585, 2574, 297, 1162, 617, 204, 1165, 628}"
452,1,376,0,0.2649382,"\int \sqrt{b \sec (e+f x)} \sqrt{a \sin (e+f x)} \, dx","Int[Sqrt[b*Sec[e + f*x]]*Sqrt[a*Sin[e + f*x]],x]","-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{\sqrt{2} \sqrt{b} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{\sqrt{2} \sqrt{b} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} \sqrt{b} f}-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} \sqrt{b} f}","-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{\sqrt{2} \sqrt{b} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{\sqrt{2} \sqrt{b} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} \sqrt{b} f}-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} \sqrt{b} f}",1,"-((Sqrt[a]*ArcTan[1 - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(Sqrt[2]*Sqrt[b]*f)) + (Sqrt[a]*ArcTan[1 + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(Sqrt[2]*Sqrt[b]*f) + (Sqrt[a]*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(2*Sqrt[2]*Sqrt[b]*f) - (Sqrt[a]*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(2*Sqrt[2]*Sqrt[b]*f)","A",11,8,25,0.3200,1,"{2585, 2574, 297, 1162, 617, 204, 1165, 628}"
453,1,33,0,0.0516478,"\int \frac{\sqrt{b \sec (e+f x)}}{(a \sin (e+f x))^{3/2}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/(a*Sin[e + f*x])^(3/2),x]","-\frac{2 b}{a f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}","-\frac{2 b}{a f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(a*f*Sqrt[b*Sec[e + f*x]]*Sqrt[a*Sin[e + f*x]])","A",1,1,25,0.04000,1,"{2578}"
454,1,71,0,0.1088415,"\int \frac{\sqrt{b \sec (e+f x)}}{(a \sin (e+f x))^{7/2}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/(a*Sin[e + f*x])^(7/2),x]","-\frac{8 b}{5 a^3 f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{2 b}{5 a f (a \sin (e+f x))^{5/2} \sqrt{b \sec (e+f x)}}","-\frac{8 b}{5 a^3 f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{2 b}{5 a f (a \sin (e+f x))^{5/2} \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(5*a*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(5/2)) - (8*b)/(5*a^3*f*Sqrt[b*Sec[e + f*x]]*Sqrt[a*Sin[e + f*x]])","A",2,2,25,0.08000,1,"{2584, 2578}"
455,1,106,0,0.1652277,"\int \frac{\sqrt{b \sec (e+f x)}}{(a \sin (e+f x))^{11/2}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/(a*Sin[e + f*x])^(11/2),x]","-\frac{64 b}{45 a^5 f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{16 b}{45 a^3 f (a \sin (e+f x))^{5/2} \sqrt{b \sec (e+f x)}}-\frac{2 b}{9 a f (a \sin (e+f x))^{9/2} \sqrt{b \sec (e+f x)}}","-\frac{64 b}{45 a^5 f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{16 b}{45 a^3 f (a \sin (e+f x))^{5/2} \sqrt{b \sec (e+f x)}}-\frac{2 b}{9 a f (a \sin (e+f x))^{9/2} \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(9*a*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(9/2)) - (16*b)/(45*a^3*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(5/2)) - (64*b)/(45*a^5*f*Sqrt[b*Sec[e + f*x]]*Sqrt[a*Sin[e + f*x]])","A",3,2,25,0.08000,1,"{2584, 2578}"
456,1,128,0,0.2147729,"\int \sqrt{b \sec (e+f x)} (a \sin (e+f x))^{7/2} \, dx","Int[Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(7/2),x]","-\frac{5 a^3 b \sqrt{a \sin (e+f x)}}{6 f \sqrt{b \sec (e+f x)}}+\frac{5 a^4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{12 f \sqrt{a \sin (e+f x)}}-\frac{a b (a \sin (e+f x))^{5/2}}{3 f \sqrt{b \sec (e+f x)}}","-\frac{5 a^3 b \sqrt{a \sin (e+f x)}}{6 f \sqrt{b \sec (e+f x)}}+\frac{5 a^4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{12 f \sqrt{a \sin (e+f x)}}-\frac{a b (a \sin (e+f x))^{5/2}}{3 f \sqrt{b \sec (e+f x)}}",1,"(-5*a^3*b*Sqrt[a*Sin[e + f*x]])/(6*f*Sqrt[b*Sec[e + f*x]]) - (a*b*(a*Sin[e + f*x])^(5/2))/(3*f*Sqrt[b*Sec[e + f*x]]) + (5*a^4*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(12*f*Sqrt[a*Sin[e + f*x]])","A",5,4,25,0.1600,1,"{2583, 2585, 2573, 2641}"
457,1,91,0,0.1506045,"\int \sqrt{b \sec (e+f x)} (a \sin (e+f x))^{3/2} \, dx","Int[Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(3/2),x]","\frac{a^2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{2 f \sqrt{a \sin (e+f x)}}-\frac{a b \sqrt{a \sin (e+f x)}}{f \sqrt{b \sec (e+f x)}}","\frac{a^2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{2 f \sqrt{a \sin (e+f x)}}-\frac{a b \sqrt{a \sin (e+f x)}}{f \sqrt{b \sec (e+f x)}}",1,"-((a*b*Sqrt[a*Sin[e + f*x]])/(f*Sqrt[b*Sec[e + f*x]])) + (a^2*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(2*f*Sqrt[a*Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2583, 2585, 2573, 2641}"
458,1,53,0,0.0990154,"\int \frac{\sqrt{b \sec (e+f x)}}{\sqrt{a \sin (e+f x)}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/Sqrt[a*Sin[e + f*x]],x]","\frac{\sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{f \sqrt{a \sin (e+f x)}}","\frac{\sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{f \sqrt{a \sin (e+f x)}}",1,"(EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(f*Sqrt[a*Sin[e + f*x]])","A",3,3,25,0.1200,1,"{2585, 2573, 2641}"
459,1,95,0,0.1536438,"\int \frac{\sqrt{b \sec (e+f x)}}{(a \sin (e+f x))^{5/2}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/(a*Sin[e + f*x])^(5/2),x]","\frac{2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{3 a^2 f \sqrt{a \sin (e+f x)}}-\frac{2 b}{3 a f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}","\frac{2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{3 a^2 f \sqrt{a \sin (e+f x)}}-\frac{2 b}{3 a f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(3*a*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(3/2)) + (2*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(3*a^2*f*Sqrt[a*Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2584, 2585, 2573, 2641}"
460,1,130,0,0.2135072,"\int \frac{\sqrt{b \sec (e+f x)}}{(a \sin (e+f x))^{9/2}} \, dx","Int[Sqrt[b*Sec[e + f*x]]/(a*Sin[e + f*x])^(9/2),x]","-\frac{4 b}{7 a^3 f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}+\frac{4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{7 a^4 f \sqrt{a \sin (e+f x)}}-\frac{2 b}{7 a f (a \sin (e+f x))^{7/2} \sqrt{b \sec (e+f x)}}","-\frac{4 b}{7 a^3 f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}+\frac{4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{7 a^4 f \sqrt{a \sin (e+f x)}}-\frac{2 b}{7 a f (a \sin (e+f x))^{7/2} \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(7*a*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(7/2)) - (4*b)/(7*a^3*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(3/2)) + (4*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(7*a^4*f*Sqrt[a*Sin[e + f*x]])","A",5,4,25,0.1600,1,"{2584, 2585, 2573, 2641}"
461,1,115,0,0.1644656,"\int \frac{\sin ^{\frac{9}{2}}(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^(9/2)/Sqrt[b*Sec[e + f*x]],x]","-\frac{b \sin ^{\frac{7}{2}}(e+f x)}{5 f (b \sec (e+f x))^{3/2}}-\frac{7 b \sin ^{\frac{3}{2}}(e+f x)}{30 f (b \sec (e+f x))^{3/2}}+\frac{7 \sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{20 f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}","-\frac{b \sin ^{\frac{7}{2}}(e+f x)}{5 f (b \sec (e+f x))^{3/2}}-\frac{7 b \sin ^{\frac{3}{2}}(e+f x)}{30 f (b \sec (e+f x))^{3/2}}+\frac{7 \sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{20 f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}",1,"(-7*b*Sin[e + f*x]^(3/2))/(30*f*(b*Sec[e + f*x])^(3/2)) - (b*Sin[e + f*x]^(7/2))/(5*f*(b*Sec[e + f*x])^(3/2)) + (7*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[Sin[e + f*x]])/(20*f*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])","A",5,4,23,0.1739,1,"{2583, 2585, 2572, 2639}"
462,1,85,0,0.1188486,"\int \frac{\sin ^{\frac{5}{2}}(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^(5/2)/Sqrt[b*Sec[e + f*x]],x]","\frac{\sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{2 f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}-\frac{b \sin ^{\frac{3}{2}}(e+f x)}{3 f (b \sec (e+f x))^{3/2}}","\frac{\sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{2 f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}-\frac{b \sin ^{\frac{3}{2}}(e+f x)}{3 f (b \sec (e+f x))^{3/2}}",1,"-(b*Sin[e + f*x]^(3/2))/(3*f*(b*Sec[e + f*x])^(3/2)) + (EllipticE[e - Pi/4 + f*x, 2]*Sqrt[Sin[e + f*x]])/(2*f*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])","A",4,4,23,0.1739,1,"{2583, 2585, 2572, 2639}"
463,1,51,0,0.0807287,"\int \frac{\sqrt{\sin (e+f x)}}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sqrt[Sin[e + f*x]]/Sqrt[b*Sec[e + f*x]],x]","\frac{\sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}","\frac{\sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}",1,"(EllipticE[e - Pi/4 + f*x, 2]*Sqrt[Sin[e + f*x]])/(f*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])","A",3,3,23,0.1304,1,"{2585, 2572, 2639}"
464,1,81,0,0.1199763,"\int \frac{1}{\sqrt{b \sec (e+f x)} \sin ^{\frac{3}{2}}(e+f x)} \, dx","Int[1/(Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^(3/2)),x]","-\frac{2 b}{f \sqrt{\sin (e+f x)} (b \sec (e+f x))^{3/2}}-\frac{2 \sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}","-\frac{2 b}{f \sqrt{\sin (e+f x)} (b \sec (e+f x))^{3/2}}-\frac{2 \sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(f*(b*Sec[e + f*x])^(3/2)*Sqrt[Sin[e + f*x]]) - (2*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[Sin[e + f*x]])/(f*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])","A",4,4,23,0.1739,1,"{2584, 2585, 2572, 2639}"
465,1,115,0,0.1624712,"\int \frac{1}{\sqrt{b \sec (e+f x)} \sin ^{\frac{7}{2}}(e+f x)} \, dx","Int[1/(Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^(7/2)),x]","-\frac{2 b}{5 f \sin ^{\frac{5}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{4 b}{5 f \sqrt{\sin (e+f x)} (b \sec (e+f x))^{3/2}}-\frac{4 \sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{5 f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}","-\frac{2 b}{5 f \sin ^{\frac{5}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{4 b}{5 f \sqrt{\sin (e+f x)} (b \sec (e+f x))^{3/2}}-\frac{4 \sqrt{\sin (e+f x)} E\left(\left.e+f x-\frac{\pi }{4}\right|2\right)}{5 f \sqrt{\sin (2 e+2 f x)} \sqrt{b \sec (e+f x)}}",1,"(-2*b)/(5*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(5/2)) - (4*b)/(5*f*(b*Sec[e + f*x])^(3/2)*Sqrt[Sin[e + f*x]]) - (4*EllipticE[e - Pi/4 + f*x, 2]*Sqrt[Sin[e + f*x]])/(5*f*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])","A",5,4,23,0.1739,1,"{2584, 2585, 2572, 2639}"
466,1,363,0,0.2679967,"\int \frac{\sin ^{\frac{3}{2}}(e+f x)}{\sqrt{b \sec (e+f x)}} \, dx","Int[Sin[e + f*x]^(3/2)/Sqrt[b*Sec[e + f*x]],x]","-\frac{b \sqrt{\sin (e+f x)}}{2 f (b \sec (e+f x))^{3/2}}+\frac{\sqrt{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}\right)}{4 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}+1\right)}{4 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{8 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)+\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{8 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}","-\frac{b \sqrt{\sin (e+f x)}}{2 f (b \sec (e+f x))^{3/2}}+\frac{\sqrt{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}\right)}{4 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}+1\right)}{4 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{8 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)+\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{8 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(Sqrt[b]*ArcTan[1 - (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/(Sqrt[b]*Sqrt[Sin[e + f*x]])])/(4*Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (Sqrt[b]*ArcTan[1 + (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/(Sqrt[b]*Sqrt[Sin[e + f*x]])])/(4*Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (Sqrt[b]*Log[Sqrt[b] + Sqrt[b]*Cot[e + f*x] - (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/Sqrt[Sin[e + f*x]]])/(8*Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) + (Sqrt[b]*Log[Sqrt[b] + Sqrt[b]*Cot[e + f*x] + (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/Sqrt[Sin[e + f*x]]])/(8*Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (b*Sqrt[Sin[e + f*x]])/(2*f*(b*Sec[e + f*x])^(3/2))","A",12,9,23,0.3913,1,"{2583, 2585, 2575, 297, 1162, 617, 204, 1165, 628}"
467,1,328,0,0.1920762,"\int \frac{1}{\sqrt{b \sec (e+f x)} \sqrt{\sin (e+f x)}} \, dx","Int[1/(Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[e + f*x]]),x]","\frac{\sqrt{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}\right)}{\sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}+1\right)}{\sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{2 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)+\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{2 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}","\frac{\sqrt{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}\right)}{\sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{b} \sqrt{\sin (e+f x)}}+1\right)}{\sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}-\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)-\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{2 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}+\frac{\sqrt{b} \log \left(\sqrt{b} \cot (e+f x)+\frac{\sqrt{2} \sqrt{b \cos (e+f x)}}{\sqrt{\sin (e+f x)}}+\sqrt{b}\right)}{2 \sqrt{2} f \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(Sqrt[b]*ArcTan[1 - (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/(Sqrt[b]*Sqrt[Sin[e + f*x]])])/(Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (Sqrt[b]*ArcTan[1 + (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/(Sqrt[b]*Sqrt[Sin[e + f*x]])])/(Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) - (Sqrt[b]*Log[Sqrt[b] + Sqrt[b]*Cot[e + f*x] - (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/Sqrt[Sin[e + f*x]]])/(2*Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]]) + (Sqrt[b]*Log[Sqrt[b] + Sqrt[b]*Cot[e + f*x] + (Sqrt[2]*Sqrt[b*Cos[e + f*x]])/Sqrt[Sin[e + f*x]]])/(2*Sqrt[2]*f*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])","A",11,8,23,0.3478,1,"{2585, 2575, 297, 1162, 617, 204, 1165, 628}"
468,1,30,0,0.0378593,"\int \frac{1}{\sqrt{b \sec (e+f x)} \sin ^{\frac{5}{2}}(e+f x)} \, dx","Int[1/(Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^(5/2)),x]","-\frac{2 b}{3 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}","-\frac{2 b}{3 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}",1,"(-2*b)/(3*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(3/2))","A",1,1,23,0.04348,1,"{2578}"
469,1,61,0,0.0780422,"\int \frac{1}{\sqrt{b \sec (e+f x)} \sin ^{\frac{9}{2}}(e+f x)} \, dx","Int[1/(Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^(9/2)),x]","-\frac{8 b}{21 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{2 b}{7 f \sin ^{\frac{7}{2}}(e+f x) (b \sec (e+f x))^{3/2}}","-\frac{8 b}{21 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{2 b}{7 f \sin ^{\frac{7}{2}}(e+f x) (b \sec (e+f x))^{3/2}}",1,"(-2*b)/(7*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(7/2)) - (8*b)/(21*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(3/2))","A",2,2,23,0.08696,1,"{2584, 2578}"
470,1,91,0,0.1218107,"\int \frac{1}{\sqrt{b \sec (e+f x)} \sin ^{\frac{13}{2}}(e+f x)} \, dx","Int[1/(Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^(13/2)),x]","-\frac{64 b}{231 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{16 b}{77 f \sin ^{\frac{7}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{2 b}{11 f \sin ^{\frac{11}{2}}(e+f x) (b \sec (e+f x))^{3/2}}","-\frac{64 b}{231 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{16 b}{77 f \sin ^{\frac{7}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{2 b}{11 f \sin ^{\frac{11}{2}}(e+f x) (b \sec (e+f x))^{3/2}}",1,"(-2*b)/(11*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(11/2)) - (16*b)/(77*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(7/2)) - (64*b)/(231*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(3/2))","A",3,2,23,0.08696,1,"{2584, 2578}"
471,1,121,0,0.1622581,"\int \frac{1}{\sqrt{b \sec (e+f x)} \sin ^{\frac{17}{2}}(e+f x)} \, dx","Int[1/(Sqrt[b*Sec[e + f*x]]*Sin[e + f*x]^(17/2)),x]","-\frac{256 b}{1155 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{64 b}{385 f \sin ^{\frac{7}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{8 b}{55 f \sin ^{\frac{11}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{2 b}{15 f \sin ^{\frac{15}{2}}(e+f x) (b \sec (e+f x))^{3/2}}","-\frac{256 b}{1155 f \sin ^{\frac{3}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{64 b}{385 f \sin ^{\frac{7}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{8 b}{55 f \sin ^{\frac{11}{2}}(e+f x) (b \sec (e+f x))^{3/2}}-\frac{2 b}{15 f \sin ^{\frac{15}{2}}(e+f x) (b \sec (e+f x))^{3/2}}",1,"(-2*b)/(15*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(15/2)) - (8*b)/(55*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(11/2)) - (64*b)/(385*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(7/2)) - (256*b)/(1155*f*(b*Sec[e + f*x])^(3/2)*Sin[e + f*x]^(3/2))","A",4,2,23,0.08696,1,"{2584, 2578}"
472,1,490,0,0.553205,"\int \frac{(a \sin (e+f x))^{9/2}}{(b \sec (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(9/2)/(b*Sec[e + f*x])^(3/2),x]","-\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{128 \sqrt{2} b^{5/2} f}+\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{128 \sqrt{2} b^{5/2} f}+\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{256 \sqrt{2} b^{5/2} f}-\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{256 \sqrt{2} b^{5/2} f}-\frac{7 a^3 (a \sin (e+f x))^{3/2}}{192 b f \sqrt{b \sec (e+f x)}}+\frac{(a \sin (e+f x))^{11/2}}{6 a b f \sqrt{b \sec (e+f x)}}-\frac{a (a \sin (e+f x))^{7/2}}{48 b f \sqrt{b \sec (e+f x)}}","-\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{128 \sqrt{2} b^{5/2} f}+\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{128 \sqrt{2} b^{5/2} f}+\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{256 \sqrt{2} b^{5/2} f}-\frac{7 a^{9/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{256 \sqrt{2} b^{5/2} f}-\frac{7 a^3 (a \sin (e+f x))^{3/2}}{192 b f \sqrt{b \sec (e+f x)}}+\frac{(a \sin (e+f x))^{11/2}}{6 a b f \sqrt{b \sec (e+f x)}}-\frac{a (a \sin (e+f x))^{7/2}}{48 b f \sqrt{b \sec (e+f x)}}",1,"(-7*a^(9/2)*ArcTan[1 - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(128*Sqrt[2]*b^(5/2)*f) + (7*a^(9/2)*ArcTan[1 + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(128*Sqrt[2]*b^(5/2)*f) + (7*a^(9/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(256*Sqrt[2]*b^(5/2)*f) - (7*a^(9/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(256*Sqrt[2]*b^(5/2)*f) - (7*a^3*(a*Sin[e + f*x])^(3/2))/(192*b*f*Sqrt[b*Sec[e + f*x]]) - (a*(a*Sin[e + f*x])^(7/2))/(48*b*f*Sqrt[b*Sec[e + f*x]]) + (a*Sin[e + f*x])^(11/2)/(6*a*b*f*Sqrt[b*Sec[e + f*x]])","A",14,10,25,0.4000,1,"{2582, 2583, 2585, 2574, 297, 1162, 617, 204, 1165, 628}"
473,1,453,0,0.447008,"\int \frac{(a \sin (e+f x))^{5/2}}{(b \sec (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(5/2)/(b*Sec[e + f*x])^(3/2),x]","-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{32 \sqrt{2} b^{5/2} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{32 \sqrt{2} b^{5/2} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} b^{5/2} f}-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} b^{5/2} f}+\frac{(a \sin (e+f x))^{7/2}}{4 a b f \sqrt{b \sec (e+f x)}}-\frac{a (a \sin (e+f x))^{3/2}}{16 b f \sqrt{b \sec (e+f x)}}","-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{32 \sqrt{2} b^{5/2} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{32 \sqrt{2} b^{5/2} f}+\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} b^{5/2} f}-\frac{3 a^{5/2} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{64 \sqrt{2} b^{5/2} f}+\frac{(a \sin (e+f x))^{7/2}}{4 a b f \sqrt{b \sec (e+f x)}}-\frac{a (a \sin (e+f x))^{3/2}}{16 b f \sqrt{b \sec (e+f x)}}",1,"(-3*a^(5/2)*ArcTan[1 - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(32*Sqrt[2]*b^(5/2)*f) + (3*a^(5/2)*ArcTan[1 + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(32*Sqrt[2]*b^(5/2)*f) + (3*a^(5/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(64*Sqrt[2]*b^(5/2)*f) - (3*a^(5/2)*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(64*Sqrt[2]*b^(5/2)*f) - (a*(a*Sin[e + f*x])^(3/2))/(16*b*f*Sqrt[b*Sec[e + f*x]]) + (a*Sin[e + f*x])^(7/2)/(4*a*b*f*Sqrt[b*Sec[e + f*x]])","A",13,10,25,0.4000,1,"{2582, 2583, 2585, 2574, 297, 1162, 617, 204, 1165, 628}"
474,1,418,0,0.3561223,"\int \frac{\sqrt{a \sin (e+f x)}}{(b \sec (e+f x))^{3/2}} \, dx","Int[Sqrt[a*Sin[e + f*x]]/(b*Sec[e + f*x])^(3/2),x]","-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{4 \sqrt{2} b^{5/2} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{4 \sqrt{2} b^{5/2} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} b^{5/2} f}-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} b^{5/2} f}+\frac{(a \sin (e+f x))^{3/2}}{2 a b f \sqrt{b \sec (e+f x)}}","-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{4 \sqrt{2} b^{5/2} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{4 \sqrt{2} b^{5/2} f}+\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} b^{5/2} f}-\frac{\sqrt{a} \sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{8 \sqrt{2} b^{5/2} f}+\frac{(a \sin (e+f x))^{3/2}}{2 a b f \sqrt{b \sec (e+f x)}}",1,"-(Sqrt[a]*ArcTan[1 - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(4*Sqrt[2]*b^(5/2)*f) + (Sqrt[a]*ArcTan[1 + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(4*Sqrt[2]*b^(5/2)*f) + (Sqrt[a]*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(8*Sqrt[2]*b^(5/2)*f) - (Sqrt[a]*Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(8*Sqrt[2]*b^(5/2)*f) + (a*Sin[e + f*x])^(3/2)/(2*a*b*f*Sqrt[b*Sec[e + f*x]])","A",12,9,25,0.3600,1,"{2582, 2585, 2574, 297, 1162, 617, 204, 1165, 628}"
475,1,411,0,0.3596295,"\int \frac{1}{(b \sec (e+f x))^{3/2} (a \sin (e+f x))^{3/2}} \, dx","Int[1/((b*Sec[e + f*x])^(3/2)*(a*Sin[e + f*x])^(3/2)),x]","\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{\sqrt{2} a^{3/2} b^{5/2} f}-\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{\sqrt{2} a^{3/2} b^{5/2} f}-\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} a^{3/2} b^{5/2} f}+\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} a^{3/2} b^{5/2} f}-\frac{2}{a b f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}","\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}\right)}{\sqrt{2} a^{3/2} b^{5/2} f}-\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{a} \sqrt{b \cos (e+f x)}}+1\right)}{\sqrt{2} a^{3/2} b^{5/2} f}-\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(-\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} a^{3/2} b^{5/2} f}+\frac{\sqrt{b \cos (e+f x)} \sqrt{b \sec (e+f x)} \log \left(\frac{\sqrt{2} \sqrt{b} \sqrt{a \sin (e+f x)}}{\sqrt{b \cos (e+f x)}}+\sqrt{a} \tan (e+f x)+\sqrt{a}\right)}{2 \sqrt{2} a^{3/2} b^{5/2} f}-\frac{2}{a b f \sqrt{a \sin (e+f x)} \sqrt{b \sec (e+f x)}}",1,"(ArcTan[1 - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(Sqrt[2]*a^(3/2)*b^(5/2)*f) - (ArcTan[1 + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/(Sqrt[a]*Sqrt[b*Cos[e + f*x]])]*Sqrt[b*Cos[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(Sqrt[2]*a^(3/2)*b^(5/2)*f) - (Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] - (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(2*Sqrt[2]*a^(3/2)*b^(5/2)*f) + (Sqrt[b*Cos[e + f*x]]*Log[Sqrt[a] + (Sqrt[2]*Sqrt[b]*Sqrt[a*Sin[e + f*x]])/Sqrt[b*Cos[e + f*x]] + Sqrt[a]*Tan[e + f*x]]*Sqrt[b*Sec[e + f*x]])/(2*Sqrt[2]*a^(3/2)*b^(5/2)*f) - 2/(a*b*f*Sqrt[b*Sec[e + f*x]]*Sqrt[a*Sin[e + f*x]])","A",12,9,25,0.3600,1,"{2581, 2585, 2574, 297, 1162, 617, 204, 1165, 628}"
476,1,35,0,0.0575665,"\int \frac{1}{(b \sec (e+f x))^{3/2} (a \sin (e+f x))^{7/2}} \, dx","Int[1/((b*Sec[e + f*x])^(3/2)*(a*Sin[e + f*x])^(7/2)),x]","-\frac{2 b}{5 a f (a \sin (e+f x))^{5/2} (b \sec (e+f x))^{5/2}}","-\frac{2 b}{5 a f (a \sin (e+f x))^{5/2} (b \sec (e+f x))^{5/2}}",1,"(-2*b)/(5*a*f*(b*Sec[e + f*x])^(5/2)*(a*Sin[e + f*x])^(5/2))","A",1,1,25,0.04000,1,"{2578}"
477,1,172,0,0.2747275,"\int \frac{(a \sin (e+f x))^{7/2}}{(b \sec (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(7/2)/(b*Sec[e + f*x])^(3/2),x]","\frac{a^4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{24 b^2 f \sqrt{a \sin (e+f x)}}-\frac{a^3 \sqrt{a \sin (e+f x)}}{12 b f \sqrt{b \sec (e+f x)}}+\frac{(a \sin (e+f x))^{9/2}}{5 a b f \sqrt{b \sec (e+f x)}}-\frac{a (a \sin (e+f x))^{5/2}}{30 b f \sqrt{b \sec (e+f x)}}","\frac{a^4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{24 b^2 f \sqrt{a \sin (e+f x)}}-\frac{a^3 \sqrt{a \sin (e+f x)}}{12 b f \sqrt{b \sec (e+f x)}}+\frac{(a \sin (e+f x))^{9/2}}{5 a b f \sqrt{b \sec (e+f x)}}-\frac{a (a \sin (e+f x))^{5/2}}{30 b f \sqrt{b \sec (e+f x)}}",1,"-(a^3*Sqrt[a*Sin[e + f*x]])/(12*b*f*Sqrt[b*Sec[e + f*x]]) - (a*(a*Sin[e + f*x])^(5/2))/(30*b*f*Sqrt[b*Sec[e + f*x]]) + (a*Sin[e + f*x])^(9/2)/(5*a*b*f*Sqrt[b*Sec[e + f*x]]) + (a^4*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(24*b^2*f*Sqrt[a*Sin[e + f*x]])","A",6,5,25,0.2000,1,"{2582, 2583, 2585, 2573, 2641}"
478,1,135,0,0.215809,"\int \frac{(a \sin (e+f x))^{3/2}}{(b \sec (e+f x))^{3/2}} \, dx","Int[(a*Sin[e + f*x])^(3/2)/(b*Sec[e + f*x])^(3/2),x]","\frac{a^2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{12 b^2 f \sqrt{a \sin (e+f x)}}+\frac{(a \sin (e+f x))^{5/2}}{3 a b f \sqrt{b \sec (e+f x)}}-\frac{a \sqrt{a \sin (e+f x)}}{6 b f \sqrt{b \sec (e+f x)}}","\frac{a^2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{12 b^2 f \sqrt{a \sin (e+f x)}}+\frac{(a \sin (e+f x))^{5/2}}{3 a b f \sqrt{b \sec (e+f x)}}-\frac{a \sqrt{a \sin (e+f x)}}{6 b f \sqrt{b \sec (e+f x)}}",1,"-(a*Sqrt[a*Sin[e + f*x]])/(6*b*f*Sqrt[b*Sec[e + f*x]]) + (a*Sin[e + f*x])^(5/2)/(3*a*b*f*Sqrt[b*Sec[e + f*x]]) + (a^2*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(12*b^2*f*Sqrt[a*Sin[e + f*x]])","A",5,5,25,0.2000,1,"{2582, 2583, 2585, 2573, 2641}"
479,1,94,0,0.1523367,"\int \frac{1}{(b \sec (e+f x))^{3/2} \sqrt{a \sin (e+f x)}} \, dx","Int[1/((b*Sec[e + f*x])^(3/2)*Sqrt[a*Sin[e + f*x]]),x]","\frac{\sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{2 b^2 f \sqrt{a \sin (e+f x)}}+\frac{\sqrt{a \sin (e+f x)}}{a b f \sqrt{b \sec (e+f x)}}","\frac{\sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{2 b^2 f \sqrt{a \sin (e+f x)}}+\frac{\sqrt{a \sin (e+f x)}}{a b f \sqrt{b \sec (e+f x)}}",1,"Sqrt[a*Sin[e + f*x]]/(a*b*f*Sqrt[b*Sec[e + f*x]]) + (EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(2*b^2*f*Sqrt[a*Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2582, 2585, 2573, 2641}"
480,1,100,0,0.1563316,"\int \frac{1}{(b \sec (e+f x))^{3/2} (a \sin (e+f x))^{5/2}} \, dx","Int[1/((b*Sec[e + f*x])^(3/2)*(a*Sin[e + f*x])^(5/2)),x]","-\frac{\sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{3 a^2 b^2 f \sqrt{a \sin (e+f x)}}-\frac{2}{3 a b f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}","-\frac{\sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{3 a^2 b^2 f \sqrt{a \sin (e+f x)}}-\frac{2}{3 a b f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}",1,"-2/(3*a*b*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(3/2)) - (EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(3*a^2*b^2*f*Sqrt[a*Sin[e + f*x]])","A",4,4,25,0.1600,1,"{2581, 2585, 2573, 2641}"
481,1,137,0,0.2189799,"\int \frac{1}{(b \sec (e+f x))^{3/2} (a \sin (e+f x))^{9/2}} \, dx","Int[1/((b*Sec[e + f*x])^(3/2)*(a*Sin[e + f*x])^(9/2)),x]","-\frac{2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{21 a^4 b^2 f \sqrt{a \sin (e+f x)}}+\frac{2}{21 a^3 b f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}-\frac{2}{7 a b f (a \sin (e+f x))^{7/2} \sqrt{b \sec (e+f x)}}","-\frac{2 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{21 a^4 b^2 f \sqrt{a \sin (e+f x)}}+\frac{2}{21 a^3 b f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}-\frac{2}{7 a b f (a \sin (e+f x))^{7/2} \sqrt{b \sec (e+f x)}}",1,"-2/(7*a*b*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(7/2)) + 2/(21*a^3*b*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(3/2)) - (2*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(21*a^4*b^2*f*Sqrt[a*Sin[e + f*x]])","A",5,5,25,0.2000,1,"{2581, 2584, 2585, 2573, 2641}"
482,1,174,0,0.2823247,"\int \frac{1}{(b \sec (e+f x))^{3/2} (a \sin (e+f x))^{13/2}} \, dx","Int[1/((b*Sec[e + f*x])^(3/2)*(a*Sin[e + f*x])^(13/2)),x]","-\frac{4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{77 a^6 b^2 f \sqrt{a \sin (e+f x)}}+\frac{4}{77 a^5 b f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}+\frac{2}{77 a^3 b f (a \sin (e+f x))^{7/2} \sqrt{b \sec (e+f x)}}-\frac{2}{11 a b f (a \sin (e+f x))^{11/2} \sqrt{b \sec (e+f x)}}","-\frac{4 \sqrt{\sin (2 e+2 f x)} F\left(\left.e+f x-\frac{\pi }{4}\right|2\right) \sqrt{b \sec (e+f x)}}{77 a^6 b^2 f \sqrt{a \sin (e+f x)}}+\frac{4}{77 a^5 b f (a \sin (e+f x))^{3/2} \sqrt{b \sec (e+f x)}}+\frac{2}{77 a^3 b f (a \sin (e+f x))^{7/2} \sqrt{b \sec (e+f x)}}-\frac{2}{11 a b f (a \sin (e+f x))^{11/2} \sqrt{b \sec (e+f x)}}",1,"-2/(11*a*b*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(11/2)) + 2/(77*a^3*b*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(7/2)) + 4/(77*a^5*b*f*Sqrt[b*Sec[e + f*x]]*(a*Sin[e + f*x])^(3/2)) - (4*EllipticF[e - Pi/4 + f*x, 2]*Sqrt[b*Sec[e + f*x]]*Sqrt[Sin[2*e + 2*f*x]])/(77*a^6*b^2*f*Sqrt[a*Sin[e + f*x]])","A",6,5,25,0.2000,1,"{2581, 2584, 2585, 2573, 2641}"
483,1,75,0,0.1088382,"\int (d \sec (a+b x))^{5/2} (c \sin (a+b x))^m \, dx","Int[(d*Sec[a + b*x])^(5/2)*(c*Sin[a + b*x])^m,x]","\frac{d \cos ^2(a+b x)^{3/4} (d \sec (a+b x))^{3/2} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{7}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}","\frac{d \cos ^2(a+b x)^{3/4} (d \sec (a+b x))^{3/2} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{7}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}",1,"(d*(Cos[a + b*x]^2)^(3/4)*Hypergeometric2F1[7/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(d*Sec[a + b*x])^(3/2)*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m))","A",2,2,23,0.08696,1,"{2587, 2577}"
484,1,75,0,0.1075662,"\int (d \sec (a+b x))^{3/2} (c \sin (a+b x))^m \, dx","Int[(d*Sec[a + b*x])^(3/2)*(c*Sin[a + b*x])^m,x]","\frac{d \sqrt[4]{\cos ^2(a+b x)} \sqrt{d \sec (a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{5}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}","\frac{d \sqrt[4]{\cos ^2(a+b x)} \sqrt{d \sec (a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{5}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c (m+1)}",1,"(d*(Cos[a + b*x]^2)^(1/4)*Hypergeometric2F1[5/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*Sqrt[d*Sec[a + b*x]]*(c*Sin[a + b*x])^(1 + m))/(b*c*(1 + m))","A",2,2,23,0.08696,1,"{2587, 2577}"
485,1,77,0,0.0952061,"\int \sqrt{d \sec (a+b x)} (c \sin (a+b x))^m \, dx","Int[Sqrt[d*Sec[a + b*x]]*(c*Sin[a + b*x])^m,x]","\frac{\cos ^2(a+b x)^{3/4} (d \sec (a+b x))^{3/2} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{3}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1)}","\frac{\cos ^2(a+b x)^{3/4} (d \sec (a+b x))^{3/2} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{3}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1)}",1,"((Cos[a + b*x]^2)^(3/4)*Hypergeometric2F1[3/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(d*Sec[a + b*x])^(3/2)*(c*Sin[a + b*x])^(1 + m))/(b*c*d*(1 + m))","A",2,2,23,0.08696,1,"{2586, 2577}"
486,1,77,0,0.0966463,"\int \frac{(c \sin (a+b x))^m}{\sqrt{d \sec (a+b x)}} \, dx","Int[(c*Sin[a + b*x])^m/Sqrt[d*Sec[a + b*x]],x]","\frac{\sqrt[4]{\cos ^2(a+b x)} \sqrt{d \sec (a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1)}","\frac{\sqrt[4]{\cos ^2(a+b x)} \sqrt{d \sec (a+b x)} (c \sin (a+b x))^{m+1} \, _2F_1\left(\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1)}",1,"((Cos[a + b*x]^2)^(1/4)*Hypergeometric2F1[1/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*Sqrt[d*Sec[a + b*x]]*(c*Sin[a + b*x])^(1 + m))/(b*c*d*(1 + m))","A",2,2,23,0.08696,1,"{2586, 2577}"
487,1,77,0,0.1071108,"\int \frac{(c \sin (a+b x))^m}{(d \sec (a+b x))^{3/2}} \, dx","Int[(c*Sin[a + b*x])^m/(d*Sec[a + b*x])^(3/2),x]","\frac{(c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1) \sqrt[4]{\cos ^2(a+b x)} \sqrt{d \sec (a+b x)}}","\frac{(c \sin (a+b x))^{m+1} \, _2F_1\left(-\frac{1}{4},\frac{m+1}{2};\frac{m+3}{2};\sin ^2(a+b x)\right)}{b c d (m+1) \sqrt[4]{\cos ^2(a+b x)} \sqrt{d \sec (a+b x)}}",1,"(Hypergeometric2F1[-1/4, (1 + m)/2, (3 + m)/2, Sin[a + b*x]^2]*(c*Sin[a + b*x])^(1 + m))/(b*c*d*(1 + m)*(Cos[a + b*x]^2)^(1/4)*Sqrt[d*Sec[a + b*x]])","A",2,2,23,0.08696,1,"{2586, 2577}"
488,1,86,0,0.0764943,"\int \sec ^n(e+f x) \sin ^m(e+f x) \, dx","Int[Sec[e + f*x]^n*Sin[e + f*x]^m,x]","-\frac{\sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} \sec ^{n-1}(e+f x) \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{\sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} \sec ^{n-1}(e+f x) \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*Sec[e + f*x]^(-1 + n)*Sin[e + f*x]^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(f*(1 - n)))","A",2,2,17,0.1176,1,"{2587, 2576}"
489,1,89,0,0.0876263,"\int \sec ^n(e+f x) (a \sin (e+f x))^m \, dx","Int[Sec[e + f*x]^n*(a*Sin[e + f*x])^m,x]","-\frac{a \sin ^2(e+f x)^{\frac{1-m}{2}} \sec ^{n-1}(e+f x) (a \sin (e+f x))^{m-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{a \sin ^2(e+f x)^{\frac{1-m}{2}} \sec ^{n-1}(e+f x) (a \sin (e+f x))^{m-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((a*Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*Sec[e + f*x]^(-1 + n)*(a*Sin[e + f*x])^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(f*(1 - n)))","A",2,2,19,0.1053,1,"{2587, 2576}"
490,1,89,0,0.0891234,"\int (b \sec (e+f x))^n \sin ^m(e+f x) \, dx","Int[(b*Sec[e + f*x])^n*Sin[e + f*x]^m,x]","-\frac{b \sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{b \sin ^{m-1}(e+f x) \sin ^2(e+f x)^{\frac{1-m}{2}} (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((b*Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*Sin[e + f*x]^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(f*(1 - n)))","A",2,2,19,0.1053,1,"{2587, 2576}"
491,1,92,0,0.1034374,"\int (b \sec (e+f x))^n (a \sin (e+f x))^m \, dx","Int[(b*Sec[e + f*x])^n*(a*Sin[e + f*x])^m,x]","-\frac{a b \sin ^2(e+f x)^{\frac{1-m}{2}} (a \sin (e+f x))^{m-1} (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{a b \sin ^2(e+f x)^{\frac{1-m}{2}} (a \sin (e+f x))^{m-1} (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{1-m}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((a*b*Hypergeometric2F1[(1 - m)/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*(a*Sin[e + f*x])^(-1 + m)*(Sin[e + f*x]^2)^((1 - m)/2))/(f*(1 - n)))","A",2,2,21,0.09524,1,"{2587, 2576}"
492,1,80,0,0.0732299,"\int (b \sec (e+f x))^n \sin ^5(e+f x) \, dx","Int[(b*Sec[e + f*x])^n*Sin[e + f*x]^5,x]","-\frac{b^5 (b \sec (e+f x))^{n-5}}{f (5-n)}+\frac{2 b^3 (b \sec (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \sec (e+f x))^{n-1}}{f (1-n)}","-\frac{b^5 (b \sec (e+f x))^{n-5}}{f (5-n)}+\frac{2 b^3 (b \sec (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \sec (e+f x))^{n-1}}{f (1-n)}",1,"-((b^5*(b*Sec[e + f*x])^(-5 + n))/(f*(5 - n))) + (2*b^3*(b*Sec[e + f*x])^(-3 + n))/(f*(3 - n)) - (b*(b*Sec[e + f*x])^(-1 + n))/(f*(1 - n))","A",3,2,19,0.1053,1,"{2622, 270}"
493,1,52,0,0.0526494,"\int (b \sec (e+f x))^n \sin ^3(e+f x) \, dx","Int[(b*Sec[e + f*x])^n*Sin[e + f*x]^3,x]","\frac{b^3 (b \sec (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \sec (e+f x))^{n-1}}{f (1-n)}","\frac{b^3 (b \sec (e+f x))^{n-3}}{f (3-n)}-\frac{b (b \sec (e+f x))^{n-1}}{f (1-n)}",1,"(b^3*(b*Sec[e + f*x])^(-3 + n))/(f*(3 - n)) - (b*(b*Sec[e + f*x])^(-1 + n))/(f*(1 - n))","A",3,2,19,0.1053,1,"{2622, 14}"
494,1,25,0,0.0333282,"\int (b \sec (e+f x))^n \sin (e+f x) \, dx","Int[(b*Sec[e + f*x])^n*Sin[e + f*x],x]","-\frac{b (b \sec (e+f x))^{n-1}}{f (1-n)}","-\frac{b (b \sec (e+f x))^{n-1}}{f (1-n)}",1,"-((b*(b*Sec[e + f*x])^(-1 + n))/(f*(1 - n)))","A",2,2,17,0.1176,1,"{2622, 30}"
495,1,49,0,0.0382708,"\int \csc (e+f x) (b \sec (e+f x))^n \, dx","Int[Csc[e + f*x]*(b*Sec[e + f*x])^n,x]","-\frac{(b \sec (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\sec ^2(e+f x)\right)}{b f (n+1)}","-\frac{(b \sec (e+f x))^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\sec ^2(e+f x)\right)}{b f (n+1)}",1,"-((Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, Sec[e + f*x]^2]*(b*Sec[e + f*x])^(1 + n))/(b*f*(1 + n)))","A",2,2,17,0.1176,1,"{2622, 364}"
496,1,48,0,0.0516906,"\int \csc ^3(e+f x) (b \sec (e+f x))^n \, dx","Int[Csc[e + f*x]^3*(b*Sec[e + f*x])^n,x]","\frac{(b \sec (e+f x))^{n+3} \, _2F_1\left(2,\frac{n+3}{2};\frac{n+5}{2};\sec ^2(e+f x)\right)}{b^3 f (n+3)}","\frac{(b \sec (e+f x))^{n+3} \, _2F_1\left(2,\frac{n+3}{2};\frac{n+5}{2};\sec ^2(e+f x)\right)}{b^3 f (n+3)}",1,"(Hypergeometric2F1[2, (3 + n)/2, (5 + n)/2, Sec[e + f*x]^2]*(b*Sec[e + f*x])^(3 + n))/(b^3*f*(3 + n))","A",2,2,19,0.1053,1,"{2622, 364}"
497,1,73,0,0.0845627,"\int (b \sec (e+f x))^n \sin ^6(e+f x) \, dx","Int[(b*Sec[e + f*x])^n*Sin[e + f*x]^6,x]","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(-\frac{5}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(-\frac{5}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}",1,"-((b*Hypergeometric2F1[-5/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*Sin[e + f*x])/(f*(1 - n)*Sqrt[Sin[e + f*x]^2]))","A",2,2,19,0.1053,1,"{2632, 2576}"
498,1,73,0,0.0818204,"\int (b \sec (e+f x))^n \sin ^4(e+f x) \, dx","Int[(b*Sec[e + f*x])^n*Sin[e + f*x]^4,x]","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(-\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(-\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}",1,"-((b*Hypergeometric2F1[-3/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*Sin[e + f*x])/(f*(1 - n)*Sqrt[Sin[e + f*x]^2]))","A",2,2,19,0.1053,1,"{2632, 2576}"
499,1,73,0,0.081193,"\int (b \sec (e+f x))^n \sin ^2(e+f x) \, dx","Int[(b*Sec[e + f*x])^n*Sin[e + f*x]^2,x]","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(-\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}",1,"-((b*Hypergeometric2F1[-1/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*Sin[e + f*x])/(f*(1 - n)*Sqrt[Sin[e + f*x]^2]))","A",2,2,19,0.1053,1,"{2632, 2576}"
500,1,73,0,0.0325035,"\int (b \sec (e+f x))^n \, dx","Int[(b*Sec[e + f*x])^n,x]","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}","-\frac{b \sin (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n) \sqrt{\sin ^2(e+f x)}}",1,"-((b*Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*Sin[e + f*x])/(f*(1 - n)*Sqrt[Sin[e + f*x]^2]))","A",2,2,10,0.2000,1,"{3772, 2643}"
501,1,73,0,0.0794675,"\int \csc ^2(e+f x) (b \sec (e+f x))^n \, dx","Int[Csc[e + f*x]^2*(b*Sec[e + f*x])^n,x]","-\frac{b \sqrt{\sin ^2(e+f x)} \csc (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{b \sqrt{\sin ^2(e+f x)} \csc (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{3}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((b*Csc[e + f*x]*Hypergeometric2F1[3/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*Sqrt[Sin[e + f*x]^2])/(f*(1 - n)))","A",2,2,19,0.1053,1,"{2632, 2576}"
502,1,73,0,0.0797302,"\int \csc ^4(e+f x) (b \sec (e+f x))^n \, dx","Int[Csc[e + f*x]^4*(b*Sec[e + f*x])^n,x]","-\frac{b \sqrt{\sin ^2(e+f x)} \csc (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{5}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}","-\frac{b \sqrt{\sin ^2(e+f x)} \csc (e+f x) (b \sec (e+f x))^{n-1} \, _2F_1\left(\frac{5}{2},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(e+f x)\right)}{f (1-n)}",1,"-((b*Csc[e + f*x]*Hypergeometric2F1[5/2, (1 - n)/2, (3 - n)/2, Cos[e + f*x]^2]*(b*Sec[e + f*x])^(-1 + n)*Sqrt[Sin[e + f*x]^2])/(f*(1 - n)))","A",2,2,19,0.1053,1,"{2632, 2576}"
503,1,76,0,0.1097715,"\int (b \sec (a+b x))^n (c \sin (a+b x))^{3/2} \, dx","Int[(b*Sec[a + b*x])^n*(c*Sin[a + b*x])^(3/2),x]","-\frac{c \sqrt{c \sin (a+b x)} (b \sec (a+b x))^{n-1} \, _2F_1\left(-\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{(1-n) \sqrt[4]{\sin ^2(a+b x)}}","-\frac{c \sqrt{c \sin (a+b x)} (b \sec (a+b x))^{n-1} \, _2F_1\left(-\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{(1-n) \sqrt[4]{\sin ^2(a+b x)}}",1,"-((c*Hypergeometric2F1[-1/4, (1 - n)/2, (3 - n)/2, Cos[a + b*x]^2]*(b*Sec[a + b*x])^(-1 + n)*Sqrt[c*Sin[a + b*x]])/((1 - n)*(Sin[a + b*x]^2)^(1/4)))","A",2,2,23,0.08696,1,"{2587, 2576}"
504,1,76,0,0.0942671,"\int (b \sec (a+b x))^n \sqrt{c \sin (a+b x)} \, dx","Int[(b*Sec[a + b*x])^n*Sqrt[c*Sin[a + b*x]],x]","-\frac{c \sqrt[4]{\sin ^2(a+b x)} (b \sec (a+b x))^{n-1} \, _2F_1\left(\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{(1-n) \sqrt{c \sin (a+b x)}}","-\frac{c \sqrt[4]{\sin ^2(a+b x)} (b \sec (a+b x))^{n-1} \, _2F_1\left(\frac{1}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{(1-n) \sqrt{c \sin (a+b x)}}",1,"-((c*Hypergeometric2F1[1/4, (1 - n)/2, (3 - n)/2, Cos[a + b*x]^2]*(b*Sec[a + b*x])^(-1 + n)*(Sin[a + b*x]^2)^(1/4))/((1 - n)*Sqrt[c*Sin[a + b*x]]))","A",2,2,23,0.08696,1,"{2587, 2576}"
505,1,76,0,0.0962568,"\int \frac{(b \sec (a+b x))^n}{\sqrt{c \sin (a+b x)}} \, dx","Int[(b*Sec[a + b*x])^n/Sqrt[c*Sin[a + b*x]],x]","-\frac{c \sin ^2(a+b x)^{3/4} (b \sec (a+b x))^{n-1} \, _2F_1\left(\frac{3}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{(1-n) (c \sin (a+b x))^{3/2}}","-\frac{c \sin ^2(a+b x)^{3/4} (b \sec (a+b x))^{n-1} \, _2F_1\left(\frac{3}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{(1-n) (c \sin (a+b x))^{3/2}}",1,"-((c*Hypergeometric2F1[3/4, (1 - n)/2, (3 - n)/2, Cos[a + b*x]^2]*(b*Sec[a + b*x])^(-1 + n)*(Sin[a + b*x]^2)^(3/4))/((1 - n)*(c*Sin[a + b*x])^(3/2)))","A",2,2,23,0.08696,1,"{2587, 2576}"
506,1,78,0,0.1166571,"\int \frac{(b \sec (a+b x))^n}{(c \sin (a+b x))^{3/2}} \, dx","Int[(b*Sec[a + b*x])^n/(c*Sin[a + b*x])^(3/2),x]","-\frac{\sqrt[4]{\sin ^2(a+b x)} (b \sec (a+b x))^{n-1} \, _2F_1\left(\frac{5}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{c (1-n) \sqrt{c \sin (a+b x)}}","-\frac{\sqrt[4]{\sin ^2(a+b x)} (b \sec (a+b x))^{n-1} \, _2F_1\left(\frac{5}{4},\frac{1-n}{2};\frac{3-n}{2};\cos ^2(a+b x)\right)}{c (1-n) \sqrt{c \sin (a+b x)}}",1,"-((Hypergeometric2F1[5/4, (1 - n)/2, (3 - n)/2, Cos[a + b*x]^2]*(b*Sec[a + b*x])^(-1 + n)*(Sin[a + b*x]^2)^(1/4))/(c*(1 - n)*Sqrt[c*Sin[a + b*x]]))","A",2,2,23,0.08696,1,"{2587, 2576}"
507,1,100,0,0.077818,"\int \sqrt{d \csc (e+f x)} \sin ^4(e+f x) \, dx","Int[Sqrt[d*Csc[e + f*x]]*Sin[e + f*x]^4,x]","-\frac{2 d^3 \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}-\frac{10 d \cos (e+f x)}{21 f \sqrt{d \csc (e+f x)}}+\frac{10 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 f}","-\frac{2 d^3 \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}-\frac{10 d \cos (e+f x)}{21 f \sqrt{d \csc (e+f x)}}+\frac{10 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 f}",1,"(-2*d^3*Cos[e + f*x])/(7*f*(d*Csc[e + f*x])^(5/2)) - (10*d*Cos[e + f*x])/(21*f*Sqrt[d*Csc[e + f*x]]) + (10*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(21*f)","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
508,1,75,0,0.0542168,"\int \sqrt{d \csc (e+f x)} \sin ^3(e+f x) \, dx","Int[Sqrt[d*Csc[e + f*x]]*Sin[e + f*x]^3,x]","\frac{6 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d^2 \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}","\frac{6 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d^2 \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}",1,"(-2*d^2*Cos[e + f*x])/(5*f*(d*Csc[e + f*x])^(3/2)) + (6*d*EllipticE[(e - Pi/2 + f*x)/2, 2])/(5*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
509,1,72,0,0.0522891,"\int \sqrt{d \csc (e+f x)} \sin ^2(e+f x) \, dx","Int[Sqrt[d*Csc[e + f*x]]*Sin[e + f*x]^2,x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 d \cos (e+f x)}{3 f \sqrt{d \csc (e+f x)}}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 d \cos (e+f x)}{3 f \sqrt{d \csc (e+f x)}}",1,"(-2*d*Cos[e + f*x])/(3*f*Sqrt[d*Csc[e + f*x]]) + (2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*f)","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
510,1,44,0,0.0284428,"\int \sqrt{d \csc (e+f x)} \sin (e+f x) \, dx","Int[Sqrt[d*Csc[e + f*x]]*Sin[e + f*x],x]","\frac{2 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","\frac{2 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(2*d*EllipticE[(e - Pi/2 + f*x)/2, 2])/(f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",3,3,19,0.1579,1,"{16, 3771, 2639}"
511,1,43,0,0.0193115,"\int \sqrt{d \csc (e+f x)} \, dx","Int[Sqrt[d*Csc[e + f*x]],x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{f}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{f}",1,"(2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/f","A",2,2,12,0.1667,1,"{3771, 2641}"
512,1,68,0,0.0391602,"\int \csc (e+f x) \sqrt{d \csc (e+f x)} \, dx","Int[Csc[e + f*x]*Sqrt[d*Csc[e + f*x]],x]","-\frac{2 \cos (e+f x) \sqrt{d \csc (e+f x)}}{f}-\frac{2 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","-\frac{2 \cos (e+f x) \sqrt{d \csc (e+f x)}}{f}-\frac{2 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(-2*Cos[e + f*x]*Sqrt[d*Csc[e + f*x]])/f - (2*d*EllipticE[(e - Pi/2 + f*x)/2, 2])/(f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,19,0.2105,1,"{16, 3768, 3771, 2639}"
513,1,74,0,0.0404922,"\int \csc ^2(e+f x) \sqrt{d \csc (e+f x)} \, dx","Int[Csc[e + f*x]^2*Sqrt[d*Csc[e + f*x]],x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 d f}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 d f}",1,"(-2*Cos[e + f*x]*(d*Csc[e + f*x])^(3/2))/(3*d*f) + (2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*f)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
514,1,100,0,0.0584073,"\int \csc ^3(e+f x) \sqrt{d \csc (e+f x)} \, dx","Int[Csc[e + f*x]^3*Sqrt[d*Csc[e + f*x]],x]","-\frac{2 \cos (e+f x) (d \csc (e+f x))^{5/2}}{5 d^2 f}-\frac{6 \cos (e+f x) \sqrt{d \csc (e+f x)}}{5 f}-\frac{6 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","-\frac{2 \cos (e+f x) (d \csc (e+f x))^{5/2}}{5 d^2 f}-\frac{6 \cos (e+f x) \sqrt{d \csc (e+f x)}}{5 f}-\frac{6 d E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(-6*Cos[e + f*x]*Sqrt[d*Csc[e + f*x]])/(5*f) - (2*Cos[e + f*x]*(d*Csc[e + f*x])^(5/2))/(5*d^2*f) - (6*d*EllipticE[(e - Pi/2 + f*x)/2, 2])/(5*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
515,1,103,0,0.0758318,"\int (d \csc (e+f x))^{3/2} \sin ^5(e+f x) \, dx","Int[(d*Csc[e + f*x])^(3/2)*Sin[e + f*x]^5,x]","-\frac{2 d^4 \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}-\frac{10 d^2 \cos (e+f x)}{21 f \sqrt{d \csc (e+f x)}}+\frac{10 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 f}","-\frac{2 d^4 \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}-\frac{10 d^2 \cos (e+f x)}{21 f \sqrt{d \csc (e+f x)}}+\frac{10 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 f}",1,"(-2*d^4*Cos[e + f*x])/(7*f*(d*Csc[e + f*x])^(5/2)) - (10*d^2*Cos[e + f*x])/(21*f*Sqrt[d*Csc[e + f*x]]) + (10*d*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(21*f)","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
516,1,77,0,0.0556424,"\int (d \csc (e+f x))^{3/2} \sin ^4(e+f x) \, dx","Int[(d*Csc[e + f*x])^(3/2)*Sin[e + f*x]^4,x]","\frac{6 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d^3 \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}","\frac{6 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d^3 \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}",1,"(-2*d^3*Cos[e + f*x])/(5*f*(d*Csc[e + f*x])^(3/2)) + (6*d^2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(5*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
517,1,75,0,0.0531429,"\int (d \csc (e+f x))^{3/2} \sin ^3(e+f x) \, dx","Int[(d*Csc[e + f*x])^(3/2)*Sin[e + f*x]^3,x]","\frac{2 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 d^2 \cos (e+f x)}{3 f \sqrt{d \csc (e+f x)}}","\frac{2 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 d^2 \cos (e+f x)}{3 f \sqrt{d \csc (e+f x)}}",1,"(-2*d^2*Cos[e + f*x])/(3*f*Sqrt[d*Csc[e + f*x]]) + (2*d*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*f)","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
518,1,46,0,0.0379558,"\int (d \csc (e+f x))^{3/2} \sin ^2(e+f x) \, dx","Int[(d*Csc[e + f*x])^(3/2)*Sin[e + f*x]^2,x]","\frac{2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","\frac{2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(2*d^2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",3,3,21,0.1429,1,"{16, 3771, 2639}"
519,1,44,0,0.0280744,"\int (d \csc (e+f x))^{3/2} \sin (e+f x) \, dx","Int[(d*Csc[e + f*x])^(3/2)*Sin[e + f*x],x]","\frac{2 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{f}","\frac{2 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{f}",1,"(2*d*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/f","A",3,3,19,0.1579,1,"{16, 3771, 2641}"
520,1,71,0,0.0334052,"\int (d \csc (e+f x))^{3/2} \, dx","Int[(d*Csc[e + f*x])^(3/2),x]","-\frac{2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d \cos (e+f x) \sqrt{d \csc (e+f x)}}{f}","-\frac{2 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d \cos (e+f x) \sqrt{d \csc (e+f x)}}{f}",1,"(-2*d*Cos[e + f*x]*Sqrt[d*Csc[e + f*x]])/f - (2*d^2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",3,3,12,0.2500,1,"{3768, 3771, 2639}"
521,1,72,0,0.0388401,"\int \csc (e+f x) (d \csc (e+f x))^{3/2} \, dx","Int[Csc[e + f*x]*(d*Csc[e + f*x])^(3/2),x]","\frac{2 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 f}","\frac{2 d \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 f}",1,"(-2*Cos[e + f*x]*(d*Csc[e + f*x])^(3/2))/(3*f) + (2*d*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*f)","A",4,4,19,0.2105,1,"{16, 3768, 3771, 2641}"
522,1,103,0,0.0580863,"\int \csc ^2(e+f x) (d \csc (e+f x))^{3/2} \, dx","Int[Csc[e + f*x]^2*(d*Csc[e + f*x])^(3/2),x]","-\frac{6 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{5/2}}{5 d f}-\frac{6 d \cos (e+f x) \sqrt{d \csc (e+f x)}}{5 f}","-\frac{6 d^2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{5/2}}{5 d f}-\frac{6 d \cos (e+f x) \sqrt{d \csc (e+f x)}}{5 f}",1,"(-6*d*Cos[e + f*x]*Sqrt[d*Csc[e + f*x]])/(5*f) - (2*Cos[e + f*x]*(d*Csc[e + f*x])^(5/2))/(5*d*f) - (6*d^2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(5*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
523,1,102,0,0.0711687,"\int \frac{\sin ^3(e+f x)}{\sqrt{d \csc (e+f x)}} \, dx","Int[Sin[e + f*x]^3/Sqrt[d*Csc[e + f*x]],x]","-\frac{2 d^2 \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}-\frac{10 \cos (e+f x)}{21 f \sqrt{d \csc (e+f x)}}+\frac{10 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 d f}","-\frac{2 d^2 \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}-\frac{10 \cos (e+f x)}{21 f \sqrt{d \csc (e+f x)}}+\frac{10 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 d f}",1,"(-2*d^2*Cos[e + f*x])/(7*f*(d*Csc[e + f*x])^(5/2)) - (10*Cos[e + f*x])/(21*f*Sqrt[d*Csc[e + f*x]]) + (10*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(21*d*f)","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
524,1,72,0,0.0514034,"\int \frac{\sin ^2(e+f x)}{\sqrt{d \csc (e+f x)}} \, dx","Int[Sin[e + f*x]^2/Sqrt[d*Csc[e + f*x]],x]","\frac{6 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}","\frac{6 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 d \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}",1,"(-2*d*Cos[e + f*x])/(5*f*(d*Csc[e + f*x])^(3/2)) + (6*EllipticE[(e - Pi/2 + f*x)/2, 2])/(5*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,21,0.1905,1,"{16, 3769, 3771, 2639}"
525,1,74,0,0.044945,"\int \frac{\sin (e+f x)}{\sqrt{d \csc (e+f x)}} \, dx","Int[Sin[e + f*x]/Sqrt[d*Csc[e + f*x]],x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d f}-\frac{2 \cos (e+f x)}{3 f \sqrt{d \csc (e+f x)}}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d f}-\frac{2 \cos (e+f x)}{3 f \sqrt{d \csc (e+f x)}}",1,"(-2*Cos[e + f*x])/(3*f*Sqrt[d*Csc[e + f*x]]) + (2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*d*f)","A",4,4,19,0.2105,1,"{16, 3769, 3771, 2641}"
526,1,43,0,0.0185217,"\int \frac{1}{\sqrt{d \csc (e+f x)}} \, dx","Int[1/Sqrt[d*Csc[e + f*x]],x]","\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",2,2,12,0.1667,1,"{3771, 2639}"
527,1,46,0,0.0214527,"\int \frac{\csc (e+f x)}{\sqrt{d \csc (e+f x)}} \, dx","Int[Csc[e + f*x]/Sqrt[d*Csc[e + f*x]],x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{d f}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{d f}",1,"(2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(d*f)","A",3,3,19,0.1579,1,"{16, 3771, 2641}"
528,1,70,0,0.0385336,"\int \frac{\csc ^2(e+f x)}{\sqrt{d \csc (e+f x)}} \, dx","Int[Csc[e + f*x]^2/Sqrt[d*Csc[e + f*x]],x]","-\frac{2 \cos (e+f x) \sqrt{d \csc (e+f x)}}{d f}-\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","-\frac{2 \cos (e+f x) \sqrt{d \csc (e+f x)}}{d f}-\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(-2*Cos[e + f*x]*Sqrt[d*Csc[e + f*x]])/(d*f) - (2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
529,1,77,0,0.0393681,"\int \frac{\csc ^3(e+f x)}{\sqrt{d \csc (e+f x)}} \, dx","Int[Csc[e + f*x]^3/Sqrt[d*Csc[e + f*x]],x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 d^2 f}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 d^2 f}",1,"(-2*Cos[e + f*x]*(d*Csc[e + f*x])^(3/2))/(3*d^2*f) + (2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*d*f)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
530,1,103,0,0.0737739,"\int \frac{\sin ^2(e+f x)}{(d \csc (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]^2/(d*Csc[e + f*x])^(3/2),x]","\frac{10 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 d^2 f}-\frac{10 \cos (e+f x)}{21 d f \sqrt{d \csc (e+f x)}}-\frac{2 d \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}","\frac{10 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{21 d^2 f}-\frac{10 \cos (e+f x)}{21 d f \sqrt{d \csc (e+f x)}}-\frac{2 d \cos (e+f x)}{7 f (d \csc (e+f x))^{5/2}}",1,"(-2*d*Cos[e + f*x])/(7*f*(d*Csc[e + f*x])^(5/2)) - (10*Cos[e + f*x])/(21*d*f*Sqrt[d*Csc[e + f*x]]) + (10*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(21*d^2*f)","A",5,4,21,0.1905,1,"{16, 3769, 3771, 2641}"
531,1,74,0,0.0456729,"\int \frac{\sin (e+f x)}{(d \csc (e+f x))^{3/2}} \, dx","Int[Sin[e + f*x]/(d*Csc[e + f*x])^(3/2),x]","\frac{6 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}","\frac{6 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}-\frac{2 \cos (e+f x)}{5 f (d \csc (e+f x))^{3/2}}",1,"(-2*Cos[e + f*x])/(5*f*(d*Csc[e + f*x])^(3/2)) + (6*EllipticE[(e - Pi/2 + f*x)/2, 2])/(5*d*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,19,0.2105,1,"{16, 3769, 3771, 2639}"
532,1,77,0,0.033067,"\int \frac{1}{(d \csc (e+f x))^{3/2}} \, dx","Int[(d*Csc[e + f*x])^(-3/2),x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d^2 f}-\frac{2 \cos (e+f x)}{3 d f \sqrt{d \csc (e+f x)}}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d^2 f}-\frac{2 \cos (e+f x)}{3 d f \sqrt{d \csc (e+f x)}}",1,"(-2*Cos[e + f*x])/(3*d*f*Sqrt[d*Csc[e + f*x]]) + (2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*d^2*f)","A",3,3,12,0.2500,1,"{3769, 3771, 2641}"
533,1,46,0,0.021443,"\int \frac{\csc (e+f x)}{(d \csc (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]/(d*Csc[e + f*x])^(3/2),x]","\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(d*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",3,3,19,0.1579,1,"{16, 3771, 2639}"
534,1,46,0,0.0219113,"\int \frac{\csc ^2(e+f x)}{(d \csc (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^2/(d*Csc[e + f*x])^(3/2),x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{d^2 f}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{d^2 f}",1,"(2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(d^2*f)","A",3,3,21,0.1429,1,"{16, 3771, 2641}"
535,1,73,0,0.0388136,"\int \frac{\csc ^3(e+f x)}{(d \csc (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^3/(d*Csc[e + f*x])^(3/2),x]","-\frac{2 \cos (e+f x) \sqrt{d \csc (e+f x)}}{d^2 f}-\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","-\frac{2 \cos (e+f x) \sqrt{d \csc (e+f x)}}{d^2 f}-\frac{2 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(-2*Cos[e + f*x]*Sqrt[d*Csc[e + f*x]])/(d^2*f) - (2*EllipticE[(e - Pi/2 + f*x)/2, 2])/(d*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
536,1,77,0,0.0388047,"\int \frac{\csc ^4(e+f x)}{(d \csc (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^4/(d*Csc[e + f*x])^(3/2),x]","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d^2 f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 d^3 f}","\frac{2 \sqrt{\sin (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right) \sqrt{d \csc (e+f x)}}{3 d^2 f}-\frac{2 \cos (e+f x) (d \csc (e+f x))^{3/2}}{3 d^3 f}",1,"(-2*Cos[e + f*x]*(d*Csc[e + f*x])^(3/2))/(3*d^3*f) + (2*Sqrt[d*Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(3*d^2*f)","A",4,4,21,0.1905,1,"{16, 3768, 3771, 2641}"
537,1,105,0,0.0590597,"\int \frac{\csc ^5(e+f x)}{(d \csc (e+f x))^{3/2}} \, dx","Int[Csc[e + f*x]^5/(d*Csc[e + f*x])^(3/2),x]","-\frac{2 \cos (e+f x) (d \csc (e+f x))^{5/2}}{5 d^4 f}-\frac{6 \cos (e+f x) \sqrt{d \csc (e+f x)}}{5 d^2 f}-\frac{6 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}","-\frac{2 \cos (e+f x) (d \csc (e+f x))^{5/2}}{5 d^4 f}-\frac{6 \cos (e+f x) \sqrt{d \csc (e+f x)}}{5 d^2 f}-\frac{6 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{5 d f \sqrt{\sin (e+f x)} \sqrt{d \csc (e+f x)}}",1,"(-6*Cos[e + f*x]*Sqrt[d*Csc[e + f*x]])/(5*d^2*f) - (2*Cos[e + f*x]*(d*Csc[e + f*x])^(5/2))/(5*d^4*f) - (6*EllipticE[(e - Pi/2 + f*x)/2, 2])/(5*d*f*Sqrt[d*Csc[e + f*x]]*Sqrt[Sin[e + f*x]])","A",5,4,21,0.1905,1,"{16, 3768, 3771, 2639}"
538,1,87,0,0.0636076,"\int (b \csc (e+f x))^n (a \sin (e+f x))^m \, dx","Int[(b*Csc[e + f*x])^n*(a*Sin[e + f*x])^m,x]","\frac{\cos (e+f x) (a \sin (e+f x))^{m+1} (b \csc (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m-n+1);\frac{1}{2} (m-n+3);\sin ^2(e+f x)\right)}{a f (m-n+1) \sqrt{\cos ^2(e+f x)}}","\frac{\cos (e+f x) (a \sin (e+f x))^{m+1} (b \csc (e+f x))^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (m-n+1);\frac{1}{2} (m-n+3);\sin ^2(e+f x)\right)}{a f (m-n+1) \sqrt{\cos ^2(e+f x)}}",1,"(Cos[e + f*x]*(b*Csc[e + f*x])^n*Hypergeometric2F1[1/2, (1 + m - n)/2, (3 + m - n)/2, Sin[e + f*x]^2]*(a*Sin[e + f*x])^(1 + m))/(a*f*(1 + m - n)*Sqrt[Cos[e + f*x]^2])","A",2,2,21,0.09524,1,"{2588, 2643}"