1,1,12,0,0.0042156,"\int \csc (a+b x) \, dx","Int[Csc[a + b*x],x]","-\frac{\tanh ^{-1}(\cos (a+b x))}{b}","-\frac{\tanh ^{-1}(\cos (a+b x))}{b}",1,"-(ArcTanh[Cos[a + b*x]]/b)","A",1,1,6,0.1667,1,"{3770}"
2,1,11,0,0.0083176,"\int \csc ^2(a+b x) \, dx","Int[Csc[a + b*x]^2,x]","-\frac{\cot (a+b x)}{b}","-\frac{\cot (a+b x)}{b}",1,"-(Cot[a + b*x]/b)","A",2,2,8,0.2500,1,"{3767, 8}"
3,1,34,0,0.0138963,"\int \csc ^3(a+b x) \, dx","Int[Csc[a + b*x]^3,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",2,2,8,0.2500,1,"{3768, 3770}"
4,1,27,0,0.0113776,"\int \csc ^4(a+b x) \, dx","Int[Csc[a + b*x]^4,x]","-\frac{\cot ^3(a+b x)}{3 b}-\frac{\cot (a+b x)}{b}","-\frac{\cot ^3(a+b x)}{3 b}-\frac{\cot (a+b x)}{b}",1,"-(Cot[a + b*x]/b) - Cot[a + b*x]^3/(3*b)","A",2,1,8,0.1250,1,"{3767}"
5,1,55,0,0.0259667,"\int \csc ^5(a+b x) \, dx","Int[Csc[a + b*x]^5,x]","-\frac{3 \tanh ^{-1}(\cos (a+b x))}{8 b}-\frac{\cot (a+b x) \csc ^3(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 (a+b x) \csc ^3(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]*Csc[a + b*x]^3)/(4*b)","A",3,2,8,0.2500,1,"{3768, 3770}"
6,1,42,0,0.0139804,"\int \csc ^6(a+b x) \, dx","Int[Csc[a + b*x]^6,x]","-\frac{\cot ^5(a+b x)}{5 b}-\frac{2 \cot ^3(a+b x)}{3 b}-\frac{\cot (a+b x)}{b}","-\frac{\cot ^5(a+b x)}{5 b}-\frac{2 \cot ^3(a+b x)}{3 b}-\frac{\cot (a+b x)}{b}",1,"-(Cot[a + b*x]/b) - (2*Cot[a + b*x]^3)/(3*b) - Cot[a + b*x]^5/(5*b)","A",2,1,8,0.1250,1,"{3767}"
7,1,76,0,0.0363369,"\int \csc ^7(a+b x) \, dx","Int[Csc[a + b*x]^7,x]","-\frac{5 \tanh ^{-1}(\cos (a+b x))}{16 b}-\frac{\cot (a+b x) \csc ^5(a+b x)}{6 b}-\frac{5 \cot (a+b x) \csc ^3(a+b x)}{24 b}-\frac{5 \cot (a+b x) \csc (a+b x)}{16 b}","-\frac{5 \tanh ^{-1}(\cos (a+b x))}{16 b}-\frac{\cot (a+b x) \csc ^5(a+b x)}{6 b}-\frac{5 \cot (a+b x) \csc ^3(a+b x)}{24 b}-\frac{5 \cot (a+b x) \csc (a+b x)}{16 b}",1,"(-5*ArcTanh[Cos[a + b*x]])/(16*b) - (5*Cot[a + b*x]*Csc[a + b*x])/(16*b) - (5*Cot[a + b*x]*Csc[a + b*x]^3)/(24*b) - (Cot[a + b*x]*Csc[a + b*x]^5)/(6*b)","A",4,2,8,0.2500,1,"{3768, 3770}"
8,1,55,0,0.0165351,"\int \csc ^8(a+b x) \, dx","Int[Csc[a + b*x]^8,x]","-\frac{\cot ^7(a+b x)}{7 b}-\frac{3 \cot ^5(a+b x)}{5 b}-\frac{\cot ^3(a+b x)}{b}-\frac{\cot (a+b x)}{b}","-\frac{\cot ^7(a+b x)}{7 b}-\frac{3 \cot ^5(a+b x)}{5 b}-\frac{\cot ^3(a+b x)}{b}-\frac{\cot (a+b x)}{b}",1,"-(Cot[a + b*x]/b) - Cot[a + b*x]^3/b - (3*Cot[a + b*x]^5)/(5*b) - Cot[a + b*x]^7/(7*b)","A",2,1,8,0.1250,1,"{3767}"
9,1,90,0,0.0367819,"\int \csc ^{\frac{7}{2}}(a+b x) \, dx","Int[Csc[a + b*x]^(7/2),x]","-\frac{2 \cos (a+b x) \csc ^{\frac{5}{2}}(a+b x)}{5 b}-\frac{6 \cos (a+b x) \sqrt{\csc (a+b x)}}{5 b}-\frac{6 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}","-\frac{2 \cos (a+b x) \csc ^{\frac{5}{2}}(a+b x)}{5 b}-\frac{6 \cos (a+b x) \sqrt{\csc (a+b x)}}{5 b}-\frac{6 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}",1,"(-6*Cos[a + b*x]*Sqrt[Csc[a + b*x]])/(5*b) - (2*Cos[a + b*x]*Csc[a + b*x]^(5/2))/(5*b) - (6*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(5*b)","A",4,3,10,0.3000,1,"{3768, 3771, 2639}"
10,1,67,0,0.0260246,"\int \csc ^{\frac{5}{2}}(a+b x) \, dx","Int[Csc[a + b*x]^(5/2),x]","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \cos (a+b x) \csc ^{\frac{3}{2}}(a+b x)}{3 b}","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \cos (a+b x) \csc ^{\frac{3}{2}}(a+b x)}{3 b}",1,"(-2*Cos[a + b*x]*Csc[a + b*x]^(3/2))/(3*b) + (2*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b)","A",3,3,10,0.3000,1,"{3768, 3771, 2641}"
11,1,63,0,0.0243478,"\int \csc ^{\frac{3}{2}}(a+b x) \, dx","Int[Csc[a + b*x]^(3/2),x]","-\frac{2 \cos (a+b x) \sqrt{\csc (a+b x)}}{b}-\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}","-\frac{2 \cos (a+b x) \sqrt{\csc (a+b x)}}{b}-\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(-2*Cos[a + b*x]*Sqrt[Csc[a + b*x]])/b - (2*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b","A",3,3,10,0.3000,1,"{3768, 3771, 2639}"
12,1,41,0,0.0166098,"\int \sqrt{\csc (a+b x)} \, dx","Int[Sqrt[Csc[a + b*x]],x]","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(2*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b","A",2,2,10,0.2000,1,"{3771, 2641}"
13,1,41,0,0.016806,"\int \frac{1}{\sqrt{\csc (a+b x)}} \, dx","Int[1/Sqrt[Csc[a + b*x]],x]","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b}",1,"(2*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b","A",2,2,10,0.2000,1,"{3771, 2639}"
14,1,67,0,0.0269316,"\int \frac{1}{\csc ^{\frac{3}{2}}(a+b x)} \, dx","Int[Csc[a + b*x]^(-3/2),x]","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \cos (a+b x)}{3 b \sqrt{\csc (a+b x)}}","\frac{2 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b}-\frac{2 \cos (a+b x)}{3 b \sqrt{\csc (a+b x)}}",1,"(-2*Cos[a + b*x])/(3*b*Sqrt[Csc[a + b*x]]) + (2*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b)","A",3,3,10,0.3000,1,"{3769, 3771, 2641}"
15,1,67,0,0.0258078,"\int \frac{1}{\csc ^{\frac{5}{2}}(a+b x)} \, dx","Int[Csc[a + b*x]^(-5/2),x]","\frac{6 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}-\frac{2 \cos (a+b x)}{5 b \csc ^{\frac{3}{2}}(a+b x)}","\frac{6 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b}-\frac{2 \cos (a+b x)}{5 b \csc ^{\frac{3}{2}}(a+b x)}",1,"(-2*Cos[a + b*x])/(5*b*Csc[a + b*x]^(3/2)) + (6*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(5*b)","A",3,3,10,0.3000,1,"{3769, 3771, 2639}"
16,1,90,0,0.0383128,"\int \frac{1}{\csc ^{\frac{7}{2}}(a+b x)} \, dx","Int[Csc[a + b*x]^(-7/2),x]","-\frac{2 \cos (a+b x)}{7 b \csc ^{\frac{5}{2}}(a+b x)}-\frac{10 \cos (a+b x)}{21 b \sqrt{\csc (a+b x)}}+\frac{10 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{21 b}","-\frac{2 \cos (a+b x)}{7 b \csc ^{\frac{5}{2}}(a+b x)}-\frac{10 \cos (a+b x)}{21 b \sqrt{\csc (a+b x)}}+\frac{10 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{21 b}",1,"(-2*Cos[a + b*x])/(7*b*Csc[a + b*x]^(5/2)) - (10*Cos[a + b*x])/(21*b*Sqrt[Csc[a + b*x]]) + (10*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(21*b)","A",4,3,10,0.3000,1,"{3769, 3771, 2641}"
17,1,103,0,0.0528121,"\int (c \csc (a+b x))^{7/2} \, dx","Int[(c*Csc[a + b*x])^(7/2),x]","-\frac{6 c^3 \cos (a+b x) \sqrt{c \csc (a+b x)}}{5 b}-\frac{6 c^4 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}-\frac{2 c \cos (a+b x) (c \csc (a+b x))^{5/2}}{5 b}","-\frac{6 c^3 \cos (a+b x) \sqrt{c \csc (a+b x)}}{5 b}-\frac{6 c^4 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}-\frac{2 c \cos (a+b x) (c \csc (a+b x))^{5/2}}{5 b}",1,"(-6*c^3*Cos[a + b*x]*Sqrt[c*Csc[a + b*x]])/(5*b) - (2*c*Cos[a + b*x]*(c*Csc[a + b*x])^(5/2))/(5*b) - (6*c^4*EllipticE[(a - Pi/2 + b*x)/2, 2])/(5*b*Sqrt[c*Csc[a + b*x]]*Sqrt[Sin[a + b*x]])","A",4,3,12,0.2500,1,"{3768, 3771, 2639}"
18,1,75,0,0.0310997,"\int (c \csc (a+b x))^{5/2} \, dx","Int[(c*Csc[a + b*x])^(5/2),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) \sqrt{c \csc (a+b x)}}{3 b}-\frac{2 c \cos (a+b x) (c \csc (a+b x))^{3/2}}{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) \sqrt{c \csc (a+b x)}}{3 b}-\frac{2 c \cos (a+b x) (c \csc (a+b x))^{3/2}}{3 b}",1,"(-2*c*Cos[a + b*x]*(c*Csc[a + b*x])^(3/2))/(3*b) + (2*c^2*Sqrt[c*Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b)","A",3,3,12,0.2500,1,"{3768, 3771, 2641}"
19,1,71,0,0.0319975,"\int (c \csc (a+b x))^{3/2} \, dx","Int[(c*Csc[a + b*x])^(3/2),x]","-\frac{2 c^2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}-\frac{2 c \cos (a+b x) \sqrt{c \csc (a+b x)}}{b}","-\frac{2 c^2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}-\frac{2 c \cos (a+b x) \sqrt{c \csc (a+b x)}}{b}",1,"(-2*c*Cos[a + b*x]*Sqrt[c*Csc[a + b*x]])/b - (2*c^2*EllipticE[(a - Pi/2 + b*x)/2, 2])/(b*Sqrt[c*Csc[a + b*x]]*Sqrt[Sin[a + b*x]])","A",3,3,12,0.2500,1,"{3768, 3771, 2639}"
20,1,43,0,0.0181133,"\int \sqrt{c \csc (a+b x)} \, dx","Int[Sqrt[c*Csc[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) \sqrt{c \csc (a+b x)}}{b}","\frac{2 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \csc (a+b x)}}{b}",1,"(2*Sqrt[c*Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b","A",2,2,12,0.1667,1,"{3771, 2641}"
21,1,43,0,0.0180977,"\int \frac{1}{\sqrt{c \csc (a+b x)}} \, dx","Int[1/Sqrt[c*Csc[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}","\frac{2 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}",1,"(2*EllipticE[(a - Pi/2 + b*x)/2, 2])/(b*Sqrt[c*Csc[a + b*x]]*Sqrt[Sin[a + b*x]])","A",2,2,12,0.1667,1,"{3771, 2639}"
22,1,77,0,0.032662,"\int \frac{1}{(c \csc (a+b x))^{3/2}} \, dx","Int[(c*Csc[a + b*x])^(-3/2),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) \sqrt{c \csc (a+b x)}}{3 b c^2}-\frac{2 \cos (a+b x)}{3 b c \sqrt{c \csc (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) \sqrt{c \csc (a+b x)}}{3 b c^2}-\frac{2 \cos (a+b x)}{3 b c \sqrt{c \csc (a+b x)}}",1,"(-2*Cos[a + b*x])/(3*b*c*Sqrt[c*Csc[a + b*x]]) + (2*Sqrt[c*Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b*c^2)","A",3,3,12,0.2500,1,"{3769, 3771, 2641}"
23,1,77,0,0.0319249,"\int \frac{1}{(c \csc (a+b x))^{5/2}} \, dx","Int[(c*Csc[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 c^2 \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}-\frac{2 \cos (a+b x)}{5 b c (c \csc (a+b x))^{3/2}}","\frac{6 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{5 b c^2 \sqrt{\sin (a+b x)} \sqrt{c \csc (a+b x)}}-\frac{2 \cos (a+b x)}{5 b c (c \csc (a+b x))^{3/2}}",1,"(-2*Cos[a + b*x])/(5*b*c*(c*Csc[a + b*x])^(3/2)) + (6*EllipticE[(a - Pi/2 + b*x)/2, 2])/(5*b*c^2*Sqrt[c*Csc[a + b*x]]*Sqrt[Sin[a + b*x]])","A",3,3,12,0.2500,1,"{3769, 3771, 2639}"
24,1,105,0,0.0491781,"\int \frac{1}{(c \csc (a+b x))^{7/2}} \, dx","Int[(c*Csc[a + b*x])^(-7/2),x]","-\frac{10 \cos (a+b x)}{21 b c^3 \sqrt{c \csc (a+b x)}}+\frac{10 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \csc (a+b x)}}{21 b c^4}-\frac{2 \cos (a+b x)}{7 b c (c \csc (a+b x))^{5/2}}","-\frac{10 \cos (a+b x)}{21 b c^3 \sqrt{c \csc (a+b x)}}+\frac{10 \sqrt{\sin (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right) \sqrt{c \csc (a+b x)}}{21 b c^4}-\frac{2 \cos (a+b x)}{7 b c (c \csc (a+b x))^{5/2}}",1,"(-2*Cos[a + b*x])/(7*b*c*(c*Csc[a + b*x])^(5/2)) - (10*Cos[a + b*x])/(21*b*c^3*Sqrt[c*Csc[a + b*x]]) + (10*Sqrt[c*Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(21*b*c^4)","A",4,3,12,0.2500,1,"{3769, 3771, 2641}"
25,1,51,0,0.0223791,"\int \csc ^{\frac{4}{3}}(a+b x) \, dx","Int[Csc[a + b*x]^(4/3),x]","-\frac{3 \cos (a+b x) \sqrt[3]{\csc (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)}}","-\frac{3 \cos (a+b x) \sqrt[3]{\csc (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)}}",1,"(-3*Cos[a + b*x]*Csc[a + b*x]^(1/3)*Hypergeometric2F1[-1/6, 1/2, 5/6, Sin[a + b*x]^2])/(b*Sqrt[Cos[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
26,1,51,0,0.021894,"\int \csc ^{\frac{2}{3}}(a+b x) \, dx","Int[Csc[a + b*x]^(2/3),x]","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)} \sqrt[3]{\csc (a+b x)}}","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)} \sqrt[3]{\csc (a+b x)}}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Sin[a + b*x]^2])/(b*Sqrt[Cos[a + b*x]^2]*Csc[a + b*x]^(1/3))","A",2,2,10,0.2000,1,"{3772, 2643}"
27,1,53,0,0.0216941,"\int \sqrt[3]{\csc (a+b x)} \, dx","Int[Csc[a + b*x]^(1/3),x]","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sin ^2(a+b x)\right)}{2 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{2}{3}}(a+b x)}","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sin ^2(a+b x)\right)}{2 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{2}{3}}(a+b x)}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sin[a + b*x]^2])/(2*b*Sqrt[Cos[a + b*x]^2]*Csc[a + b*x]^(2/3))","A",2,2,10,0.2000,1,"{3772, 2643}"
28,1,53,0,0.0213129,"\int \frac{1}{\sqrt[3]{\csc (a+b x)}} \, dx","Int[Csc[a + b*x]^(-1/3),x]","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(a+b x)\right)}{4 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{4}{3}}(a+b x)}","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(a+b x)\right)}{4 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{4}{3}}(a+b x)}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sin[a + b*x]^2])/(4*b*Sqrt[Cos[a + b*x]^2]*Csc[a + b*x]^(4/3))","A",2,2,10,0.2000,1,"{3772, 2643}"
29,1,53,0,0.0212965,"\int \frac{1}{\csc ^{\frac{2}{3}}(a+b x)} \, dx","Int[Csc[a + b*x]^(-2/3),x]","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\sin ^2(a+b x)\right)}{5 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{5}{3}}(a+b x)}","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\sin ^2(a+b x)\right)}{5 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{5}{3}}(a+b x)}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Sin[a + b*x]^2])/(5*b*Sqrt[Cos[a + b*x]^2]*Csc[a + b*x]^(5/3))","A",2,2,10,0.2000,1,"{3772, 2643}"
30,1,53,0,0.0213212,"\int \frac{1}{\csc ^{\frac{4}{3}}(a+b x)} \, dx","Int[Csc[a + b*x]^(-4/3),x]","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sin ^2(a+b x)\right)}{7 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{7}{3}}(a+b x)}","\frac{3 \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sin ^2(a+b x)\right)}{7 b \sqrt{\cos ^2(a+b x)} \csc ^{\frac{7}{3}}(a+b x)}",1,"(3*Cos[a + b*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Sin[a + b*x]^2])/(7*b*Sqrt[Cos[a + b*x]^2]*Csc[a + b*x]^(7/3))","A",2,2,10,0.2000,1,"{3772, 2643}"
31,1,54,0,0.0295966,"\int (c \csc (a+b x))^{4/3} \, dx","Int[(c*Csc[a + b*x])^(4/3),x]","-\frac{3 c \cos (a+b x) \sqrt[3]{c \csc (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)}}","-\frac{3 c \cos (a+b x) \sqrt[3]{c \csc (a+b x)} \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)}}",1,"(-3*c*Cos[a + b*x]*(c*Csc[a + b*x])^(1/3)*Hypergeometric2F1[-1/6, 1/2, 5/6, Sin[a + b*x]^2])/(b*Sqrt[Cos[a + b*x]^2])","A",2,2,12,0.1667,1,"{3772, 2643}"
32,1,54,0,0.0271586,"\int (c \csc (a+b x))^{2/3} \, dx","Int[(c*Csc[a + b*x])^(2/3),x]","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)} \sqrt[3]{c \csc (a+b x)}}","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};\sin ^2(a+b x)\right)}{b \sqrt{\cos ^2(a+b x)} \sqrt[3]{c \csc (a+b x)}}",1,"(3*c*Cos[a + b*x]*Hypergeometric2F1[1/6, 1/2, 7/6, Sin[a + b*x]^2])/(b*Sqrt[Cos[a + b*x]^2]*(c*Csc[a + b*x])^(1/3))","A",2,2,12,0.1667,1,"{3772, 2643}"
33,1,56,0,0.0263249,"\int \sqrt[3]{c \csc (a+b x)} \, dx","Int[(c*Csc[a + b*x])^(1/3),x]","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sin ^2(a+b x)\right)}{2 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{2/3}}","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};\sin ^2(a+b x)\right)}{2 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{2/3}}",1,"(3*c*Cos[a + b*x]*Hypergeometric2F1[1/3, 1/2, 4/3, Sin[a + b*x]^2])/(2*b*Sqrt[Cos[a + b*x]^2]*(c*Csc[a + b*x])^(2/3))","A",2,2,12,0.1667,1,"{3772, 2643}"
34,1,56,0,0.0262917,"\int \frac{1}{\sqrt[3]{c \csc (a+b x)}} \, dx","Int[(c*Csc[a + b*x])^(-1/3),x]","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(a+b x)\right)}{4 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{4/3}}","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};\sin ^2(a+b x)\right)}{4 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{4/3}}",1,"(3*c*Cos[a + b*x]*Hypergeometric2F1[1/2, 2/3, 5/3, Sin[a + b*x]^2])/(4*b*Sqrt[Cos[a + b*x]^2]*(c*Csc[a + b*x])^(4/3))","A",2,2,12,0.1667,1,"{3772, 2643}"
35,1,56,0,0.0271572,"\int \frac{1}{(c \csc (a+b x))^{2/3}} \, dx","Int[(c*Csc[a + b*x])^(-2/3),x]","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\sin ^2(a+b x)\right)}{5 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{5/3}}","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};\sin ^2(a+b x)\right)}{5 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{5/3}}",1,"(3*c*Cos[a + b*x]*Hypergeometric2F1[1/2, 5/6, 11/6, Sin[a + b*x]^2])/(5*b*Sqrt[Cos[a + b*x]^2]*(c*Csc[a + b*x])^(5/3))","A",2,2,12,0.1667,1,"{3772, 2643}"
36,1,56,0,0.0272993,"\int \frac{1}{(c \csc (a+b x))^{4/3}} \, dx","Int[(c*Csc[a + b*x])^(-4/3),x]","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sin ^2(a+b x)\right)}{7 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{7/3}}","\frac{3 c \cos (a+b x) \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};\sin ^2(a+b x)\right)}{7 b \sqrt{\cos ^2(a+b x)} (c \csc (a+b x))^{7/3}}",1,"(3*c*Cos[a + b*x]*Hypergeometric2F1[1/2, 7/6, 13/6, Sin[a + b*x]^2])/(7*b*Sqrt[Cos[a + b*x]^2]*(c*Csc[a + b*x])^(7/3))","A",2,2,12,0.1667,1,"{3772, 2643}"
37,1,69,0,0.0259089,"\int \csc ^n(a+b x) \, dx","Int[Csc[a + b*x]^n,x]","\frac{\cos (a+b x) \csc ^{n-1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(a+b x)\right)}{b (1-n) \sqrt{\cos ^2(a+b x)}}","\frac{\cos (a+b x) \csc ^{n-1}(a+b x) \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(a+b x)\right)}{b (1-n) \sqrt{\cos ^2(a+b x)}}",1,"(Cos[a + b*x]*Csc[a + b*x]^(-1 + n)*Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Sin[a + b*x]^2])/(b*(1 - n)*Sqrt[Cos[a + b*x]^2])","A",2,2,8,0.2500,1,"{3772, 2643}"
38,1,72,0,0.0297544,"\int (c \csc (a+b x))^n \, dx","Int[(c*Csc[a + b*x])^n,x]","\frac{c \cos (a+b x) (c \csc (a+b x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(a+b x)\right)}{b (1-n) \sqrt{\cos ^2(a+b x)}}","\frac{c \cos (a+b x) (c \csc (a+b x))^{n-1} \, _2F_1\left(\frac{1}{2},\frac{1-n}{2};\frac{3-n}{2};\sin ^2(a+b x)\right)}{b (1-n) \sqrt{\cos ^2(a+b x)}}",1,"(c*Cos[a + b*x]*(c*Csc[a + b*x])^(-1 + n)*Hypergeometric2F1[1/2, (1 - n)/2, (3 - n)/2, Sin[a + b*x]^2])/(b*(1 - n)*Sqrt[Cos[a + b*x]^2])","A",2,2,10,0.2000,1,"{3772, 2643}"
39,1,50,0,0.0168905,"\int \csc ^2(x)^{7/2} \, dx","Int[(Csc[x]^2)^(7/2),x]","-\frac{1}{6} \cot (x) \csc ^2(x)^{5/2}-\frac{5}{24} \cot (x) \csc ^2(x)^{3/2}-\frac{5}{16} \cot (x) \sqrt{\csc ^2(x)}-\frac{5}{16} \sinh ^{-1}(\cot (x))","-\frac{1}{6} \cot (x) \csc ^2(x)^{5/2}-\frac{5}{24} \cot (x) \csc ^2(x)^{3/2}-\frac{5}{16} \cot (x) \sqrt{\csc ^2(x)}-\frac{5}{16} \sinh ^{-1}(\cot (x))",1,"(-5*ArcSinh[Cot[x]])/16 - (5*Cot[x]*Sqrt[Csc[x]^2])/16 - (5*Cot[x]*(Csc[x]^2)^(3/2))/24 - (Cot[x]*(Csc[x]^2)^(5/2))/6","A",5,3,8,0.3750,1,"{4122, 195, 215}"
40,1,36,0,0.0123468,"\int \csc ^2(x)^{5/2} \, dx","Int[(Csc[x]^2)^(5/2),x]","-\frac{1}{4} \cot (x) \csc ^2(x)^{3/2}-\frac{3}{8} \cot (x) \sqrt{\csc ^2(x)}-\frac{3}{8} \sinh ^{-1}(\cot (x))","-\frac{1}{4} \cot (x) \csc ^2(x)^{3/2}-\frac{3}{8} \cot (x) \sqrt{\csc ^2(x)}-\frac{3}{8} \sinh ^{-1}(\cot (x))",1,"(-3*ArcSinh[Cot[x]])/8 - (3*Cot[x]*Sqrt[Csc[x]^2])/8 - (Cot[x]*(Csc[x]^2)^(3/2))/4","A",4,3,8,0.3750,1,"{4122, 195, 215}"
41,1,22,0,0.0094297,"\int \csc ^2(x)^{3/2} \, dx","Int[(Csc[x]^2)^(3/2),x]","-\frac{1}{2} \cot (x) \sqrt{\csc ^2(x)}-\frac{1}{2} \sinh ^{-1}(\cot (x))","-\frac{1}{2} \cot (x) \sqrt{\csc ^2(x)}-\frac{1}{2} \sinh ^{-1}(\cot (x))",1,"-ArcSinh[Cot[x]]/2 - (Cot[x]*Sqrt[Csc[x]^2])/2","A",3,3,8,0.3750,1,"{4122, 195, 215}"
42,1,5,0,0.0066315,"\int \sqrt{\csc ^2(x)} \, dx","Int[Sqrt[Csc[x]^2],x]","-\sinh ^{-1}(\cot (x))","-\sinh ^{-1}(\cot (x))",1,"-ArcSinh[Cot[x]]","A",2,2,8,0.2500,1,"{4122, 215}"
43,1,12,0,0.0093475,"\int \frac{1}{\sqrt{\csc ^2(x)}} \, dx","Int[1/Sqrt[Csc[x]^2],x]","-\frac{\cot (x)}{\sqrt{\csc ^2(x)}}","-\frac{\cot (x)}{\sqrt{\csc ^2(x)}}",1,"-(Cot[x]/Sqrt[Csc[x]^2])","A",2,2,8,0.2500,1,"{4122, 191}"
44,1,29,0,0.011221,"\int \frac{1}{\csc ^2(x)^{3/2}} \, dx","Int[(Csc[x]^2)^(-3/2),x]","-\frac{2 \cot (x)}{3 \sqrt{\csc ^2(x)}}-\frac{\cot (x)}{3 \csc ^2(x)^{3/2}}","-\frac{2 \cot (x)}{3 \sqrt{\csc ^2(x)}}-\frac{\cot (x)}{3 \csc ^2(x)^{3/2}}",1,"-Cot[x]/(3*(Csc[x]^2)^(3/2)) - (2*Cot[x])/(3*Sqrt[Csc[x]^2])","A",3,3,8,0.3750,1,"{4122, 192, 191}"
45,1,43,0,0.0147414,"\int \frac{1}{\csc ^2(x)^{5/2}} \, dx","Int[(Csc[x]^2)^(-5/2),x]","-\frac{8 \cot (x)}{15 \sqrt{\csc ^2(x)}}-\frac{4 \cot (x)}{15 \csc ^2(x)^{3/2}}-\frac{\cot (x)}{5 \csc ^2(x)^{5/2}}","-\frac{8 \cot (x)}{15 \sqrt{\csc ^2(x)}}-\frac{4 \cot (x)}{15 \csc ^2(x)^{3/2}}-\frac{\cot (x)}{5 \csc ^2(x)^{5/2}}",1,"-Cot[x]/(5*(Csc[x]^2)^(5/2)) - (4*Cot[x])/(15*(Csc[x]^2)^(3/2)) - (8*Cot[x])/(15*Sqrt[Csc[x]^2])","A",4,3,8,0.3750,1,"{4122, 192, 191}"
46,1,57,0,0.0188562,"\int \frac{1}{\csc ^2(x)^{7/2}} \, dx","Int[(Csc[x]^2)^(-7/2),x]","-\frac{16 \cot (x)}{35 \sqrt{\csc ^2(x)}}-\frac{8 \cot (x)}{35 \csc ^2(x)^{3/2}}-\frac{6 \cot (x)}{35 \csc ^2(x)^{5/2}}-\frac{\cot (x)}{7 \csc ^2(x)^{7/2}}","-\frac{16 \cot (x)}{35 \sqrt{\csc ^2(x)}}-\frac{8 \cot (x)}{35 \csc ^2(x)^{3/2}}-\frac{6 \cot (x)}{35 \csc ^2(x)^{5/2}}-\frac{\cot (x)}{7 \csc ^2(x)^{7/2}}",1,"-Cot[x]/(7*(Csc[x]^2)^(7/2)) - (6*Cot[x])/(35*(Csc[x]^2)^(5/2)) - (8*Cot[x])/(35*(Csc[x]^2)^(3/2)) - (16*Cot[x])/(35*Sqrt[Csc[x]^2])","A",5,3,8,0.3750,1,"{4122, 192, 191}"
47,1,84,0,0.0395658,"\int \left(a \csc ^2(x)\right)^{7/2} \, dx","Int[(a*Csc[x]^2)^(7/2),x]","-\frac{5}{16} a^3 \cot (x) \sqrt{a \csc ^2(x)}-\frac{5}{24} a^2 \cot (x) \left(a \csc ^2(x)\right)^{3/2}-\frac{5}{16} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)-\frac{1}{6} a \cot (x) \left(a \csc ^2(x)\right)^{5/2}","-\frac{5}{16} a^3 \cot (x) \sqrt{a \csc ^2(x)}-\frac{5}{24} a^2 \cot (x) \left(a \csc ^2(x)\right)^{3/2}-\frac{5}{16} a^{7/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)-\frac{1}{6} a \cot (x) \left(a \csc ^2(x)\right)^{5/2}",1,"(-5*a^(7/2)*ArcTanh[(Sqrt[a]*Cot[x])/Sqrt[a*Csc[x]^2]])/16 - (5*a^3*Cot[x]*Sqrt[a*Csc[x]^2])/16 - (5*a^2*Cot[x]*(a*Csc[x]^2)^(3/2))/24 - (a*Cot[x]*(a*Csc[x]^2)^(5/2))/6","A",6,4,10,0.4000,1,"{4122, 195, 217, 206}"
48,1,65,0,0.0291973,"\int \left(a \csc ^2(x)\right)^{5/2} \, dx","Int[(a*Csc[x]^2)^(5/2),x]","-\frac{3}{8} a^2 \cot (x) \sqrt{a \csc ^2(x)}-\frac{3}{8} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)-\frac{1}{4} a \cot (x) \left(a \csc ^2(x)\right)^{3/2}","-\frac{3}{8} a^2 \cot (x) \sqrt{a \csc ^2(x)}-\frac{3}{8} a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)-\frac{1}{4} a \cot (x) \left(a \csc ^2(x)\right)^{3/2}",1,"(-3*a^(5/2)*ArcTanh[(Sqrt[a]*Cot[x])/Sqrt[a*Csc[x]^2]])/8 - (3*a^2*Cot[x]*Sqrt[a*Csc[x]^2])/8 - (a*Cot[x]*(a*Csc[x]^2)^(3/2))/4","A",5,4,10,0.4000,1,"{4122, 195, 217, 206}"
49,1,46,0,0.0219625,"\int \left(a \csc ^2(x)\right)^{3/2} \, dx","Int[(a*Csc[x]^2)^(3/2),x]","-\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)-\frac{1}{2} a \cot (x) \sqrt{a \csc ^2(x)}","-\frac{1}{2} a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)-\frac{1}{2} a \cot (x) \sqrt{a \csc ^2(x)}",1,"-(a^(3/2)*ArcTanh[(Sqrt[a]*Cot[x])/Sqrt[a*Csc[x]^2]])/2 - (a*Cot[x]*Sqrt[a*Csc[x]^2])/2","A",4,4,10,0.4000,1,"{4122, 195, 217, 206}"
50,1,26,0,0.0156433,"\int \sqrt{a \csc ^2(x)} \, dx","Int[Sqrt[a*Csc[x]^2],x]","-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)","-\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \cot (x)}{\sqrt{a \csc ^2(x)}}\right)",1,"-(Sqrt[a]*ArcTanh[(Sqrt[a]*Cot[x])/Sqrt[a*Csc[x]^2]])","A",3,3,10,0.3000,1,"{4122, 217, 206}"
51,1,14,0,0.0134393,"\int \frac{1}{\sqrt{a \csc ^2(x)}} \, dx","Int[1/Sqrt[a*Csc[x]^2],x]","-\frac{\cot (x)}{\sqrt{a \csc ^2(x)}}","-\frac{\cot (x)}{\sqrt{a \csc ^2(x)}}",1,"-(Cot[x]/Sqrt[a*Csc[x]^2])","A",2,2,10,0.2000,1,"{4122, 191}"
52,1,36,0,0.0183318,"\int \frac{1}{\left(a \csc ^2(x)\right)^{3/2}} \, dx","Int[(a*Csc[x]^2)^(-3/2),x]","-\frac{2 \cot (x)}{3 a \sqrt{a \csc ^2(x)}}-\frac{\cot (x)}{3 \left(a \csc ^2(x)\right)^{3/2}}","-\frac{2 \cot (x)}{3 a \sqrt{a \csc ^2(x)}}-\frac{\cot (x)}{3 \left(a \csc ^2(x)\right)^{3/2}}",1,"-Cot[x]/(3*(a*Csc[x]^2)^(3/2)) - (2*Cot[x])/(3*a*Sqrt[a*Csc[x]^2])","A",3,3,10,0.3000,1,"{4122, 192, 191}"
53,1,55,0,0.026984,"\int \frac{1}{\left(a \csc ^2(x)\right)^{5/2}} \, dx","Int[(a*Csc[x]^2)^(-5/2),x]","-\frac{8 \cot (x)}{15 a^2 \sqrt{a \csc ^2(x)}}-\frac{4 \cot (x)}{15 a \left(a \csc ^2(x)\right)^{3/2}}-\frac{\cot (x)}{5 \left(a \csc ^2(x)\right)^{5/2}}","-\frac{8 \cot (x)}{15 a^2 \sqrt{a \csc ^2(x)}}-\frac{4 \cot (x)}{15 a \left(a \csc ^2(x)\right)^{3/2}}-\frac{\cot (x)}{5 \left(a \csc ^2(x)\right)^{5/2}}",1,"-Cot[x]/(5*(a*Csc[x]^2)^(5/2)) - (4*Cot[x])/(15*a*(a*Csc[x]^2)^(3/2)) - (8*Cot[x])/(15*a^2*Sqrt[a*Csc[x]^2])","A",4,3,10,0.3000,1,"{4122, 192, 191}"
54,1,74,0,0.0357382,"\int \frac{1}{\left(a \csc ^2(x)\right)^{7/2}} \, dx","Int[(a*Csc[x]^2)^(-7/2),x]","-\frac{16 \cot (x)}{35 a^3 \sqrt{a \csc ^2(x)}}-\frac{8 \cot (x)}{35 a^2 \left(a \csc ^2(x)\right)^{3/2}}-\frac{6 \cot (x)}{35 a \left(a \csc ^2(x)\right)^{5/2}}-\frac{\cot (x)}{7 \left(a \csc ^2(x)\right)^{7/2}}","-\frac{16 \cot (x)}{35 a^3 \sqrt{a \csc ^2(x)}}-\frac{8 \cot (x)}{35 a^2 \left(a \csc ^2(x)\right)^{3/2}}-\frac{6 \cot (x)}{35 a \left(a \csc ^2(x)\right)^{5/2}}-\frac{\cot (x)}{7 \left(a \csc ^2(x)\right)^{7/2}}",1,"-Cot[x]/(7*(a*Csc[x]^2)^(7/2)) - (6*Cot[x])/(35*a*(a*Csc[x]^2)^(5/2)) - (8*Cot[x])/(35*a^2*(a*Csc[x]^2)^(3/2)) - (16*Cot[x])/(35*a^3*Sqrt[a*Csc[x]^2])","A",5,3,10,0.3000,1,"{4122, 192, 191}"
55,1,123,0,0.0595877,"\int \left(a \csc ^3(x)\right)^{5/2} \, dx","Int[(a*Csc[x]^3)^(5/2),x]","-\frac{2}{13} a^2 \cot (x) \csc ^4(x) \sqrt{a \csc ^3(x)}-\frac{22}{117} a^2 \cot (x) \csc ^2(x) \sqrt{a \csc ^3(x)}-\frac{154}{585} a^2 \cot (x) \sqrt{a \csc ^3(x)}-\frac{154}{195} a^2 \sin (x) \cos (x) \sqrt{a \csc ^3(x)}+\frac{154}{195} a^2 \sin ^{\frac{3}{2}}(x) E\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) \sqrt{a \csc ^3(x)}","-\frac{2}{13} a^2 \cot (x) \csc ^4(x) \sqrt{a \csc ^3(x)}-\frac{22}{117} a^2 \cot (x) \csc ^2(x) \sqrt{a \csc ^3(x)}-\frac{154}{585} a^2 \cot (x) \sqrt{a \csc ^3(x)}-\frac{154}{195} a^2 \sin (x) \cos (x) \sqrt{a \csc ^3(x)}+\frac{154}{195} a^2 \sin ^{\frac{3}{2}}(x) E\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) \sqrt{a \csc ^3(x)}",1,"(-154*a^2*Cot[x]*Sqrt[a*Csc[x]^3])/585 - (22*a^2*Cot[x]*Csc[x]^2*Sqrt[a*Csc[x]^3])/117 - (2*a^2*Cot[x]*Csc[x]^4*Sqrt[a*Csc[x]^3])/13 - (154*a^2*Cos[x]*Sqrt[a*Csc[x]^3]*Sin[x])/195 + (154*a^2*Sqrt[a*Csc[x]^3]*EllipticE[Pi/4 - x/2, 2]*Sin[x]^(3/2))/195","A",7,4,10,0.4000,1,"{4123, 3768, 3771, 2639}"
56,1,71,0,0.0375206,"\int \left(a \csc ^3(x)\right)^{3/2} \, dx","Int[(a*Csc[x]^3)^(3/2),x]","-\frac{10}{21} a \cos (x) \sqrt{a \csc ^3(x)}-\frac{2}{7} a \cot (x) \csc (x) \sqrt{a \csc ^3(x)}-\frac{10}{21} a \sin ^{\frac{3}{2}}(x) F\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) \sqrt{a \csc ^3(x)}","-\frac{10}{21} a \cos (x) \sqrt{a \csc ^3(x)}-\frac{2}{7} a \cot (x) \csc (x) \sqrt{a \csc ^3(x)}-\frac{10}{21} a \sin ^{\frac{3}{2}}(x) F\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) \sqrt{a \csc ^3(x)}",1,"(-10*a*Cos[x]*Sqrt[a*Csc[x]^3])/21 - (2*a*Cot[x]*Csc[x]*Sqrt[a*Csc[x]^3])/7 - (10*a*Sqrt[a*Csc[x]^3]*EllipticF[Pi/4 - x/2, 2]*Sin[x]^(3/2))/21","A",5,4,10,0.4000,1,"{4123, 3768, 3771, 2641}"
57,1,48,0,0.0270866,"\int \sqrt{a \csc ^3(x)} \, dx","Int[Sqrt[a*Csc[x]^3],x]","2 \sin ^{\frac{3}{2}}(x) E\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) \sqrt{a \csc ^3(x)}-2 \sin (x) \cos (x) \sqrt{a \csc ^3(x)}","2 \sin ^{\frac{3}{2}}(x) E\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right) \sqrt{a \csc ^3(x)}-2 \sin (x) \cos (x) \sqrt{a \csc ^3(x)}",1,"-2*Cos[x]*Sqrt[a*Csc[x]^3]*Sin[x] + 2*Sqrt[a*Csc[x]^3]*EllipticE[Pi/4 - x/2, 2]*Sin[x]^(3/2)","A",4,4,10,0.4000,1,"{4123, 3768, 3771, 2639}"
58,1,50,0,0.0296832,"\int \frac{1}{\sqrt{a \csc ^3(x)}} \, dx","Int[1/Sqrt[a*Csc[x]^3],x]","-\frac{2 \cot (x)}{3 \sqrt{a \csc ^3(x)}}-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right)}{3 \sin ^{\frac{3}{2}}(x) \sqrt{a \csc ^3(x)}}","-\frac{2 \cot (x)}{3 \sqrt{a \csc ^3(x)}}-\frac{2 F\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right)}{3 \sin ^{\frac{3}{2}}(x) \sqrt{a \csc ^3(x)}}",1,"(-2*Cot[x])/(3*Sqrt[a*Csc[x]^3]) - (2*EllipticF[Pi/4 - x/2, 2])/(3*Sqrt[a*Csc[x]^3]*Sin[x]^(3/2))","A",4,4,10,0.4000,1,"{4123, 3769, 3771, 2641}"
59,1,79,0,0.0383605,"\int \frac{1}{\left(a \csc ^3(x)\right)^{3/2}} \, dx","Int[(a*Csc[x]^3)^(-3/2),x]","-\frac{14 \cos (x)}{45 a \sqrt{a \csc ^3(x)}}-\frac{2 \sin ^2(x) \cos (x)}{9 a \sqrt{a \csc ^3(x)}}-\frac{14 E\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right)}{15 a \sin ^{\frac{3}{2}}(x) \sqrt{a \csc ^3(x)}}","-\frac{14 \cos (x)}{45 a \sqrt{a \csc ^3(x)}}-\frac{2 \sin ^2(x) \cos (x)}{9 a \sqrt{a \csc ^3(x)}}-\frac{14 E\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right)}{15 a \sin ^{\frac{3}{2}}(x) \sqrt{a \csc ^3(x)}}",1,"(-14*Cos[x])/(45*a*Sqrt[a*Csc[x]^3]) - (14*EllipticE[Pi/4 - x/2, 2])/(15*a*Sqrt[a*Csc[x]^3]*Sin[x]^(3/2)) - (2*Cos[x]*Sin[x]^2)/(9*a*Sqrt[a*Csc[x]^3])","A",5,4,10,0.4000,1,"{4123, 3769, 3771, 2639}"
60,1,123,0,0.0611232,"\int \frac{1}{\left(a \csc ^3(x)\right)^{5/2}} \, dx","Int[(a*Csc[x]^3)^(-5/2),x]","-\frac{26 \cot (x)}{77 a^2 \sqrt{a \csc ^3(x)}}-\frac{2 \sin ^5(x) \cos (x)}{15 a^2 \sqrt{a \csc ^3(x)}}-\frac{26 \sin ^3(x) \cos (x)}{165 a^2 \sqrt{a \csc ^3(x)}}-\frac{78 \sin (x) \cos (x)}{385 a^2 \sqrt{a \csc ^3(x)}}-\frac{26 F\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right)}{77 a^2 \sin ^{\frac{3}{2}}(x) \sqrt{a \csc ^3(x)}}","-\frac{26 \cot (x)}{77 a^2 \sqrt{a \csc ^3(x)}}-\frac{2 \sin ^5(x) \cos (x)}{15 a^2 \sqrt{a \csc ^3(x)}}-\frac{26 \sin ^3(x) \cos (x)}{165 a^2 \sqrt{a \csc ^3(x)}}-\frac{78 \sin (x) \cos (x)}{385 a^2 \sqrt{a \csc ^3(x)}}-\frac{26 F\left(\left.\frac{\pi }{4}-\frac{x}{2}\right|2\right)}{77 a^2 \sin ^{\frac{3}{2}}(x) \sqrt{a \csc ^3(x)}}",1,"(-26*Cot[x])/(77*a^2*Sqrt[a*Csc[x]^3]) - (26*EllipticF[Pi/4 - x/2, 2])/(77*a^2*Sqrt[a*Csc[x]^3]*Sin[x]^(3/2)) - (78*Cos[x]*Sin[x])/(385*a^2*Sqrt[a*Csc[x]^3]) - (26*Cos[x]*Sin[x]^3)/(165*a^2*Sqrt[a*Csc[x]^3]) - (2*Cos[x]*Sin[x]^5)/(15*a^2*Sqrt[a*Csc[x]^3])","A",7,4,10,0.4000,1,"{4123, 3769, 3771, 2641}"
61,1,164,0,0.0352601,"\int \left(a \csc ^4(x)\right)^{7/2} \, dx","Int[(a*Csc[x]^4)^(7/2),x]","-\frac{1}{13} a^3 \cos ^2(x) \cot ^{11}(x) \sqrt{a \csc ^4(x)}-\frac{6}{11} a^3 \cos ^2(x) \cot ^9(x) \sqrt{a \csc ^4(x)}-\frac{5}{3} a^3 \cos ^2(x) \cot ^7(x) \sqrt{a \csc ^4(x)}-\frac{20}{7} a^3 \cos ^2(x) \cot ^5(x) \sqrt{a \csc ^4(x)}-3 a^3 \cos ^2(x) \cot ^3(x) \sqrt{a \csc ^4(x)}-2 a^3 \cos ^2(x) \cot (x) \sqrt{a \csc ^4(x)}-a^3 \sin (x) \cos (x) \sqrt{a \csc ^4(x)}","-\frac{1}{13} a^3 \cos ^2(x) \cot ^{11}(x) \sqrt{a \csc ^4(x)}-\frac{6}{11} a^3 \cos ^2(x) \cot ^9(x) \sqrt{a \csc ^4(x)}-\frac{5}{3} a^3 \cos ^2(x) \cot ^7(x) \sqrt{a \csc ^4(x)}-\frac{20}{7} a^3 \cos ^2(x) \cot ^5(x) \sqrt{a \csc ^4(x)}-3 a^3 \cos ^2(x) \cot ^3(x) \sqrt{a \csc ^4(x)}-2 a^3 \cos ^2(x) \cot (x) \sqrt{a \csc ^4(x)}-a^3 \sin (x) \cos (x) \sqrt{a \csc ^4(x)}",1,"-2*a^3*Cos[x]^2*Cot[x]*Sqrt[a*Csc[x]^4] - 3*a^3*Cos[x]^2*Cot[x]^3*Sqrt[a*Csc[x]^4] - (20*a^3*Cos[x]^2*Cot[x]^5*Sqrt[a*Csc[x]^4])/7 - (5*a^3*Cos[x]^2*Cot[x]^7*Sqrt[a*Csc[x]^4])/3 - (6*a^3*Cos[x]^2*Cot[x]^9*Sqrt[a*Csc[x]^4])/11 - (a^3*Cos[x]^2*Cot[x]^11*Sqrt[a*Csc[x]^4])/13 - a^3*Cos[x]*Sqrt[a*Csc[x]^4]*Sin[x]","A",3,2,10,0.2000,1,"{4123, 3767}"
62,1,118,0,0.027743,"\int \left(a \csc ^4(x)\right)^{5/2} \, dx","Int[(a*Csc[x]^4)^(5/2),x]","-\frac{1}{9} a^2 \cos ^2(x) \cot ^7(x) \sqrt{a \csc ^4(x)}-\frac{4}{7} a^2 \cos ^2(x) \cot ^5(x) \sqrt{a \csc ^4(x)}-\frac{6}{5} a^2 \cos ^2(x) \cot ^3(x) \sqrt{a \csc ^4(x)}-\frac{4}{3} a^2 \cos ^2(x) \cot (x) \sqrt{a \csc ^4(x)}-a^2 \sin (x) \cos (x) \sqrt{a \csc ^4(x)}","-\frac{1}{9} a^2 \cos ^2(x) \cot ^7(x) \sqrt{a \csc ^4(x)}-\frac{4}{7} a^2 \cos ^2(x) \cot ^5(x) \sqrt{a \csc ^4(x)}-\frac{6}{5} a^2 \cos ^2(x) \cot ^3(x) \sqrt{a \csc ^4(x)}-\frac{4}{3} a^2 \cos ^2(x) \cot (x) \sqrt{a \csc ^4(x)}-a^2 \sin (x) \cos (x) \sqrt{a \csc ^4(x)}",1,"(-4*a^2*Cos[x]^2*Cot[x]*Sqrt[a*Csc[x]^4])/3 - (6*a^2*Cos[x]^2*Cot[x]^3*Sqrt[a*Csc[x]^4])/5 - (4*a^2*Cos[x]^2*Cot[x]^5*Sqrt[a*Csc[x]^4])/7 - (a^2*Cos[x]^2*Cot[x]^7*Sqrt[a*Csc[x]^4])/9 - a^2*Cos[x]*Sqrt[a*Csc[x]^4]*Sin[x]","A",3,2,10,0.2000,1,"{4123, 3767}"
63,1,62,0,0.0209453,"\int \left(a \csc ^4(x)\right)^{3/2} \, dx","Int[(a*Csc[x]^4)^(3/2),x]","-\frac{1}{5} a \cos ^2(x) \cot ^3(x) \sqrt{a \csc ^4(x)}-\frac{2}{3} a \cos ^2(x) \cot (x) \sqrt{a \csc ^4(x)}-a \sin (x) \cos (x) \sqrt{a \csc ^4(x)}","-\frac{1}{5} a \cos ^2(x) \cot ^3(x) \sqrt{a \csc ^4(x)}-\frac{2}{3} a \cos ^2(x) \cot (x) \sqrt{a \csc ^4(x)}-a \sin (x) \cos (x) \sqrt{a \csc ^4(x)}",1,"(-2*a*Cos[x]^2*Cot[x]*Sqrt[a*Csc[x]^4])/3 - (a*Cos[x]^2*Cot[x]^3*Sqrt[a*Csc[x]^4])/5 - a*Cos[x]*Sqrt[a*Csc[x]^4]*Sin[x]","A",3,2,10,0.2000,1,"{4123, 3767}"
64,1,16,0,0.0147763,"\int \sqrt{a \csc ^4(x)} \, dx","Int[Sqrt[a*Csc[x]^4],x]","\sin (x) (-\cos (x)) \sqrt{a \csc ^4(x)}","\sin (x) (-\cos (x)) \sqrt{a \csc ^4(x)}",1,"-(Cos[x]*Sqrt[a*Csc[x]^4]*Sin[x])","A",3,3,10,0.3000,1,"{4123, 3767, 8}"
65,1,36,0,0.01555,"\int \frac{1}{\sqrt{a \csc ^4(x)}} \, dx","Int[1/Sqrt[a*Csc[x]^4],x]","\frac{x \csc ^2(x)}{2 \sqrt{a \csc ^4(x)}}-\frac{\cot (x)}{2 \sqrt{a \csc ^4(x)}}","\frac{x \csc ^2(x)}{2 \sqrt{a \csc ^4(x)}}-\frac{\cot (x)}{2 \sqrt{a \csc ^4(x)}}",1,"-Cot[x]/(2*Sqrt[a*Csc[x]^4]) + (x*Csc[x]^2)/(2*Sqrt[a*Csc[x]^4])","A",3,3,10,0.3000,1,"{4123, 2635, 8}"
66,1,86,0,0.0294559,"\int \frac{1}{\left(a \csc ^4(x)\right)^{3/2}} \, dx","Int[(a*Csc[x]^4)^(-3/2),x]","\frac{5 x \csc ^2(x)}{16 a \sqrt{a \csc ^4(x)}}-\frac{5 \cot (x)}{16 a \sqrt{a \csc ^4(x)}}-\frac{\sin ^3(x) \cos (x)}{6 a \sqrt{a \csc ^4(x)}}-\frac{5 \sin (x) \cos (x)}{24 a \sqrt{a \csc ^4(x)}}","\frac{5 x \csc ^2(x)}{16 a \sqrt{a \csc ^4(x)}}-\frac{5 \cot (x)}{16 a \sqrt{a \csc ^4(x)}}-\frac{\sin ^3(x) \cos (x)}{6 a \sqrt{a \csc ^4(x)}}-\frac{5 \sin (x) \cos (x)}{24 a \sqrt{a \csc ^4(x)}}",1,"(-5*Cot[x])/(16*a*Sqrt[a*Csc[x]^4]) + (5*x*Csc[x]^2)/(16*a*Sqrt[a*Csc[x]^4]) - (5*Cos[x]*Sin[x])/(24*a*Sqrt[a*Csc[x]^4]) - (Cos[x]*Sin[x]^3)/(6*a*Sqrt[a*Csc[x]^4])","A",5,3,10,0.3000,1,"{4123, 2635, 8}"
67,1,132,0,0.0446798,"\int \frac{1}{\left(a \csc ^4(x)\right)^{5/2}} \, dx","Int[(a*Csc[x]^4)^(-5/2),x]","\frac{63 x \csc ^2(x)}{256 a^2 \sqrt{a \csc ^4(x)}}-\frac{63 \cot (x)}{256 a^2 \sqrt{a \csc ^4(x)}}-\frac{\sin ^7(x) \cos (x)}{10 a^2 \sqrt{a \csc ^4(x)}}-\frac{9 \sin ^5(x) \cos (x)}{80 a^2 \sqrt{a \csc ^4(x)}}-\frac{21 \sin ^3(x) \cos (x)}{160 a^2 \sqrt{a \csc ^4(x)}}-\frac{21 \sin (x) \cos (x)}{128 a^2 \sqrt{a \csc ^4(x)}}","\frac{63 x \csc ^2(x)}{256 a^2 \sqrt{a \csc ^4(x)}}-\frac{63 \cot (x)}{256 a^2 \sqrt{a \csc ^4(x)}}-\frac{\sin ^7(x) \cos (x)}{10 a^2 \sqrt{a \csc ^4(x)}}-\frac{9 \sin ^5(x) \cos (x)}{80 a^2 \sqrt{a \csc ^4(x)}}-\frac{21 \sin ^3(x) \cos (x)}{160 a^2 \sqrt{a \csc ^4(x)}}-\frac{21 \sin (x) \cos (x)}{128 a^2 \sqrt{a \csc ^4(x)}}",1,"(-63*Cot[x])/(256*a^2*Sqrt[a*Csc[x]^4]) + (63*x*Csc[x]^2)/(256*a^2*Sqrt[a*Csc[x]^4]) - (21*Cos[x]*Sin[x])/(128*a^2*Sqrt[a*Csc[x]^4]) - (21*Cos[x]*Sin[x]^3)/(160*a^2*Sqrt[a*Csc[x]^4]) - (9*Cos[x]*Sin[x]^5)/(80*a^2*Sqrt[a*Csc[x]^4]) - (Cos[x]*Sin[x]^7)/(10*a^2*Sqrt[a*Csc[x]^4])","A",7,3,10,0.3000,1,"{4123, 2635, 8}"
68,1,80,0,0.0495435,"\int \left((b \csc (c+d x))^p\right)^n \, dx","Int[((b*Csc[c + d*x])^p)^n,x]","\frac{\sin (c+d x) \cos (c+d x) \left((b \csc (c+d x))^p\right)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\sin ^2(c+d x)\right)}{d (1-n p) \sqrt{\cos ^2(c+d x)}}","\frac{\sin (c+d x) \cos (c+d x) \left((b \csc (c+d x))^p\right)^n \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\sin ^2(c+d x)\right)}{d (1-n p) \sqrt{\cos ^2(c+d x)}}",1,"(Cos[c + d*x]*((b*Csc[c + d*x])^p)^n*Hypergeometric2F1[1/2, (1 - n*p)/2, (3 - n*p)/2, Sin[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n*p)*Sqrt[Cos[c + d*x]^2])","A",3,3,12,0.2500,1,"{4123, 3772, 2643}"
69,1,82,0,0.0491908,"\int \left(a (b \csc (c+d x))^p\right)^n \, dx","Int[(a*(b*Csc[c + d*x])^p)^n,x]","\frac{\sin (c+d x) \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\sin ^2(c+d x)\right) \left(a (b \csc (c+d x))^p\right)^n}{d (1-n p) \sqrt{\cos ^2(c+d x)}}","\frac{\sin (c+d x) \cos (c+d x) \, _2F_1\left(\frac{1}{2},\frac{1}{2} (1-n p);\frac{1}{2} (3-n p);\sin ^2(c+d x)\right) \left(a (b \csc (c+d x))^p\right)^n}{d (1-n p) \sqrt{\cos ^2(c+d x)}}",1,"(Cos[c + d*x]*(a*(b*Csc[c + d*x])^p)^n*Hypergeometric2F1[1/2, (1 - n*p)/2, (3 - n*p)/2, Sin[c + d*x]^2]*Sin[c + d*x])/(d*(1 - n*p)*Sqrt[Cos[c + d*x]^2])","A",3,3,14,0.2143,1,"{4123, 3772, 2643}"
70,1,91,0,0.0448884,"\int (a \csc (e+f x))^m (b \csc (e+f x))^n \, dx","Int[(a*Csc[e + f*x])^m*(b*Csc[e + f*x])^n,x]","\frac{a \cos (e+f x) (a \csc (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)}{f (-m-n+1) \sqrt{\cos ^2(e+f x)}}","\frac{a \cos (e+f x) (a \csc (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)}{f (-m-n+1) \sqrt{\cos ^2(e+f x)}}",1,"(a*Cos[e + f*x]*(a*Csc[e + f*x])^(-1 + m)*(b*Csc[e + f*x])^n*Hypergeometric2F1[1/2, (1 - m - n)/2, (3 - m - n)/2, Sin[e + f*x]^2])/(f*(1 - m - n)*Sqrt[Cos[e + f*x]^2])","A",3,3,21,0.1429,1,"{20, 3772, 2643}"