1,1,114,0,0.0614145,"\int x^6 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^6*(a + b*ArcCsc[c*x]),x]","\frac{1}{7} x^7 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^6 \sqrt{1-\frac{1}{c^2 x^2}}}{42 c}+\frac{5 b x^4 \sqrt{1-\frac{1}{c^2 x^2}}}{168 c^3}+\frac{5 b x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{112 c^5}+\frac{5 b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{112 c^7}","\frac{1}{7} x^7 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^6 \sqrt{1-\frac{1}{c^2 x^2}}}{42 c}+\frac{5 b x^4 \sqrt{1-\frac{1}{c^2 x^2}}}{168 c^3}+\frac{5 b x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{112 c^5}+\frac{5 b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{112 c^7}",1,"(5*b*Sqrt[1 - 1/(c^2*x^2)]*x^2)/(112*c^5) + (5*b*Sqrt[1 - 1/(c^2*x^2)]*x^4)/(168*c^3) + (b*Sqrt[1 - 1/(c^2*x^2)]*x^6)/(42*c) + (x^7*(a + b*ArcCsc[c*x]))/7 + (5*b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(112*c^7)","A",7,5,12,0.4167,1,"{5221, 266, 51, 63, 208}"
2,1,89,0,0.0418436,"\int x^5 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^5*(a + b*ArcCsc[c*x]),x]","\frac{1}{6} x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^5 \sqrt{1-\frac{1}{c^2 x^2}}}{30 c}+\frac{2 b x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{45 c^3}+\frac{4 b x \sqrt{1-\frac{1}{c^2 x^2}}}{45 c^5}","\frac{1}{6} x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^5 \sqrt{1-\frac{1}{c^2 x^2}}}{30 c}+\frac{2 b x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{45 c^3}+\frac{4 b x \sqrt{1-\frac{1}{c^2 x^2}}}{45 c^5}",1,"(4*b*Sqrt[1 - 1/(c^2*x^2)]*x)/(45*c^5) + (2*b*Sqrt[1 - 1/(c^2*x^2)]*x^3)/(45*c^3) + (b*Sqrt[1 - 1/(c^2*x^2)]*x^5)/(30*c) + (x^6*(a + b*ArcCsc[c*x]))/6","A",4,3,12,0.2500,1,"{5221, 271, 191}"
3,1,89,0,0.0475787,"\int x^4 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^4*(a + b*ArcCsc[c*x]),x]","\frac{1}{5} x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^4 \sqrt{1-\frac{1}{c^2 x^2}}}{20 c}+\frac{3 b x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{40 c^3}+\frac{3 b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{40 c^5}","\frac{1}{5} x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^4 \sqrt{1-\frac{1}{c^2 x^2}}}{20 c}+\frac{3 b x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{40 c^3}+\frac{3 b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{40 c^5}",1,"(3*b*Sqrt[1 - 1/(c^2*x^2)]*x^2)/(40*c^3) + (b*Sqrt[1 - 1/(c^2*x^2)]*x^4)/(20*c) + (x^5*(a + b*ArcCsc[c*x]))/5 + (3*b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(40*c^5)","A",6,5,12,0.4167,1,"{5221, 266, 51, 63, 208}"
4,1,64,0,0.0265763,"\int x^3 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcCsc[c*x]),x]","\frac{1}{4} x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{12 c}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}}}{6 c^3}","\frac{1}{4} x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{12 c}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}}}{6 c^3}",1,"(b*Sqrt[1 - 1/(c^2*x^2)]*x)/(6*c^3) + (b*Sqrt[1 - 1/(c^2*x^2)]*x^3)/(12*c) + (x^4*(a + b*ArcCsc[c*x]))/4","A",3,3,12,0.2500,1,"{5221, 271, 191}"
5,1,64,0,0.035954,"\int x^2 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcCsc[c*x]),x]","\frac{1}{3} x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{6 c}+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{6 c^3}","\frac{1}{3} x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{6 c}+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{6 c^3}",1,"(b*Sqrt[1 - 1/(c^2*x^2)]*x^2)/(6*c) + (x^3*(a + b*ArcCsc[c*x]))/3 + (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(6*c^3)","A",5,5,12,0.4167,1,"{5221, 266, 51, 63, 208}"
6,1,39,0,0.0119133,"\int x \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcCsc[c*x]),x]","\frac{1}{2} x^2 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}","\frac{1}{2} x^2 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}",1,"(b*Sqrt[1 - 1/(c^2*x^2)]*x)/(2*c) + (x^2*(a + b*ArcCsc[c*x]))/2","A",2,2,10,0.2000,1,"{5221, 191}"
7,1,31,0,0.0205758,"\int \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[a + b*ArcCsc[c*x],x]","a x+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \csc ^{-1}(c x)","a x+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \csc ^{-1}(c x)",1,"a*x + b*x*ArcCsc[c*x] + (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c","A",5,4,8,0.5000,1,"{5215, 266, 63, 208}"
8,1,64,0,0.0847952,"\int \frac{a+b \csc ^{-1}(c x)}{x} \, dx","Int[(a + b*ArcCsc[c*x])/x,x]","\frac{1}{2} i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b}-\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)","\frac{1}{2} i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b}-\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)",1,"((I/2)*(a + b*ArcCsc[c*x])^2)/b - (a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])] + (I/2)*b*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",6,6,12,0.5000,1,"{5219, 4625, 3717, 2190, 2279, 2391}"
9,1,32,0,0.0197825,"\int \frac{a+b \csc ^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcCsc[c*x])/x^2,x]","-\frac{a+b \csc ^{-1}(c x)}{x}-b c \sqrt{1-\frac{1}{c^2 x^2}}","-\frac{a+b \csc ^{-1}(c x)}{x}-b c \sqrt{1-\frac{1}{c^2 x^2}}",1,"-(b*c*Sqrt[1 - 1/(c^2*x^2)]) - (a + b*ArcCsc[c*x])/x","A",2,2,12,0.1667,1,"{5221, 261}"
10,1,51,0,0.0315293,"\int \frac{a+b \csc ^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcCsc[c*x])/x^3,x]","-\frac{a+b \csc ^{-1}(c x)}{2 x^2}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{4 x}+\frac{1}{4} b c^2 \csc ^{-1}(c x)","-\frac{a+b \csc ^{-1}(c x)}{2 x^2}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{4 x}+\frac{1}{4} b c^2 \csc ^{-1}(c x)",1,"-(b*c*Sqrt[1 - 1/(c^2*x^2)])/(4*x) + (b*c^2*ArcCsc[c*x])/4 - (a + b*ArcCsc[c*x])/(2*x^2)","A",4,4,12,0.3333,1,"{5221, 335, 321, 216}"
11,1,60,0,0.0379044,"\int \frac{a+b \csc ^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcCsc[c*x])/x^4,x]","-\frac{a+b \csc ^{-1}(c x)}{3 x^3}+\frac{1}{9} b c^3 \left(1-\frac{1}{c^2 x^2}\right)^{3/2}-\frac{1}{3} b c^3 \sqrt{1-\frac{1}{c^2 x^2}}","-\frac{a+b \csc ^{-1}(c x)}{3 x^3}+\frac{1}{9} b c^3 \left(1-\frac{1}{c^2 x^2}\right)^{3/2}-\frac{1}{3} b c^3 \sqrt{1-\frac{1}{c^2 x^2}}",1,"-(b*c^3*Sqrt[1 - 1/(c^2*x^2)])/3 + (b*c^3*(1 - 1/(c^2*x^2))^(3/2))/9 - (a + b*ArcCsc[c*x])/(3*x^3)","A",4,3,12,0.2500,1,"{5221, 266, 43}"
12,1,76,0,0.0449829,"\int \frac{a+b \csc ^{-1}(c x)}{x^5} \, dx","Int[(a + b*ArcCsc[c*x])/x^5,x]","-\frac{a+b \csc ^{-1}(c x)}{4 x^4}-\frac{3 b c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{32 x}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{16 x^3}+\frac{3}{32} b c^4 \csc ^{-1}(c x)","-\frac{a+b \csc ^{-1}(c x)}{4 x^4}-\frac{3 b c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{32 x}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{16 x^3}+\frac{3}{32} b c^4 \csc ^{-1}(c x)",1,"-(b*c*Sqrt[1 - 1/(c^2*x^2)])/(16*x^3) - (3*b*c^3*Sqrt[1 - 1/(c^2*x^2)])/(32*x) + (3*b*c^4*ArcCsc[c*x])/32 - (a + b*ArcCsc[c*x])/(4*x^4)","A",5,4,12,0.3333,1,"{5221, 335, 321, 216}"
13,1,82,0,0.0491578,"\int \frac{a+b \csc ^{-1}(c x)}{x^6} \, dx","Int[(a + b*ArcCsc[c*x])/x^6,x]","-\frac{a+b \csc ^{-1}(c x)}{5 x^5}-\frac{1}{25} b c^5 \left(1-\frac{1}{c^2 x^2}\right)^{5/2}+\frac{2}{15} b c^5 \left(1-\frac{1}{c^2 x^2}\right)^{3/2}-\frac{1}{5} b c^5 \sqrt{1-\frac{1}{c^2 x^2}}","-\frac{a+b \csc ^{-1}(c x)}{5 x^5}-\frac{1}{25} b c^5 \left(1-\frac{1}{c^2 x^2}\right)^{5/2}+\frac{2}{15} b c^5 \left(1-\frac{1}{c^2 x^2}\right)^{3/2}-\frac{1}{5} b c^5 \sqrt{1-\frac{1}{c^2 x^2}}",1,"-(b*c^5*Sqrt[1 - 1/(c^2*x^2)])/5 + (2*b*c^5*(1 - 1/(c^2*x^2))^(3/2))/15 - (b*c^5*(1 - 1/(c^2*x^2))^(5/2))/25 - (a + b*ArcCsc[c*x])/(5*x^5)","A",4,3,12,0.2500,1,"{5221, 266, 43}"
14,1,101,0,0.0624712,"\int \frac{a+b \csc ^{-1}(c x)}{x^7} \, dx","Int[(a + b*ArcCsc[c*x])/x^7,x]","-\frac{a+b \csc ^{-1}(c x)}{6 x^6}-\frac{5 b c^5 \sqrt{1-\frac{1}{c^2 x^2}}}{96 x}-\frac{5 b c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{144 x^3}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{36 x^5}+\frac{5}{96} b c^6 \csc ^{-1}(c x)","-\frac{a+b \csc ^{-1}(c x)}{6 x^6}-\frac{5 b c^5 \sqrt{1-\frac{1}{c^2 x^2}}}{96 x}-\frac{5 b c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{144 x^3}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{36 x^5}+\frac{5}{96} b c^6 \csc ^{-1}(c x)",1,"-(b*c*Sqrt[1 - 1/(c^2*x^2)])/(36*x^5) - (5*b*c^3*Sqrt[1 - 1/(c^2*x^2)])/(144*x^3) - (5*b*c^5*Sqrt[1 - 1/(c^2*x^2)])/(96*x) + (5*b*c^6*ArcCsc[c*x])/96 - (a + b*ArcCsc[c*x])/(6*x^6)","A",6,4,12,0.3333,1,"{5221, 335, 321, 216}"
15,1,107,0,0.1062369,"\int x^3 \left(a+b \csc ^{-1}(c x)\right)^2 \, dx","Int[x^3*(a + b*ArcCsc[c*x])^2,x]","\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{6 c}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} x^4 \left(a+b \csc ^{-1}(c x)\right)^2+\frac{b^2 x^2}{12 c^2}+\frac{b^2 \log (x)}{3 c^4}","\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{6 c}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} x^4 \left(a+b \csc ^{-1}(c x)\right)^2+\frac{b^2 x^2}{12 c^2}+\frac{b^2 \log (x)}{3 c^4}",1,"(b^2*x^2)/(12*c^2) + (b*Sqrt[1 - 1/(c^2*x^2)]*x*(a + b*ArcCsc[c*x]))/(3*c^3) + (b*Sqrt[1 - 1/(c^2*x^2)]*x^3*(a + b*ArcCsc[c*x]))/(6*c) + (x^4*(a + b*ArcCsc[c*x])^2)/4 + (b^2*Log[x])/(3*c^4)","A",5,5,14,0.3571,1,"{5223, 4410, 4185, 4184, 3475}"
16,1,139,0,0.1190064,"\int x^2 \left(a+b \csc ^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcCsc[c*x])^2,x]","-\frac{i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right)}{3 c^3}+\frac{i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right)}{3 c^3}+\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{3 c}+\frac{2 b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \csc ^{-1}(c x)\right)^2+\frac{b^2 x}{3 c^2}","-\frac{i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right)}{3 c^3}+\frac{i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right)}{3 c^3}+\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{3 c}+\frac{2 b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \csc ^{-1}(c x)\right)^2+\frac{b^2 x}{3 c^2}",1,"(b^2*x)/(3*c^2) + (b*Sqrt[1 - 1/(c^2*x^2)]*x^2*(a + b*ArcCsc[c*x]))/(3*c) + (x^3*(a + b*ArcCsc[c*x])^2)/3 + (2*b*(a + b*ArcCsc[c*x])*ArcTanh[E^(I*ArcCsc[c*x])])/(3*c^3) - ((I/3)*b^2*PolyLog[2, -E^(I*ArcCsc[c*x])])/c^3 + ((I/3)*b^2*PolyLog[2, E^(I*ArcCsc[c*x])])/c^3","A",8,6,14,0.4286,1,"{5223, 4410, 4185, 4183, 2279, 2391}"
17,1,55,0,0.0700716,"\int x \left(a+b \csc ^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcCsc[c*x])^2,x]","\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{c}+\frac{1}{2} x^2 \left(a+b \csc ^{-1}(c x)\right)^2+\frac{b^2 \log (x)}{c^2}","\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{c}+\frac{1}{2} x^2 \left(a+b \csc ^{-1}(c x)\right)^2+\frac{b^2 \log (x)}{c^2}",1,"(b*Sqrt[1 - 1/(c^2*x^2)]*x*(a + b*ArcCsc[c*x]))/c + (x^2*(a + b*ArcCsc[c*x])^2)/2 + (b^2*Log[x])/c^2","A",4,4,12,0.3333,1,"{5223, 4410, 4184, 3475}"
18,1,84,0,0.0675351,"\int \left(a+b \csc ^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcCsc[c*x])^2,x]","-\frac{2 i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right)}{c}+\frac{2 i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right)}{c}+x \left(a+b \csc ^{-1}(c x)\right)^2+\frac{4 b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c}","-\frac{2 i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right)}{c}+\frac{2 i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right)}{c}+x \left(a+b \csc ^{-1}(c x)\right)^2+\frac{4 b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c}",1,"x*(a + b*ArcCsc[c*x])^2 + (4*b*(a + b*ArcCsc[c*x])*ArcTanh[E^(I*ArcCsc[c*x])])/c - ((2*I)*b^2*PolyLog[2, -E^(I*ArcCsc[c*x])])/c + ((2*I)*b^2*PolyLog[2, E^(I*ArcCsc[c*x])])/c","A",7,5,10,0.5000,1,"{5217, 4410, 4183, 2279, 2391}"
19,1,91,0,0.1233985,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcCsc[c*x])^2/x,x]","i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(c x)}\right)+\frac{i \left(a+b \csc ^{-1}(c x)\right)^3}{3 b}-\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2","i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(c x)}\right)+\frac{i \left(a+b \csc ^{-1}(c x)\right)^3}{3 b}-\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2",1,"((I/3)*(a + b*ArcCsc[c*x])^3)/b - (a + b*ArcCsc[c*x])^2*Log[1 - E^((2*I)*ArcCsc[c*x])] + I*b*(a + b*ArcCsc[c*x])*PolyLog[2, E^((2*I)*ArcCsc[c*x])] - (b^2*PolyLog[3, E^((2*I)*ArcCsc[c*x])])/2","A",6,6,14,0.4286,1,"{5223, 3717, 2190, 2531, 2282, 6589}"
20,1,50,0,0.0608282,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcCsc[c*x])^2/x^2,x]","-2 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{x}+\frac{2 b^2}{x}","-2 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{x}+\frac{2 b^2}{x}",1,"(2*b^2)/x - 2*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x]) - (a + b*ArcCsc[c*x])^2/x","A",4,3,14,0.2143,1,"{5223, 3296, 2637}"
21,1,88,0,0.0779932,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^2}{x^3} \, dx","Int[(a + b*ArcCsc[c*x])^2/x^3,x]","-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{2 x}+\frac{1}{2} a b c^2 \csc ^{-1}(c x)-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{2 x^2}+\frac{1}{4} b^2 c^2 \csc ^{-1}(c x)^2+\frac{b^2}{4 x^2}","-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{2 x}+\frac{1}{2} a b c^2 \csc ^{-1}(c x)-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{2 x^2}+\frac{1}{4} b^2 c^2 \csc ^{-1}(c x)^2+\frac{b^2}{4 x^2}",1,"b^2/(4*x^2) + (a*b*c^2*ArcCsc[c*x])/2 + (b^2*c^2*ArcCsc[c*x]^2)/4 - (b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x]))/(2*x) - (a + b*ArcCsc[c*x])^2/(2*x^2)","A",4,3,14,0.2143,1,"{5223, 4404, 3310}"
22,1,102,0,0.0963057,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^2}{x^4} \, dx","Int[(a + b*ArcCsc[c*x])^2/x^4,x]","-\frac{4}{9} b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)-\frac{2 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{9 x^2}-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{3 x^3}+\frac{4 b^2 c^2}{9 x}+\frac{2 b^2}{27 x^3}","-\frac{4}{9} b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)-\frac{2 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{9 x^2}-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{3 x^3}+\frac{4 b^2 c^2}{9 x}+\frac{2 b^2}{27 x^3}",1,"(2*b^2)/(27*x^3) + (4*b^2*c^2)/(9*x) - (4*b*c^3*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x]))/9 - (2*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x]))/(9*x^2) - (a + b*ArcCsc[c*x])^2/(3*x^3)","A",5,5,14,0.3571,1,"{5223, 4404, 3310, 3296, 2637}"
23,1,134,0,0.1122841,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^2}{x^5} \, dx","Int[(a + b*ArcCsc[c*x])^2/x^5,x]","-\frac{3 b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{16 x}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{8 x^3}+\frac{3}{16} a b c^4 \csc ^{-1}(c x)-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{4 x^4}+\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \csc ^{-1}(c x)^2+\frac{b^2}{32 x^4}","-\frac{3 b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{16 x}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)}{8 x^3}+\frac{3}{16} a b c^4 \csc ^{-1}(c x)-\frac{\left(a+b \csc ^{-1}(c x)\right)^2}{4 x^4}+\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \csc ^{-1}(c x)^2+\frac{b^2}{32 x^4}",1,"b^2/(32*x^4) + (3*b^2*c^2)/(32*x^2) + (3*a*b*c^4*ArcCsc[c*x])/16 + (3*b^2*c^4*ArcCsc[c*x]^2)/32 - (b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x]))/(8*x^3) - (3*b*c^3*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x]))/(16*x) - (a + b*ArcCsc[c*x])^2/(4*x^4)","A",5,3,14,0.2143,1,"{5223, 4404, 3310}"
24,1,207,0,0.2171416,"\int x^3 \left(a+b \csc ^{-1}(c x)\right)^3 \, dx","Int[x^3*(a + b*ArcCsc[c*x])^3,x]","\frac{i b^3 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 c^4}+\frac{b^2 x^2 \left(a+b \csc ^{-1}(c x)\right)}{4 c^2}-\frac{b^2 \log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^4}+\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{4 c}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{2 c^3}+\frac{i b \left(a+b \csc ^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \csc ^{-1}(c x)\right)^3+\frac{b^3 x \sqrt{1-\frac{1}{c^2 x^2}}}{4 c^3}","\frac{i b^3 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 c^4}+\frac{b^2 x^2 \left(a+b \csc ^{-1}(c x)\right)}{4 c^2}-\frac{b^2 \log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^4}+\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{4 c}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{2 c^3}+\frac{i b \left(a+b \csc ^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \csc ^{-1}(c x)\right)^3+\frac{b^3 x \sqrt{1-\frac{1}{c^2 x^2}}}{4 c^3}",1,"(b^3*Sqrt[1 - 1/(c^2*x^2)]*x)/(4*c^3) + (b^2*x^2*(a + b*ArcCsc[c*x]))/(4*c^2) + ((I/2)*b*(a + b*ArcCsc[c*x])^2)/c^4 + (b*Sqrt[1 - 1/(c^2*x^2)]*x*(a + b*ArcCsc[c*x])^2)/(2*c^3) + (b*Sqrt[1 - 1/(c^2*x^2)]*x^3*(a + b*ArcCsc[c*x])^2)/(4*c) + (x^4*(a + b*ArcCsc[c*x])^3)/4 - (b^2*(a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])])/c^4 + ((I/2)*b^3*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/c^4","A",10,10,14,0.7143,1,"{5223, 4410, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
25,1,220,0,0.1881116,"\int x^2 \left(a+b \csc ^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcCsc[c*x])^3,x]","-\frac{i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^3}+\frac{i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(c x)}\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,e^{i \csc ^{-1}(c x)}\right)}{c^3}+\frac{b^2 x \left(a+b \csc ^{-1}(c x)\right)}{c^2}+\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{2 c}+\frac{b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \csc ^{-1}(c x)\right)^3+\frac{b^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c^3}","-\frac{i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^3}+\frac{i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(c x)}\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,e^{i \csc ^{-1}(c x)}\right)}{c^3}+\frac{b^2 x \left(a+b \csc ^{-1}(c x)\right)}{c^2}+\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{2 c}+\frac{b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \csc ^{-1}(c x)\right)^3+\frac{b^3 \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c^3}",1,"(b^2*x*(a + b*ArcCsc[c*x]))/c^2 + (b*Sqrt[1 - 1/(c^2*x^2)]*x^2*(a + b*ArcCsc[c*x])^2)/(2*c) + (x^3*(a + b*ArcCsc[c*x])^3)/3 + (b*(a + b*ArcCsc[c*x])^2*ArcTanh[E^(I*ArcCsc[c*x])])/c^3 + (b^3*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c^3 - (I*b^2*(a + b*ArcCsc[c*x])*PolyLog[2, -E^(I*ArcCsc[c*x])])/c^3 + (I*b^2*(a + b*ArcCsc[c*x])*PolyLog[2, E^(I*ArcCsc[c*x])])/c^3 + (b^3*PolyLog[3, -E^(I*ArcCsc[c*x])])/c^3 - (b^3*PolyLog[3, E^(I*ArcCsc[c*x])])/c^3","A",11,8,14,0.5714,1,"{5223, 4410, 4186, 3770, 4183, 2531, 2282, 6589}"
26,1,126,0,0.1473189,"\int x \left(a+b \csc ^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcCsc[c*x])^3,x]","\frac{3 i b^3 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 c^2}-\frac{3 b^2 \log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^2}+\frac{3 b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{2 c}+\frac{3 i b \left(a+b \csc ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \csc ^{-1}(c x)\right)^3","\frac{3 i b^3 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 c^2}-\frac{3 b^2 \log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c^2}+\frac{3 b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{2 c}+\frac{3 i b \left(a+b \csc ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \csc ^{-1}(c x)\right)^3",1,"(((3*I)/2)*b*(a + b*ArcCsc[c*x])^2)/c^2 + (3*b*Sqrt[1 - 1/(c^2*x^2)]*x*(a + b*ArcCsc[c*x])^2)/(2*c) + (x^2*(a + b*ArcCsc[c*x])^3)/2 - (3*b^2*(a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])])/c^2 + (((3*I)/2)*b^3*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/c^2","A",7,7,12,0.5833,1,"{5223, 4410, 4184, 3717, 2190, 2279, 2391}"
27,1,144,0,0.1121792,"\int \left(a+b \csc ^{-1}(c x)\right)^3 \, dx","Int[(a + b*ArcCsc[c*x])^3,x]","-\frac{6 i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c}+\frac{6 i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c}+\frac{6 b^3 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(c x)}\right)}{c}-\frac{6 b^3 \text{PolyLog}\left(3,e^{i \csc ^{-1}(c x)}\right)}{c}+x \left(a+b \csc ^{-1}(c x)\right)^3+\frac{6 b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2}{c}","-\frac{6 i b^2 \text{PolyLog}\left(2,-e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c}+\frac{6 i b^2 \text{PolyLog}\left(2,e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{c}+\frac{6 b^3 \text{PolyLog}\left(3,-e^{i \csc ^{-1}(c x)}\right)}{c}-\frac{6 b^3 \text{PolyLog}\left(3,e^{i \csc ^{-1}(c x)}\right)}{c}+x \left(a+b \csc ^{-1}(c x)\right)^3+\frac{6 b \tanh ^{-1}\left(e^{i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2}{c}",1,"x*(a + b*ArcCsc[c*x])^3 + (6*b*(a + b*ArcCsc[c*x])^2*ArcTanh[E^(I*ArcCsc[c*x])])/c - ((6*I)*b^2*(a + b*ArcCsc[c*x])*PolyLog[2, -E^(I*ArcCsc[c*x])])/c + ((6*I)*b^2*(a + b*ArcCsc[c*x])*PolyLog[2, E^(I*ArcCsc[c*x])])/c + (6*b^3*PolyLog[3, -E^(I*ArcCsc[c*x])])/c - (6*b^3*PolyLog[3, E^(I*ArcCsc[c*x])])/c","A",9,6,10,0.6000,1,"{5217, 4410, 4183, 2531, 2282, 6589}"
28,1,124,0,0.1431583,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcCsc[c*x])^3/x,x]","-\frac{3}{2} b^2 \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)+\frac{3}{2} i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2-\frac{3}{4} i b^3 \text{PolyLog}\left(4,e^{2 i \csc ^{-1}(c x)}\right)+\frac{i \left(a+b \csc ^{-1}(c x)\right)^4}{4 b}-\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^3","-\frac{3}{2} b^2 \text{PolyLog}\left(3,e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)+\frac{3}{2} i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^2-\frac{3}{4} i b^3 \text{PolyLog}\left(4,e^{2 i \csc ^{-1}(c x)}\right)+\frac{i \left(a+b \csc ^{-1}(c x)\right)^4}{4 b}-\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)^3",1,"((I/4)*(a + b*ArcCsc[c*x])^4)/b - (a + b*ArcCsc[c*x])^3*Log[1 - E^((2*I)*ArcCsc[c*x])] + ((3*I)/2)*b*(a + b*ArcCsc[c*x])^2*PolyLog[2, E^((2*I)*ArcCsc[c*x])] - (3*b^2*(a + b*ArcCsc[c*x])*PolyLog[3, E^((2*I)*ArcCsc[c*x])])/2 - ((3*I)/4)*b^3*PolyLog[4, E^((2*I)*ArcCsc[c*x])]","A",7,7,14,0.5000,1,"{5223, 3717, 2190, 2531, 6609, 2282, 6589}"
29,1,80,0,0.0857982,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcCsc[c*x])^3/x^2,x]","\frac{6 b^2 \left(a+b \csc ^{-1}(c x)\right)}{x}-3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{x}+6 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}","\frac{6 b^2 \left(a+b \csc ^{-1}(c x)\right)}{x}-3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{x}+6 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}",1,"6*b^3*c*Sqrt[1 - 1/(c^2*x^2)] + (6*b^2*(a + b*ArcCsc[c*x]))/x - 3*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x])^2 - (a + b*ArcCsc[c*x])^3/x","A",5,3,14,0.2143,1,"{5223, 3296, 2638}"
30,1,125,0,0.1049949,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^3}{x^3} \, dx","Int[(a + b*ArcCsc[c*x])^3/x^3,x]","\frac{3 b^2 \left(a+b \csc ^{-1}(c x)\right)}{4 x^2}-\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{4 x}+\frac{1}{4} c^2 \left(a+b \csc ^{-1}(c x)\right)^3-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{2 x^2}+\frac{3 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}}{8 x}-\frac{3}{8} b^3 c^2 \csc ^{-1}(c x)","\frac{3 b^2 \left(a+b \csc ^{-1}(c x)\right)}{4 x^2}-\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{4 x}+\frac{1}{4} c^2 \left(a+b \csc ^{-1}(c x)\right)^3-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{2 x^2}+\frac{3 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}}{8 x}-\frac{3}{8} b^3 c^2 \csc ^{-1}(c x)",1,"(3*b^3*c*Sqrt[1 - 1/(c^2*x^2)])/(8*x) - (3*b^3*c^2*ArcCsc[c*x])/8 + (3*b^2*(a + b*ArcCsc[c*x]))/(4*x^2) - (3*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x])^2)/(4*x) + (c^2*(a + b*ArcCsc[c*x])^3)/4 - (a + b*ArcCsc[c*x])^3/(2*x^2)","A",6,6,14,0.4286,1,"{5223, 4404, 3311, 32, 2635, 8}"
31,1,170,0,0.149797,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^3}{x^4} \, dx","Int[(a + b*ArcCsc[c*x])^3/x^4,x]","\frac{4 b^2 c^2 \left(a+b \csc ^{-1}(c x)\right)}{3 x}+\frac{2 b^2 \left(a+b \csc ^{-1}(c x)\right)}{9 x^3}-\frac{2}{3} b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{3 x^2}-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{3 x^3}-\frac{2}{27} b^3 c^3 \left(1-\frac{1}{c^2 x^2}\right)^{3/2}+\frac{14}{9} b^3 c^3 \sqrt{1-\frac{1}{c^2 x^2}}","\frac{4 b^2 c^2 \left(a+b \csc ^{-1}(c x)\right)}{3 x}+\frac{2 b^2 \left(a+b \csc ^{-1}(c x)\right)}{9 x^3}-\frac{2}{3} b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{3 x^2}-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{3 x^3}-\frac{2}{27} b^3 c^3 \left(1-\frac{1}{c^2 x^2}\right)^{3/2}+\frac{14}{9} b^3 c^3 \sqrt{1-\frac{1}{c^2 x^2}}",1,"(14*b^3*c^3*Sqrt[1 - 1/(c^2*x^2)])/9 - (2*b^3*c^3*(1 - 1/(c^2*x^2))^(3/2))/27 + (2*b^2*(a + b*ArcCsc[c*x]))/(9*x^3) + (4*b^2*c^2*(a + b*ArcCsc[c*x]))/(3*x) - (2*b*c^3*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x])^2)/3 - (b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x])^2)/(3*x^2) - (a + b*ArcCsc[c*x])^3/(3*x^3)","A",8,6,14,0.4286,1,"{5223, 4404, 3311, 3296, 2638, 2633}"
32,1,208,0,0.1759476,"\int \frac{\left(a+b \csc ^{-1}(c x)\right)^3}{x^5} \, dx","Int[(a + b*ArcCsc[c*x])^3/x^5,x]","\frac{9 b^2 c^2 \left(a+b \csc ^{-1}(c x)\right)}{32 x^2}+\frac{3 b^2 \left(a+b \csc ^{-1}(c x)\right)}{32 x^4}-\frac{9 b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{32 x}-\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{16 x^3}+\frac{3}{32} c^4 \left(a+b \csc ^{-1}(c x)\right)^3-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{4 x^4}+\frac{45 b^3 c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{256 x}+\frac{3 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}}{128 x^3}-\frac{45}{256} b^3 c^4 \csc ^{-1}(c x)","\frac{9 b^2 c^2 \left(a+b \csc ^{-1}(c x)\right)}{32 x^2}+\frac{3 b^2 \left(a+b \csc ^{-1}(c x)\right)}{32 x^4}-\frac{9 b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{32 x}-\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \csc ^{-1}(c x)\right)^2}{16 x^3}+\frac{3}{32} c^4 \left(a+b \csc ^{-1}(c x)\right)^3-\frac{\left(a+b \csc ^{-1}(c x)\right)^3}{4 x^4}+\frac{45 b^3 c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{256 x}+\frac{3 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}}{128 x^3}-\frac{45}{256} b^3 c^4 \csc ^{-1}(c x)",1,"(3*b^3*c*Sqrt[1 - 1/(c^2*x^2)])/(128*x^3) + (45*b^3*c^3*Sqrt[1 - 1/(c^2*x^2)])/(256*x) - (45*b^3*c^4*ArcCsc[c*x])/256 + (3*b^2*(a + b*ArcCsc[c*x]))/(32*x^4) + (9*b^2*c^2*(a + b*ArcCsc[c*x]))/(32*x^2) - (3*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x])^2)/(16*x^3) - (9*b*c^3*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcCsc[c*x])^2)/(32*x) + (3*c^4*(a + b*ArcCsc[c*x])^3)/32 - (a + b*ArcCsc[c*x])^3/(4*x^4)","A",10,6,14,0.4286,1,"{5223, 4404, 3311, 32, 2635, 8}"
33,0,0,0,0.0150766,"\int \frac{x}{a+b \csc ^{-1}(c x)} \, dx","Int[x/(a + b*ArcCsc[c*x]),x]","\int \frac{x}{a+b \csc ^{-1}(c x)} \, dx","\text{Int}\left(\frac{x}{a+b \csc ^{-1}(c x)},x\right)",0,"Defer[Int][x/(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
34,0,0,0,0.005974,"\int \frac{1}{a+b \csc ^{-1}(c x)} \, dx","Int[(a + b*ArcCsc[c*x])^(-1),x]","\int \frac{1}{a+b \csc ^{-1}(c x)} \, dx","\text{Int}\left(\frac{1}{a+b \csc ^{-1}(c x)},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])^(-1), x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0244585,"\int \frac{1}{x \left(a+b \csc ^{-1}(c x)\right)} \, dx","Int[1/(x*(a + b*ArcCsc[c*x])),x]","\int \frac{1}{x \left(a+b \csc ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \csc ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*ArcCsc[c*x])), x]","A",0,0,0,0,-1,"{}"
36,1,47,0,0.1061071,"\int \frac{1}{x^2 \left(a+b \csc ^{-1}(c x)\right)} \, dx","Int[1/(x^2*(a + b*ArcCsc[c*x])),x]","-\frac{c \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{b}-\frac{c \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{b}","-\frac{c \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{b}-\frac{c \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{b}",1,"-((c*Cos[a/b]*CosIntegral[a/b + ArcCsc[c*x]])/b) - (c*Sin[a/b]*SinIntegral[a/b + ArcCsc[c*x]])/b","A",4,4,14,0.2857,1,"{5223, 3303, 3299, 3302}"
37,1,63,0,0.1342879,"\int \frac{1}{x^3 \left(a+b \csc ^{-1}(c x)\right)} \, dx","Int[1/(x^3*(a + b*ArcCsc[c*x])),x]","\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \csc ^{-1}(c x)\right)}{2 b}-\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \csc ^{-1}(c x)\right)}{2 b}","\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \csc ^{-1}(c x)\right)}{2 b}-\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \csc ^{-1}(c x)\right)}{2 b}",1,"(c^2*CosIntegral[(2*a)/b + 2*ArcCsc[c*x]]*Sin[(2*a)/b])/(2*b) - (c^2*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcCsc[c*x]])/(2*b)","A",6,6,14,0.4286,1,"{5223, 4406, 12, 3303, 3299, 3302}"
38,1,117,0,0.2287545,"\int \frac{1}{x^4 \left(a+b \csc ^{-1}(c x)\right)} \, dx","Int[1/(x^4*(a + b*ArcCsc[c*x])),x]","-\frac{c^3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{4 b}+\frac{c^3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \csc ^{-1}(c x)\right)}{4 b}-\frac{c^3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{4 b}+\frac{c^3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \csc ^{-1}(c x)\right)}{4 b}","-\frac{c^3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{4 b}+\frac{c^3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \csc ^{-1}(c x)\right)}{4 b}-\frac{c^3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\csc ^{-1}(c x)\right)}{4 b}+\frac{c^3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \csc ^{-1}(c x)\right)}{4 b}",1,"-(c^3*Cos[a/b]*CosIntegral[a/b + ArcCsc[c*x]])/(4*b) + (c^3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcCsc[c*x]])/(4*b) - (c^3*Sin[a/b]*SinIntegral[a/b + ArcCsc[c*x]])/(4*b) + (c^3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcCsc[c*x]])/(4*b)","A",9,5,14,0.3571,1,"{5223, 4406, 3303, 3299, 3302}"
39,0,0,0,0.0235343,"\int (d x)^m \left(a+b \csc ^{-1}(c x)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcCsc[c*x])^3,x]","\int (d x)^m \left(a+b \csc ^{-1}(c x)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \csc ^{-1}(c x)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcCsc[c*x])^3, x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.024169,"\int (d x)^m \left(a+b \csc ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcCsc[c*x])^2,x]","\int (d x)^m \left(a+b \csc ^{-1}(c x)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \csc ^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcCsc[c*x])^2, x]","A",0,0,0,0,-1,"{}"
41,1,66,0,0.043359,"\int (d x)^m \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d*x)^m*(a + b*ArcCsc[c*x]),x]","\frac{(d x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{d (m+1)}+\frac{b (d x)^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{c^2 x^2}\right)}{c m (m+1)}","\frac{(d x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{d (m+1)}+\frac{b (d x)^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};\frac{1}{c^2 x^2}\right)}{c m (m+1)}",1,"((d*x)^(1 + m)*(a + b*ArcCsc[c*x]))/(d*(1 + m)) + (b*(d*x)^m*Hypergeometric2F1[1/2, -m/2, 1 - m/2, 1/(c^2*x^2)])/(c*m*(1 + m))","A",3,3,14,0.2143,1,"{5221, 339, 364}"
42,0,0,0,0.0257448,"\int \frac{(d x)^m}{a+b \csc ^{-1}(c x)} \, dx","Int[(d*x)^m/(a + b*ArcCsc[c*x]),x]","\int \frac{(d x)^m}{a+b \csc ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \csc ^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
43,0,0,0,0.0255385,"\int \frac{(d x)^m}{\left(a+b \csc ^{-1}(c x)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcCsc[c*x])^2,x]","\int \frac{(d x)^m}{\left(a+b \csc ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \csc ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcCsc[c*x])^2, x]","A",0,0,0,0,-1,"{}"
44,1,167,0,0.4018393,"\int (d+e x)^3 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcCsc[c*x]),x]","\frac{(d+e x)^4 \left(a+b \csc ^{-1}(c x)\right)}{4 e}+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}} \left(9 c^2 d^2+e^2\right)}{6 c^3}+\frac{b d \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{2 c^3}+\frac{b d e^2 x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}+\frac{b e^3 x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{12 c}-\frac{b d^4 \csc ^{-1}(c x)}{4 e}","\frac{(d+e x)^4 \left(a+b \csc ^{-1}(c x)\right)}{4 e}+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}} \left(9 c^2 d^2+e^2\right)}{6 c^3}+\frac{b d \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{2 c^3}+\frac{b d e^2 x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}+\frac{b e^3 x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{12 c}-\frac{b d^4 \csc ^{-1}(c x)}{4 e}",1,"(b*e*(9*c^2*d^2 + e^2)*Sqrt[1 - 1/(c^2*x^2)]*x)/(6*c^3) + (b*d*e^2*Sqrt[1 - 1/(c^2*x^2)]*x^2)/(2*c) + (b*e^3*Sqrt[1 - 1/(c^2*x^2)]*x^3)/(12*c) - (b*d^4*ArcCsc[c*x])/(4*e) + ((d + e*x)^4*(a + b*ArcCsc[c*x]))/(4*e) + (b*d*(2*c^2*d^2 + e^2)*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(2*c^3)","A",11,9,16,0.5625,1,"{5227, 1568, 1475, 1807, 844, 216, 266, 63, 208}"
45,1,123,0,0.2767662,"\int (d+e x)^2 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcCsc[c*x]),x]","\frac{(d+e x)^3 \left(a+b \csc ^{-1}(c x)\right)}{3 e}+\frac{b \left(6 c^2 d^2+e^2\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{6 c^3}+\frac{b d e x \sqrt{1-\frac{1}{c^2 x^2}}}{c}+\frac{b e^2 x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{6 c}-\frac{b d^3 \csc ^{-1}(c x)}{3 e}","\frac{(d+e x)^3 \left(a+b \csc ^{-1}(c x)\right)}{3 e}+\frac{b \left(6 c^2 d^2+e^2\right) \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{6 c^3}+\frac{b d e x \sqrt{1-\frac{1}{c^2 x^2}}}{c}+\frac{b e^2 x^2 \sqrt{1-\frac{1}{c^2 x^2}}}{6 c}-\frac{b d^3 \csc ^{-1}(c x)}{3 e}",1,"(b*d*e*Sqrt[1 - 1/(c^2*x^2)]*x)/c + (b*e^2*Sqrt[1 - 1/(c^2*x^2)]*x^2)/(6*c) - (b*d^3*ArcCsc[c*x])/(3*e) + ((d + e*x)^3*(a + b*ArcCsc[c*x]))/(3*e) + (b*(6*c^2*d^2 + e^2)*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(6*c^3)","A",10,9,16,0.5625,1,"{5227, 1568, 1475, 1807, 844, 216, 266, 63, 208}"
46,1,83,0,0.1666651,"\int (d+e x) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcCsc[c*x]),x]","\frac{(d+e x)^2 \left(a+b \csc ^{-1}(c x)\right)}{2 e}+\frac{b d \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}-\frac{b d^2 \csc ^{-1}(c x)}{2 e}","\frac{(d+e x)^2 \left(a+b \csc ^{-1}(c x)\right)}{2 e}+\frac{b d \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}-\frac{b d^2 \csc ^{-1}(c x)}{2 e}",1,"(b*e*Sqrt[1 - 1/(c^2*x^2)]*x)/(2*c) - (b*d^2*ArcCsc[c*x])/(2*e) + ((d + e*x)^2*(a + b*ArcCsc[c*x]))/(2*e) + (b*d*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c","A",9,9,14,0.6429,1,"{5227, 1568, 1396, 1807, 844, 216, 266, 63, 208}"
47,1,31,0,0.0229732,"\int \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[a + b*ArcCsc[c*x],x]","a x+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \csc ^{-1}(c x)","a x+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \csc ^{-1}(c x)",1,"a*x + b*x*ArcCsc[c*x] + (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c","A",5,4,8,0.5000,1,"{5215, 266, 63, 208}"
48,1,257,0,0.4059788,"\int \frac{a+b \csc ^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x),x]","-\frac{i b \text{PolyLog}\left(2,\frac{i \left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}-\frac{i b \text{PolyLog}\left(2,\frac{i \left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i \left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i \left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e}","-\frac{i b \text{PolyLog}\left(2,\frac{i \left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}-\frac{i b \text{PolyLog}\left(2,\frac{i \left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i \left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i \left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \csc ^{-1}(c x)}}{c d}\right)}{e}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e}",1,"((a + b*ArcCsc[c*x])*Log[1 - (I*(e - Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcCsc[c*x]))/(c*d)])/e + ((a + b*ArcCsc[c*x])*Log[1 - (I*(e + Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcCsc[c*x]))/(c*d)])/e - ((a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])])/e - (I*b*PolyLog[2, (I*(e - Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcCsc[c*x]))/(c*d)])/e - (I*b*PolyLog[2, (I*(e + Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcCsc[c*x]))/(c*d)])/e + ((I/2)*b*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/e","A",4,2,16,0.1250,1,"{5225, 2518}"
49,1,102,0,0.1554732,"\int \frac{a+b \csc ^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x)^2,x]","-\frac{a+b \csc ^{-1}(c x)}{e (d+e x)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{e}{x}}{c \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d^2-e^2}}\right)}{d \sqrt{c^2 d^2-e^2}}+\frac{b \csc ^{-1}(c x)}{d e}","-\frac{a+b \csc ^{-1}(c x)}{e (d+e x)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{e}{x}}{c \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d^2-e^2}}\right)}{d \sqrt{c^2 d^2-e^2}}+\frac{b \csc ^{-1}(c x)}{d e}",1,"(b*ArcCsc[c*x])/(d*e) - (a + b*ArcCsc[c*x])/(e*(d + e*x)) + (b*ArcTanh[(c^2*d + e/x)/(c*Sqrt[c^2*d^2 - e^2]*Sqrt[1 - 1/(c^2*x^2)])])/(d*Sqrt[c^2*d^2 - e^2])","A",7,7,16,0.4375,1,"{5227, 1568, 1475, 844, 216, 725, 206}"
50,1,172,0,0.2919052,"\int \frac{a+b \csc ^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x)^3,x]","-\frac{a+b \csc ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c e \sqrt{1-\frac{1}{c^2 x^2}}}{2 d \left(c^2 d^2-e^2\right) \left(\frac{d}{x}+e\right)}+\frac{b \left(2 c^2 d^2-e^2\right) \tanh ^{-1}\left(\frac{c^2 d+\frac{e}{x}}{c \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d^2-e^2}}\right)}{2 d^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b \csc ^{-1}(c x)}{2 d^2 e}","-\frac{a+b \csc ^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c e \sqrt{1-\frac{1}{c^2 x^2}}}{2 d \left(c^2 d^2-e^2\right) \left(\frac{d}{x}+e\right)}+\frac{b \left(2 c^2 d^2-e^2\right) \tanh ^{-1}\left(\frac{c^2 d+\frac{e}{x}}{c \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d^2-e^2}}\right)}{2 d^2 \left(c^2 d^2-e^2\right)^{3/2}}+\frac{b \csc ^{-1}(c x)}{2 d^2 e}",1,"-(b*c*e*Sqrt[1 - 1/(c^2*x^2)])/(2*d*(c^2*d^2 - e^2)*(e + d/x)) + (b*ArcCsc[c*x])/(2*d^2*e) - (a + b*ArcCsc[c*x])/(2*e*(d + e*x)^2) + (b*(2*c^2*d^2 - e^2)*ArcTanh[(c^2*d + e/x)/(c*Sqrt[c^2*d^2 - e^2]*Sqrt[1 - 1/(c^2*x^2)])])/(2*d^2*(c^2*d^2 - e^2)^(3/2))","A",8,8,16,0.5000,1,"{5227, 1568, 1475, 1651, 844, 216, 725, 206}"
51,1,693,0,2.8272952,"\int x^2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]),x]","\frac{2 d^2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}-\frac{4 d (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}+\frac{2 (d+e x)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^3}-\frac{32 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{32 b d^2 \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \sqrt{1-c^2 x^2} \left(c^2 d^2+3 e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{35 c^4 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{32 b d^4 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b d \sqrt{1-c^2 x^2} (c d-e) (c d+e) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^4 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b d \left(1-c^2 x^2\right) \sqrt{d+e x}}{105 c^3 e x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{4 b \left(1-c^2 x^2\right) (d+e x)^{3/2}}{35 c^3 e x \sqrt{1-\frac{1}{c^2 x^2}}}","\frac{2 d^2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}-\frac{4 d (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}+\frac{2 (d+e x)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^3}-\frac{4 b d \sqrt{1-c^2 x^2} \left(9 c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^4 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b \sqrt{1-c^2 x^2} \left(5 c^2 d^2-9 e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^4 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{32 b d^4 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b d \left(1-c^2 x^2\right) \sqrt{d+e x}}{105 c^3 e x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{4 b \left(1-c^2 x^2\right) (d+e x)^{3/2}}{35 c^3 e x \sqrt{1-\frac{1}{c^2 x^2}}}",1,"(4*b*d*Sqrt[d + e*x]*(1 - c^2*x^2))/(105*c^3*e*Sqrt[1 - 1/(c^2*x^2)]*x) - (4*b*(d + e*x)^(3/2)*(1 - c^2*x^2))/(35*c^3*e*Sqrt[1 - 1/(c^2*x^2)]*x) + (2*d^2*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^3) - (4*d*(d + e*x)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^3) + (2*(d + e*x)^(7/2)*(a + b*ArcCsc[c*x]))/(7*e^3) + (32*b*d^2*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(105*c^2*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*(c^2*d^2 + 3*e^2)*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(35*c^4*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (32*b*d^3*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(105*c^2*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*d*(c*d - e)*(c*d + e)*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(105*c^4*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*d^4*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(105*c*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",31,16,21,0.7619,1,"{43, 5247, 12, 6721, 6742, 743, 844, 719, 424, 419, 958, 932, 168, 538, 537, 833}"
52,1,502,0,2.1949149,"\int x \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]),x]","-\frac{2 d (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^2}+\frac{8 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{8 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{4 b \sqrt{1-c^2 x^2} (c d-e) (c d+e) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{8 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}","-\frac{2 d (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^2}+\frac{4 b \sqrt{1-c^2 x^2} \left(3 c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{8 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{8 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(-4*b*Sqrt[d + e*x]*(1 - c^2*x^2))/(15*c^3*Sqrt[1 - 1/(c^2*x^2)]*x) - (2*d*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^2) + (2*(d + e*x)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^2) - (8*b*d*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^2*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (8*b*d^2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^2*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (4*b*(c*d - e)*(c*d + e)*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^4*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (8*b*d^3*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",24,15,19,0.7895,1,"{43, 5247, 12, 6721, 6742, 743, 844, 719, 424, 419, 958, 932, 168, 538, 537}"
53,1,315,0,0.4849103,"\int \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x]*(a + b*ArcCsc[c*x]),x]","\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e}-\frac{4 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}","\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e}-\frac{4 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(2*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e) - (4*b*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*d*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*d^2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",15,11,18,0.6111,1,"{5227, 1574, 958, 719, 419, 933, 168, 538, 537, 844, 424}"
54,0,0,0,0.0708815,"\int \frac{\sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/x,x]","\int \frac{\sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][(Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
55,0,0,0,0.0757837,"\int \frac{\sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/x^2,x]","\int \frac{\sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][(Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
56,1,372,0,0.754832,"\int (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]),x]","\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e}-\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2+e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b e \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{28 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}","\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e}-\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2+e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b e \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{28 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(-4*b*e*Sqrt[d + e*x]*(1 - c^2*x^2))/(15*c^3*Sqrt[1 - 1/(c^2*x^2)]*x) + (2*(d + e*x)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e) - (28*b*d*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*(2*c^2*d^2 + e^2)*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^4*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*d^3*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*c*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",22,13,18,0.7222,1,"{5227, 1574, 958, 719, 419, 933, 168, 538, 537, 844, 424, 931, 1584}"
57,1,714,0,2.5894459,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x}} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x],x]","-\frac{2 d^3 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^4}+\frac{2 d^2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{e^4}-\frac{6 d (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^4}+\frac{2 (d+e x)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^4}+\frac{64 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{35 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{24 b d^2 \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{35 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2-9 e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^4 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{64 b d^4 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{35 c e^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b d \left(1-c^2 x^2\right) \sqrt{d+e x}}{21 c^3 e^2 x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{32 b d \sqrt{1-c^2 x^2} (c d-e) (c d+e) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^4 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{35 c^3 e \sqrt{1-\frac{1}{c^2 x^2}}}","-\frac{2 d^3 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^4}+\frac{2 d^2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{e^4}-\frac{6 d (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^4}+\frac{2 (d+e x)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^4}+\frac{64 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{35 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{24 b d^2 \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{35 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2-9 e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^4 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{64 b d^4 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{35 c e^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b d \left(1-c^2 x^2\right) \sqrt{d+e x}}{21 c^3 e^2 x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{32 b d \sqrt{1-c^2 x^2} (c d-e) (c d+e) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{105 c^4 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{35 c^3 e \sqrt{1-\frac{1}{c^2 x^2}}}",1,"(-4*b*Sqrt[d + e*x]*(1 - c^2*x^2))/(35*c^3*e*Sqrt[1 - 1/(c^2*x^2)]) + (4*b*d*Sqrt[d + e*x]*(1 - c^2*x^2))/(21*c^3*e^2*Sqrt[1 - 1/(c^2*x^2)]*x) - (2*d^3*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^4 + (2*d^2*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/e^4 - (6*d*(d + e*x)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^4) + (2*(d + e*x)^(7/2)*(a + b*ArcCsc[c*x]))/(7*e^4) - (24*b*d^2*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(35*c^2*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (4*b*(2*c^2*d^2 - 9*e^2)*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(105*c^4*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (64*b*d^3*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(35*c^2*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*d*(c*d - e)*(c*d + e)*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(105*c^4*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (64*b*d^4*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(35*c*e^4*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",27,17,21,0.8095,1,"{43, 5247, 12, 6721, 6742, 719, 424, 944, 419, 932, 168, 538, 537, 833, 844, 942, 1654}"
58,1,530,0,1.9073679,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x}} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x],x]","\frac{2 d^2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^3}-\frac{4 d (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}-\frac{32 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{32 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b \sqrt{1-c^2 x^2} (c d-e) (c d+e) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 e x \sqrt{1-\frac{1}{c^2 x^2}}}","\frac{2 d^2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^3}-\frac{4 d (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}-\frac{32 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{32 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b \sqrt{1-c^2 x^2} (c d-e) (c d+e) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 e x \sqrt{1-\frac{1}{c^2 x^2}}}",1,"(-4*b*Sqrt[d + e*x]*(1 - c^2*x^2))/(15*c^3*e*Sqrt[1 - 1/(c^2*x^2)]*x) + (2*d^2*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^3 - (4*d*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^3) + (2*(d + e*x)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^3) + (4*b*d*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*c^2*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (32*b*d^2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^2*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (4*b*(c*d - e)*(c*d + e)*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^4*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*d^3*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",20,15,21,0.7143,1,"{43, 5247, 12, 6721, 6742, 719, 424, 944, 419, 932, 168, 538, 537, 833, 844}"
59,1,344,0,1.6002797,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x}} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x],x]","-\frac{2 d \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{8 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{8 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}","-\frac{2 d \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{8 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{8 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(-2*d*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^2 + (2*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^2) - (4*b*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (8*b*d*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (8*b*d^2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",14,13,19,0.6842,1,"{43, 5247, 12, 6721, 6742, 719, 424, 944, 419, 932, 168, 538, 537}"
60,1,212,0,0.318515,"\int \frac{a+b \csc ^{-1}(c x)}{\sqrt{d+e x}} \, dx","Int[(a + b*ArcCsc[c*x])/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(2*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e - (4*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*d*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",9,9,18,0.5000,1,"{5227, 1574, 944, 719, 419, 933, 168, 538, 537}"
61,0,0,0,0.0722318,"\int \frac{a+b \csc ^{-1}(c x)}{x \sqrt{d+e x}} \, dx","Int[(a + b*ArcCsc[c*x])/(x*Sqrt[d + e*x]),x]","\int \frac{a+b \csc ^{-1}(c x)}{x \sqrt{d+e x}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x \sqrt{d+e x}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x*Sqrt[d + e*x]), x]","A",0,0,0,0,-1,"{}"
62,0,0,0,0.079183,"\int \frac{a+b \csc ^{-1}(c x)}{x^2 \sqrt{d+e x}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^2*Sqrt[d + e*x]),x]","\int \frac{a+b \csc ^{-1}(c x)}{x^2 \sqrt{d+e x}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x^2 \sqrt{d+e x}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x^2*Sqrt[d + e*x]), x]","A",0,0,0,0,-1,"{}"
63,1,551,0,2.4740435,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{(d+e x)^{3/2}} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/(d + e*x)^(3/2),x]","\frac{2 d^3 \left(a+b \csc ^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}+\frac{6 d^2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^4}-\frac{2 d (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^4}-\frac{8 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2+e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{64 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c e^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 e^2 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{32 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}","\frac{2 d^3 \left(a+b \csc ^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}+\frac{6 d^2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^4}-\frac{2 d (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^4}-\frac{8 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2+e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^4 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{64 b d^3 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c e^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \left(1-c^2 x^2\right) \sqrt{d+e x}}{15 c^3 e^2 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{32 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(-4*b*Sqrt[d + e*x]*(1 - c^2*x^2))/(15*c^3*e^2*Sqrt[1 - 1/(c^2*x^2)]*x) + (2*d^3*(a + b*ArcCsc[c*x]))/(e^4*Sqrt[d + e*x]) + (6*d^2*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^4 - (2*d*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/e^4 + (2*(d + e*x)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^4) + (32*b*d*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^2*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (8*b*d^2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c^2*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*(2*c^2*d^2 + e^2)*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*c^4*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (64*b*d^3*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*c*e^4*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",23,15,21,0.7143,1,"{43, 5247, 12, 6721, 6742, 719, 419, 932, 168, 538, 537, 844, 424, 931, 1584}"
64,1,369,0,1.8135079,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{(d+e x)^{3/2}} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/(d + e*x)^(3/2),x]","-\frac{2 d^2 \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}-\frac{4 d \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{32 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{20 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}","-\frac{2 d^2 \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}-\frac{4 d \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{32 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{20 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{\frac{c (d+e x)}{c d+e}}}",1,"(-2*d^2*(a + b*ArcCsc[c*x]))/(e^3*Sqrt[d + e*x]) - (4*d*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^3 + (2*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^3) - (4*b*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (20*b*d*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (32*b*d^2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",16,13,21,0.6190,1,"{43, 5247, 12, 6721, 6742, 719, 419, 932, 168, 538, 537, 844, 424}"
65,1,238,0,1.575277,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{(d+e x)^{3/2}} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{2 d \left(a+b \csc ^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}-\frac{8 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{2 d \left(a+b \csc ^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}-\frac{8 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(2*d*(a + b*ArcCsc[c*x]))/(e^2*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^2 - (4*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c^2*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (8*b*d*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",11,11,19,0.5789,1,"{43, 5247, 12, 6721, 6742, 719, 419, 932, 168, 538, 537}"
66,1,119,0,0.2253704,"\int \frac{a+b \csc ^{-1}(c x)}{(d+e x)^{3/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x)^(3/2),x]","\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{e \sqrt{d+e x}}","\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{e \sqrt{d+e x}}",1,"(-2*(a + b*ArcCsc[c*x]))/(e*Sqrt[d + e*x]) + (4*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",6,6,18,0.3333,1,"{5227, 1574, 933, 168, 538, 537}"
67,0,0,0,0.0889813,"\int \frac{a+b \csc ^{-1}(c x)}{x (d+e x)^{3/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x*(d + e*x)^(3/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x (d+e x)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x (d+e x)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x*(d + e*x)^(3/2)), x]","A",0,0,0,0,-1,"{}"
68,0,0,0,0.0938657,"\int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^2*(d + e*x)^(3/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x^2*(d + e*x)^(3/2)), x]","A",0,0,0,0,-1,"{}"
69,1,602,0,2.8957156,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{(d+e x)^{5/2}} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/(d + e*x)^(5/2),x]","\frac{2 d^3 \left(a+b \csc ^{-1}(c x)\right)}{3 e^4 (d+e x)^{3/2}}-\frac{6 d^2 \left(a+b \csc ^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}-\frac{6 d \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^4}-\frac{4 b d^2 \left(1-c^2 x^2\right)}{3 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{8 b d^2 \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2-e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{64 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{32 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","\frac{2 d^3 \left(a+b \csc ^{-1}(c x)\right)}{3 e^4 (d+e x)^{3/2}}-\frac{6 d^2 \left(a+b \csc ^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}-\frac{6 d \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^4}-\frac{4 b d^2 \left(1-c^2 x^2\right)}{3 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{8 b d^2 \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \sqrt{1-c^2 x^2} \left(2 c^2 d^2-e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{64 b d^2 \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^4 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}+\frac{32 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c^2 e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(-4*b*d^2*(1 - c^2*x^2))/(3*c*e^2*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (2*d^3*(a + b*ArcCsc[c*x]))/(3*e^4*(d + e*x)^(3/2)) - (6*d^2*(a + b*ArcCsc[c*x]))/(e^4*Sqrt[d + e*x]) - (6*d*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^4 + (2*(d + e*x)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^4) + (8*b*d^2*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*e^3*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*(2*c^2*d^2 - e^2)*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*e^3*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (32*b*d*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c^2*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (64*b*d^2*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*e^4*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",31,18,21,0.8571,1,"{43, 5247, 12, 6721, 6742, 745, 21, 719, 424, 958, 932, 168, 538, 537, 835, 844, 419, 1651}"
70,1,440,0,2.1847688,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{(d+e x)^{5/2}} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/(d + e*x)^(5/2),x]","-\frac{2 d^2 \left(a+b \csc ^{-1}(c x)\right)}{3 e^3 (d+e x)^{3/2}}+\frac{4 d \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{4 b d \left(1-c^2 x^2\right)}{3 c e x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{32 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","-\frac{2 d^2 \left(a+b \csc ^{-1}(c x)\right)}{3 e^3 (d+e x)^{3/2}}+\frac{4 d \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{4 b d \left(1-c^2 x^2\right)}{3 c e x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{4 b d \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{c^2 e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}-\frac{32 b d \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^3 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(4*b*d*(1 - c^2*x^2))/(3*c*e*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (2*d^2*(a + b*ArcCsc[c*x]))/(3*e^3*(d + e*x)^(3/2)) + (4*d*(a + b*ArcCsc[c*x]))/(e^3*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a + b*ArcCsc[c*x]))/e^3 - (4*b*d*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*e^2*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(c^2*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*d*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*e^3*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",25,17,21,0.8095,1,"{43, 5247, 12, 6721, 6742, 745, 21, 719, 424, 958, 932, 168, 538, 537, 835, 844, 419}"
71,1,314,0,2.0008222,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{(d+e x)^{5/2}} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/(d + e*x)^(5/2),x]","-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}+\frac{2 d \left(a+b \csc ^{-1}(c x)\right)}{3 e^2 (d+e x)^{3/2}}-\frac{4 b \left(1-c^2 x^2\right)}{3 c x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{8 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}+\frac{2 d \left(a+b \csc ^{-1}(c x)\right)}{3 e^2 (d+e x)^{3/2}}-\frac{4 b \left(1-c^2 x^2\right)}{3 c x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 e x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{8 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c e^2 x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(-4*b*(1 - c^2*x^2))/(3*c*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (2*d*(a + b*ArcCsc[c*x]))/(3*e^2*(d + e*x)^(3/2)) - (2*(a + b*ArcCsc[c*x]))/(e^2*Sqrt[d + e*x]) + (4*b*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*e*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (8*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*e^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",19,14,19,0.7368,1,"{43, 5247, 12, 6721, 6742, 745, 21, 719, 424, 958, 932, 168, 538, 537}"
72,1,298,0,0.4089263,"\int \frac{a+b \csc ^{-1}(c x)}{(d+e x)^{5/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x)^(5/2),x]","-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{3 e (d+e x)^{3/2}}+\frac{4 b e \left(1-c^2 x^2\right)}{3 c d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c d e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{3 e (d+e x)^{3/2}}+\frac{4 b e \left(1-c^2 x^2\right)}{3 c d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{3 c d e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(4*b*e*(1 - c^2*x^2))/(3*c*d*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (2*(a + b*ArcCsc[c*x]))/(3*e*(d + e*x)^(3/2)) - (4*b*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*d*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (4*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(3*c*d*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",12,11,18,0.6111,1,"{5227, 1574, 958, 745, 21, 719, 424, 933, 168, 538, 537}"
73,0,0,0,0.0881453,"\int \frac{a+b \csc ^{-1}(c x)}{x (d+e x)^{5/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x*(d + e*x)^(5/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x (d+e x)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x (d+e x)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x*(d + e*x)^(5/2)), x]","A",0,0,0,0,-1,"{}"
74,0,0,0,0.101364,"\int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{5/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^2*(d + e*x)^(5/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x^2 (d+e x)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x^2*(d + e*x)^(5/2)), x]","A",0,0,0,0,-1,"{}"
75,1,637,0,0.7516933,"\int \frac{a+b \csc ^{-1}(c x)}{(d+e x)^{7/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x)^(7/2),x]","-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{5 e (d+e x)^{5/2}}+\frac{16 b c e \left(1-c^2 x^2\right)}{15 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right)^2 \sqrt{d+e x}}+\frac{4 b e \left(1-c^2 x^2\right)}{5 c d^2 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{4 b e \left(1-c^2 x^2\right)}{15 c d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) (d+e x)^{3/2}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{16 b c^2 \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right)^2 \sqrt{\frac{c (d+e x)}{c d+e}}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 d^2 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c d^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}","-\frac{2 \left(a+b \csc ^{-1}(c x)\right)}{5 e (d+e x)^{5/2}}+\frac{4 b e \left(1-c^2 x^2\right)}{5 c d^2 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}+\frac{16 b c e \left(1-c^2 x^2\right)}{15 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right)^2 \sqrt{d+e x}}+\frac{4 b e \left(1-c^2 x^2\right)}{15 c d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) (d+e x)^{3/2}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 d x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^2-e^2\right) \sqrt{d+e x}}-\frac{4 b \sqrt{1-c^2 x^2} \left(7 c^2 d^2-3 e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{15 x \sqrt{1-\frac{1}{c^2 x^2}} \left(c^2 d^3-d e^2\right)^2 \sqrt{\frac{c (d+e x)}{c d+e}}}+\frac{4 b \sqrt{1-c^2 x^2} \sqrt{\frac{c (d+e x)}{c d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{2}}\right)|\frac{2 e}{c d+e}\right)}{5 c d^2 e x \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{d+e x}}",1,"(4*b*e*(1 - c^2*x^2))/(15*c*d*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*(d + e*x)^(3/2)) + (16*b*c*e*(1 - c^2*x^2))/(15*(c^2*d^2 - e^2)^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (4*b*e*(1 - c^2*x^2))/(5*c*d^2*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (2*(a + b*ArcCsc[c*x]))/(5*e*(d + e*x)^(5/2)) - (16*b*c^2*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*(c^2*d^2 - e^2)^2*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) - (4*b*Sqrt[d + e*x]*Sqrt[1 - c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*d^2*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[(c*(d + e*x))/(c*d + e)]) + (4*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(15*d*(c^2*d^2 - e^2)*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (4*b*Sqrt[(c*(d + e*x))/(c*d + e)]*Sqrt[1 - c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - c*x]/Sqrt[2]], (2*e)/(c*d + e)])/(5*c*d^2*e*Sqrt[1 - 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",19,14,18,0.7778,1,"{5227, 1574, 958, 745, 835, 844, 719, 424, 419, 21, 933, 168, 538, 537}"
76,1,206,0,0.125028,"\int x^4 \left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)*(a + b*ArcCsc[c*x]),x]","\frac{1}{5} d x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^4 \sqrt{c^2 x^2-1} \left(42 c^2 d+25 e\right)}{840 c^3 \sqrt{c^2 x^2}}+\frac{b x^2 \sqrt{c^2 x^2-1} \left(42 c^2 d+25 e\right)}{560 c^5 \sqrt{c^2 x^2}}+\frac{b x \left(42 c^2 d+25 e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{560 c^6 \sqrt{c^2 x^2}}+\frac{b e x^6 \sqrt{c^2 x^2-1}}{42 c \sqrt{c^2 x^2}}","\frac{1}{5} d x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^4 \sqrt{c^2 x^2-1} \left(42 c^2 d+25 e\right)}{840 c^3 \sqrt{c^2 x^2}}+\frac{b x^2 \sqrt{c^2 x^2-1} \left(42 c^2 d+25 e\right)}{560 c^5 \sqrt{c^2 x^2}}+\frac{b x \left(42 c^2 d+25 e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{560 c^6 \sqrt{c^2 x^2}}+\frac{b e x^6 \sqrt{c^2 x^2-1}}{42 c \sqrt{c^2 x^2}}",1,"(b*(42*c^2*d + 25*e)*x^2*Sqrt[-1 + c^2*x^2])/(560*c^5*Sqrt[c^2*x^2]) + (b*(42*c^2*d + 25*e)*x^4*Sqrt[-1 + c^2*x^2])/(840*c^3*Sqrt[c^2*x^2]) + (b*e*x^6*Sqrt[-1 + c^2*x^2])/(42*c*Sqrt[c^2*x^2]) + (d*x^5*(a + b*ArcCsc[c*x]))/5 + (e*x^7*(a + b*ArcCsc[c*x]))/7 + (b*(42*c^2*d + 25*e)*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(560*c^6*Sqrt[c^2*x^2])","A",7,7,19,0.3684,1,"{14, 5239, 12, 459, 321, 217, 206}"
77,1,161,0,0.1077956,"\int x^2 \left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)*(a + b*ArcCsc[c*x]),x]","\frac{1}{3} d x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^2 \sqrt{c^2 x^2-1} \left(20 c^2 d+9 e\right)}{120 c^3 \sqrt{c^2 x^2}}+\frac{b x \left(20 c^2 d+9 e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{120 c^4 \sqrt{c^2 x^2}}+\frac{b e x^4 \sqrt{c^2 x^2-1}}{20 c \sqrt{c^2 x^2}}","\frac{1}{3} d x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^2 \sqrt{c^2 x^2-1} \left(20 c^2 d+9 e\right)}{120 c^3 \sqrt{c^2 x^2}}+\frac{b x \left(20 c^2 d+9 e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{120 c^4 \sqrt{c^2 x^2}}+\frac{b e x^4 \sqrt{c^2 x^2-1}}{20 c \sqrt{c^2 x^2}}",1,"(b*(20*c^2*d + 9*e)*x^2*Sqrt[-1 + c^2*x^2])/(120*c^3*Sqrt[c^2*x^2]) + (b*e*x^4*Sqrt[-1 + c^2*x^2])/(20*c*Sqrt[c^2*x^2]) + (d*x^3*(a + b*ArcCsc[c*x]))/3 + (e*x^5*(a + b*ArcCsc[c*x]))/5 + (b*(20*c^2*d + 9*e)*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(120*c^4*Sqrt[c^2*x^2])","A",6,7,19,0.3684,1,"{14, 5239, 12, 459, 321, 217, 206}"
78,1,109,0,0.0509346,"\int \left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)*(a + b*ArcCsc[c*x]),x]","d x \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(6 c^2 d+e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{6 c^2 \sqrt{c^2 x^2}}+\frac{b e x^2 \sqrt{c^2 x^2-1}}{6 c \sqrt{c^2 x^2}}","d x \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(6 c^2 d+e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{6 c^2 \sqrt{c^2 x^2}}+\frac{b e x^2 \sqrt{c^2 x^2-1}}{6 c \sqrt{c^2 x^2}}",1,"(b*e*x^2*Sqrt[-1 + c^2*x^2])/(6*c*Sqrt[c^2*x^2]) + d*x*(a + b*ArcCsc[c*x]) + (e*x^3*(a + b*ArcCsc[c*x]))/3 + (b*(6*c^2*d + e)*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(6*c^2*Sqrt[c^2*x^2])","A",5,5,16,0.3125,1,"{5229, 12, 388, 217, 206}"
79,1,87,0,0.0645933,"\int \frac{\left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)*(a + b*ArcCsc[c*x]))/x^2,x]","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{x}+e x \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d \sqrt{c^2 x^2-1}}{\sqrt{c^2 x^2}}+\frac{b e x \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{\sqrt{c^2 x^2}}","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{x}+e x \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d \sqrt{c^2 x^2-1}}{\sqrt{c^2 x^2}}+\frac{b e x \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{\sqrt{c^2 x^2}}",1,"-((b*c*d*Sqrt[-1 + c^2*x^2])/Sqrt[c^2*x^2]) - (d*(a + b*ArcCsc[c*x]))/x + e*x*(a + b*ArcCsc[c*x]) + (b*e*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/Sqrt[c^2*x^2]","A",4,5,19,0.2632,1,"{14, 5239, 451, 217, 206}"
80,1,105,0,0.0783417,"\int \frac{\left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)*(a + b*ArcCsc[c*x]))/x^4,x]","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{x}-\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d+9 e\right)}{9 \sqrt{c^2 x^2}}-\frac{b c d \sqrt{c^2 x^2-1}}{9 x^2 \sqrt{c^2 x^2}}","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{x}-\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d+9 e\right)}{9 \sqrt{c^2 x^2}}-\frac{b c d \sqrt{c^2 x^2-1}}{9 x^2 \sqrt{c^2 x^2}}",1,"-(b*c*(2*c^2*d + 9*e)*Sqrt[-1 + c^2*x^2])/(9*Sqrt[c^2*x^2]) - (b*c*d*Sqrt[-1 + c^2*x^2])/(9*x^2*Sqrt[c^2*x^2]) - (d*(a + b*ArcCsc[c*x]))/(3*x^3) - (e*(a + b*ArcCsc[c*x]))/x","A",4,5,19,0.2632,1,"{14, 5239, 12, 453, 264}"
81,1,152,0,0.0921755,"\int \frac{\left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)*(a + b*ArcCsc[c*x]))/x^6,x]","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{2 b c^3 \sqrt{c^2 x^2-1} \left(12 c^2 d+25 e\right)}{225 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(12 c^2 d+25 e\right)}{225 x^2 \sqrt{c^2 x^2}}-\frac{b c d \sqrt{c^2 x^2-1}}{25 x^4 \sqrt{c^2 x^2}}","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{2 b c^3 \sqrt{c^2 x^2-1} \left(12 c^2 d+25 e\right)}{225 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(12 c^2 d+25 e\right)}{225 x^2 \sqrt{c^2 x^2}}-\frac{b c d \sqrt{c^2 x^2-1}}{25 x^4 \sqrt{c^2 x^2}}",1,"(-2*b*c^3*(12*c^2*d + 25*e)*Sqrt[-1 + c^2*x^2])/(225*Sqrt[c^2*x^2]) - (b*c*d*Sqrt[-1 + c^2*x^2])/(25*x^4*Sqrt[c^2*x^2]) - (b*c*(12*c^2*d + 25*e)*Sqrt[-1 + c^2*x^2])/(225*x^2*Sqrt[c^2*x^2]) - (d*(a + b*ArcCsc[c*x]))/(5*x^5) - (e*(a + b*ArcCsc[c*x]))/(3*x^3)","A",5,6,19,0.3158,1,"{14, 5239, 12, 453, 271, 264}"
82,1,197,0,0.1180375,"\int \frac{\left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)*(a + b*ArcCsc[c*x]))/x^8,x]","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{8 b c^5 \sqrt{c^2 x^2-1} \left(30 c^2 d+49 e\right)}{3675 \sqrt{c^2 x^2}}-\frac{4 b c^3 \sqrt{c^2 x^2-1} \left(30 c^2 d+49 e\right)}{3675 x^2 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(30 c^2 d+49 e\right)}{1225 x^4 \sqrt{c^2 x^2}}-\frac{b c d \sqrt{c^2 x^2-1}}{49 x^6 \sqrt{c^2 x^2}}","-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{8 b c^5 \sqrt{c^2 x^2-1} \left(30 c^2 d+49 e\right)}{3675 \sqrt{c^2 x^2}}-\frac{4 b c^3 \sqrt{c^2 x^2-1} \left(30 c^2 d+49 e\right)}{3675 x^2 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(30 c^2 d+49 e\right)}{1225 x^4 \sqrt{c^2 x^2}}-\frac{b c d \sqrt{c^2 x^2-1}}{49 x^6 \sqrt{c^2 x^2}}",1,"(-8*b*c^5*(30*c^2*d + 49*e)*Sqrt[-1 + c^2*x^2])/(3675*Sqrt[c^2*x^2]) - (b*c*d*Sqrt[-1 + c^2*x^2])/(49*x^6*Sqrt[c^2*x^2]) - (b*c*(30*c^2*d + 49*e)*Sqrt[-1 + c^2*x^2])/(1225*x^4*Sqrt[c^2*x^2]) - (4*b*c^3*(30*c^2*d + 49*e)*Sqrt[-1 + c^2*x^2])/(3675*x^2*Sqrt[c^2*x^2]) - (d*(a + b*ArcCsc[c*x]))/(7*x^7) - (e*(a + b*ArcCsc[c*x]))/(5*x^5)","A",6,6,19,0.3158,1,"{14, 5239, 12, 453, 271, 264}"
83,1,196,0,0.1503328,"\int x^5 \left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^5*(d + e*x^2)*(a + b*ArcCsc[c*x]),x]","\frac{1}{6} d x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(c^2 x^2-1\right)^{5/2} \left(4 c^2 d+9 e\right)}{120 c^7 \sqrt{c^2 x^2}}+\frac{b x \left(c^2 x^2-1\right)^{3/2} \left(8 c^2 d+9 e\right)}{72 c^7 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(4 c^2 d+3 e\right)}{24 c^7 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{c^2 x^2}}","\frac{1}{6} d x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(c^2 x^2-1\right)^{5/2} \left(4 c^2 d+9 e\right)}{120 c^7 \sqrt{c^2 x^2}}+\frac{b x \left(c^2 x^2-1\right)^{3/2} \left(8 c^2 d+9 e\right)}{72 c^7 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(4 c^2 d+3 e\right)}{24 c^7 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{c^2 x^2}}",1,"(b*(4*c^2*d + 3*e)*x*Sqrt[-1 + c^2*x^2])/(24*c^7*Sqrt[c^2*x^2]) + (b*(8*c^2*d + 9*e)*x*(-1 + c^2*x^2)^(3/2))/(72*c^7*Sqrt[c^2*x^2]) + (b*(4*c^2*d + 9*e)*x*(-1 + c^2*x^2)^(5/2))/(120*c^7*Sqrt[c^2*x^2]) + (b*e*x*(-1 + c^2*x^2)^(7/2))/(56*c^7*Sqrt[c^2*x^2]) + (d*x^6*(a + b*ArcCsc[c*x]))/6 + (e*x^8*(a + b*ArcCsc[c*x]))/8","A",5,5,19,0.2632,1,"{14, 5239, 12, 446, 77}"
84,1,153,0,0.121809,"\int x^3 \left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)*(a + b*ArcCsc[c*x]),x]","\frac{1}{4} d x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(c^2 x^2-1\right)^{3/2} \left(3 c^2 d+4 e\right)}{36 c^5 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(3 c^2 d+2 e\right)}{12 c^5 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{c^2 x^2}}","\frac{1}{4} d x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(c^2 x^2-1\right)^{3/2} \left(3 c^2 d+4 e\right)}{36 c^5 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(3 c^2 d+2 e\right)}{12 c^5 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{c^2 x^2}}",1,"(b*(3*c^2*d + 2*e)*x*Sqrt[-1 + c^2*x^2])/(12*c^5*Sqrt[c^2*x^2]) + (b*(3*c^2*d + 4*e)*x*(-1 + c^2*x^2)^(3/2))/(36*c^5*Sqrt[c^2*x^2]) + (b*e*x*(-1 + c^2*x^2)^(5/2))/(30*c^5*Sqrt[c^2*x^2]) + (d*x^4*(a + b*ArcCsc[c*x]))/4 + (e*x^6*(a + b*ArcCsc[c*x]))/6","A",5,5,19,0.2632,1,"{14, 5239, 12, 446, 77}"
85,1,138,0,0.0957639,"\int x \left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)*(a + b*ArcCsc[c*x]),x]","\frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{4 e}+\frac{b c d^2 x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{4 e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right)}{4 c^3 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{3/2}}{12 c^3 \sqrt{c^2 x^2}}","\frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{4 e}+\frac{b c d^2 x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{4 e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(2 c^2 d+e\right)}{4 c^3 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{3/2}}{12 c^3 \sqrt{c^2 x^2}}",1,"(b*(2*c^2*d + e)*x*Sqrt[-1 + c^2*x^2])/(4*c^3*Sqrt[c^2*x^2]) + (b*e*x*(-1 + c^2*x^2)^(3/2))/(12*c^3*Sqrt[c^2*x^2]) + ((d + e*x^2)^2*(a + b*ArcCsc[c*x]))/(4*e) + (b*c*d^2*x*ArcTan[Sqrt[-1 + c^2*x^2]])/(4*e*Sqrt[c^2*x^2])","A",6,5,17,0.2941,1,"{5237, 446, 88, 63, 205}"
86,1,124,0,0.2861937,"\int \frac{\left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)*(a + b*ArcCsc[c*x]))/x,x]","\frac{1}{2} i b d \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-d \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \csc ^{-1}(c x)\right)+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}+\frac{1}{2} i b d \csc ^{-1}(c x)^2-b d \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+b d \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)","\frac{1}{2} i b d \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-d \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \csc ^{-1}(c x)\right)+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}+\frac{1}{2} i b d \csc ^{-1}(c x)^2-b d \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+b d \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)",1,"(b*e*Sqrt[1 - 1/(c^2*x^2)]*x)/(2*c) + (I/2)*b*d*ArcCsc[c*x]^2 + (e*x^2*(a + b*ArcCsc[c*x]))/2 - b*d*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])] + b*d*ArcCsc[c*x]*Log[x^(-1)] - d*(a + b*ArcCsc[c*x])*Log[x^(-1)] + (I/2)*b*d*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",11,11,19,0.5789,1,"{5241, 14, 4731, 6742, 264, 2326, 4625, 3717, 2190, 2279, 2391}"
87,1,137,0,0.3023966,"\int \frac{\left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)*(a + b*ArcCsc[c*x]))/x^3,x]","\frac{1}{2} i b e \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d \sqrt{1-\frac{1}{c^2 x^2}}}{4 x}+\frac{1}{4} b c^2 d \csc ^{-1}(c x)+\frac{1}{2} i b e \csc ^{-1}(c x)^2-b e \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+b e \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)","\frac{1}{2} i b e \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d \sqrt{1-\frac{1}{c^2 x^2}}}{4 x}+\frac{1}{4} b c^2 d \csc ^{-1}(c x)+\frac{1}{2} i b e \csc ^{-1}(c x)^2-b e \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+b e \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)",1,"-(b*c*d*Sqrt[1 - 1/(c^2*x^2)])/(4*x) + (b*c^2*d*ArcCsc[c*x])/4 + (I/2)*b*e*ArcCsc[c*x]^2 - (d*(a + b*ArcCsc[c*x]))/(2*x^2) - b*e*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])] + b*e*ArcCsc[c*x]*Log[x^(-1)] - e*(a + b*ArcCsc[c*x])*Log[x^(-1)] + (I/2)*b*e*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",13,13,19,0.6842,1,"{5241, 14, 4731, 12, 6742, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
88,1,252,0,0.2371424,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*ArcCsc[c*x]),x]","\frac{1}{3} d^2 x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^2 \sqrt{c^2 x^2-1} \left(280 c^4 d^2+252 c^2 d e+75 e^2\right)}{1680 c^5 \sqrt{c^2 x^2}}+\frac{b x \left(280 c^4 d^2+252 c^2 d e+75 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{1680 c^6 \sqrt{c^2 x^2}}+\frac{b e x^4 \sqrt{c^2 x^2-1} \left(84 c^2 d+25 e\right)}{840 c^3 \sqrt{c^2 x^2}}+\frac{b e^2 x^6 \sqrt{c^2 x^2-1}}{42 c \sqrt{c^2 x^2}}","\frac{1}{3} d^2 x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x^2 \sqrt{c^2 x^2-1} \left(280 c^4 d^2+252 c^2 d e+75 e^2\right)}{1680 c^5 \sqrt{c^2 x^2}}+\frac{b x \left(280 c^4 d^2+252 c^2 d e+75 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{1680 c^6 \sqrt{c^2 x^2}}+\frac{b e x^4 \sqrt{c^2 x^2-1} \left(84 c^2 d+25 e\right)}{840 c^3 \sqrt{c^2 x^2}}+\frac{b e^2 x^6 \sqrt{c^2 x^2-1}}{42 c \sqrt{c^2 x^2}}",1,"(b*(280*c^4*d^2 + 252*c^2*d*e + 75*e^2)*x^2*Sqrt[-1 + c^2*x^2])/(1680*c^5*Sqrt[c^2*x^2]) + (b*e*(84*c^2*d + 25*e)*x^4*Sqrt[-1 + c^2*x^2])/(840*c^3*Sqrt[c^2*x^2]) + (b*e^2*x^6*Sqrt[-1 + c^2*x^2])/(42*c*Sqrt[c^2*x^2]) + (d^2*x^3*(a + b*ArcCsc[c*x]))/3 + (2*d*e*x^5*(a + b*ArcCsc[c*x]))/5 + (e^2*x^7*(a + b*ArcCsc[c*x]))/7 + (b*(280*c^4*d^2 + 252*c^2*d*e + 75*e^2)*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(1680*c^6*Sqrt[c^2*x^2])","A",7,8,21,0.3810,1,"{270, 5239, 12, 1267, 459, 321, 217, 206}"
89,1,191,0,0.1141116,"\int \left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^2*(a + b*ArcCsc[c*x]),x]","d^2 x \left(a+b \csc ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(120 c^4 d^2+40 c^2 d e+9 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{120 c^4 \sqrt{c^2 x^2}}+\frac{b e x^2 \sqrt{c^2 x^2-1} \left(40 c^2 d+9 e\right)}{120 c^3 \sqrt{c^2 x^2}}+\frac{b e^2 x^4 \sqrt{c^2 x^2-1}}{20 c \sqrt{c^2 x^2}}","d^2 x \left(a+b \csc ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(120 c^4 d^2+40 c^2 d e+9 e^2\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{120 c^4 \sqrt{c^2 x^2}}+\frac{b e x^2 \sqrt{c^2 x^2-1} \left(40 c^2 d+9 e\right)}{120 c^3 \sqrt{c^2 x^2}}+\frac{b e^2 x^4 \sqrt{c^2 x^2-1}}{20 c \sqrt{c^2 x^2}}",1,"(b*e*(40*c^2*d + 9*e)*x^2*Sqrt[-1 + c^2*x^2])/(120*c^3*Sqrt[c^2*x^2]) + (b*e^2*x^4*Sqrt[-1 + c^2*x^2])/(20*c*Sqrt[c^2*x^2]) + d^2*x*(a + b*ArcCsc[c*x]) + (2*d*e*x^3*(a + b*ArcCsc[c*x]))/3 + (e^2*x^5*(a + b*ArcCsc[c*x]))/5 + (b*(120*c^4*d^2 + 40*c^2*d*e + 9*e^2)*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(120*c^4*Sqrt[c^2*x^2])","A",6,7,18,0.3889,1,"{194, 5229, 12, 1159, 388, 217, 206}"
90,1,163,0,0.1295229,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsc[c*x]))/x^2,x]","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{c^2 x^2-1}}{\sqrt{c^2 x^2}}+\frac{b e x \left(12 c^2 d+e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{6 c^2 \sqrt{c^2 x^2}}+\frac{b e^2 x^2 \sqrt{c^2 x^2-1}}{6 c \sqrt{c^2 x^2}}","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{c^2 x^2-1}}{\sqrt{c^2 x^2}}+\frac{b e x \left(12 c^2 d+e\right) \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{6 c^2 \sqrt{c^2 x^2}}+\frac{b e^2 x^2 \sqrt{c^2 x^2-1}}{6 c \sqrt{c^2 x^2}}",1,"-((b*c*d^2*Sqrt[-1 + c^2*x^2])/Sqrt[c^2*x^2]) + (b*e^2*x^2*Sqrt[-1 + c^2*x^2])/(6*c*Sqrt[c^2*x^2]) - (d^2*(a + b*ArcCsc[c*x]))/x + 2*d*e*x*(a + b*ArcCsc[c*x]) + (e^2*x^3*(a + b*ArcCsc[c*x]))/3 + (b*e*(12*c^2*d + e)*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/(6*c^2*Sqrt[c^2*x^2])","A",6,7,21,0.3333,1,"{270, 5239, 12, 1265, 388, 217, 206}"
91,1,157,0,0.1324832,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsc[c*x]))/x^4,x]","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \csc ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{c^2 x^2-1}}{9 x^2 \sqrt{c^2 x^2}}-\frac{2 b c d \sqrt{c^2 x^2-1} \left(c^2 d+9 e\right)}{9 \sqrt{c^2 x^2}}+\frac{b e^2 x \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{\sqrt{c^2 x^2}}","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \csc ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{c^2 x^2-1}}{9 x^2 \sqrt{c^2 x^2}}-\frac{2 b c d \sqrt{c^2 x^2-1} \left(c^2 d+9 e\right)}{9 \sqrt{c^2 x^2}}+\frac{b e^2 x \tanh ^{-1}\left(\frac{c x}{\sqrt{c^2 x^2-1}}\right)}{\sqrt{c^2 x^2}}",1,"(-2*b*c*d*(c^2*d + 9*e)*Sqrt[-1 + c^2*x^2])/(9*Sqrt[c^2*x^2]) - (b*c*d^2*Sqrt[-1 + c^2*x^2])/(9*x^2*Sqrt[c^2*x^2]) - (d^2*(a + b*ArcCsc[c*x]))/(3*x^3) - (2*d*e*(a + b*ArcCsc[c*x]))/x + e^2*x*(a + b*ArcCsc[c*x]) + (b*e^2*x*ArcTanh[(c*x)/Sqrt[-1 + c^2*x^2]])/Sqrt[c^2*x^2]","A",6,7,21,0.3333,1,"{270, 5239, 12, 1265, 451, 217, 206}"
92,1,183,0,0.1601781,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsc[c*x]))/x^6,x]","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \csc ^{-1}(c x)\right)}{x}-\frac{b c \sqrt{c^2 x^2-1} \left(24 c^4 d^2+100 c^2 d e+225 e^2\right)}{225 \sqrt{c^2 x^2}}-\frac{b c d^2 \sqrt{c^2 x^2-1}}{25 x^4 \sqrt{c^2 x^2}}-\frac{2 b c d \sqrt{c^2 x^2-1} \left(6 c^2 d+25 e\right)}{225 x^2 \sqrt{c^2 x^2}}","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \csc ^{-1}(c x)\right)}{x}-\frac{b c \sqrt{c^2 x^2-1} \left(24 c^4 d^2+100 c^2 d e+225 e^2\right)}{225 \sqrt{c^2 x^2}}-\frac{b c d^2 \sqrt{c^2 x^2-1}}{25 x^4 \sqrt{c^2 x^2}}-\frac{2 b c d \sqrt{c^2 x^2-1} \left(6 c^2 d+25 e\right)}{225 x^2 \sqrt{c^2 x^2}}",1,"-(b*c*(24*c^4*d^2 + 100*c^2*d*e + 225*e^2)*Sqrt[-1 + c^2*x^2])/(225*Sqrt[c^2*x^2]) - (b*c*d^2*Sqrt[-1 + c^2*x^2])/(25*x^4*Sqrt[c^2*x^2]) - (2*b*c*d*(6*c^2*d + 25*e)*Sqrt[-1 + c^2*x^2])/(225*x^2*Sqrt[c^2*x^2]) - (d^2*(a + b*ArcCsc[c*x]))/(5*x^5) - (2*d*e*(a + b*ArcCsc[c*x]))/(3*x^3) - (e^2*(a + b*ArcCsc[c*x]))/x","A",5,6,21,0.2857,1,"{270, 5239, 12, 1265, 453, 264}"
93,1,241,0,0.1969189,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsc[c*x]))/x^8,x]","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{2 b c^3 \sqrt{c^2 x^2-1} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 x^2 \sqrt{c^2 x^2}}-\frac{b c d^2 \sqrt{c^2 x^2-1}}{49 x^6 \sqrt{c^2 x^2}}-\frac{2 b c d \sqrt{c^2 x^2-1} \left(15 c^2 d+49 e\right)}{1225 x^4 \sqrt{c^2 x^2}}","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \csc ^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \csc ^{-1}(c x)\right)}{3 x^3}-\frac{2 b c^3 \sqrt{c^2 x^2-1} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(360 c^4 d^2+1176 c^2 d e+1225 e^2\right)}{11025 x^2 \sqrt{c^2 x^2}}-\frac{b c d^2 \sqrt{c^2 x^2-1}}{49 x^6 \sqrt{c^2 x^2}}-\frac{2 b c d \sqrt{c^2 x^2-1} \left(15 c^2 d+49 e\right)}{1225 x^4 \sqrt{c^2 x^2}}",1,"(-2*b*c^3*(360*c^4*d^2 + 1176*c^2*d*e + 1225*e^2)*Sqrt[-1 + c^2*x^2])/(11025*Sqrt[c^2*x^2]) - (b*c*d^2*Sqrt[-1 + c^2*x^2])/(49*x^6*Sqrt[c^2*x^2]) - (2*b*c*d*(15*c^2*d + 49*e)*Sqrt[-1 + c^2*x^2])/(1225*x^4*Sqrt[c^2*x^2]) - (b*c*(360*c^4*d^2 + 1176*c^2*d*e + 1225*e^2)*Sqrt[-1 + c^2*x^2])/(11025*x^2*Sqrt[c^2*x^2]) - (d^2*(a + b*ArcCsc[c*x]))/(7*x^7) - (2*d*e*(a + b*ArcCsc[c*x]))/(5*x^5) - (e^2*(a + b*ArcCsc[c*x]))/(3*x^3)","A",6,7,21,0.3333,1,"{270, 5239, 12, 1265, 453, 271, 264}"
94,1,242,0,0.2231235,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*ArcCsc[c*x]),x]","\frac{1}{4} d^2 x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(c^2 x^2-1\right)^{3/2} \left(6 c^4 d^2+16 c^2 d e+9 e^2\right)}{72 c^7 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(6 c^4 d^2+8 c^2 d e+3 e^2\right)}{24 c^7 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{5/2} \left(8 c^2 d+9 e\right)}{120 c^7 \sqrt{c^2 x^2}}+\frac{b e^2 x \left(c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{c^2 x^2}}","\frac{1}{4} d^2 x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \csc ^{-1}(c x)\right)+\frac{b x \left(c^2 x^2-1\right)^{3/2} \left(6 c^4 d^2+16 c^2 d e+9 e^2\right)}{72 c^7 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(6 c^4 d^2+8 c^2 d e+3 e^2\right)}{24 c^7 \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{5/2} \left(8 c^2 d+9 e\right)}{120 c^7 \sqrt{c^2 x^2}}+\frac{b e^2 x \left(c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{c^2 x^2}}",1,"(b*(6*c^4*d^2 + 8*c^2*d*e + 3*e^2)*x*Sqrt[-1 + c^2*x^2])/(24*c^7*Sqrt[c^2*x^2]) + (b*(6*c^4*d^2 + 16*c^2*d*e + 9*e^2)*x*(-1 + c^2*x^2)^(3/2))/(72*c^7*Sqrt[c^2*x^2]) + (b*e*(8*c^2*d + 9*e)*x*(-1 + c^2*x^2)^(5/2))/(120*c^7*Sqrt[c^2*x^2]) + (b*e^2*x*(-1 + c^2*x^2)^(7/2))/(56*c^7*Sqrt[c^2*x^2]) + (d^2*x^4*(a + b*ArcCsc[c*x]))/4 + (d*e*x^6*(a + b*ArcCsc[c*x]))/3 + (e^2*x^8*(a + b*ArcCsc[c*x]))/8","A",5,6,21,0.2857,1,"{266, 43, 5239, 12, 1251, 771}"
95,1,195,0,0.1442222,"\int x \left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*ArcCsc[c*x]),x]","\frac{\left(d+e x^2\right)^3 \left(a+b \csc ^{-1}(c x)\right)}{6 e}+\frac{b x \sqrt{c^2 x^2-1} \left(3 c^4 d^2+3 c^2 d e+e^2\right)}{6 c^5 \sqrt{c^2 x^2}}+\frac{b c d^3 x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 e \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{3/2} \left(3 c^2 d+2 e\right)}{18 c^5 \sqrt{c^2 x^2}}+\frac{b e^2 x \left(c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{c^2 x^2}}","\frac{\left(d+e x^2\right)^3 \left(a+b \csc ^{-1}(c x)\right)}{6 e}+\frac{b x \sqrt{c^2 x^2-1} \left(3 c^4 d^2+3 c^2 d e+e^2\right)}{6 c^5 \sqrt{c^2 x^2}}+\frac{b c d^3 x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{6 e \sqrt{c^2 x^2}}+\frac{b e x \left(c^2 x^2-1\right)^{3/2} \left(3 c^2 d+2 e\right)}{18 c^5 \sqrt{c^2 x^2}}+\frac{b e^2 x \left(c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{c^2 x^2}}",1,"(b*(3*c^4*d^2 + 3*c^2*d*e + e^2)*x*Sqrt[-1 + c^2*x^2])/(6*c^5*Sqrt[c^2*x^2]) + (b*e*(3*c^2*d + 2*e)*x*(-1 + c^2*x^2)^(3/2))/(18*c^5*Sqrt[c^2*x^2]) + (b*e^2*x*(-1 + c^2*x^2)^(5/2))/(30*c^5*Sqrt[c^2*x^2]) + ((d + e*x^2)^3*(a + b*ArcCsc[c*x]))/(6*e) + (b*c*d^3*x*ArcTan[Sqrt[-1 + c^2*x^2]])/(6*e*Sqrt[c^2*x^2])","A",6,5,19,0.2632,1,"{5237, 446, 88, 63, 205}"
96,1,186,0,0.4222628,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsc[c*x]))/x,x]","\frac{1}{2} i b d^2 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-d^2 \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)+d e x^2 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}} \left(6 c^2 d+e\right)}{6 c^3}+\frac{b e^2 x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{12 c}+\frac{1}{2} i b d^2 \csc ^{-1}(c x)^2-b d^2 \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+b d^2 \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)","\frac{1}{2} i b d^2 \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-d^2 \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)+d e x^2 \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \csc ^{-1}(c x)\right)+\frac{b e x \sqrt{1-\frac{1}{c^2 x^2}} \left(6 c^2 d+e\right)}{6 c^3}+\frac{b e^2 x^3 \sqrt{1-\frac{1}{c^2 x^2}}}{12 c}+\frac{1}{2} i b d^2 \csc ^{-1}(c x)^2-b d^2 \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+b d^2 \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)",1,"(b*e*(6*c^2*d + e)*Sqrt[1 - 1/(c^2*x^2)]*x)/(6*c^3) + (b*e^2*Sqrt[1 - 1/(c^2*x^2)]*x^3)/(12*c) + (I/2)*b*d^2*ArcCsc[c*x]^2 + d*e*x^2*(a + b*ArcCsc[c*x]) + (e^2*x^4*(a + b*ArcCsc[c*x]))/4 - b*d^2*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])] + b*d^2*ArcCsc[c*x]*Log[x^(-1)] - d^2*(a + b*ArcCsc[c*x])*Log[x^(-1)] + (I/2)*b*d^2*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",12,13,21,0.6190,1,"{5241, 266, 43, 4731, 6742, 453, 264, 2326, 4625, 3717, 2190, 2279, 2391}"
97,1,189,0,0.4296123,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsc[c*x]))/x^3,x]","i b d e \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{1-\frac{1}{c^2 x^2}}}{4 x}+\frac{1}{4} b c^2 d^2 \csc ^{-1}(c x)+\frac{b e^2 x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}+i b d e \csc ^{-1}(c x)^2-2 b d e \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+2 b d e \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)","i b d e \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \csc ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \csc ^{-1}(c x)\right)-\frac{b c d^2 \sqrt{1-\frac{1}{c^2 x^2}}}{4 x}+\frac{1}{4} b c^2 d^2 \csc ^{-1}(c x)+\frac{b e^2 x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c}+i b d e \csc ^{-1}(c x)^2-2 b d e \csc ^{-1}(c x) \log \left(1-e^{2 i \csc ^{-1}(c x)}\right)+2 b d e \log \left(\frac{1}{x}\right) \csc ^{-1}(c x)",1,"-(b*c*d^2*Sqrt[1 - 1/(c^2*x^2)])/(4*x) + (b*e^2*Sqrt[1 - 1/(c^2*x^2)]*x)/(2*c) + (b*c^2*d^2*ArcCsc[c*x])/4 + I*b*d*e*ArcCsc[c*x]^2 - (d^2*(a + b*ArcCsc[c*x]))/(2*x^2) + (e^2*x^2*(a + b*ArcCsc[c*x]))/2 - 2*b*d*e*ArcCsc[c*x]*Log[1 - E^((2*I)*ArcCsc[c*x])] + 2*b*d*e*ArcCsc[c*x]*Log[x^(-1)] - 2*d*e*(a + b*ArcCsc[c*x])*Log[x^(-1)] + I*b*d*e*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",14,15,21,0.7143,1,"{5241, 266, 43, 4731, 12, 6742, 264, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
98,1,565,0,1.2570296,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/(d + e*x^2),x]","-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{x \left(a+b \csc ^{-1}(c x)\right)}{e}+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c e}","-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{x \left(a+b \csc ^{-1}(c x)\right)}{e}+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c e}",1,"(x*(a + b*ArcCsc[c*x]))/e + (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(c*e) - (Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^(3/2)) + (Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^(3/2)) + (Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^(3/2)) - ((I/2)*b*Sqrt[-d]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^(3/2) + ((I/2)*b*Sqrt[-d]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^(3/2) - ((I/2)*b*Sqrt[-d]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^(3/2) + ((I/2)*b*Sqrt[-d]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^(3/2)","A",25,12,21,0.5714,1,"{5241, 4733, 4627, 266, 63, 208, 4667, 4741, 4519, 2190, 2279, 2391}"
99,1,507,0,1.1385638,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/(d + e*x^2),x]","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e}","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e}",1,"((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e) - ((a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])])/e - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e - ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e - ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e + ((I/2)*b*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/e","A",26,9,19,0.4737,1,"{5241, 4733, 4625, 3717, 2190, 2279, 2391, 4741, 4519}"
100,1,529,0,0.8702925,"\int \frac{a+b \csc ^{-1}(c x)}{d+e x^2} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x^2),x]","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"-((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e])","A",19,7,18,0.3889,1,"{5231, 4667, 4741, 4519, 2190, 2279, 2391}"
101,1,479,0,0.9004074,"\int \frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCsc[c*x])/(x*(d + e*x^2)),x]","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b d}","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b d}",1,"((I/2)*(a + b*ArcCsc[c*x])^2)/(b*d) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d) + ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d + ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d","A",19,7,21,0.3333,1,"{5241, 4733, 4741, 4519, 2190, 2279, 2391}"
102,1,572,0,1.0998229,"\int \frac{a+b \csc ^{-1}(c x)}{x^2 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCsc[c*x])/(x^2*(d + e*x^2)),x]","-\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{a}{d x}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{d}-\frac{b \csc ^{-1}(c x)}{d x}","-\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{a}{d x}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{d}-\frac{b \csc ^{-1}(c x)}{d x}",1,"-((b*c*Sqrt[1 - 1/(c^2*x^2)])/d) - a/(d*x) - (b*ArcCsc[c*x])/(d*x) - (Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) + (Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) + (Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - ((I/2)*b*Sqrt[e]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(-d)^(3/2) + ((I/2)*b*Sqrt[e]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(-d)^(3/2) - ((I/2)*b*Sqrt[e]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(-d)^(3/2) + ((I/2)*b*Sqrt[e]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(-d)^(3/2)","A",24,10,21,0.4762,1,"{5241, 4733, 4619, 261, 4667, 4741, 4519, 2190, 2279, 2391}"
103,1,628,0,1.3206061,"\int \frac{x^5 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^5*(a + b*ArcCsc[c*x]))/(d + e*x^2)^2,x]","\frac{i b d \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{i b d \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{2 e^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 e^{5/2} \sqrt{c^2 d+e}}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c e^2}","\frac{i b d \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{i b d \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{2 e^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 e^{5/2} \sqrt{c^2 d+e}}+\frac{b x \sqrt{1-\frac{1}{c^2 x^2}}}{2 c e^2}",1,"(b*Sqrt[1 - 1/(c^2*x^2)]*x)/(2*c*e^2) + (d*(a + b*ArcCsc[c*x]))/(2*e^2*(e + d/x^2)) + (x^2*(a + b*ArcCsc[c*x]))/(2*e^2) - (b*d*ArcTan[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)]*x)])/(2*e^(5/2)*Sqrt[c^2*d + e]) - (d*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 + (2*d*(a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])])/e^3 + (I*b*d*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 + (I*b*d*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 + (I*b*d*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 + (I*b*d*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 - (I*b*d*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/e^3","A",31,14,21,0.6667,1,"{5241, 4733, 4627, 264, 4625, 3717, 2190, 2279, 2391, 4729, 377, 205, 4741, 4519}"
104,1,590,0,1.2384508,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/(d + e*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{a+b \csc ^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 e^{3/2} \sqrt{c^2 d+e}}","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{a+b \csc ^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 e^{3/2} \sqrt{c^2 d+e}}",1,"-(a + b*ArcCsc[c*x])/(2*e*(e + d/x^2)) + (b*ArcTan[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)]*x)])/(2*e^(3/2)*Sqrt[c^2*d + e]) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^2) - ((a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])])/e^2 - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^2 - ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^2 - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^2 - ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^2 + ((I/2)*b*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/e^2","A",29,12,21,0.5714,1,"{5241, 4733, 4625, 3717, 2190, 2279, 2391, 4729, 377, 205, 4741, 4519}"
105,1,131,0,0.1210131,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/(d + e*x^2)^2,x]","-\frac{a+b \csc ^{-1}(c x)}{2 e \left(d+e x^2\right)}-\frac{b c x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{2 d e \sqrt{c^2 x^2}}+\frac{b c x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{\sqrt{c^2 d+e}}\right)}{2 d \sqrt{e} \sqrt{c^2 x^2} \sqrt{c^2 d+e}}","-\frac{a+b \csc ^{-1}(c x)}{2 e \left(d+e x^2\right)}-\frac{b c x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{2 d e \sqrt{c^2 x^2}}+\frac{b c x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{\sqrt{c^2 d+e}}\right)}{2 d \sqrt{e} \sqrt{c^2 x^2} \sqrt{c^2 d+e}}",1,"-(a + b*ArcCsc[c*x])/(2*e*(d + e*x^2)) - (b*c*x*ArcTan[Sqrt[-1 + c^2*x^2]])/(2*d*e*Sqrt[c^2*x^2]) + (b*c*x*ArcTan[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/Sqrt[c^2*d + e]])/(2*d*Sqrt[e]*Sqrt[c^2*d + e]*Sqrt[c^2*x^2])","A",7,5,19,0.2632,1,"{5237, 446, 86, 63, 205}"
106,1,566,0,1.161308,"\int \frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCsc[c*x])/(x*(d + e*x^2)^2),x]","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b d^2}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 d^2 \sqrt{c^2 d+e}}","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b d^2}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 d^2 \sqrt{c^2 d+e}}",1,"-(e*(a + b*ArcCsc[c*x]))/(2*d^2*(e + d/x^2)) + ((I/2)*(a + b*ArcCsc[c*x])^2)/(b*d^2) + (b*Sqrt[e]*ArcTan[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)]*x)])/(2*d^2*Sqrt[c^2*d + e]) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^2) + ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d^2 + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d^2 + ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d^2 + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d^2","A",24,10,21,0.4762,1,"{5241, 4733, 4729, 377, 205, 4741, 4519, 2190, 2279, 2391}"
107,1,803,0,2.4003875,"\int \frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcCsc[c*x]))/(d + e*x^2)^2,x]","\frac{x \left(a+b \csc ^{-1}(c x)\right)}{e^2}-\frac{3 \sqrt{-d} \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{4 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c e^2}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 e^2 \sqrt{d c^2+e}}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 e^2 \sqrt{d c^2+e}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}","\frac{x \left(a+b \csc ^{-1}(c x)\right)}{e^2}-\frac{3 \sqrt{-d} \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right) \left(a+b \csc ^{-1}(c x)\right)}{4 e^{5/2}}-\frac{d \left(a+b \csc ^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{4 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c e^2}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 e^2 \sqrt{d c^2+e}}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 e^2 \sqrt{d c^2+e}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 e^{5/2}}",1,"-(d*(a + b*ArcCsc[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) + (d*(a + b*ArcCsc[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] + d/x)) + (x*(a + b*ArcCsc[c*x]))/e^2 + (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(c*e^2) + (b*Sqrt[d]*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*e^2*Sqrt[c^2*d + e]) + (b*Sqrt[d]*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*e^2*Sqrt[c^2*d + e]) - (3*Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*e^(5/2)) - (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^(5/2) + (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^(5/2) - (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^(5/2) + (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^(5/2)","A",51,15,21,0.7143,1,"{5241, 4733, 4627, 266, 63, 208, 4667, 4743, 725, 206, 4741, 4519, 2190, 2279, 2391}"
108,1,765,0,1.2547448,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/(d + e*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \csc ^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \csc ^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d+e}}-\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d+e}}","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \csc ^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \csc ^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d+e}}-\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d+e}}",1,"(a + b*ArcCsc[c*x])/(4*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcCsc[c*x])/(4*e*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*Sqrt[d]*e*Sqrt[c^2*d + e]) - (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*Sqrt[d]*e*Sqrt[c^2*d + e]) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((I/4)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2)) + ((I/4)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2)) - ((I/4)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2)) + ((I/4)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2))","A",27,10,21,0.4762,1,"{5241, 4667, 4743, 725, 206, 4741, 4519, 2190, 2279, 2391}"
109,1,759,0,2.2881605,"\int \frac{a+b \csc ^{-1}(c x)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x^2)^2,x]","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \csc ^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \csc ^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 d^{3/2} \sqrt{c^2 d+e}}+\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 d^{3/2} \sqrt{c^2 d+e}}","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \csc ^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \csc ^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 d^{3/2} \sqrt{c^2 d+e}}+\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{1-\frac{1}{c^2 x^2}} \sqrt{c^2 d+e}}\right)}{4 d^{3/2} \sqrt{c^2 d+e}}",1,"-(a + b*ArcCsc[c*x])/(4*d*(Sqrt[-d]*Sqrt[e] - d/x)) + (a + b*ArcCsc[c*x])/(4*d*(Sqrt[-d]*Sqrt[e] + d/x)) + (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*d^(3/2)*Sqrt[c^2*d + e]) + (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*d^(3/2)*Sqrt[c^2*d + e]) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((I/4)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e]) - ((I/4)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e]) + ((I/4)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e]) - ((I/4)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e])","A",47,11,18,0.6111,1,"{5231, 4733, 4667, 4743, 725, 206, 4741, 4519, 2190, 2279, 2391}"
110,1,806,0,2.3640739,"\int \frac{a+b \csc ^{-1}(c x)}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCsc[c*x])/(x^2*(d + e*x^2)^2),x]","-\frac{a}{d^2 x}-\frac{b \csc ^{-1}(c x)}{d^2 x}+\frac{e \left(a+b \csc ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{4 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 d^{5/2} \sqrt{d c^2+e}}-\frac{b e \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 d^{5/2} \sqrt{d c^2+e}}+\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{d^2}","-\frac{a}{d^2 x}-\frac{b \csc ^{-1}(c x)}{d^2 x}+\frac{e \left(a+b \csc ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{4 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 d^{5/2} \sqrt{d c^2+e}}-\frac{b e \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{4 d^{5/2} \sqrt{d c^2+e}}+\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{4 (-d)^{5/2}}-\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{d^2}",1,"-((b*c*Sqrt[1 - 1/(c^2*x^2)])/d^2) - a/(d^2*x) - (b*ArcCsc[c*x])/(d^2*x) + (e*(a + b*ArcCsc[c*x]))/(4*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (e*(a + b*ArcCsc[c*x]))/(4*d^2*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*e*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*d^(5/2)*Sqrt[c^2*d + e]) - (b*e*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(4*d^(5/2)*Sqrt[c^2*d + e]) + (3*Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) - (3*Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) - (3*Sqrt[e]*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (((3*I)/4)*b*Sqrt[e]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(-d)^(5/2) - (((3*I)/4)*b*Sqrt[e]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(-d)^(5/2) + (((3*I)/4)*b*Sqrt[e]*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(-d)^(5/2) - (((3*I)/4)*b*Sqrt[e]*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(-d)^(5/2)","A",50,13,21,0.6190,1,"{5241, 4733, 4619, 261, 4667, 4743, 725, 206, 4741, 4519, 2190, 2279, 2391}"
111,1,727,0,1.4419887,"\int \frac{x^5 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^5*(a + b*ArcCsc[c*x]))/(d + e*x^2)^3,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{a+b \csc ^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \csc ^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{b c d \sqrt{1-\frac{1}{c^2 x^2}}}{8 e^2 x \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \left(c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{8 e^{5/2} \left(c^2 d+e\right)^{3/2}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 e^{5/2} \sqrt{c^2 d+e}}","-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{i b \text{PolyLog}\left(2,e^{2 i \csc ^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{a+b \csc ^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \csc ^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\log \left(1-e^{2 i \csc ^{-1}(c x)}\right) \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{b c d \sqrt{1-\frac{1}{c^2 x^2}}}{8 e^2 x \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \left(c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{8 e^{5/2} \left(c^2 d+e\right)^{3/2}}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{2 e^{5/2} \sqrt{c^2 d+e}}",1,"(b*c*d*Sqrt[1 - 1/(c^2*x^2)])/(8*e^2*(c^2*d + e)*(e + d/x^2)*x) - (a + b*ArcCsc[c*x])/(4*e*(e + d/x^2)^2) - (a + b*ArcCsc[c*x])/(2*e^2*(e + d/x^2)) + (b*ArcTan[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)]*x)])/(2*e^(5/2)*Sqrt[c^2*d + e]) + (b*(c^2*d + 2*e)*ArcTan[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)]*x)])/(8*e^(5/2)*(c^2*d + e)^(3/2)) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^3) - ((a + b*ArcCsc[c*x])*Log[1 - E^((2*I)*ArcCsc[c*x])])/e^3 - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 - ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 + ((I/2)*b*PolyLog[2, E^((2*I)*ArcCsc[c*x])])/e^3","A",33,13,21,0.6190,1,"{5241, 4733, 4625, 3717, 2190, 2279, 2391, 4729, 382, 377, 205, 4741, 4519}"
112,1,157,0,0.1820811,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/(d + e*x^2)^3,x]","\frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}+\frac{b c x \left(c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{\sqrt{c^2 d+e}}\right)}{8 d e^{3/2} \sqrt{c^2 x^2} \left(c^2 d+e\right)^{3/2}}-\frac{b c x \sqrt{c^2 x^2-1}}{8 e \sqrt{c^2 x^2} \left(c^2 d+e\right) \left(d+e x^2\right)}","\frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}+\frac{b c x \left(c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{\sqrt{c^2 d+e}}\right)}{8 d e^{3/2} \sqrt{c^2 x^2} \left(c^2 d+e\right)^{3/2}}-\frac{b c x \sqrt{c^2 x^2-1}}{8 e \sqrt{c^2 x^2} \left(c^2 d+e\right) \left(d+e x^2\right)}",1,"-(b*c*x*Sqrt[-1 + c^2*x^2])/(8*e*(c^2*d + e)*Sqrt[c^2*x^2]*(d + e*x^2)) + (x^4*(a + b*ArcCsc[c*x]))/(4*d*(d + e*x^2)^2) + (b*c*(c^2*d + 2*e)*x*ArcTan[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/Sqrt[c^2*d + e]])/(8*d*e^(3/2)*(c^2*d + e)^(3/2)*Sqrt[c^2*x^2])","A",6,7,21,0.3333,1,"{264, 5239, 12, 446, 78, 63, 205}"
113,1,193,0,0.1911026,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/(d + e*x^2)^3,x]","-\frac{a+b \csc ^{-1}(c x)}{4 e \left(d+e x^2\right)^2}-\frac{b c x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{4 d^2 e \sqrt{c^2 x^2}}+\frac{b c x \left(3 c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{\sqrt{c^2 d+e}}\right)}{8 d^2 \sqrt{e} \sqrt{c^2 x^2} \left(c^2 d+e\right)^{3/2}}+\frac{b c x \sqrt{c^2 x^2-1}}{8 d \sqrt{c^2 x^2} \left(c^2 d+e\right) \left(d+e x^2\right)}","-\frac{a+b \csc ^{-1}(c x)}{4 e \left(d+e x^2\right)^2}-\frac{b c x \tan ^{-1}\left(\sqrt{c^2 x^2-1}\right)}{4 d^2 e \sqrt{c^2 x^2}}+\frac{b c x \left(3 c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{\sqrt{c^2 d+e}}\right)}{8 d^2 \sqrt{e} \sqrt{c^2 x^2} \left(c^2 d+e\right)^{3/2}}+\frac{b c x \sqrt{c^2 x^2-1}}{8 d \sqrt{c^2 x^2} \left(c^2 d+e\right) \left(d+e x^2\right)}",1,"(b*c*x*Sqrt[-1 + c^2*x^2])/(8*d*(c^2*d + e)*Sqrt[c^2*x^2]*(d + e*x^2)) - (a + b*ArcCsc[c*x])/(4*e*(d + e*x^2)^2) - (b*c*x*ArcTan[Sqrt[-1 + c^2*x^2]])/(4*d^2*e*Sqrt[c^2*x^2]) + (b*c*(3*c^2*d + 2*e)*x*ArcTan[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/Sqrt[c^2*d + e]])/(8*d^2*Sqrt[e]*(c^2*d + e)^(3/2)*Sqrt[c^2*x^2])","A",8,6,19,0.3158,1,"{5237, 446, 103, 156, 63, 205}"
114,1,704,0,1.3176933,"\int \frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcCsc[c*x])/(x*(d + e*x^2)^3),x]","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{e^2 \left(a+b \csc ^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b d^3}-\frac{b c e \sqrt{1-\frac{1}{c^2 x^2}}}{8 d^2 x \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}-\frac{b \sqrt{e} \left(c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{8 d^3 \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{d^3 \sqrt{c^2 d+e}}","\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1+\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{e^2 \left(a+b \csc ^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \csc ^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \csc ^{-1}(c x)\right)^2}{2 b d^3}-\frac{b c e \sqrt{1-\frac{1}{c^2 x^2}}}{8 d^2 x \left(c^2 d+e\right) \left(\frac{d}{x^2}+e\right)}-\frac{b \sqrt{e} \left(c^2 d+2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{8 d^3 \left(c^2 d+e\right)^{3/2}}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d+e}}{c \sqrt{e} x \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{d^3 \sqrt{c^2 d+e}}",1,"-(b*c*e*Sqrt[1 - 1/(c^2*x^2)])/(8*d^2*(c^2*d + e)*(e + d/x^2)*x) + (e^2*(a + b*ArcCsc[c*x]))/(4*d^3*(e + d/x^2)^2) - (e*(a + b*ArcCsc[c*x]))/(d^3*(e + d/x^2)) + ((I/2)*(a + b*ArcCsc[c*x])^2)/(b*d^3) + (b*Sqrt[e]*ArcTan[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)]*x)])/(d^3*Sqrt[c^2*d + e]) - (b*Sqrt[e]*(c^2*d + 2*e)*ArcTan[Sqrt[c^2*d + e]/(c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)]*x)])/(8*d^3*(c^2*d + e)^(3/2)) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^3) + ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d^3 + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d^3 + ((I/2)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d^3 + ((I/2)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d^3","A",28,11,21,0.5238,1,"{5241, 4733, 4729, 382, 377, 205, 4741, 4519, 2190, 2279, 2391}"
115,1,1144,0,1.6001287,"\int \frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcCsc[c*x]))/(d + e*x^2)^3,x]","-\frac{b \sqrt{-d} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{-d} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{3 \left(a+b \csc ^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \csc ^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right)}{16 e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{3 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e^2 \sqrt{d c^2+e}}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e \left(d c^2+e\right)^{3/2}}-\frac{3 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e^2 \sqrt{d c^2+e}}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e \left(d c^2+e\right)^{3/2}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}","-\frac{b \sqrt{-d} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{-d} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 e^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{3 \left(a+b \csc ^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \csc ^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \csc ^{-1}(c x)\right)}{16 e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{3 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e^2 \sqrt{d c^2+e}}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e \left(d c^2+e\right)^{3/2}}-\frac{3 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e^2 \sqrt{d c^2+e}}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} e \left(d c^2+e\right)^{3/2}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}",1,"-(b*c*Sqrt[-d]*Sqrt[1 - 1/(c^2*x^2)])/(16*e^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] - d/x)) - (b*c*Sqrt[-d]*Sqrt[1 - 1/(c^2*x^2)])/(16*e^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] + d/x)) + (Sqrt[-d]*(a + b*ArcCsc[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (3*(a + b*ArcCsc[c*x]))/(16*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[-d]*(a + b*ArcCsc[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (3*(a + b*ArcCsc[c*x]))/(16*e^2*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*Sqrt[d]*e*(c^2*d + e)^(3/2)) - (3*b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*Sqrt[d]*e^2*Sqrt[c^2*d + e]) - (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*Sqrt[d]*e*(c^2*d + e)^(3/2)) - (3*b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*Sqrt[d]*e^2*Sqrt[c^2*d + e]) - (3*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) + (3*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) + (3*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (((3*I)/16)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2)) + (((3*I)/16)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2)) - (((3*I)/16)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2)) + (((3*I)/16)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2))","A",35,11,21,0.5238,1,"{5241, 4667, 4743, 731, 725, 206, 4741, 4519, 2190, 2279, 2391}"
116,1,1144,0,3.0688669,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/(d + e*x^2)^3,x]","-\frac{b \sqrt{1-\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{1-\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \csc ^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \csc ^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \csc ^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \csc ^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} e \sqrt{d c^2+e}}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(d c^2+e\right)^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} e \sqrt{d c^2+e}}+\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(d c^2+e\right)^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}","-\frac{b \sqrt{1-\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{1-\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \sqrt{e} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \csc ^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \csc ^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \csc ^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \csc ^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} e \sqrt{d c^2+e}}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(d c^2+e\right)^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} e \sqrt{d c^2+e}}+\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(d c^2+e\right)^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}",1,"-(b*c*Sqrt[1 - 1/(c^2*x^2)])/(16*Sqrt[-d]*Sqrt[e]*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] - d/x)) - (b*c*Sqrt[1 - 1/(c^2*x^2)])/(16*Sqrt[-d]*Sqrt[e]*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] + d/x)) + (a + b*ArcCsc[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (a + b*ArcCsc[c*x])/(16*d*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcCsc[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (a + b*ArcCsc[c*x])/(16*d*e*(Sqrt[-d]*Sqrt[e] + d/x)) + (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(3/2)*(c^2*d + e)^(3/2)) - (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(3/2)*e*Sqrt[c^2*d + e]) + (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(3/2)*(c^2*d + e)^(3/2)) - (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(3/2)*e*Sqrt[c^2*d + e]) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((I/16)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2)) - ((I/16)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2)) + ((I/16)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2)) - ((I/16)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2))","A",63,12,21,0.5714,1,"{5241, 4733, 4667, 4743, 731, 725, 206, 4741, 4519, 2190, 2279, 2391}"
117,1,1134,0,4.0488551,"\int \frac{a+b \csc ^{-1}(c x)}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x^2)^3,x]","-\frac{b \sqrt{e} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{e} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{5 \left(a+b \csc ^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \csc ^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}+\frac{5 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{d c^2+e}}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(d c^2+e\right)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{d c^2+e}}-\frac{b e \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(d c^2+e\right)^{3/2}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}","-\frac{b \sqrt{e} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{e} \sqrt{1-\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(d c^2+e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{5 \left(a+b \csc ^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \csc ^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \csc ^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}+\frac{5 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{d c^2+e}}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(d c^2+e\right)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{d c^2+e}}-\frac{b e \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{d c^2+e} \sqrt{1-\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(d c^2+e\right)^{3/2}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(1-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \csc ^{-1}(c x)\right) \log \left(\frac{i \sqrt{-d} e^{i \csc ^{-1}(c x)} c}{\sqrt{e}+\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 i b \text{PolyLog}\left(2,-\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 i b \text{PolyLog}\left(2,\frac{i c \sqrt{-d} e^{i \csc ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}",1,"-(b*c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] - d/x)) - (b*c*Sqrt[e]*Sqrt[1 - 1/(c^2*x^2)])/(16*(-d)^(3/2)*(c^2*d + e)*(Sqrt[-d]*Sqrt[e] + d/x)) + (Sqrt[e]*(a + b*ArcCsc[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) - (5*(a + b*ArcCsc[c*x]))/(16*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[e]*(a + b*ArcCsc[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) + (5*(a + b*ArcCsc[c*x]))/(16*d^2*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*e*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(5/2)*(c^2*d + e)^(3/2)) + (5*b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(5/2)*Sqrt[c^2*d + e]) - (b*e*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(5/2)*(c^2*d + e)^(3/2)) + (5*b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d + e]*Sqrt[1 - 1/(c^2*x^2)])])/(16*d^(5/2)*Sqrt[c^2*d + e]) - (3*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (3*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcCsc[c*x])*Log[1 - (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (3*(a + b*ArcCsc[c*x])*Log[1 + (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (((3*I)/16)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e]) + (((3*I)/16)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e]) - (((3*I)/16)*b*PolyLog[2, ((-I)*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e]) + (((3*I)/16)*b*PolyLog[2, (I*c*Sqrt[-d]*E^(I*ArcCsc[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e])","A",81,12,18,0.6667,1,"{5231, 4733, 4667, 4743, 731, 725, 206, 4741, 4519, 2190, 2279, 2391}"
118,1,403,0,1.3122266,"\int x^5 \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^5*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]),x]","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^3}-\frac{b x \sqrt{c^2 x^2-1} \left(23 c^4 d^2+12 c^2 d e-75 e^2\right) \sqrt{d+e x^2}}{1680 c^5 e^2 \sqrt{c^2 x^2}}-\frac{8 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{105 e^3 \sqrt{c^2 x^2}}+\frac{b x \left(-35 c^4 d^2 e+105 c^6 d^3+63 c^2 d e^2+75 e^3\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{1680 c^6 e^{5/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{c^2 x^2-1} \left(29 c^2 d-25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e^2 \sqrt{c^2 x^2}}","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^3}-\frac{b x \sqrt{c^2 x^2-1} \left(23 c^4 d^2+12 c^2 d e-75 e^2\right) \sqrt{d+e x^2}}{1680 c^5 e^2 \sqrt{c^2 x^2}}-\frac{8 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{105 e^3 \sqrt{c^2 x^2}}+\frac{b x \left(-35 c^4 d^2 e+105 c^6 d^3+63 c^2 d e^2+75 e^3\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{1680 c^6 e^{5/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{c^2 x^2-1} \left(29 c^2 d-25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e^2 \sqrt{c^2 x^2}}",1,"-(b*(23*c^4*d^2 + 12*c^2*d*e - 75*e^2)*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(1680*c^5*e^2*Sqrt[c^2*x^2]) - (b*(29*c^2*d - 25*e)*x*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(840*c^3*e^2*Sqrt[c^2*x^2]) + (b*x*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(5/2))/(42*c*e^2*Sqrt[c^2*x^2]) + (d^2*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^3) - (2*d*(d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^3) + ((d + e*x^2)^(7/2)*(a + b*ArcCsc[c*x]))/(7*e^3) - (8*b*c*d^(7/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(105*e^3*Sqrt[c^2*x^2]) + (b*(105*c^6*d^3 - 35*c^4*d^2*e + 63*c^2*d*e^2 + 75*e^3)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(1680*c^6*e^(5/2)*Sqrt[c^2*x^2])","A",12,12,23,0.5217,1,"{266, 43, 5239, 12, 1615, 154, 157, 63, 217, 206, 93, 204}"
119,1,294,0,0.4088104,"\int x^3 \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]),x]","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^2}+\frac{2 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{15 e^2 \sqrt{c^2 x^2}}-\frac{b x \left(15 c^4 d^2-10 c^2 d e-9 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{3/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(c^2 d+9 e\right) \sqrt{d+e x^2}}{120 c^3 e \sqrt{c^2 x^2}}","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^2}+\frac{2 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{15 e^2 \sqrt{c^2 x^2}}-\frac{b x \left(15 c^4 d^2-10 c^2 d e-9 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{3/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(c^2 d+9 e\right) \sqrt{d+e x^2}}{120 c^3 e \sqrt{c^2 x^2}}",1,"(b*(c^2*d + 9*e)*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(120*c^3*e*Sqrt[c^2*x^2]) + (b*x*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(20*c*e*Sqrt[c^2*x^2]) - (d*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^2) + ((d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^2) + (2*b*c*d^(5/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(15*e^2*Sqrt[c^2*x^2]) - (b*(15*c^4*d^2 - 10*c^2*d*e - 9*e^2)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(120*c^4*e^(3/2)*Sqrt[c^2*x^2])","A",11,12,23,0.5217,1,"{266, 43, 5239, 12, 573, 154, 157, 63, 217, 206, 93, 204}"
120,1,195,0,0.2115781,"\int x \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]),x]","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e}-\frac{b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{6 c \sqrt{c^2 x^2}}+\frac{b x \left(3 c^2 d+e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 \sqrt{e} \sqrt{c^2 x^2}}","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e}-\frac{b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{6 c \sqrt{c^2 x^2}}+\frac{b x \left(3 c^2 d+e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 \sqrt{e} \sqrt{c^2 x^2}}",1,"(b*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(6*c*Sqrt[c^2*x^2]) + ((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e) - (b*c*d^(3/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(3*e*Sqrt[c^2*x^2]) + (b*(3*c^2*d + e)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^2*Sqrt[e]*Sqrt[c^2*x^2])","A",9,9,21,0.4286,1,"{5237, 446, 102, 157, 63, 217, 206, 93, 204}"
121,0,0,0,0.1015467,"\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
122,0,0,0,0.1067184,"\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x^3,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
123,0,0,0,0.096438,"\int x^2 \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]),x]","\int x^2 \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
124,0,0,0,0.0337974,"\int \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]),x]","\int \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right),x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
125,0,0,0,0.0869433,"\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x^2,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
126,1,328,0,0.4317645,"\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x^4,x]","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 d x^3}-\frac{2 b c \sqrt{c^2 x^2-1} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{9 d \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{9 x^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(2 c^2 d+3 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{2 b c^2 x \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 d x^3}-\frac{2 b c \sqrt{c^2 x^2-1} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{9 d \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{9 x^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(2 c^2 d+3 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{2 b c^2 x \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}",1,"(-2*b*c*(c^2*d + 2*e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(9*d*Sqrt[c^2*x^2]) - (b*c*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(9*x^2*Sqrt[c^2*x^2]) - ((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(3*d*x^3) + (2*b*c^2*(c^2*d + 2*e)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(9*d*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*(2*c^2*d + 3*e)*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(9*d*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",11,11,23,0.4783,1,"{264, 5239, 12, 474, 583, 524, 427, 426, 424, 421, 419}"
127,1,453,0,0.6200644,"\int \frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{x^6} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/x^6,x]","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{5 d x^5}-\frac{b c \sqrt{c^2 x^2-1} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(24 c^4 d^2+7 c^2 d e-30 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 d x^4 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(12 c^2 d-e\right) \sqrt{d+e x^2}}{225 d x^2 \sqrt{c^2 x^2}}","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{5 d x^5}-\frac{b c \sqrt{c^2 x^2-1} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(24 c^4 d^2+7 c^2 d e-30 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(24 c^4 d^2+19 c^2 d e-31 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 d x^4 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(12 c^2 d-e\right) \sqrt{d+e x^2}}{225 d x^2 \sqrt{c^2 x^2}}",1,"-(b*c*(24*c^4*d^2 + 19*c^2*d*e - 31*e^2)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(225*d^2*Sqrt[c^2*x^2]) - (b*c*(12*c^2*d - e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(225*d*x^2*Sqrt[c^2*x^2]) - (b*c*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(25*d*x^4*Sqrt[c^2*x^2]) - ((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(5*d*x^5) + (2*e*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(15*d^2*x^3) + (b*c^2*(24*c^4*d^2 + 19*c^2*d*e - 31*e^2)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(225*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*(24*c^4*d^2 + 7*c^2*d*e - 30*e^2)*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(225*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",12,12,23,0.5217,1,"{271, 264, 5239, 12, 580, 583, 524, 427, 426, 424, 421, 419}"
128,1,374,0,0.5378572,"\int x^3 \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]),x]","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^2}-\frac{b x \sqrt{c^2 x^2-1} \left(3 c^4 d^2-38 c^2 d e-25 e^2\right) \sqrt{d+e x^2}}{560 c^5 e \sqrt{c^2 x^2}}+\frac{2 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{35 e^2 \sqrt{c^2 x^2}}-\frac{b x \left(-35 c^4 d^2 e+35 c^6 d^3-63 c^2 d e^2-25 e^3\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{560 c^6 e^{3/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(13 c^2 d+25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e \sqrt{c^2 x^2}}","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \csc ^{-1}(c x)\right)}{7 e^2}-\frac{b x \sqrt{c^2 x^2-1} \left(3 c^4 d^2-38 c^2 d e-25 e^2\right) \sqrt{d+e x^2}}{560 c^5 e \sqrt{c^2 x^2}}+\frac{2 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{35 e^2 \sqrt{c^2 x^2}}-\frac{b x \left(-35 c^4 d^2 e+35 c^6 d^3-63 c^2 d e^2-25 e^3\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{560 c^6 e^{3/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(13 c^2 d+25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e \sqrt{c^2 x^2}}",1,"-(b*(3*c^4*d^2 - 38*c^2*d*e - 25*e^2)*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(560*c^5*e*Sqrt[c^2*x^2]) + (b*(13*c^2*d + 25*e)*x*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(840*c^3*e*Sqrt[c^2*x^2]) + (b*x*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(5/2))/(42*c*e*Sqrt[c^2*x^2]) - (d*(d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^2) + ((d + e*x^2)^(7/2)*(a + b*ArcCsc[c*x]))/(7*e^2) + (2*b*c*d^(7/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(35*e^2*Sqrt[c^2*x^2]) - (b*(35*c^6*d^3 - 35*c^4*d^2*e - 63*c^2*d*e^2 - 25*e^3)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(560*c^6*e^(3/2)*Sqrt[c^2*x^2])","A",12,12,23,0.5217,1,"{266, 43, 5239, 12, 573, 154, 157, 63, 217, 206, 93, 204}"
129,1,262,0,0.2883907,"\int x \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]),x]","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e}+\frac{b x \left(15 c^4 d^2+10 c^2 d e+3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{40 c^4 \sqrt{e} \sqrt{c^2 x^2}}-\frac{b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{5 e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(7 c^2 d+3 e\right) \sqrt{d+e x^2}}{40 c^3 \sqrt{c^2 x^2}}","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e}+\frac{b x \left(15 c^4 d^2+10 c^2 d e+3 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{40 c^4 \sqrt{e} \sqrt{c^2 x^2}}-\frac{b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{5 e \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(7 c^2 d+3 e\right) \sqrt{d+e x^2}}{40 c^3 \sqrt{c^2 x^2}}",1,"(b*(7*c^2*d + 3*e)*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(40*c^3*Sqrt[c^2*x^2]) + (b*x*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(20*c*Sqrt[c^2*x^2]) + ((d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e) - (b*c*d^(5/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(5*e*Sqrt[c^2*x^2]) + (b*(15*c^4*d^2 + 10*c^2*d*e + 3*e^2)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(40*c^4*Sqrt[e]*Sqrt[c^2*x^2])","A",10,10,21,0.4762,1,"{5237, 446, 102, 154, 157, 63, 217, 206, 93, 204}"
130,0,0,0,0.1160809,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
131,0,0,0,0.1220814,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^3,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
132,0,0,0,0.123709,"\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]),x]","\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
133,0,0,0,0.0452941,"\int \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]),x]","\int \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right),x\right)",0,"Defer[Int][(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
134,0,0,0,0.1063173,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^2,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
135,0,0,0,0.1066396,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^4,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^4} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^4},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^4, x]","A",0,0,0,0,-1,"{}"
136,1,416,0,0.5725675,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^6,x]","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 d x^5}-\frac{b c \sqrt{c^2 x^2-1} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(8 c^4 d^2+19 c^2 d e+15 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 x^4 \sqrt{c^2 x^2}}-\frac{4 b c \sqrt{c^2 x^2-1} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{75 x^2 \sqrt{c^2 x^2}}","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 d x^5}-\frac{b c \sqrt{c^2 x^2-1} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(8 c^4 d^2+19 c^2 d e+15 e^2\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(8 c^4 d^2+23 c^2 d e+23 e^2\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{75 d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 x^4 \sqrt{c^2 x^2}}-\frac{4 b c \sqrt{c^2 x^2-1} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{75 x^2 \sqrt{c^2 x^2}}",1,"-(b*c*(8*c^4*d^2 + 23*c^2*d*e + 23*e^2)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(75*d*Sqrt[c^2*x^2]) - (4*b*c*(c^2*d + 2*e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(75*x^2*Sqrt[c^2*x^2]) - (b*c*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(25*x^4*Sqrt[c^2*x^2]) - ((d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(5*d*x^5) + (b*c^2*(8*c^4*d^2 + 23*c^2*d*e + 23*e^2)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(75*d*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*(8*c^4*d^2 + 19*c^2*d*e + 15*e^2)*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(75*d*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",12,12,23,0.5217,1,"{264, 5239, 12, 474, 580, 583, 524, 427, 426, 424, 421, 419}"
137,1,554,0,0.8911121,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/x^8,x]","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{7 d x^7}-\frac{b c \sqrt{c^2 x^2-1} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(120 c^4 d^2+159 c^2 d e-37 e^2\right) \sqrt{d+e x^2}}{3675 d x^2 \sqrt{c^2 x^2}}-\frac{2 b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(204 c^4 d^2 e+120 c^6 d^3+17 c^2 d e^2-105 e^3\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{49 d x^6 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(30 c^2 d+11 e\right) \left(d+e x^2\right)^{3/2}}{1225 d x^4 \sqrt{c^2 x^2}}","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{7 d x^7}-\frac{b c \sqrt{c^2 x^2-1} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(120 c^4 d^2+159 c^2 d e-37 e^2\right) \sqrt{d+e x^2}}{3675 d x^2 \sqrt{c^2 x^2}}-\frac{2 b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \left(204 c^4 d^2 e+120 c^6 d^3+17 c^2 d e^2-105 e^3\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2-247 e^3\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{49 d x^6 \sqrt{c^2 x^2}}-\frac{b c \sqrt{c^2 x^2-1} \left(30 c^2 d+11 e\right) \left(d+e x^2\right)^{3/2}}{1225 d x^4 \sqrt{c^2 x^2}}",1,"-(b*c*(240*c^6*d^3 + 528*c^4*d^2*e + 193*c^2*d*e^2 - 247*e^3)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(3675*d^2*Sqrt[c^2*x^2]) - (b*c*(120*c^4*d^2 + 159*c^2*d*e - 37*e^2)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(3675*d*x^2*Sqrt[c^2*x^2]) - (b*c*(30*c^2*d + 11*e)*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(1225*d*x^4*Sqrt[c^2*x^2]) - (b*c*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(5/2))/(49*d*x^6*Sqrt[c^2*x^2]) - ((d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(7*d*x^7) + (2*e*(d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(35*d^2*x^5) + (b*c^2*(240*c^6*d^3 + 528*c^4*d^2*e + 193*c^2*d*e^2 - 247*e^3)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3675*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (2*b*(c^2*d + e)*(120*c^6*d^3 + 204*c^4*d^2*e + 17*c^2*d*e^2 - 105*e^3)*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3675*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",13,12,23,0.5217,1,"{271, 264, 5239, 12, 580, 583, 524, 427, 426, 424, 421, 419}"
138,1,321,0,1.0481948,"\int \frac{x^5 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^5*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x^2],x]","\frac{d^2 \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}-\frac{8 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{15 e^3 \sqrt{c^2 x^2}}+\frac{b x \left(45 c^4 d^2-10 c^2 d e+9 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{5/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{c^2 x^2-1} \left(19 c^2 d-9 e\right) \sqrt{d+e x^2}}{120 c^3 e^2 \sqrt{c^2 x^2}}","\frac{d^2 \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{5 e^3}-\frac{8 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{15 e^3 \sqrt{c^2 x^2}}+\frac{b x \left(45 c^4 d^2-10 c^2 d e+9 e^2\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{5/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{c^2 x^2-1} \left(19 c^2 d-9 e\right) \sqrt{d+e x^2}}{120 c^3 e^2 \sqrt{c^2 x^2}}",1,"-(b*(19*c^2*d - 9*e)*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(120*c^3*e^2*Sqrt[c^2*x^2]) + (b*x*Sqrt[-1 + c^2*x^2]*(d + e*x^2)^(3/2))/(20*c*e^2*Sqrt[c^2*x^2]) + (d^2*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/e^3 - (2*d*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^3) + ((d + e*x^2)^(5/2)*(a + b*ArcCsc[c*x]))/(5*e^3) - (8*b*c*d^(5/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(15*e^3*Sqrt[c^2*x^2]) + (b*(45*c^4*d^2 - 10*c^2*d*e + 9*e^2)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(120*c^4*e^(5/2)*Sqrt[c^2*x^2])","A",11,12,23,0.5217,1,"{266, 43, 5239, 12, 1615, 154, 157, 63, 217, 206, 93, 204}"
139,1,225,0,0.3273743,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x^2],x]","-\frac{d \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{2 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e^2 \sqrt{c^2 x^2}}-\frac{b x \left(3 c^2 d-e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{3/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{6 c e \sqrt{c^2 x^2}}","-\frac{d \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^2}+\frac{2 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e^2 \sqrt{c^2 x^2}}-\frac{b x \left(3 c^2 d-e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{3/2} \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{6 c e \sqrt{c^2 x^2}}",1,"(b*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(6*c*e*Sqrt[c^2*x^2]) - (d*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/e^2 + ((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^2) + (2*b*c*d^(3/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(3*e^2*Sqrt[c^2*x^2]) - (b*(3*c^2*d - e)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^2*e^(3/2)*Sqrt[c^2*x^2])","A",10,12,23,0.5217,1,"{266, 43, 5239, 12, 573, 154, 157, 63, 217, 206, 93, 204}"
140,1,132,0,0.1508414,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x^2],x]","\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e}-\frac{b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{e \sqrt{c^2 x^2}}+\frac{b x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{\sqrt{e} \sqrt{c^2 x^2}}","\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e}-\frac{b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{e \sqrt{c^2 x^2}}+\frac{b x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{\sqrt{e} \sqrt{c^2 x^2}}",1,"(Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/e - (b*c*Sqrt[d]*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(e*Sqrt[c^2*x^2]) + (b*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(Sqrt[e]*Sqrt[c^2*x^2])","A",8,8,21,0.3810,1,"{5237, 446, 105, 63, 217, 206, 93, 204}"
141,0,0,0,0.096927,"\int \frac{a+b \csc ^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x*Sqrt[d + e*x^2]),x]","\int \frac{a+b \csc ^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
142,0,0,0,0.1106582,"\int \frac{a+b \csc ^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^3*Sqrt[d + e*x^2]),x]","\int \frac{a+b \csc ^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x^3 \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x^3*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.092479,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.0307962,"\int \frac{a+b \csc ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsc[c*x])/Sqrt[d + e*x^2],x]","\int \frac{a+b \csc ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
145,1,247,0,0.2664995,"\int \frac{a+b \csc ^{-1}(c x)}{x^2 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^2*Sqrt[d + e*x^2]),x]","-\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{d x}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{d \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}","-\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{d x}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{d \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}",1,"-((b*c*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(d*Sqrt[c^2*x^2])) - (Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/(d*x) + (b*c^2*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(d*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + e)*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(d*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",11,11,23,0.4783,1,"{264, 5239, 12, 475, 21, 423, 427, 426, 424, 421, 419}"
146,1,362,0,0.5687871,"\int \frac{a+b \csc ^{-1}(c x)}{x^4 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^4*Sqrt[d + e*x^2]),x]","\frac{2 e \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2}}{9 d^2 \sqrt{c^2 x^2}}-\frac{2 b x \sqrt{1-c^2 x^2} \left(c^2 d-3 e\right) \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{9 d x^2 \sqrt{c^2 x^2}}","\frac{2 e \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{3 d x^3}-\frac{b c \sqrt{c^2 x^2-1} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2}}{9 d^2 \sqrt{c^2 x^2}}-\frac{2 b x \sqrt{1-c^2 x^2} \left(c^2 d-3 e\right) \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(2 c^2 d-5 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{9 d x^2 \sqrt{c^2 x^2}}",1,"-(b*c*(2*c^2*d - 5*e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(9*d^2*Sqrt[c^2*x^2]) - (b*c*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(9*d*x^2*Sqrt[c^2*x^2]) - (Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/(3*d*x^3) + (2*e*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/(3*d^2*x) + (b*c^2*(2*c^2*d - 5*e)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(9*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (2*b*(c^2*d - 3*e)*(c^2*d + e)*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(9*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",11,12,23,0.5217,1,"{271, 264, 5239, 12, 580, 583, 524, 427, 426, 424, 421, 419}"
147,1,252,0,1.0735374,"\int \frac{x^5 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2),x]","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{8 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e^3 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{6 c e^2 \sqrt{c^2 x^2}}-\frac{b x \left(9 c^2 d-e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{5/2} \sqrt{c^2 x^2}}","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 e^3}+\frac{8 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e^3 \sqrt{c^2 x^2}}+\frac{b x \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{6 c e^2 \sqrt{c^2 x^2}}-\frac{b x \left(9 c^2 d-e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{5/2} \sqrt{c^2 x^2}}",1,"(b*x*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(6*c*e^2*Sqrt[c^2*x^2]) - (d^2*(a + b*ArcCsc[c*x]))/(e^3*Sqrt[d + e*x^2]) - (2*d*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/e^3 + ((d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]))/(3*e^3) + (8*b*c*d^(3/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(3*e^3*Sqrt[c^2*x^2]) - (b*(9*c^2*d - e)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^2*e^(5/2)*Sqrt[c^2*x^2])","A",10,11,23,0.4783,1,"{266, 43, 5239, 12, 1615, 157, 63, 217, 206, 93, 204}"
148,1,156,0,0.3213089,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2),x]","\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{e^2 \sqrt{d+e x^2}}-\frac{2 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{e^2 \sqrt{c^2 x^2}}+\frac{b x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{3/2} \sqrt{c^2 x^2}}","\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{e^2 \sqrt{d+e x^2}}-\frac{2 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{e^2 \sqrt{c^2 x^2}}+\frac{b x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{3/2} \sqrt{c^2 x^2}}",1,"(d*(a + b*ArcCsc[c*x]))/(e^2*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/e^2 - (2*b*c*Sqrt[d]*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(e^2*Sqrt[c^2*x^2]) + (b*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(e^(3/2)*Sqrt[c^2*x^2])","A",9,11,23,0.4783,1,"{266, 43, 5239, 12, 573, 157, 63, 217, 206, 93, 204}"
149,1,79,0,0.1172384,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2),x]","\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{\sqrt{d} e \sqrt{c^2 x^2}}-\frac{a+b \csc ^{-1}(c x)}{e \sqrt{d+e x^2}}","\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{\sqrt{d} e \sqrt{c^2 x^2}}-\frac{a+b \csc ^{-1}(c x)}{e \sqrt{d+e x^2}}",1,"-((a + b*ArcCsc[c*x])/(e*Sqrt[d + e*x^2])) + (b*c*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(Sqrt[d]*e*Sqrt[c^2*x^2])","A",4,4,21,0.1905,1,"{5237, 446, 93, 204}"
150,0,0,0,0.124985,"\int \frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
151,0,0,0,0.136165,"\int \frac{a+b \csc ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^3*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x^3*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
152,0,0,0,0.1131193,"\int \frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
153,0,0,0,0.101641,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
154,1,108,0,0.0911184,"\int \frac{a+b \csc ^{-1}(c x)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x^2)^(3/2),x]","\frac{x \left(a+b \csc ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}+\frac{b x \sqrt{1-c^2 x^2} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}","\frac{x \left(a+b \csc ^{-1}(c x)\right)}{d \sqrt{d+e x^2}}+\frac{b x \sqrt{1-c^2 x^2} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}",1,"(x*(a + b*ArcCsc[c*x]))/(d*Sqrt[d + e*x^2]) + (b*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(d*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",5,5,20,0.2500,1,"{191, 5229, 12, 421, 419}"
155,1,275,0,0.3175261,"\int \frac{a+b \csc ^{-1}(c x)}{x^2 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^2*(d + e*x^2)^(3/2)),x]","-\frac{2 e x \left(a+b \csc ^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \csc ^{-1}(c x)}{d x \sqrt{d+e x^2}}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{d^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}","-\frac{2 e x \left(a+b \csc ^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \csc ^{-1}(c x)}{d x \sqrt{d+e x^2}}-\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{d^2 \sqrt{c^2 x^2}}-\frac{b x \sqrt{1-c^2 x^2} \left(c^2 d+2 e\right) \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}",1,"-((b*c*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(d^2*Sqrt[c^2*x^2])) - (a + b*ArcCsc[c*x])/(d*x*Sqrt[d + e*x^2]) - (2*e*x*(a + b*ArcCsc[c*x]))/(d^2*Sqrt[d + e*x^2]) + (b*c^2*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (b*(c^2*d + 2*e)*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",10,11,23,0.4783,1,"{271, 191, 5239, 12, 583, 524, 427, 426, 424, 421, 419}"
156,1,243,0,1.056596,"\int \frac{x^5 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{b c d x \sqrt{c^2 x^2-1}}{3 e^2 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}-\frac{8 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e^3 \sqrt{c^2 x^2}}+\frac{b x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{5/2} \sqrt{c^2 x^2}}","-\frac{d^2 \left(a+b \csc ^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \csc ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right)}{e^3}+\frac{b c d x \sqrt{c^2 x^2-1}}{3 e^2 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}-\frac{8 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 e^3 \sqrt{c^2 x^2}}+\frac{b x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{5/2} \sqrt{c^2 x^2}}",1,"(b*c*d*x*Sqrt[-1 + c^2*x^2])/(3*e^2*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[d + e*x^2]) - (d^2*(a + b*ArcCsc[c*x]))/(3*e^3*(d + e*x^2)^(3/2)) + (2*d*(a + b*ArcCsc[c*x]))/(e^3*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]))/e^3 - (8*b*c*Sqrt[d]*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(3*e^3*Sqrt[c^2*x^2]) + (b*x*ArcTanh[(Sqrt[e]*Sqrt[-1 + c^2*x^2])/(c*Sqrt[d + e*x^2])])/(e^(5/2)*Sqrt[c^2*x^2])","A",10,11,23,0.4783,1,"{266, 43, 5239, 12, 1614, 157, 63, 217, 206, 93, 204}"
157,1,163,0,0.246188,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \csc ^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}+\frac{2 b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 \sqrt{d} e^2 \sqrt{c^2 x^2}}-\frac{b c x \sqrt{c^2 x^2-1}}{3 e \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}","-\frac{a+b \csc ^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \csc ^{-1}(c x)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}+\frac{2 b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 \sqrt{d} e^2 \sqrt{c^2 x^2}}-\frac{b c x \sqrt{c^2 x^2-1}}{3 e \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}",1,"-(b*c*x*Sqrt[-1 + c^2*x^2])/(3*e*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[d + e*x^2]) + (d*(a + b*ArcCsc[c*x]))/(3*e^2*(d + e*x^2)^(3/2)) - (a + b*ArcCsc[c*x])/(e^2*Sqrt[d + e*x^2]) + (2*b*c*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(3*Sqrt[d]*e^2*Sqrt[c^2*x^2])","A",7,8,23,0.3478,1,"{266, 43, 5239, 12, 573, 152, 93, 204}"
158,1,138,0,0.1350407,"\int \frac{x \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \csc ^{-1}(c x)}{3 e \left(d+e x^2\right)^{3/2}}+\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 d^{3/2} e \sqrt{c^2 x^2}}+\frac{b c x \sqrt{c^2 x^2-1}}{3 d \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}","-\frac{a+b \csc ^{-1}(c x)}{3 e \left(d+e x^2\right)^{3/2}}+\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{c^2 x^2-1}}\right)}{3 d^{3/2} e \sqrt{c^2 x^2}}+\frac{b c x \sqrt{c^2 x^2-1}}{3 d \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}",1,"(b*c*x*Sqrt[-1 + c^2*x^2])/(3*d*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[d + e*x^2]) - (a + b*ArcCsc[c*x])/(3*e*(d + e*x^2)^(3/2)) + (b*c*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 + c^2*x^2])])/(3*d^(3/2)*e*Sqrt[c^2*x^2])","A",5,5,21,0.2381,1,"{5237, 446, 96, 93, 204}"
159,0,0,0,0.1232047,"\int \frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
160,0,0,0,0.1404131,"\int \frac{a+b \csc ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^3*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \csc ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x^3*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
161,0,0,0,0.1208364,"\int \frac{x^6 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^6 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^6 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^6*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
162,0,0,0,0.1095612,"\int \frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
163,1,276,0,0.2833727,"\int \frac{x^2 \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(5/2),x]","\frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{b c x^2 \sqrt{c^2 x^2-1}}{3 d \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b x \sqrt{1-c^2 x^2} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d e \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}-\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d e \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}","\frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{b c x^2 \sqrt{c^2 x^2-1}}{3 d \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b x \sqrt{1-c^2 x^2} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d e \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}-\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d e \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}",1,"(b*c*x^2*Sqrt[-1 + c^2*x^2])/(3*d*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[d + e*x^2]) + (x^3*(a + b*ArcCsc[c*x]))/(3*d*(d + e*x^2)^(3/2)) - (b*c^2*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3*d*e*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) + (b*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3*d*e*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",10,10,23,0.4348,1,"{264, 5239, 12, 471, 423, 427, 426, 424, 421, 419}"
164,1,296,0,0.2376143,"\int \frac{a+b \csc ^{-1}(c x)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCsc[c*x])/(d + e*x^2)^(5/2),x]","\frac{2 x \left(a+b \csc ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \csc ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b c e x^2 \sqrt{c^2 x^2-1}}{3 d^2 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{2 b x \sqrt{1-c^2 x^2} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}","\frac{2 x \left(a+b \csc ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \csc ^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b c e x^2 \sqrt{c^2 x^2-1}}{3 d^2 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{2 b x \sqrt{1-c^2 x^2} \sqrt{\frac{e x^2}{d}+1} F\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{3 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \left(c^2 d+e\right) \sqrt{\frac{e x^2}{d}+1}}",1,"-(b*c*e*x^2*Sqrt[-1 + c^2*x^2])/(3*d^2*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[d + e*x^2]) + (x*(a + b*ArcCsc[c*x]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*ArcCsc[c*x]))/(3*d^2*Sqrt[d + e*x^2]) + (b*c^2*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3*d^2*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) + (2*b*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",10,11,20,0.5500,1,"{192, 191, 5229, 12, 527, 524, 427, 426, 424, 421, 419}"
165,1,566,0,2.4048877,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^3*(a + b*ArcCsc[c*x]),x]","\frac{3 d^2 e (f x)^{m+3} \left(a+b \csc ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \csc ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \csc ^{-1}(c x)\right)}{f^7 (m+7)}+\frac{b c x \sqrt{1-c^2 x^2} (f x)^{m+1} \left(\frac{e \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^6 (m+2) (m+3) (m+4) (m+5) (m+6) (m+7)}+\frac{d^3}{(m+1)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{f \sqrt{c^2 x^2} \sqrt{c^2 x^2-1}}+\frac{b e x \sqrt{c^2 x^2-1} (f x)^{m+1} \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^5 f (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) \sqrt{c^2 x^2}}+\frac{b e^2 x \sqrt{c^2 x^2-1} (f x)^{m+3} \left(3 c^2 d \left(m^2+13 m+42\right)+e (m+5)^2\right)}{c^3 f^3 (m+4) (m+5) (m+6) (m+7) \sqrt{c^2 x^2}}+\frac{b e^3 x \sqrt{c^2 x^2-1} (f x)^{m+5}}{c f^5 (m+6) (m+7) \sqrt{c^2 x^2}}","\frac{3 d^2 e (f x)^{m+3} \left(a+b \csc ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \csc ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \csc ^{-1}(c x)\right)}{f^7 (m+7)}+\frac{b x \sqrt{1-c^2 x^2} (f x)^{m+1} \left(\frac{e (m+1) \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{(m+3) (m+5) (m+7)}+\frac{c^6 d^3 (m+2) (m+4) (m+6)}{m+1}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{c^5 f (m+1) (m+2) (m+4) (m+6) \sqrt{c^2 x^2} \sqrt{c^2 x^2-1}}+\frac{b e x \sqrt{c^2 x^2-1} (f x)^{m+1} \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)+3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^5 f (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) \sqrt{c^2 x^2}}+\frac{b e^2 x \sqrt{c^2 x^2-1} (f x)^{m+3} \left(3 c^2 d \left(m^2+13 m+42\right)+e (m+5)^2\right)}{c^3 f^3 (m+4) (m+5) (m+6) (m+7) \sqrt{c^2 x^2}}+\frac{b e^3 x \sqrt{c^2 x^2-1} (f x)^{m+5}}{c f^5 (m+6) (m+7) \sqrt{c^2 x^2}}",1,"(b*e*(e^2*(15 + 8*m + m^2)^2 + 3*c^2*d*e*(3 + m)^2*(42 + 13*m + m^2) + 3*c^4*d^2*(840 + 638*m + 179*m^2 + 22*m^3 + m^4))*x*(f*x)^(1 + m)*Sqrt[-1 + c^2*x^2])/(c^5*f*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*Sqrt[c^2*x^2]) + (b*e^2*(e*(5 + m)^2 + 3*c^2*d*(42 + 13*m + m^2))*x*(f*x)^(3 + m)*Sqrt[-1 + c^2*x^2])/(c^3*f^3*(4 + m)*(5 + m)*(6 + m)*(7 + m)*Sqrt[c^2*x^2]) + (b*e^3*x*(f*x)^(5 + m)*Sqrt[-1 + c^2*x^2])/(c*f^5*(6 + m)*(7 + m)*Sqrt[c^2*x^2]) + (d^3*(f*x)^(1 + m)*(a + b*ArcCsc[c*x]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*ArcCsc[c*x]))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*ArcCsc[c*x]))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*ArcCsc[c*x]))/(f^7*(7 + m)) + (b*c*(d^3/(1 + m)^2 + (e*(e^2*(15 + 8*m + m^2)^2 + 3*c^2*d*e*(3 + m)^2*(42 + 13*m + m^2) + 3*c^4*d^2*(840 + 638*m + 179*m^2 + 22*m^3 + m^4)))/(c^6*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)))*x*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2])","A",6,7,23,0.3043,1,"{270, 5239, 1809, 1267, 459, 365, 364}"
166,1,352,0,0.4320322,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^2*(a + b*ArcCsc[c*x]),x]","\frac{d^2 (f x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \csc ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \csc ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{b c x \sqrt{1-c^2 x^2} (f x)^{m+1} \left(\frac{e \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)}{c^4 (m+2) (m+3) (m+4) (m+5)}+\frac{d^2}{(m+1)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{f \sqrt{c^2 x^2} \sqrt{c^2 x^2-1}}+\frac{b e x \sqrt{c^2 x^2-1} (f x)^{m+1} \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)}{c^3 f (m+2) (m+3) (m+4) (m+5) \sqrt{c^2 x^2}}+\frac{b e^2 x \sqrt{c^2 x^2-1} (f x)^{m+3}}{c f^3 (m+4) (m+5) \sqrt{c^2 x^2}}","\frac{d^2 (f x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \csc ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \csc ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{b x \sqrt{1-c^2 x^2} (f x)^{m+1} \left(c^4 d^2 (m+2) (m+3) (m+4) (m+5)+e (m+1)^2 \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{c^3 f (m+1)^2 (m+2) (m+3) (m+4) (m+5) \sqrt{c^2 x^2} \sqrt{c^2 x^2-1}}+\frac{b e x \sqrt{c^2 x^2-1} (f x)^{m+1} \left(2 c^2 d \left(m^2+9 m+20\right)+e (m+3)^2\right)}{c^3 f (m+2) (m+3) (m+4) (m+5) \sqrt{c^2 x^2}}+\frac{b e^2 x \sqrt{c^2 x^2-1} (f x)^{m+3}}{c f^3 (m+4) (m+5) \sqrt{c^2 x^2}}",1,"(b*e*(e*(3 + m)^2 + 2*c^2*d*(20 + 9*m + m^2))*x*(f*x)^(1 + m)*Sqrt[-1 + c^2*x^2])/(c^3*f*(2 + m)*(3 + m)*(4 + m)*(5 + m)*Sqrt[c^2*x^2]) + (b*e^2*x*(f*x)^(3 + m)*Sqrt[-1 + c^2*x^2])/(c*f^3*(4 + m)*(5 + m)*Sqrt[c^2*x^2]) + (d^2*(f*x)^(1 + m)*(a + b*ArcCsc[c*x]))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*ArcCsc[c*x]))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*ArcCsc[c*x]))/(f^5*(5 + m)) + (b*c*(d^2/(1 + m)^2 + (e*(e*(3 + m)^2 + 2*c^2*d*(20 + 9*m + m^2)))/(c^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)))*x*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2])","A",6,7,23,0.3043,1,"{270, 5239, 12, 1267, 459, 365, 364}"
167,1,202,0,0.1938284,"\int (f x)^m \left(d+e x^2\right) \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*ArcCsc[c*x]),x]","\frac{d (f x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \csc ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{b c x \sqrt{1-c^2 x^2} (f x)^{m+1} \left(\frac{e}{c^2 (m+2) (m+3)}+\frac{d}{(m+1)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{f \sqrt{c^2 x^2} \sqrt{c^2 x^2-1}}+\frac{b e x \sqrt{c^2 x^2-1} (f x)^{m+1}}{c f \left(m^2+5 m+6\right) \sqrt{c^2 x^2}}","\frac{d (f x)^{m+1} \left(a+b \csc ^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \csc ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{b x \sqrt{1-c^2 x^2} (f x)^{m+1} \left(c^2 d (m+2) (m+3)+e (m+1)^2\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};c^2 x^2\right)}{c f (m+1)^2 (m+2) (m+3) \sqrt{c^2 x^2} \sqrt{c^2 x^2-1}}+\frac{b e x \sqrt{c^2 x^2-1} (f x)^{m+1}}{c f \left(m^2+5 m+6\right) \sqrt{c^2 x^2}}",1,"(b*e*x*(f*x)^(1 + m)*Sqrt[-1 + c^2*x^2])/(c*f*(6 + 5*m + m^2)*Sqrt[c^2*x^2]) + (d*(f*x)^(1 + m)*(a + b*ArcCsc[c*x]))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*ArcCsc[c*x]))/(f^3*(3 + m)) + (b*c*(d/(1 + m)^2 + e/(c^2*(2 + m)*(3 + m)))*x*(f*x)^(1 + m)*Sqrt[1 - c^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, c^2*x^2])/(f*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2])","A",5,6,21,0.2857,1,"{14, 5239, 12, 459, 365, 364}"
168,0,0,0,0.0751858,"\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[((f*x)^m*(a + b*ArcCsc[c*x]))/(d + e*x^2),x]","\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{d+e x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{d+e x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsc[c*x]))/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
169,0,0,0,0.0741915,"\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcCsc[c*x]))/(d + e*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsc[c*x]))/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
170,0,0,0,0.1154804,"\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]),x]","\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} (f x)^m \left(a+b \csc ^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
171,0,0,0,0.0972978,"\int (f x)^m \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","Int[(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]),x]","\int (f x)^m \sqrt{d+e x^2} \left(a+b \csc ^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} (f x)^m \left(a+b \csc ^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcCsc[c*x]), x]","A",0,0,0,0,-1,"{}"
172,0,0,0,0.1000588,"\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[((f*x)^m*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsc[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
173,0,0,0,0.1172093,"\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \csc ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsc[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
174,1,401,0,2.5272284,"\int \frac{x^{11} \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^11*(a + b*ArcCsc[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\left(1-c^4 x^4\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \csc ^{-1}(c x)\right)}{2 c^{12}}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{9/2}}{90 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{3 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{7/2}}{70 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{13 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{150 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{7 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{90 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{15 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{4 b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{15 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}","-\frac{\left(1-c^4 x^4\right)^{5/2} \left(a+b \csc ^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \csc ^{-1}(c x)\right)}{2 c^{12}}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{9/2}}{90 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{3 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{7/2}}{70 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{13 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{150 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{7 b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{90 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{4 b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{15 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{4 b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{15 c^{13} x \sqrt{1-\frac{1}{c^2 x^2}}}",1,"(-4*b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(15*c^13*Sqrt[1 - 1/(c^2*x^2)]*x) + (7*b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(3/2))/(90*c^13*Sqrt[1 - 1/(c^2*x^2)]*x) - (13*b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(5/2))/(150*c^13*Sqrt[1 - 1/(c^2*x^2)]*x) + (3*b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(7/2))/(70*c^13*Sqrt[1 - 1/(c^2*x^2)]*x) - (b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(9/2))/(90*c^13*Sqrt[1 - 1/(c^2*x^2)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcCsc[c*x]))/(2*c^12) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcCsc[c*x]))/(3*c^12) - ((1 - c^4*x^4)^(5/2)*(a + b*ArcCsc[c*x]))/(10*c^12) + (4*b*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(15*c^13*Sqrt[1 - 1/(c^2*x^2)]*x)","A",16,11,26,0.4231,1,"{266, 43, 5247, 12, 6721, 6742, 848, 50, 63, 208, 783}"
175,1,268,0,2.0272021,"\int \frac{x^7 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^7*(a + b*ArcCsc[c*x]))/Sqrt[1 - c^4*x^4],x]","\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \csc ^{-1}(c x)\right)}{2 c^8}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{30 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{18 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{3 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{3 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}","\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \csc ^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \csc ^{-1}(c x)\right)}{2 c^8}-\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{5/2}}{30 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{b \sqrt{1-c^2 x^2} \left(c^2 x^2+1\right)^{3/2}}{18 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{3 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{3 c^9 x \sqrt{1-\frac{1}{c^2 x^2}}}",1,"-(b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(3*c^9*Sqrt[1 - 1/(c^2*x^2)]*x) + (b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(3/2))/(18*c^9*Sqrt[1 - 1/(c^2*x^2)]*x) - (b*Sqrt[1 - c^2*x^2]*(1 + c^2*x^2)^(5/2))/(30*c^9*Sqrt[1 - 1/(c^2*x^2)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcCsc[c*x]))/(2*c^8) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcCsc[c*x]))/(6*c^8) + (b*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(3*c^9*Sqrt[1 - 1/(c^2*x^2)]*x)","A",13,11,26,0.4231,1,"{266, 43, 5247, 12, 6721, 6742, 848, 50, 63, 208, 783}"
176,1,135,0,0.2120741,"\int \frac{x^3 \left(a+b \csc ^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^3*(a + b*ArcCsc[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\sqrt{1-c^4 x^4} \left(a+b \csc ^{-1}(c x)\right)}{2 c^4}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{2 c^5 x \sqrt{1-\frac{1}{c^2 x^2}}}+\frac{b \sqrt{1-c^2 x^2} \tanh ^{-1}\left(\sqrt{c^2 x^2+1}\right)}{2 c^5 x \sqrt{1-\frac{1}{c^2 x^2}}}","-\frac{\sqrt{1-c^4 x^4} \left(a+b \csc ^{-1}(c x)\right)}{2 c^4}-\frac{b x \sqrt{1-c^4 x^4}}{2 c^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1}}+\frac{b x \tan ^{-1}\left(\frac{\sqrt{1-c^4 x^4}}{\sqrt{c^2 x^2-1}}\right)}{2 c^3 \sqrt{c^2 x^2}}",1,"-(b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(2*c^5*Sqrt[1 - 1/(c^2*x^2)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcCsc[c*x]))/(2*c^4) + (b*Sqrt[1 - c^2*x^2]*ArcTanh[Sqrt[1 + c^2*x^2]])/(2*c^5*Sqrt[1 - 1/(c^2*x^2)]*x)","A",8,9,26,0.3462,1,"{261, 5247, 12, 1572, 1252, 848, 50, 63, 208}"
177,0,0,0,0.0890698,"\int \frac{a+b \csc ^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcCsc[c*x])/(x*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \csc ^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"
178,0,0,0,0.1005546,"\int \frac{a+b \csc ^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcCsc[c*x])/(x^5*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \csc ^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \csc ^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcCsc[c*x])/(x^5*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"