1,1,114,0,0.0608637,"\int x^6 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^6*(a + b*ArcSec[c*x]),x]","\frac{1}{7} x^7 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x]))/7 - (5*b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(112*c^7)","A",7,5,12,0.4167,1,"{5220, 266, 51, 63, 208}"
2,1,89,0,0.0413837,"\int x^5 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^5*(a + b*ArcSec[c*x]),x]","\frac{1}{6} x^6 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x]))/6","A",4,3,12,0.2500,1,"{5220, 271, 191}"
3,1,89,0,0.0463687,"\int x^4 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^4*(a + b*ArcSec[c*x]),x]","\frac{1}{5} x^5 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x]))/5 - (3*b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(40*c^5)","A",6,5,12,0.4167,1,"{5220, 266, 51, 63, 208}"
4,1,64,0,0.0265671,"\int x^3 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcSec[c*x]),x]","\frac{1}{4} x^4 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x]))/4","A",3,3,12,0.2500,1,"{5220, 271, 191}"
5,1,64,0,0.0348788,"\int x^2 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcSec[c*x]),x]","\frac{1}{3} x^3 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x]))/3 - (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(6*c^3)","A",5,5,12,0.4167,1,"{5220, 266, 51, 63, 208}"
6,1,39,0,0.0119012,"\int x \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcSec[c*x]),x]","\frac{1}{2} x^2 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x]))/2","A",2,2,10,0.2000,1,"{5220, 191}"
7,1,32,0,0.0203169,"\int \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[a + b*ArcSec[c*x],x]","a x-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \sec ^{-1}(c x)","a x-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \sec ^{-1}(c x)",1,"a*x + b*x*ArcSec[c*x] - (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c","A",5,4,8,0.5000,1,"{5214, 266, 63, 208}"
8,1,64,0,0.0843917,"\int \frac{a+b \sec ^{-1}(c x)}{x} \, dx","Int[(a + b*ArcSec[c*x])/x,x]","\frac{1}{2} i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)+\frac{i \left(a+b \sec ^{-1}(c x)\right)^2}{2 b}-\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)","\frac{1}{2} i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)+\frac{i \left(a+b \sec ^{-1}(c x)\right)^2}{2 b}-\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)",1,"((I/2)*(a + b*ArcSec[c*x])^2)/b - (a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])] + (I/2)*b*PolyLog[2, -E^((2*I)*ArcSec[c*x])]","A",6,6,12,0.5000,1,"{5218, 4626, 3719, 2190, 2279, 2391}"
9,1,31,0,0.0202613,"\int \frac{a+b \sec ^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcSec[c*x])/x^2,x]","b c \sqrt{1-\frac{1}{c^2 x^2}}-\frac{a+b \sec ^{-1}(c x)}{x}","b c \sqrt{1-\frac{1}{c^2 x^2}}-\frac{a+b \sec ^{-1}(c x)}{x}",1,"b*c*Sqrt[1 - 1/(c^2*x^2)] - (a + b*ArcSec[c*x])/x","A",2,2,12,0.1667,1,"{5220, 261}"
10,1,51,0,0.0332673,"\int \frac{a+b \sec ^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcSec[c*x])/x^3,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x])/(2*x^2)","A",4,4,12,0.3333,1,"{5220, 335, 321, 216}"
11,1,60,0,0.0390767,"\int \frac{a+b \sec ^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcSec[c*x])/x^4,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x])/(3*x^3)","A",4,3,12,0.2500,1,"{5220, 266, 43}"
12,1,76,0,0.0453043,"\int \frac{a+b \sec ^{-1}(c x)}{x^5} \, dx","Int[(a + b*ArcSec[c*x])/x^5,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x])/(4*x^4)","A",5,4,12,0.3333,1,"{5220, 335, 321, 216}"
13,1,82,0,0.0493282,"\int \frac{a+b \sec ^{-1}(c x)}{x^6} \, dx","Int[(a + b*ArcSec[c*x])/x^6,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x])/(5*x^5)","A",4,3,12,0.2500,1,"{5220, 266, 43}"
14,1,101,0,0.0588217,"\int \frac{a+b \sec ^{-1}(c x)}{x^7} \, dx","Int[(a + b*ArcSec[c*x])/x^7,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x])/(6*x^6)","A",6,4,12,0.3333,1,"{5220, 335, 321, 216}"
15,1,107,0,0.1067238,"\int x^3 \left(a+b \sec ^{-1}(c x)\right)^2 \, dx","Int[x^3*(a + b*ArcSec[c*x])^2,x]","-\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{6 c}-\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} x^4 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{6 c}-\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} x^4 \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*c^3) - (b*Sqrt[1 - 1/(c^2*x^2)]*x^3*(a + b*ArcSec[c*x]))/(6*c) + (x^4*(a + b*ArcSec[c*x])^2)/4 + (b^2*Log[x])/(3*c^4)","A",5,5,14,0.3571,1,"{5222, 4409, 4185, 4184, 3475}"
16,1,147,0,0.1231324,"\int x^2 \left(a+b \sec ^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcSec[c*x])^2,x]","-\frac{i b^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(c x)}\right)}{3 c^3}+\frac{i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right)}{3 c^3}-\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{3 c}+\frac{2 i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \sec ^{-1}(c x)\right)^2+\frac{b^2 x}{3 c^2}","-\frac{i b^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(c x)}\right)}{3 c^3}+\frac{i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right)}{3 c^3}-\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{3 c}+\frac{2 i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*c) + (x^3*(a + b*ArcSec[c*x])^2)/3 + (((2*I)/3)*b*(a + b*ArcSec[c*x])*ArcTan[E^(I*ArcSec[c*x])])/c^3 - ((I/3)*b^2*PolyLog[2, (-I)*E^(I*ArcSec[c*x])])/c^3 + ((I/3)*b^2*PolyLog[2, I*E^(I*ArcSec[c*x])])/c^3","A",8,6,14,0.4286,1,"{5222, 4409, 4185, 4181, 2279, 2391}"
17,1,56,0,0.0682639,"\int x \left(a+b \sec ^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcSec[c*x])^2,x]","-\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{c}+\frac{1}{2} x^2 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{c}+\frac{1}{2} x^2 \left(a+b \sec ^{-1}(c x)\right)^2+\frac{b^2 \log (x)}{c^2}",1,"-((b*Sqrt[1 - 1/(c^2*x^2)]*x*(a + b*ArcSec[c*x]))/c) + (x^2*(a + b*ArcSec[c*x])^2)/2 + (b^2*Log[x])/c^2","A",4,4,12,0.3333,1,"{5222, 4409, 4184, 3475}"
18,1,92,0,0.0719971,"\int \left(a+b \sec ^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcSec[c*x])^2,x]","-\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(c x)}\right)}{c}+\frac{2 i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right)}{c}+x \left(a+b \sec ^{-1}(c x)\right)^2+\frac{4 i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c}","-\frac{2 i b^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(c x)}\right)}{c}+\frac{2 i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right)}{c}+x \left(a+b \sec ^{-1}(c x)\right)^2+\frac{4 i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c}",1,"x*(a + b*ArcSec[c*x])^2 + ((4*I)*b*(a + b*ArcSec[c*x])*ArcTan[E^(I*ArcSec[c*x])])/c - ((2*I)*b^2*PolyLog[2, (-I)*E^(I*ArcSec[c*x])])/c + ((2*I)*b^2*PolyLog[2, I*E^(I*ArcSec[c*x])])/c","A",7,5,10,0.5000,1,"{5216, 4409, 4181, 2279, 2391}"
19,1,93,0,0.1189867,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcSec[c*x])^2/x,x]","i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(c x)}\right)+\frac{i \left(a+b \sec ^{-1}(c x)\right)^3}{3 b}-\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2","i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)-\frac{1}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(c x)}\right)+\frac{i \left(a+b \sec ^{-1}(c x)\right)^3}{3 b}-\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2",1,"((I/3)*(a + b*ArcSec[c*x])^3)/b - (a + b*ArcSec[c*x])^2*Log[1 + E^((2*I)*ArcSec[c*x])] + I*b*(a + b*ArcSec[c*x])*PolyLog[2, -E^((2*I)*ArcSec[c*x])] - (b^2*PolyLog[3, -E^((2*I)*ArcSec[c*x])])/2","A",6,6,14,0.4286,1,"{5222, 3719, 2190, 2531, 2282, 6589}"
20,1,50,0,0.0586854,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcSec[c*x])^2/x^2,x]","2 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)-\frac{\left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)-\frac{\left(a+b \sec ^{-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*ArcSec[c*x]) - (a + b*ArcSec[c*x])^2/x","A",4,3,14,0.2143,1,"{5222, 3296, 2638}"
21,1,94,0,0.0793479,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^2}{x^3} \, dx","Int[(a + b*ArcSec[c*x])^2/x^3,x]","\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{2 x}+\frac{1}{2} \left(c^2-\frac{1}{x^2}\right) \left(a+b \sec ^{-1}(c x)\right)^2-\frac{1}{2} a b c^2 \sec ^{-1}(c x)-\frac{1}{4} b^2 c^2 \sec ^{-1}(c x)^2+\frac{b^2}{4 x^2}","\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{2 x}+\frac{1}{2} \left(c^2-\frac{1}{x^2}\right) \left(a+b \sec ^{-1}(c x)\right)^2-\frac{1}{2} a b c^2 \sec ^{-1}(c x)-\frac{1}{4} b^2 c^2 \sec ^{-1}(c x)^2+\frac{b^2}{4 x^2}",1,"b^2/(4*x^2) - (a*b*c^2*ArcSec[c*x])/2 - (b^2*c^2*ArcSec[c*x]^2)/4 + (b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x]))/(2*x) + ((c^2 - x^(-2))*(a + b*ArcSec[c*x])^2)/2","A",4,3,14,0.2143,1,"{5222, 4404, 3310}"
22,1,102,0,0.0940474,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^2}{x^4} \, dx","Int[(a + b*ArcSec[c*x])^2/x^4,x]","\frac{4}{9} b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)+\frac{2 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{9 x^2}-\frac{\left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{2 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{9 x^2}-\frac{\left(a+b \sec ^{-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*ArcSec[c*x]))/9 + (2*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x]))/(9*x^2) - (a + b*ArcSec[c*x])^2/(3*x^3)","A",5,5,14,0.3571,1,"{5222, 4405, 3310, 3296, 2638}"
23,1,134,0,0.1111332,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^2}{x^5} \, dx","Int[(a + b*ArcSec[c*x])^2/x^5,x]","\frac{3 b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{16 x}+\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{8 x^3}+\frac{3}{16} a b c^4 \sec ^{-1}(c x)-\frac{\left(a+b \sec ^{-1}(c x)\right)^2}{4 x^4}+\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \sec ^{-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 \sec ^{-1}(c x)\right)}{16 x}+\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)}{8 x^3}+\frac{3}{16} a b c^4 \sec ^{-1}(c x)-\frac{\left(a+b \sec ^{-1}(c x)\right)^2}{4 x^4}+\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \sec ^{-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*ArcSec[c*x])/16 + (3*b^2*c^4*ArcSec[c*x]^2)/32 + (b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x]))/(8*x^3) + (3*b*c^3*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x]))/(16*x) - (a + b*ArcSec[c*x])^2/(4*x^4)","A",5,3,14,0.2143,1,"{5222, 4405, 3310}"
24,1,207,0,0.2112031,"\int x^3 \left(a+b \sec ^{-1}(c x)\right)^3 \, dx","Int[x^3*(a + b*ArcSec[c*x])^3,x]","\frac{i b^3 \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 c^4}+\frac{b^2 x^2 \left(a+b \sec ^{-1}(c x)\right)}{4 c^2}-\frac{b^2 \log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^4}-\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{4 c}-\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{2 c^3}+\frac{i b \left(a+b \sec ^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \sec ^{-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 \sec ^{-1}(c x)}\right)}{2 c^4}+\frac{b^2 x^2 \left(a+b \sec ^{-1}(c x)\right)}{4 c^2}-\frac{b^2 \log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^4}-\frac{b x^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{4 c}-\frac{b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{2 c^3}+\frac{i b \left(a+b \sec ^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \sec ^{-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*ArcSec[c*x]))/(4*c^2) + ((I/2)*b*(a + b*ArcSec[c*x])^2)/c^4 - (b*Sqrt[1 - 1/(c^2*x^2)]*x*(a + b*ArcSec[c*x])^2)/(2*c^3) - (b*Sqrt[1 - 1/(c^2*x^2)]*x^3*(a + b*ArcSec[c*x])^2)/(4*c) + (x^4*(a + b*ArcSec[c*x])^3)/4 - (b^2*(a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])])/c^4 + ((I/2)*b^3*PolyLog[2, -E^((2*I)*ArcSec[c*x])])/c^4","A",10,10,14,0.7143,1,"{5222, 4409, 4186, 3767, 8, 4184, 3719, 2190, 2279, 2391}"
25,1,236,0,0.1922311,"\int x^2 \left(a+b \sec ^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcSec[c*x])^3,x]","-\frac{i b^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^3}+\frac{i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(c x)}\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(c x)}\right)}{c^3}+\frac{b^2 x \left(a+b \sec ^{-1}(c x)\right)}{c^2}-\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{2 c}+\frac{i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \sec ^{-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,-i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^3}+\frac{i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(c x)}\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(c x)}\right)}{c^3}+\frac{b^2 x \left(a+b \sec ^{-1}(c x)\right)}{c^2}-\frac{b x^2 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{2 c}+\frac{i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \sec ^{-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*ArcSec[c*x]))/c^2 - (b*Sqrt[1 - 1/(c^2*x^2)]*x^2*(a + b*ArcSec[c*x])^2)/(2*c) + (x^3*(a + b*ArcSec[c*x])^3)/3 + (I*b*(a + b*ArcSec[c*x])^2*ArcTan[E^(I*ArcSec[c*x])])/c^3 - (b^3*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c^3 - (I*b^2*(a + b*ArcSec[c*x])*PolyLog[2, (-I)*E^(I*ArcSec[c*x])])/c^3 + (I*b^2*(a + b*ArcSec[c*x])*PolyLog[2, I*E^(I*ArcSec[c*x])])/c^3 + (b^3*PolyLog[3, (-I)*E^(I*ArcSec[c*x])])/c^3 - (b^3*PolyLog[3, I*E^(I*ArcSec[c*x])])/c^3","A",11,8,14,0.5714,1,"{5222, 4409, 4186, 3770, 4181, 2531, 2282, 6589}"
26,1,126,0,0.1424305,"\int x \left(a+b \sec ^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcSec[c*x])^3,x]","\frac{3 i b^3 \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 c^2}-\frac{3 b^2 \log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^2}-\frac{3 b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{2 c}+\frac{3 i b \left(a+b \sec ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \sec ^{-1}(c x)\right)^3","\frac{3 i b^3 \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 c^2}-\frac{3 b^2 \log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c^2}-\frac{3 b x \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{2 c}+\frac{3 i b \left(a+b \sec ^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \sec ^{-1}(c x)\right)^3",1,"(((3*I)/2)*b*(a + b*ArcSec[c*x])^2)/c^2 - (3*b*Sqrt[1 - 1/(c^2*x^2)]*x*(a + b*ArcSec[c*x])^2)/(2*c) + (x^2*(a + b*ArcSec[c*x])^3)/2 - (3*b^2*(a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])])/c^2 + (((3*I)/2)*b^3*PolyLog[2, -E^((2*I)*ArcSec[c*x])])/c^2","A",7,7,12,0.5833,1,"{5222, 4409, 4184, 3719, 2190, 2279, 2391}"
27,1,158,0,0.1182916,"\int \left(a+b \sec ^{-1}(c x)\right)^3 \, dx","Int[(a + b*ArcSec[c*x])^3,x]","-\frac{6 i b^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c}+\frac{6 i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c}+\frac{6 b^3 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(c x)}\right)}{c}-\frac{6 b^3 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(c x)}\right)}{c}+x \left(a+b \sec ^{-1}(c x)\right)^3+\frac{6 i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2}{c}","-\frac{6 i b^2 \text{PolyLog}\left(2,-i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c}+\frac{6 i b^2 \text{PolyLog}\left(2,i e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{c}+\frac{6 b^3 \text{PolyLog}\left(3,-i e^{i \sec ^{-1}(c x)}\right)}{c}-\frac{6 b^3 \text{PolyLog}\left(3,i e^{i \sec ^{-1}(c x)}\right)}{c}+x \left(a+b \sec ^{-1}(c x)\right)^3+\frac{6 i b \tan ^{-1}\left(e^{i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2}{c}",1,"x*(a + b*ArcSec[c*x])^3 + ((6*I)*b*(a + b*ArcSec[c*x])^2*ArcTan[E^(I*ArcSec[c*x])])/c - ((6*I)*b^2*(a + b*ArcSec[c*x])*PolyLog[2, (-I)*E^(I*ArcSec[c*x])])/c + ((6*I)*b^2*(a + b*ArcSec[c*x])*PolyLog[2, I*E^(I*ArcSec[c*x])])/c + (6*b^3*PolyLog[3, (-I)*E^(I*ArcSec[c*x])])/c - (6*b^3*PolyLog[3, I*E^(I*ArcSec[c*x])])/c","A",9,6,10,0.6000,1,"{5216, 4409, 4181, 2531, 2282, 6589}"
28,1,128,0,0.140944,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcSec[c*x])^3/x,x]","-\frac{3}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)+\frac{3}{2} i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2-\frac{3}{4} i b^3 \text{PolyLog}\left(4,-e^{2 i \sec ^{-1}(c x)}\right)+\frac{i \left(a+b \sec ^{-1}(c x)\right)^4}{4 b}-\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^3","-\frac{3}{2} b^2 \text{PolyLog}\left(3,-e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)+\frac{3}{2} i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^2-\frac{3}{4} i b^3 \text{PolyLog}\left(4,-e^{2 i \sec ^{-1}(c x)}\right)+\frac{i \left(a+b \sec ^{-1}(c x)\right)^4}{4 b}-\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)^3",1,"((I/4)*(a + b*ArcSec[c*x])^4)/b - (a + b*ArcSec[c*x])^3*Log[1 + E^((2*I)*ArcSec[c*x])] + ((3*I)/2)*b*(a + b*ArcSec[c*x])^2*PolyLog[2, -E^((2*I)*ArcSec[c*x])] - (3*b^2*(a + b*ArcSec[c*x])*PolyLog[3, -E^((2*I)*ArcSec[c*x])])/2 - ((3*I)/4)*b^3*PolyLog[4, -E^((2*I)*ArcSec[c*x])]","A",7,7,14,0.5000,1,"{5222, 3719, 2190, 2531, 6609, 2282, 6589}"
29,1,80,0,0.0831653,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcSec[c*x])^3/x^2,x]","\frac{6 b^2 \left(a+b \sec ^{-1}(c x)\right)}{x}+3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2-\frac{\left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{x}+3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2-\frac{\left(a+b \sec ^{-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*ArcSec[c*x]))/x + 3*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x])^2 - (a + b*ArcSec[c*x])^3/x","A",5,3,14,0.2143,1,"{5222, 3296, 2637}"
30,1,137,0,0.1045495,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^3}{x^3} \, dx","Int[(a + b*ArcSec[c*x])^3/x^3,x]","-\frac{3}{4} b^2 \left(c^2-\frac{1}{x^2}\right) \left(a+b \sec ^{-1}(c x)\right)+\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{4 x}+\frac{1}{2} \left(c^2-\frac{1}{x^2}\right) \left(a+b \sec ^{-1}(c x)\right)^3-\frac{1}{4} c^2 \left(a+b \sec ^{-1}(c x)\right)^3-\frac{3 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}}{8 x}+\frac{3}{8} b^3 c^2 \sec ^{-1}(c x)","-\frac{3}{4} b^2 \left(c^2-\frac{1}{x^2}\right) \left(a+b \sec ^{-1}(c x)\right)+\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{4 x}+\frac{1}{2} \left(c^2-\frac{1}{x^2}\right) \left(a+b \sec ^{-1}(c x)\right)^3-\frac{1}{4} c^2 \left(a+b \sec ^{-1}(c x)\right)^3-\frac{3 b^3 c \sqrt{1-\frac{1}{c^2 x^2}}}{8 x}+\frac{3}{8} b^3 c^2 \sec ^{-1}(c x)",1,"(-3*b^3*c*Sqrt[1 - 1/(c^2*x^2)])/(8*x) + (3*b^3*c^2*ArcSec[c*x])/8 - (3*b^2*(c^2 - x^(-2))*(a + b*ArcSec[c*x]))/4 + (3*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x])^2)/(4*x) - (c^2*(a + b*ArcSec[c*x])^3)/4 + ((c^2 - x^(-2))*(a + b*ArcSec[c*x])^3)/2","A",6,6,14,0.4286,1,"{5222, 4404, 3311, 32, 2635, 8}"
31,1,170,0,0.1468382,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^3}{x^4} \, dx","Int[(a + b*ArcSec[c*x])^3/x^4,x]","\frac{4 b^2 c^2 \left(a+b \sec ^{-1}(c x)\right)}{3 x}+\frac{2 b^2 \left(a+b \sec ^{-1}(c x)\right)}{9 x^3}+\frac{2}{3} b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2+\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{3 x^2}-\frac{\left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 x}+\frac{2 b^2 \left(a+b \sec ^{-1}(c x)\right)}{9 x^3}+\frac{2}{3} b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2+\frac{b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{3 x^2}-\frac{\left(a+b \sec ^{-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*ArcSec[c*x]))/(9*x^3) + (4*b^2*c^2*(a + b*ArcSec[c*x]))/(3*x) + (2*b*c^3*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x])^2)/3 + (b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x])^2)/(3*x^2) - (a + b*ArcSec[c*x])^3/(3*x^3)","A",8,6,14,0.4286,1,"{5222, 4405, 3311, 3296, 2637, 2633}"
32,1,208,0,0.173491,"\int \frac{\left(a+b \sec ^{-1}(c x)\right)^3}{x^5} \, dx","Int[(a + b*ArcSec[c*x])^3/x^5,x]","\frac{9 b^2 c^2 \left(a+b \sec ^{-1}(c x)\right)}{32 x^2}+\frac{3 b^2 \left(a+b \sec ^{-1}(c x)\right)}{32 x^4}+\frac{9 b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{32 x}+\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{16 x^3}+\frac{3}{32} c^4 \left(a+b \sec ^{-1}(c x)\right)^3-\frac{\left(a+b \sec ^{-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 \sec ^{-1}(c x)","\frac{9 b^2 c^2 \left(a+b \sec ^{-1}(c x)\right)}{32 x^2}+\frac{3 b^2 \left(a+b \sec ^{-1}(c x)\right)}{32 x^4}+\frac{9 b c^3 \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{32 x}+\frac{3 b c \sqrt{1-\frac{1}{c^2 x^2}} \left(a+b \sec ^{-1}(c x)\right)^2}{16 x^3}+\frac{3}{32} c^4 \left(a+b \sec ^{-1}(c x)\right)^3-\frac{\left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x])/256 + (3*b^2*(a + b*ArcSec[c*x]))/(32*x^4) + (9*b^2*c^2*(a + b*ArcSec[c*x]))/(32*x^2) + (3*b*c*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x])^2)/(16*x^3) + (9*b*c^3*Sqrt[1 - 1/(c^2*x^2)]*(a + b*ArcSec[c*x])^2)/(32*x) + (3*c^4*(a + b*ArcSec[c*x])^3)/32 - (a + b*ArcSec[c*x])^3/(4*x^4)","A",10,6,14,0.4286,1,"{5222, 4405, 3311, 32, 2635, 8}"
33,0,0,0,0.0144259,"\int \frac{x}{a+b \sec ^{-1}(c x)} \, dx","Int[x/(a + b*ArcSec[c*x]),x]","\int \frac{x}{a+b \sec ^{-1}(c x)} \, dx","\text{Int}\left(\frac{x}{a+b \sec ^{-1}(c x)},x\right)",0,"Defer[Int][x/(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
34,0,0,0,0.0057647,"\int \frac{1}{a+b \sec ^{-1}(c x)} \, dx","Int[(a + b*ArcSec[c*x])^(-1),x]","\int \frac{1}{a+b \sec ^{-1}(c x)} \, dx","\text{Int}\left(\frac{1}{a+b \sec ^{-1}(c x)},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])^(-1), x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0252971,"\int \frac{1}{x \left(a+b \sec ^{-1}(c x)\right)} \, dx","Int[1/(x*(a + b*ArcSec[c*x])),x]","\int \frac{1}{x \left(a+b \sec ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sec ^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*ArcSec[c*x])), x]","A",0,0,0,0,-1,"{}"
36,1,46,0,0.1051622,"\int \frac{1}{x^2 \left(a+b \sec ^{-1}(c x)\right)} \, dx","Int[1/(x^2*(a + b*ArcSec[c*x])),x]","\frac{c \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b}-\frac{c \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b}","\frac{c \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b}-\frac{c \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b}",1,"-((c*CosIntegral[a/b + ArcSec[c*x]]*Sin[a/b])/b) + (c*Cos[a/b]*SinIntegral[a/b + ArcSec[c*x]])/b","A",4,4,14,0.2857,1,"{5222, 3303, 3299, 3302}"
37,1,63,0,0.1357682,"\int \frac{1}{x^3 \left(a+b \sec ^{-1}(c x)\right)} \, dx","Int[1/(x^3*(a + b*ArcSec[c*x])),x]","\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{2 b}-\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{2 b}","\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{2 b}-\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{2 b}",1,"-(c^2*CosIntegral[(2*a)/b + 2*ArcSec[c*x]]*Sin[(2*a)/b])/(2*b) + (c^2*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSec[c*x]])/(2*b)","A",6,6,14,0.4286,1,"{5222, 4406, 12, 3303, 3299, 3302}"
38,1,117,0,0.2246956,"\int \frac{1}{x^4 \left(a+b \sec ^{-1}(c x)\right)} \, dx","Int[1/(x^4*(a + b*ArcSec[c*x])),x]","-\frac{c^3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b}-\frac{c^3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b}+\frac{c^3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b}+\frac{c^3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b}","-\frac{c^3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b}-\frac{c^3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b}+\frac{c^3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b}+\frac{c^3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b}",1,"-(c^3*CosIntegral[a/b + ArcSec[c*x]]*Sin[a/b])/(4*b) - (c^3*CosIntegral[(3*a)/b + 3*ArcSec[c*x]]*Sin[(3*a)/b])/(4*b) + (c^3*Cos[a/b]*SinIntegral[a/b + ArcSec[c*x]])/(4*b) + (c^3*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSec[c*x]])/(4*b)","A",9,5,14,0.3571,1,"{5222, 4406, 3303, 3299, 3302}"
39,0,0,0,0.0145601,"\int \frac{x}{\left(a+b \sec ^{-1}(c x)\right)^2} \, dx","Int[x/(a + b*ArcSec[c*x])^2,x]","\int \frac{x}{\left(a+b \sec ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(a+b \sec ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][x/(a + b*ArcSec[c*x])^2, x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.0056968,"\int \frac{1}{\left(a+b \sec ^{-1}(c x)\right)^2} \, dx","Int[(a + b*ArcSec[c*x])^(-2),x]","\int \frac{1}{\left(a+b \sec ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \sec ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])^(-2), x]","A",0,0,0,0,-1,"{}"
41,0,0,0,0.0242067,"\int \frac{1}{x \left(a+b \sec ^{-1}(c x)\right)^2} \, dx","Int[1/(x*(a + b*ArcSec[c*x])^2),x]","\int \frac{1}{x \left(a+b \sec ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sec ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*ArcSec[c*x])^2), x]","A",0,0,0,0,-1,"{}"
42,1,75,0,0.128973,"\int \frac{1}{x^2 \left(a+b \sec ^{-1}(c x)\right)^2} \, dx","Int[1/(x^2*(a + b*ArcSec[c*x])^2),x]","\frac{c \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b^2}+\frac{c \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b^2}-\frac{c \sqrt{1-\frac{1}{c^2 x^2}}}{b \left(a+b \sec ^{-1}(c x)\right)}","\frac{c \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b^2}+\frac{c \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{b^2}-\frac{c \sqrt{1-\frac{1}{c^2 x^2}}}{b \left(a+b \sec ^{-1}(c x)\right)}",1,"-((c*Sqrt[1 - 1/(c^2*x^2)])/(b*(a + b*ArcSec[c*x]))) + (c*Cos[a/b]*CosIntegral[a/b + ArcSec[c*x]])/b^2 + (c*Sin[a/b]*SinIntegral[a/b + ArcSec[c*x]])/b^2","A",5,5,14,0.3571,1,"{5222, 3297, 3303, 3299, 3302}"
43,1,84,0,0.1493509,"\int \frac{1}{x^3 \left(a+b \sec ^{-1}(c x)\right)^2} \, dx","Int[1/(x^3*(a + b*ArcSec[c*x])^2),x]","\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^2}+\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^2}-\frac{c^2 \sin \left(2 \sec ^{-1}(c x)\right)}{2 b \left(a+b \sec ^{-1}(c x)\right)}","\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^2}+\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^2}-\frac{c^2 \sin \left(2 \sec ^{-1}(c x)\right)}{2 b \left(a+b \sec ^{-1}(c x)\right)}",1,"(c^2*Cos[(2*a)/b]*CosIntegral[(2*a)/b + 2*ArcSec[c*x]])/b^2 - (c^2*Sin[2*ArcSec[c*x]])/(2*b*(a + b*ArcSec[c*x])) + (c^2*Sin[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSec[c*x]])/b^2","A",7,7,14,0.5000,1,"{5222, 4406, 12, 3297, 3303, 3299, 3302}"
44,1,178,0,0.2665264,"\int \frac{1}{x^4 \left(a+b \sec ^{-1}(c x)\right)^2} \, dx","Int[1/(x^4*(a + b*ArcSec[c*x])^2),x]","\frac{c^3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b^2}+\frac{3 c^3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b^2}+\frac{c^3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b^2}+\frac{3 c^3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b^2}-\frac{c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{4 b \left(a+b \sec ^{-1}(c x)\right)}-\frac{c^3 \sin \left(3 \sec ^{-1}(c x)\right)}{4 b \left(a+b \sec ^{-1}(c x)\right)}","\frac{c^3 \cos \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b^2}+\frac{3 c^3 \cos \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b^2}+\frac{c^3 \sin \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{4 b^2}+\frac{3 c^3 \sin \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{4 b^2}-\frac{c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{4 b \left(a+b \sec ^{-1}(c x)\right)}-\frac{c^3 \sin \left(3 \sec ^{-1}(c x)\right)}{4 b \left(a+b \sec ^{-1}(c x)\right)}",1,"-(c^3*Sqrt[1 - 1/(c^2*x^2)])/(4*b*(a + b*ArcSec[c*x])) + (c^3*Cos[a/b]*CosIntegral[a/b + ArcSec[c*x]])/(4*b^2) + (3*c^3*Cos[(3*a)/b]*CosIntegral[(3*a)/b + 3*ArcSec[c*x]])/(4*b^2) - (c^3*Sin[3*ArcSec[c*x]])/(4*b*(a + b*ArcSec[c*x])) + (c^3*Sin[a/b]*SinIntegral[a/b + ArcSec[c*x]])/(4*b^2) + (3*c^3*Sin[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSec[c*x]])/(4*b^2)","A",11,6,14,0.4286,1,"{5222, 4406, 3297, 3303, 3299, 3302}"
45,0,0,0,0.014366,"\int \frac{x}{\left(a+b \sec ^{-1}(c x)\right)^3} \, dx","Int[x/(a + b*ArcSec[c*x])^3,x]","\int \frac{x}{\left(a+b \sec ^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{x}{\left(a+b \sec ^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][x/(a + b*ArcSec[c*x])^3, x]","A",0,0,0,0,-1,"{}"
46,0,0,0,0.0061648,"\int \frac{1}{\left(a+b \sec ^{-1}(c x)\right)^3} \, dx","Int[(a + b*ArcSec[c*x])^(-3),x]","\int \frac{1}{\left(a+b \sec ^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{\left(a+b \sec ^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])^(-3), x]","A",0,0,0,0,-1,"{}"
47,0,0,0,0.0249043,"\int \frac{1}{x \left(a+b \sec ^{-1}(c x)\right)^3} \, dx","Int[1/(x*(a + b*ArcSec[c*x])^3),x]","\int \frac{1}{x \left(a+b \sec ^{-1}(c x)\right)^3} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sec ^{-1}(c x)\right)^3},x\right)",0,"Defer[Int][1/(x*(a + b*ArcSec[c*x])^3), x]","A",0,0,0,0,-1,"{}"
48,1,103,0,0.1472645,"\int \frac{1}{x^2 \left(a+b \sec ^{-1}(c x)\right)^3} \, dx","Int[1/(x^2*(a + b*ArcSec[c*x])^3),x]","\frac{c \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{2 b^3}-\frac{c \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{2 b^3}-\frac{1}{2 b^2 x \left(a+b \sec ^{-1}(c x)\right)}-\frac{c \sqrt{1-\frac{1}{c^2 x^2}}}{2 b \left(a+b \sec ^{-1}(c x)\right)^2}","\frac{c \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{2 b^3}-\frac{c \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{2 b^3}-\frac{1}{2 b^2 x \left(a+b \sec ^{-1}(c x)\right)}-\frac{c \sqrt{1-\frac{1}{c^2 x^2}}}{2 b \left(a+b \sec ^{-1}(c x)\right)^2}",1,"-(c*Sqrt[1 - 1/(c^2*x^2)])/(2*b*(a + b*ArcSec[c*x])^2) - 1/(2*b^2*x*(a + b*ArcSec[c*x])) + (c*CosIntegral[a/b + ArcSec[c*x]]*Sin[a/b])/(2*b^3) - (c*Cos[a/b]*SinIntegral[a/b + ArcSec[c*x]])/(2*b^3)","A",6,5,14,0.3571,1,"{5222, 3297, 3303, 3299, 3302}"
49,1,112,0,0.1795015,"\int \frac{1}{x^3 \left(a+b \sec ^{-1}(c x)\right)^3} \, dx","Int[1/(x^3*(a + b*ArcSec[c*x])^3),x]","\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^3}-\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^3}-\frac{c^2 \cos \left(2 \sec ^{-1}(c x)\right)}{2 b^2 \left(a+b \sec ^{-1}(c x)\right)}-\frac{c^2 \sin \left(2 \sec ^{-1}(c x)\right)}{4 b \left(a+b \sec ^{-1}(c x)\right)^2}","\frac{c^2 \sin \left(\frac{2 a}{b}\right) \text{CosIntegral}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^3}-\frac{c^2 \cos \left(\frac{2 a}{b}\right) \text{Si}\left(\frac{2 a}{b}+2 \sec ^{-1}(c x)\right)}{b^3}-\frac{c^2 \cos \left(2 \sec ^{-1}(c x)\right)}{2 b^2 \left(a+b \sec ^{-1}(c x)\right)}-\frac{c^2 \sin \left(2 \sec ^{-1}(c x)\right)}{4 b \left(a+b \sec ^{-1}(c x)\right)^2}",1,"-(c^2*Cos[2*ArcSec[c*x]])/(2*b^2*(a + b*ArcSec[c*x])) + (c^2*CosIntegral[(2*a)/b + 2*ArcSec[c*x]]*Sin[(2*a)/b])/b^3 - (c^2*Sin[2*ArcSec[c*x]])/(4*b*(a + b*ArcSec[c*x])^2) - (c^2*Cos[(2*a)/b]*SinIntegral[(2*a)/b + 2*ArcSec[c*x]])/b^3","A",8,7,14,0.5000,1,"{5222, 4406, 12, 3297, 3303, 3299, 3302}"
50,1,228,0,0.3127177,"\int \frac{1}{x^4 \left(a+b \sec ^{-1}(c x)\right)^3} \, dx","Int[1/(x^4*(a + b*ArcSec[c*x])^3),x]","\frac{c^3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{8 b^3}+\frac{9 c^3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{8 b^3}-\frac{c^3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{8 b^3}-\frac{9 c^3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{8 b^3}-\frac{c^2}{8 b^2 x \left(a+b \sec ^{-1}(c x)\right)}-\frac{3 c^3 \cos \left(3 \sec ^{-1}(c x)\right)}{8 b^2 \left(a+b \sec ^{-1}(c x)\right)}-\frac{c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{8 b \left(a+b \sec ^{-1}(c x)\right)^2}-\frac{c^3 \sin \left(3 \sec ^{-1}(c x)\right)}{8 b \left(a+b \sec ^{-1}(c x)\right)^2}","\frac{c^3 \sin \left(\frac{a}{b}\right) \text{CosIntegral}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{8 b^3}+\frac{9 c^3 \sin \left(\frac{3 a}{b}\right) \text{CosIntegral}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{8 b^3}-\frac{c^3 \cos \left(\frac{a}{b}\right) \text{Si}\left(\frac{a}{b}+\sec ^{-1}(c x)\right)}{8 b^3}-\frac{9 c^3 \cos \left(\frac{3 a}{b}\right) \text{Si}\left(\frac{3 a}{b}+3 \sec ^{-1}(c x)\right)}{8 b^3}-\frac{c^2}{8 b^2 x \left(a+b \sec ^{-1}(c x)\right)}-\frac{3 c^3 \cos \left(3 \sec ^{-1}(c x)\right)}{8 b^2 \left(a+b \sec ^{-1}(c x)\right)}-\frac{c^3 \sqrt{1-\frac{1}{c^2 x^2}}}{8 b \left(a+b \sec ^{-1}(c x)\right)^2}-\frac{c^3 \sin \left(3 \sec ^{-1}(c x)\right)}{8 b \left(a+b \sec ^{-1}(c x)\right)^2}",1,"-(c^3*Sqrt[1 - 1/(c^2*x^2)])/(8*b*(a + b*ArcSec[c*x])^2) - c^2/(8*b^2*x*(a + b*ArcSec[c*x])) - (3*c^3*Cos[3*ArcSec[c*x]])/(8*b^2*(a + b*ArcSec[c*x])) + (c^3*CosIntegral[a/b + ArcSec[c*x]]*Sin[a/b])/(8*b^3) + (9*c^3*CosIntegral[(3*a)/b + 3*ArcSec[c*x]]*Sin[(3*a)/b])/(8*b^3) - (c^3*Sin[3*ArcSec[c*x]])/(8*b*(a + b*ArcSec[c*x])^2) - (c^3*Cos[a/b]*SinIntegral[a/b + ArcSec[c*x]])/(8*b^3) - (9*c^3*Cos[(3*a)/b]*SinIntegral[(3*a)/b + 3*ArcSec[c*x]])/(8*b^3)","A",13,6,14,0.4286,1,"{5222, 4406, 3297, 3303, 3299, 3302}"
51,0,0,0,0.0220289,"\int (d x)^m \left(a+b \sec ^{-1}(c x)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcSec[c*x])^3,x]","\int (d x)^m \left(a+b \sec ^{-1}(c x)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \sec ^{-1}(c x)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcSec[c*x])^3, x]","A",0,0,0,0,-1,"{}"
52,0,0,0,0.0222411,"\int (d x)^m \left(a+b \sec ^{-1}(c x)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcSec[c*x])^2,x]","\int (d x)^m \left(a+b \sec ^{-1}(c x)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \sec ^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcSec[c*x])^2, x]","A",0,0,0,0,-1,"{}"
53,1,67,0,0.0426474,"\int (d x)^m \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d*x)^m*(a + b*ArcSec[c*x]),x]","\frac{(d x)^{m+1} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5220, 339, 364}"
54,0,0,0,0.0255718,"\int \frac{(d x)^m}{a+b \sec ^{-1}(c x)} \, dx","Int[(d*x)^m/(a + b*ArcSec[c*x]),x]","\int \frac{(d x)^m}{a+b \sec ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \sec ^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
55,0,0,0,0.0240248,"\int \frac{(d x)^m}{\left(a+b \sec ^{-1}(c x)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcSec[c*x])^2,x]","\int \frac{(d x)^m}{\left(a+b \sec ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \sec ^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcSec[c*x])^2, x]","A",0,0,0,0,-1,"{}"
56,1,167,0,0.4014039,"\int (d+e x)^3 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcSec[c*x]),x]","\frac{(d+e x)^4 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1568, 1475, 1807, 844, 216, 266, 63, 208}"
57,1,124,0,0.266256,"\int (d+e x)^2 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcSec[c*x]),x]","\frac{(d+e x)^3 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1568, 1475, 1807, 844, 216, 266, 63, 208}"
58,1,84,0,0.1667266,"\int (d+e x) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcSec[c*x]),x]","\frac{(d+e x)^2 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[c*x]))/(2*e) - (b*d*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c","A",9,9,14,0.6429,1,"{5226, 1568, 1396, 1807, 844, 216, 266, 63, 208}"
59,1,32,0,0.0221793,"\int \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[a + b*ArcSec[c*x],x]","a x-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \sec ^{-1}(c x)","a x-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c}+b x \sec ^{-1}(c x)",1,"a*x + b*x*ArcSec[c*x] - (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/c","A",5,4,8,0.5000,1,"{5214, 266, 63, 208}"
60,1,247,0,0.3727604,"\int \frac{a+b \sec ^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x),x]","-\frac{i b \text{PolyLog}\left(2,-\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}-\frac{i b \text{PolyLog}\left(2,-\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{e}","-\frac{i b \text{PolyLog}\left(2,-\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}-\frac{i b \text{PolyLog}\left(2,-\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{\left(e-\sqrt{e^2-c^2 d^2}\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{\left(\sqrt{e^2-c^2 d^2}+e\right) e^{i \sec ^{-1}(c x)}}{c d}\right)}{e}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{e}",1,"((a + b*ArcSec[c*x])*Log[1 + ((e - Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcSec[c*x]))/(c*d)])/e + ((a + b*ArcSec[c*x])*Log[1 + ((e + Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcSec[c*x]))/(c*d)])/e - ((a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])])/e - (I*b*PolyLog[2, -(((e - Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcSec[c*x]))/(c*d))])/e - (I*b*PolyLog[2, -(((e + Sqrt[-(c^2*d^2) + e^2])*E^(I*ArcSec[c*x]))/(c*d))])/e + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSec[c*x])])/e","A",4,2,16,0.1250,1,"{5224, 2518}"
61,1,104,0,0.1560081,"\int \frac{a+b \sec ^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x)^2,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1568, 1475, 844, 216, 725, 206}"
62,1,172,0,0.2922602,"\int \frac{a+b \sec ^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x)^3,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1568, 1475, 1651, 844, 216, 725, 206}"
63,1,372,0,0.7593518,"\int (d+e x)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d + e*x)^(3/2)*(a + b*ArcSec[c*x]),x]","\frac{2 (d+e x)^{5/2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1574, 958, 719, 419, 933, 168, 538, 537, 844, 424, 931, 1584}"
64,1,315,0,0.4633576,"\int \sqrt{d+e x} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x]*(a + b*ArcSec[c*x]),x]","\frac{2 (d+e x)^{3/2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1574, 958, 719, 419, 933, 168, 538, 537, 844, 424}"
65,1,212,0,0.3035535,"\int \frac{a+b \sec ^{-1}(c x)}{\sqrt{d+e x}} \, dx","Int[(a + b*ArcSec[c*x])/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1574, 944, 719, 419, 933, 168, 538, 537}"
66,1,119,0,0.2191722,"\int \frac{a+b \sec ^{-1}(c x)}{(d+e x)^{3/2}} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x)^(3/2),x]","-\frac{2 \left(a+b \sec ^{-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 \sec ^{-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}}",1,"(-2*(a + b*ArcSec[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,"{5226, 1574, 933, 168, 538, 537}"
67,1,298,0,0.4056322,"\int \frac{a+b \sec ^{-1}(c x)}{(d+e x)^{5/2}} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x)^(5/2),x]","-\frac{2 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1574, 958, 745, 21, 719, 424, 933, 168, 538, 537}"
68,1,637,0,0.7108782,"\int \frac{a+b \sec ^{-1}(c x)}{(d+e x)^{7/2}} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x)^(7/2),x]","-\frac{2 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5226, 1574, 958, 745, 835, 844, 719, 424, 419, 21, 933, 168, 538, 537}"
69,1,206,0,0.12817,"\int x^4 \left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)*(a + b*ArcSec[c*x]),x]","\frac{1}{5} d x^5 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \sec ^{-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*ArcSec[c*x]))/5 + (e*x^7*(a + b*ArcSec[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, 5238, 12, 459, 321, 217, 206}"
70,1,161,0,0.1032484,"\int x^2 \left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)*(a + b*ArcSec[c*x]),x]","\frac{1}{3} d x^3 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \sec ^{-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*ArcSec[c*x]))/3 + (e*x^5*(a + b*ArcSec[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, 5238, 12, 459, 321, 217, 206}"
71,1,109,0,0.0513458,"\int \left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)*(a + b*ArcSec[c*x]),x]","d x \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \sec ^{-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*ArcSec[c*x]) + (e*x^3*(a + b*ArcSec[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,"{5228, 12, 388, 217, 206}"
72,1,87,0,0.0628026,"\int \frac{\left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)*(a + b*ArcSec[c*x]))/x^2,x]","-\frac{d \left(a+b \sec ^{-1}(c x)\right)}{x}+e x \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{x}+e x \left(a+b \sec ^{-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*ArcSec[c*x]))/x + e*x*(a + b*ArcSec[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, 5238, 451, 217, 206}"
73,1,105,0,0.0748212,"\int \frac{\left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)*(a + b*ArcSec[c*x]))/x^4,x]","-\frac{d \left(a+b \sec ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*x^3) - (e*(a + b*ArcSec[c*x]))/x","A",4,5,19,0.2632,1,"{14, 5238, 12, 453, 264}"
74,1,152,0,0.0944528,"\int \frac{\left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)*(a + b*ArcSec[c*x]))/x^6,x]","-\frac{d \left(a+b \sec ^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \sec ^{-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*ArcSec[c*x]))/(5*x^5) - (e*(a + b*ArcSec[c*x]))/(3*x^3)","A",5,6,19,0.3158,1,"{14, 5238, 12, 453, 271, 264}"
75,1,197,0,0.1171437,"\int \frac{\left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)*(a + b*ArcSec[c*x]))/x^8,x]","-\frac{d \left(a+b \sec ^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \sec ^{-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*ArcSec[c*x]))/(7*x^7) - (e*(a + b*ArcSec[c*x]))/(5*x^5)","A",6,6,19,0.3158,1,"{14, 5238, 12, 453, 271, 264}"
76,1,196,0,0.1468225,"\int x^5 \left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^5*(d + e*x^2)*(a + b*ArcSec[c*x]),x]","\frac{1}{6} d x^6 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \sec ^{-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*ArcSec[c*x]))/6 + (e*x^8*(a + b*ArcSec[c*x]))/8","A",5,5,19,0.2632,1,"{14, 5238, 12, 446, 77}"
77,1,153,0,0.1219894,"\int x^3 \left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)*(a + b*ArcSec[c*x]),x]","\frac{1}{4} d x^4 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \sec ^{-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*ArcSec[c*x]))/4 + (e*x^6*(a + b*ArcSec[c*x]))/6","A",5,5,19,0.2632,1,"{14, 5238, 12, 446, 77}"
78,1,138,0,0.0926902,"\int x \left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)*(a + b*ArcSec[c*x]),x]","\frac{\left(d+e x^2\right)^2 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 88, 63, 205}"
79,1,124,0,0.2835542,"\int \frac{\left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)*(a + b*ArcSec[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 \sec ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \sec ^{-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*ArcSec[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*ArcSec[c*x])*Log[x^(-1)] - (I/2)*b*d*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",11,11,19,0.5789,1,"{5240, 14, 4732, 6742, 264, 2326, 4625, 3717, 2190, 2279, 2391}"
80,1,137,0,0.2913751,"\int \frac{\left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)*(a + b*ArcSec[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 \sec ^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \sec ^{-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*ArcSec[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*ArcSec[c*x])*Log[x^(-1)] - (I/2)*b*e*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",13,13,19,0.6842,1,"{5240, 14, 4732, 12, 6742, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
81,1,252,0,0.2357314,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*ArcSec[c*x]),x]","\frac{1}{3} d^2 x^3 \left(a+b \sec ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \sec ^{-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*ArcSec[c*x]))/3 + (2*d*e*x^5*(a + b*ArcSec[c*x]))/5 + (e^2*x^7*(a + b*ArcSec[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, 5238, 12, 1267, 459, 321, 217, 206}"
82,1,191,0,0.1146838,"\int \left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^2*(a + b*ArcSec[c*x]),x]","d^2 x \left(a+b \sec ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \sec ^{-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*ArcSec[c*x]) + (2*d*e*x^3*(a + b*ArcSec[c*x]))/3 + (e^2*x^5*(a + b*ArcSec[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, 5228, 12, 1159, 388, 217, 206}"
83,1,162,0,0.1271889,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSec[c*x]))/x^2,x]","-\frac{d^2 \left(a+b \sec ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{x}+2 d e x \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \sec ^{-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*ArcSec[c*x]))/x + 2*d*e*x*(a + b*ArcSec[c*x]) + (e^2*x^3*(a + b*ArcSec[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, 5238, 12, 1265, 388, 217, 206}"
84,1,158,0,0.1312015,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSec[c*x]))/x^4,x]","-\frac{d^2 \left(a+b \sec ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \sec ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \sec ^{-1}(c x)\right)}{x}+e^2 x \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*x^3) - (2*d*e*(a + b*ArcSec[c*x]))/x + e^2*x*(a + b*ArcSec[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, 5238, 12, 1265, 451, 217, 206}"
85,1,183,0,0.1574661,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSec[c*x]))/x^6,x]","-\frac{d^2 \left(a+b \sec ^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \sec ^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \sec ^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \sec ^{-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*ArcSec[c*x]))/(5*x^5) - (2*d*e*(a + b*ArcSec[c*x]))/(3*x^3) - (e^2*(a + b*ArcSec[c*x]))/x","A",5,6,21,0.2857,1,"{270, 5238, 12, 1265, 453, 264}"
86,1,241,0,0.1933053,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSec[c*x]))/x^8,x]","-\frac{d^2 \left(a+b \sec ^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \sec ^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \sec ^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \sec ^{-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*ArcSec[c*x]))/(7*x^7) - (2*d*e*(a + b*ArcSec[c*x]))/(5*x^5) - (e^2*(a + b*ArcSec[c*x]))/(3*x^3)","A",6,7,21,0.3333,1,"{270, 5238, 12, 1265, 453, 271, 264}"
87,1,242,0,0.2235694,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*ArcSec[c*x]),x]","\frac{1}{4} d^2 x^4 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \sec ^{-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*ArcSec[c*x]))/4 + (d*e*x^6*(a + b*ArcSec[c*x]))/3 + (e^2*x^8*(a + b*ArcSec[c*x]))/8","A",5,6,21,0.2857,1,"{266, 43, 5238, 12, 1251, 771}"
88,1,195,0,0.1484035,"\int x \left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*ArcSec[c*x]),x]","\frac{\left(d+e x^2\right)^3 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 88, 63, 205}"
89,1,186,0,0.4118938,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSec[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 \sec ^{-1}(c x)\right)+d e x^2 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)+d e x^2 \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \sec ^{-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*ArcSec[c*x]) + (e^2*x^4*(a + b*ArcSec[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*ArcSec[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,"{5240, 266, 43, 4732, 6742, 453, 264, 2326, 4625, 3717, 2190, 2279, 2391}"
90,1,189,0,0.4173494,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*ArcSec[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 \sec ^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \sec ^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \sec ^{-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*ArcSec[c*x]))/(2*x^2) + (e^2*x^2*(a + b*ArcSec[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*ArcSec[c*x])*Log[x^(-1)] - I*b*d*e*PolyLog[2, E^((2*I)*ArcCsc[c*x])]","A",14,15,21,0.7143,1,"{5240, 266, 43, 4732, 12, 6742, 264, 321, 216, 2326, 4625, 3717, 2190, 2279, 2391}"
91,1,546,0,1.2943029,"\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^2*(a + b*ArcSec[c*x]))/(d + e*x^2),x]","\frac{i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{x \left(a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{x \left(a+b \sec ^{-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*ArcSec[c*x]))/e - (b*ArcTanh[Sqrt[1 - 1/(c^2*x^2)]])/(c*e) + (Sqrt[-d]*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^(3/2)) + (Sqrt[-d]*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^(3/2)) + ((I/2)*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/e^(3/2) - ((I/2)*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^(3/2) + ((I/2)*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/e^(3/2) - ((I/2)*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^(3/2)","A",25,12,21,0.5714,1,"{5240, 4734, 4628, 266, 63, 208, 4668, 4742, 4520, 2190, 2279, 2391}"
92,1,487,0,1.1516092,"\int \frac{x \left(a+b \sec ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x*(a + b*ArcSec[c*x]))/(d + e*x^2),x]","-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{e}","-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{e}",1,"((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e) - ((a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])])/e - ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/e - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e - ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/e - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSec[c*x])])/e","A",26,9,19,0.4737,1,"{5240, 4734, 4626, 3719, 2190, 2279, 2391, 4742, 4520}"
93,1,509,0,0.8690305,"\int \frac{a+b \sec ^{-1}(c x)}{d+e x^2} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x^2),x]","\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}","\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e]) + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*Sqrt[e]) - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*Sqrt[e])","A",19,7,18,0.3889,1,"{5230, 4668, 4742, 4520, 2190, 2279, 2391}"
94,1,459,0,0.8955206,"\int \frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSec[c*x])/(x*(d + e*x^2)),x]","\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i \left(a+b \sec ^{-1}(c x)\right)^2}{2 b d}","\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d}+\frac{i \left(a+b \sec ^{-1}(c x)\right)^2}{2 b d}",1,"((I/2)*(a + b*ArcSec[c*x])^2)/(b*d) - ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d) + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/d + ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/d + ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d","A",19,7,21,0.3333,1,"{5240, 4734, 4742, 4520, 2190, 2279, 2391}"
95,1,551,0,1.0959163,"\int \frac{a+b \sec ^{-1}(c x)}{x^2 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcSec[c*x])/(x^2*(d + e*x^2)),x]","\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-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 \sec ^{-1}(c x)}{d x}","\frac{i b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-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 \sec ^{-1}(c x)}{d x}",1,"(b*c*Sqrt[1 - 1/(c^2*x^2)])/d - a/(d*x) - (b*ArcSec[c*x])/(d*x) + (Sqrt[e]*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) + (Sqrt[e]*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*(-d)^(3/2)) + ((I/2)*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/(-d)^(3/2) - ((I/2)*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(-d)^(3/2) + ((I/2)*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/(-d)^(3/2) - ((I/2)*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(-d)^(3/2)","A",24,10,21,0.4762,1,"{5240, 4734, 4620, 261, 4668, 4742, 4520, 2190, 2279, 2391}"
96,1,608,0,1.3058642,"\int \frac{x^5 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^5*(a + b*ArcSec[c*x]))/(d + e*x^2)^2,x]","\frac{i b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{i b d \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{d \left(a+b \sec ^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{i b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{i b d \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{e^3}+\frac{d \left(a+b \sec ^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \sec ^{-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*ArcSec[c*x]))/(2*e^2*(e + d/x^2)) + (x^2*(a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 - (d*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 + (2*d*(a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])])/e^3 + (I*b*d*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/e^3 + (I*b*d*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 + (I*b*d*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/e^3 + (I*b*d*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 - (I*b*d*PolyLog[2, -E^((2*I)*ArcSec[c*x])])/e^3","A",31,14,21,0.6667,1,"{5240, 4734, 4628, 264, 4626, 3719, 2190, 2279, 2391, 4730, 377, 205, 4742, 4520}"
97,1,570,0,1.2156294,"\int \frac{x^3 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcSec[c*x]))/(d + e*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{a+b \sec ^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^2}-\frac{a+b \sec ^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-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*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^2) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^2) - ((a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])])/e^2 - ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/e^2 - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^2 - ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/e^2 - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^2 + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSec[c*x])])/e^2","A",29,12,21,0.5714,1,"{5240, 4734, 4626, 3719, 2190, 2279, 2391, 4730, 377, 205, 4742, 4520}"
98,1,131,0,0.1206757,"\int \frac{x \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x*(a + b*ArcSec[c*x]))/(d + e*x^2)^2,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 86, 63, 205}"
99,1,546,0,1.1398012,"\int \frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSec[c*x])/(x*(d + e*x^2)^2),x]","\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{e \left(a+b \sec ^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^2}-\frac{e \left(a+b \sec ^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \sec ^{-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*ArcSec[c*x]))/(2*d^2*(e + d/x^2)) + ((I/2)*(a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^2) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^2) + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/d^2 + ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d^2 + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/d^2 + ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d^2","A",24,10,21,0.4762,1,"{5240, 4734, 4730, 377, 205, 4742, 4520, 2190, 2279, 2391}"
100,1,784,0,2.3535349,"\int \frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcSec[c*x]))/(d + e*x^2)^2,x]","\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{d \left(a+b \sec ^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \sec ^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{x \left(a+b \sec ^{-1}(c x)\right)}{e^2}-\frac{b \sqrt{d} \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 e^2 \sqrt{c^2 d+e}}-\frac{b \sqrt{d} \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 e^2 \sqrt{c^2 d+e}}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c e^2}","\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}+\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{3 i b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{d \left(a+b \sec ^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \sec ^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{x \left(a+b \sec ^{-1}(c x)\right)}{e^2}-\frac{b \sqrt{d} \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 e^2 \sqrt{c^2 d+e}}-\frac{b \sqrt{d} \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 e^2 \sqrt{c^2 d+e}}-\frac{b \tanh ^{-1}\left(\sqrt{1-\frac{1}{c^2 x^2}}\right)}{c e^2}",1,"-(d*(a + b*ArcSec[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) + (d*(a + b*ArcSec[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] + d/x)) + (x*(a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*e^(5/2)) + (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/e^(5/2) - (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^(5/2) + (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/e^(5/2) - (((3*I)/4)*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^(5/2)","A",51,15,21,0.7143,1,"{5240, 4734, 4628, 266, 63, 208, 4668, 4744, 725, 206, 4742, 4520, 2190, 2279, 2391}"
101,1,745,0,1.2166393,"\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcSec[c*x]))/(d + e*x^2)^2,x]","\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \sec ^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \sec ^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \sec ^{-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*ArcSec[c*x])/(4*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) + ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*Sqrt[-d]*e^(3/2)) + ((I/4)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(3/2)) - ((I/4)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2)) + ((I/4)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(3/2)) - ((I/4)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(3/2))","A",27,10,21,0.4762,1,"{5240, 4668, 4744, 725, 206, 4742, 4520, 2190, 2279, 2391}"
102,1,739,0,2.2111605,"\int \frac{a+b \sec ^{-1}(c x)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x^2)^2,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \sec ^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \sec ^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \sec ^{-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*ArcSec[c*x])/(4*d*(Sqrt[-d]*Sqrt[e] - d/x)) + (a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((I/4)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/((-d)^(3/2)*Sqrt[e]) + ((I/4)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e]) - ((I/4)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/((-d)^(3/2)*Sqrt[e]) + ((I/4)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(3/2)*Sqrt[e])","A",47,11,18,0.6111,1,"{5230, 4734, 4668, 4744, 725, 206, 4742, 4520, 2190, 2279, 2391}"
103,1,785,0,2.3072973,"\int \frac{a+b \sec ^{-1}(c x)}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcSec[c*x])/(x^2*(d + e*x^2)^2),x]","-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{e \left(a+b \sec ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \sec ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{a}{d^2 x}+\frac{b e \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^{5/2} \sqrt{c^2 d+e}}+\frac{b e \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^{5/2} \sqrt{c^2 d+e}}+\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{d^2}-\frac{b \sec ^{-1}(c x)}{d^2 x}","-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}-\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{3 i b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{e \left(a+b \sec ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \sec ^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{a}{d^2 x}+\frac{b e \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^{5/2} \sqrt{c^2 d+e}}+\frac{b e \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^{5/2} \sqrt{c^2 d+e}}+\frac{b c \sqrt{1-\frac{1}{c^2 x^2}}}{d^2}-\frac{b \sec ^{-1}(c x)}{d^2 x}",1,"(b*c*Sqrt[1 - 1/(c^2*x^2)])/d^2 - a/(d^2*x) - (b*ArcSec[c*x])/(d^2*x) + (e*(a + b*ArcSec[c*x]))/(4*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (e*(a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) - (3*Sqrt[e]*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(4*(-d)^(5/2)) - (((3*I)/4)*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/(-d)^(5/2) + (((3*I)/4)*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(-d)^(5/2) - (((3*I)/4)*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/(-d)^(5/2) + (((3*I)/4)*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(-d)^(5/2)","A",50,13,21,0.6190,1,"{5240, 4734, 4620, 261, 4668, 4744, 725, 206, 4742, 4520, 2190, 2279, 2391}"
104,1,707,0,1.4038404,"\int \frac{x^5 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^5*(a + b*ArcSec[c*x]))/(d + e*x^2)^3,x]","-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{a+b \sec ^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \sec ^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{i b \text{PolyLog}\left(2,-e^{2 i \sec ^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 e^3}-\frac{a+b \sec ^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \sec ^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\log \left(1+e^{2 i \sec ^{-1}(c x)}\right) \left(a+b \sec ^{-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*ArcSec[c*x])/(4*e*(e + d/x^2)^2) - (a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^3) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*e^3) - ((a + b*ArcSec[c*x])*Log[1 + E^((2*I)*ArcSec[c*x])])/e^3 - ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/e^3 - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/e^3 - ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/e^3 - ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/e^3 + ((I/2)*b*PolyLog[2, -E^((2*I)*ArcSec[c*x])])/e^3","A",33,13,21,0.6190,1,"{5240, 4734, 4626, 3719, 2190, 2279, 2391, 4730, 382, 377, 205, 4742, 4520}"
105,1,157,0,0.1745122,"\int \frac{x^3 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcSec[c*x]))/(d + e*x^2)^3,x]","\frac{x^4 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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, 5238, 12, 446, 78, 63, 205}"
106,1,193,0,0.1896896,"\int \frac{x \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x*(a + b*ArcSec[c*x]))/(d + e*x^2)^3,x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 103, 156, 63, 205}"
107,1,685,0,1.291204,"\int \frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcSec[c*x])/(x*(d + e*x^2)^3),x]","\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{e^2 \left(a+b \sec ^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \sec ^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{i b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{c^2 d+e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1+\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{c^2 d+e}+\sqrt{e}}\right)}{2 d^3}+\frac{e^2 \left(a+b \sec ^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \sec ^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{i \left(a+b \sec ^{-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*ArcSec[c*x]))/(4*d^3*(e + d/x^2)^2) - (e*(a + b*ArcSec[c*x]))/(d^3*(e + d/x^2)) + ((I/2)*(a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^3) - ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(2*d^3) + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/d^3 + ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/d^3 + ((I/2)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/d^3 + ((I/2)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/d^3","A",28,11,21,0.5238,1,"{5240, 4734, 4730, 382, 377, 205, 4742, 4520, 2190, 2279, 2391}"
108,1,1124,0,1.5832062,"\int \frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcSec[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 \sec ^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \sec ^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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 \sec ^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \sec ^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \sec ^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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*ArcSec[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (3*(a + b*ArcSec[c*x]))/(16*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[-d]*(a + b*ArcSec[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (3*(a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) + (3*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*Sqrt[-d]*e^(5/2)) + (((3*I)/16)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(5/2)) - (((3*I)/16)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2)) + (((3*I)/16)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/(Sqrt[-d]*e^(5/2)) - (((3*I)/16)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(Sqrt[-d]*e^(5/2))","A",35,11,21,0.5238,1,"{5240, 4668, 4744, 731, 725, 206, 4742, 4520, 2190, 2279, 2391}"
109,1,1124,0,3.021818,"\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcSec[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 \sec ^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \sec ^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \sec ^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \sec ^{-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 \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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 \sec ^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \sec ^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \sec ^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \sec ^{-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 \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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*ArcSec[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (a + b*ArcSec[c*x])/(16*d*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcSec[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((I/16)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/((-d)^(3/2)*e^(3/2)) + ((I/16)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2)) - ((I/16)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/((-d)^(3/2)*e^(3/2)) + ((I/16)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(3/2)*e^(3/2))","A",63,12,21,0.5714,1,"{5240, 4734, 4668, 4744, 731, 725, 206, 4742, 4520, 2190, 2279, 2391}"
110,1,1114,0,3.791304,"\int \frac{a+b \sec ^{-1}(c x)}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcSec[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 \sec ^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \sec ^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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 \sec ^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \sec ^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \sec ^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}-\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-1}(c x)} c}{\sqrt{e}-\sqrt{d c^2+e}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{i \sec ^{-1}(c x)}}{\sqrt{e}+\sqrt{d c^2+e}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \sec ^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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{c \sqrt{-d} e^{i \sec ^{-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*ArcSec[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) - (5*(a + b*ArcSec[c*x]))/(16*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[e]*(a + b*ArcSec[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) + (5*(a + b*ArcSec[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*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (3*(a + b*ArcSec[c*x])*Log[1 - (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcSec[c*x])*Log[1 + (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (((3*I)/16)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e]))])/((-d)^(5/2)*Sqrt[e]) - (((3*I)/16)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] - Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e]) + (((3*I)/16)*b*PolyLog[2, -((c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e]))])/((-d)^(5/2)*Sqrt[e]) - (((3*I)/16)*b*PolyLog[2, (c*Sqrt[-d]*E^(I*ArcSec[c*x]))/(Sqrt[e] + Sqrt[c^2*d + e])])/((-d)^(5/2)*Sqrt[e])","A",81,12,18,0.6667,1,"{5230, 4734, 4668, 4744, 731, 725, 206, 4742, 4520, 2190, 2279, 2391}"
111,1,403,0,1.2748726,"\int x^5 \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^5*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]),x]","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*e^3) - (2*d*(d + e*x^2)^(5/2)*(a + b*ArcSec[c*x]))/(5*e^3) + ((d + e*x^2)^(7/2)*(a + b*ArcSec[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, 5238, 12, 1615, 154, 157, 63, 217, 206, 93, 204}"
112,1,294,0,0.3981064,"\int x^3 \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]),x]","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*e^2) + ((d + e*x^2)^(5/2)*(a + b*ArcSec[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, 5238, 12, 573, 154, 157, 63, 217, 206, 93, 204}"
113,1,195,0,0.1902923,"\int x \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]),x]","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 102, 157, 63, 217, 206, 93, 204}"
114,0,0,0,0.0977567,"\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
115,0,0,0,0.1012812,"\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x^3,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
116,0,0,0,0.0936754,"\int x^2 \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]),x]","\int x^2 \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
117,0,0,0,0.0337469,"\int \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]),x]","\int \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right),x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
118,0,0,0,0.0860681,"\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x^2,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
119,1,328,0,0.4240428,"\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x^4,x]","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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, 5238, 12, 474, 583, 524, 427, 426, 424, 421, 419}"
120,1,453,0,0.6007792,"\int \frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{x^6} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/x^6,x]","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(5*d*x^5) + (2*e*(d + e*x^2)^(3/2)*(a + b*ArcSec[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, 5238, 12, 580, 583, 524, 427, 426, 424, 421, 419}"
121,1,374,0,0.5076816,"\int x^3 \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]),x]","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(5*e^2) + ((d + e*x^2)^(7/2)*(a + b*ArcSec[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, 5238, 12, 573, 154, 157, 63, 217, 206, 93, 204}"
122,1,262,0,0.2704252,"\int x \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]),x]","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 102, 154, 157, 63, 217, 206, 93, 204}"
123,0,0,0,0.1149189,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
124,0,0,0,0.1191547,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^3,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
125,0,0,0,0.1120094,"\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]),x]","\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
126,0,0,0,0.0416049,"\int \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]),x]","\int \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right),x\right)",0,"Defer[Int][(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
127,0,0,0,0.1029871,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^2,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
128,0,0,0,0.1042255,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^4,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^4} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^4},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^4, x]","A",0,0,0,0,-1,"{}"
129,1,416,0,0.5392782,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^6,x]","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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, 5238, 12, 474, 580, 583, 524, 427, 426, 424, 421, 419}"
130,1,554,0,0.7779618,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/x^8,x]","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(7*d*x^7) + (2*e*(d + e*x^2)^(5/2)*(a + b*ArcSec[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, 5238, 12, 580, 583, 524, 427, 426, 424, 421, 419}"
131,1,321,0,1.0120863,"\int \frac{x^5 \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^5*(a + b*ArcSec[c*x]))/Sqrt[d + e*x^2],x]","\frac{d^2 \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/e^3 - (2*d*(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]))/(3*e^3) + ((d + e*x^2)^(5/2)*(a + b*ArcSec[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, 5238, 12, 1615, 154, 157, 63, 217, 206, 93, 204}"
132,1,225,0,0.3075329,"\int \frac{x^3 \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^3*(a + b*ArcSec[c*x]))/Sqrt[d + e*x^2],x]","-\frac{d \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/e^2 + ((d + e*x^2)^(3/2)*(a + b*ArcSec[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, 5238, 12, 573, 154, 157, 63, 217, 206, 93, 204}"
133,1,132,0,0.1455766,"\int \frac{x \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x*(a + b*ArcSec[c*x]))/Sqrt[d + e*x^2],x]","\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 105, 63, 217, 206, 93, 204}"
134,0,0,0,0.0968381,"\int \frac{a+b \sec ^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSec[c*x])/(x*Sqrt[d + e*x^2]),x]","\int \frac{a+b \sec ^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
135,0,0,0,0.10804,"\int \frac{a+b \sec ^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^3*Sqrt[d + e*x^2]),x]","\int \frac{a+b \sec ^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x^3 \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x^3*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
136,0,0,0,0.0905409,"\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^2*(a + b*ArcSec[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcSec[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
137,0,0,0,0.0299236,"\int \frac{a+b \sec ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSec[c*x])/Sqrt[d + e*x^2],x]","\int \frac{a+b \sec ^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
138,1,246,0,0.2550633,"\int \frac{a+b \sec ^{-1}(c x)}{x^2 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^2*Sqrt[d + e*x^2]),x]","-\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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, 5238, 12, 475, 21, 423, 427, 426, 424, 421, 419}"
139,1,362,0,0.4466286,"\int \frac{a+b \sec ^{-1}(c x)}{x^4 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^4*Sqrt[d + e*x^2]),x]","\frac{2 e \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*d*x^3) + (2*e*Sqrt[d + e*x^2]*(a + b*ArcSec[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, 5238, 12, 580, 583, 524, 427, 426, 424, 421, 419}"
140,1,1006,0,1.7803032,"\int \frac{a+b \sec ^{-1}(c x)}{x^6 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^6*Sqrt[d + e*x^2]),x]","-\frac{8 b e^2 x \sqrt{1-c^2 x^2} \sqrt{e x^2+d} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right) c^2}{15 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}+\frac{4 b e \left(2 d c^2+e\right) x \sqrt{1-c^2 x^2} \sqrt{e x^2+d} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right) c^2}{45 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b \left(8 d^2 c^4+3 d e c^2-2 e^2\right) x \sqrt{1-c^2 x^2} \sqrt{e x^2+d} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right) c^2}{75 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}+\frac{b \left(8 c^2 d-e\right) \left(d c^2+e\right) 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) c^2}{75 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{e x^2+d}}-\frac{8 b e \left(d c^2+e\right) 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) c^2}{45 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{e x^2+d}}+\frac{8 b e^2 \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{15 d^3 \sqrt{c^2 x^2}}-\frac{4 b e \left(2 d c^2+e\right) \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{45 d^3 \sqrt{c^2 x^2}}+\frac{b \left(8 d^2 c^4+3 d e c^2-2 e^2\right) \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{75 d^3 \sqrt{c^2 x^2}}-\frac{4 b e \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{45 d^2 x^2 \sqrt{c^2 x^2}}+\frac{b \left(4 d c^2+e\right) \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{75 d^2 x^2 \sqrt{c^2 x^2}}+\frac{b \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{25 d x^4 \sqrt{c^2 x^2}}-\frac{8 e^2 \sqrt{e x^2+d} \left(a+b \sec ^{-1}(c x)\right)}{15 d^3 x}+\frac{4 e \sqrt{e x^2+d} \left(a+b \sec ^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\sqrt{e x^2+d} \left(a+b \sec ^{-1}(c x)\right)}{5 d x^5}+\frac{8 b e^2 \left(d c^2+e\right) 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)}{15 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{e x^2+d}}","-\frac{8 b e^2 x \sqrt{1-c^2 x^2} \sqrt{e x^2+d} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right) c^2}{15 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}+\frac{4 b e \left(2 d c^2+e\right) x \sqrt{1-c^2 x^2} \sqrt{e x^2+d} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right) c^2}{45 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}-\frac{b \left(8 d^2 c^4+3 d e c^2-2 e^2\right) x \sqrt{1-c^2 x^2} \sqrt{e x^2+d} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right) c^2}{75 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}+\frac{b \left(8 c^2 d-e\right) \left(d c^2+e\right) 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) c^2}{75 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{e x^2+d}}-\frac{8 b e \left(d c^2+e\right) 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) c^2}{45 d^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{e x^2+d}}+\frac{8 b e^2 \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{15 d^3 \sqrt{c^2 x^2}}-\frac{4 b e \left(2 d c^2+e\right) \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{45 d^3 \sqrt{c^2 x^2}}+\frac{b \left(8 d^2 c^4+3 d e c^2-2 e^2\right) \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{75 d^3 \sqrt{c^2 x^2}}-\frac{4 b e \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{45 d^2 x^2 \sqrt{c^2 x^2}}+\frac{b \left(4 d c^2+e\right) \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{75 d^2 x^2 \sqrt{c^2 x^2}}+\frac{b \sqrt{c^2 x^2-1} \sqrt{e x^2+d} c}{25 d x^4 \sqrt{c^2 x^2}}-\frac{8 e^2 \sqrt{e x^2+d} \left(a+b \sec ^{-1}(c x)\right)}{15 d^3 x}+\frac{4 e \sqrt{e x^2+d} \left(a+b \sec ^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\sqrt{e x^2+d} \left(a+b \sec ^{-1}(c x)\right)}{5 d x^5}+\frac{8 b e^2 \left(d c^2+e\right) 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)}{15 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{e x^2+d}}",1,"(8*b*c*e^2*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(15*d^3*Sqrt[c^2*x^2]) - (4*b*c*e*(2*c^2*d + e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(45*d^3*Sqrt[c^2*x^2]) + (b*c*(8*c^4*d^2 + 3*c^2*d*e - 2*e^2)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(75*d^3*Sqrt[c^2*x^2]) + (b*c*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(25*d*x^4*Sqrt[c^2*x^2]) - (4*b*c*e*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(45*d^2*x^2*Sqrt[c^2*x^2]) + (b*c*(4*c^2*d + e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(75*d^2*x^2*Sqrt[c^2*x^2]) - (Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/(5*d*x^5) + (4*e*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/(15*d^2*x^3) - (8*e^2*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/(15*d^3*x) - (8*b*c^2*e^2*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(15*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) + (4*b*c^2*e*(2*c^2*d + e)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(45*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (b*c^2*(8*c^4*d^2 + 3*c^2*d*e - 2*e^2)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(75*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) + (b*c^2*(8*c^2*d - 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))])/(75*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2]) - (8*b*c^2*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))])/(45*d^2*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2]) + (8*b*e^2*(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))])/(15*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",32,15,23,0.6522,1,"{271, 264, 5238, 12, 6742, 475, 583, 524, 427, 426, 424, 421, 419, 21, 423}"
141,1,252,0,1.0062556,"\int \frac{x^5 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2),x]","-\frac{d^2 \left(a+b \sec ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(e^3*Sqrt[d + e*x^2]) - (2*d*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]))/e^3 + ((d + e*x^2)^(3/2)*(a + b*ArcSec[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, 5238, 12, 1615, 157, 63, 217, 206, 93, 204}"
142,1,157,0,0.2591378,"\int \frac{x^3 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2),x]","\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \sec ^{-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*ArcSec[c*x]))/(e^2*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcSec[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, 5238, 12, 573, 157, 63, 217, 206, 93, 204}"
143,1,80,0,0.101998,"\int \frac{x \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2),x]","-\frac{a+b \sec ^{-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 \sec ^{-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}}",1,"-((a + b*ArcSec[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,"{5236, 446, 93, 204}"
144,0,0,0,0.1103162,"\int \frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSec[c*x])/(x*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.122635,"\int \frac{a+b \sec ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^3*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \sec ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x^3*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
146,0,0,0,0.1064557,"\int \frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
147,0,0,0,0.0986639,"\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
148,1,109,0,0.0877321,"\int \frac{a+b \sec ^{-1}(c x)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x^2)^(3/2),x]","\frac{x \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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, 5228, 12, 421, 419}"
149,1,274,0,0.3103691,"\int \frac{a+b \sec ^{-1}(c x)}{x^2 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^2*(d + e*x^2)^(3/2)),x]","-\frac{2 e x \left(a+b \sec ^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \sec ^{-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*ArcSec[c*x])/(d*x*Sqrt[d + e*x^2]) - (2*e*x*(a + b*ArcSec[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, 5238, 12, 583, 524, 427, 426, 424, 421, 419}"
150,1,701,0,1.3917798,"\int \frac{a+b \sec ^{-1}(c x)}{x^4 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^4*(d + e*x^2)^(3/2)),x]","\frac{8 e^2 x \left(a+b \sec ^{-1}(c x)\right)}{3 d^3 \sqrt{d+e x^2}}+\frac{4 e \left(a+b \sec ^{-1}(c x)\right)}{3 d^2 x \sqrt{d+e x^2}}-\frac{a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt{d+e x^2}}-\frac{8 b e^2 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^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{2 b c \sqrt{c^2 x^2-1} \left(c^2 d-e\right) \sqrt{d+e x^2}}{9 d^3 \sqrt{c^2 x^2}}-\frac{4 b c e \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{3 d^3 \sqrt{c^2 x^2}}+\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{9 d^2 x^2 \sqrt{c^2 x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(2 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{4 b c^2 e 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{2 b c^2 x \sqrt{1-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}+\frac{4 b c^2 e 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^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}","\frac{8 e^2 x \left(a+b \sec ^{-1}(c x)\right)}{3 d^3 \sqrt{d+e x^2}}+\frac{4 e \left(a+b \sec ^{-1}(c x)\right)}{3 d^2 x \sqrt{d+e x^2}}-\frac{a+b \sec ^{-1}(c x)}{3 d x^3 \sqrt{d+e x^2}}-\frac{8 b e^2 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^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{2 b c \sqrt{c^2 x^2-1} \left(c^2 d-e\right) \sqrt{d+e x^2}}{9 d^3 \sqrt{c^2 x^2}}-\frac{4 b c e \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{3 d^3 \sqrt{c^2 x^2}}+\frac{b c \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}{9 d^2 x^2 \sqrt{c^2 x^2}}+\frac{b c^2 x \sqrt{1-c^2 x^2} \left(2 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{4 b c^2 e 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{2 b c^2 x \sqrt{1-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{9 d^3 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{\frac{e x^2}{d}+1}}+\frac{4 b c^2 e 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^3 \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 - e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(9*d^3*Sqrt[c^2*x^2]) - (4*b*c*e*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(3*d^3*Sqrt[c^2*x^2]) + (b*c*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(9*d^2*x^2*Sqrt[c^2*x^2]) - (a + b*ArcSec[c*x])/(3*d*x^3*Sqrt[d + e*x^2]) + (4*e*(a + b*ArcSec[c*x]))/(3*d^2*x*Sqrt[d + e*x^2]) + (8*e^2*x*(a + b*ArcSec[c*x]))/(3*d^3*Sqrt[d + e*x^2]) - (2*b*c^2*(c^2*d - e)*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(9*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) + (4*b*c^2*e*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) + (b*c^2*(2*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]) - (4*b*c^2*e*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]) - (8*b*e^2*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",25,14,23,0.6087,1,"{271, 191, 5238, 12, 6742, 421, 419, 480, 583, 524, 427, 426, 424, 493}"
151,1,244,0,1.0630413,"\int \frac{x^5 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{d^2 \left(a+b \sec ^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \sec ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \sec ^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*e^3*(d + e*x^2)^(3/2)) + (2*d*(a + b*ArcSec[c*x]))/(e^3*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcSec[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, 5238, 12, 1614, 157, 63, 217, 206, 93, 204}"
152,1,163,0,0.2429737,"\int \frac{x^3 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \sec ^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \sec ^{-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 \sec ^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*e^2*(d + e*x^2)^(3/2)) - (a + b*ArcSec[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, 5238, 12, 573, 152, 93, 204}"
153,1,138,0,0.1314059,"\int \frac{x \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \sec ^{-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 \sec ^{-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*ArcSec[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,"{5236, 446, 96, 93, 204}"
154,0,0,0,0.1197845,"\int \frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSec[c*x])/(x*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
155,0,0,0,0.138226,"\int \frac{a+b \sec ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^3*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \sec ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x^3*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
156,0,0,0,0.1158878,"\int \frac{x^6 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^6 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^6 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^6*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
157,0,0,0,0.1063078,"\int \frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
158,1,276,0,0.2762254,"\int \frac{x^2 \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcSec[c*x]))/(d + e*x^2)^(5/2),x]","\frac{x^3 \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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, 5238, 12, 471, 423, 427, 426, 424, 421, 419}"
159,1,296,0,0.2350801,"\int \frac{a+b \sec ^{-1}(c x)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSec[c*x])/(d + e*x^2)^(5/2),x]","\frac{2 x \left(a+b \sec ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \sec ^{-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*ArcSec[c*x]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*ArcSec[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, 5228, 12, 527, 524, 427, 426, 424, 421, 419}"
160,1,631,0,1.3959256,"\int \frac{a+b \sec ^{-1}(c x)}{x^2 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcSec[c*x])/(x^2*(d + e*x^2)^(5/2)),x]","-\frac{8 e x \left(a+b \sec ^{-1}(c x)\right)}{3 d^3 \sqrt{d+e x^2}}-\frac{4 e x \left(a+b \sec ^{-1}(c x)\right)}{3 d^2 \left(d+e x^2\right)^{3/2}}-\frac{a+b \sec ^{-1}(c x)}{d x \left(d+e x^2\right)^{3/2}}-\frac{4 b c e^2 x^2 \sqrt{c^2 x^2-1}}{3 d^3 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b c \sqrt{c^2 x^2-1} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{d^3 \sqrt{c^2 x^2} \left(c^2 d+e\right)}-\frac{b c e \sqrt{c^2 x^2-1}}{d^2 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b c^2 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^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{8 b e 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^3 \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(c^2 d+2 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^3 \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{4 b c^2 e 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^3 \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{8 e x \left(a+b \sec ^{-1}(c x)\right)}{3 d^3 \sqrt{d+e x^2}}-\frac{4 e x \left(a+b \sec ^{-1}(c x)\right)}{3 d^2 \left(d+e x^2\right)^{3/2}}-\frac{a+b \sec ^{-1}(c x)}{d x \left(d+e x^2\right)^{3/2}}-\frac{4 b c e^2 x^2 \sqrt{c^2 x^2-1}}{3 d^3 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b c \sqrt{c^2 x^2-1} \left(c^2 d+2 e\right) \sqrt{d+e x^2}}{d^3 \sqrt{c^2 x^2} \left(c^2 d+e\right)}-\frac{b c e \sqrt{c^2 x^2-1}}{d^2 \sqrt{c^2 x^2} \left(c^2 d+e\right) \sqrt{d+e x^2}}+\frac{b c^2 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^2 \sqrt{c^2 x^2} \sqrt{c^2 x^2-1} \sqrt{d+e x^2}}+\frac{8 b e 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^3 \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(c^2 d+2 e\right) \sqrt{d+e x^2} E\left(\sin ^{-1}(c x)|-\frac{e}{c^2 d}\right)}{d^3 \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{4 b c^2 e 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^3 \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*Sqrt[-1 + c^2*x^2])/(d^2*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[d + e*x^2])) - (4*b*c*e^2*x^2*Sqrt[-1 + c^2*x^2])/(3*d^3*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[d + e*x^2]) + (b*c*(c^2*d + 2*e)*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])/(d^3*(c^2*d + e)*Sqrt[c^2*x^2]) - (a + b*ArcSec[c*x])/(d*x*(d + e*x^2)^(3/2)) - (4*e*x*(a + b*ArcSec[c*x]))/(3*d^2*(d + e*x^2)^(3/2)) - (8*e*x*(a + b*ArcSec[c*x]))/(3*d^3*Sqrt[d + e*x^2]) + (4*b*c^2*e*x*Sqrt[1 - c^2*x^2]*Sqrt[d + e*x^2]*EllipticE[ArcSin[c*x], -(e/(c^2*d))])/(3*d^3*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) - (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))])/(d^3*(c^2*d + e)*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[1 + (e*x^2)/d]) + (b*c^2*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]) + (8*b*e*x*Sqrt[1 - c^2*x^2]*Sqrt[1 + (e*x^2)/d]*EllipticF[ArcSin[c*x], -(e/(c^2*d))])/(3*d^3*Sqrt[c^2*x^2]*Sqrt[-1 + c^2*x^2]*Sqrt[d + e*x^2])","A",26,18,23,0.7826,1,"{271, 192, 191, 5238, 12, 6742, 414, 21, 427, 426, 424, 472, 583, 524, 421, 419, 471, 423}"
161,1,570,0,2.4152964,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^3*(a + b*ArcSec[c*x]),x]","\frac{3 d^2 e (f x)^{m+3} \left(a+b \sec ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \sec ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \sec ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \sec ^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \sec ^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \sec ^{-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*ArcSec[c*x]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*ArcSec[c*x]))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*ArcSec[c*x]))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*ArcSec[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, 5238, 1809, 1267, 459, 365, 364}"
162,1,355,0,0.4323809,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^2*(a + b*ArcSec[c*x]),x]","\frac{d^2 (f x)^{m+1} \left(a+b \sec ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \sec ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \sec ^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \sec ^{-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*ArcSec[c*x]))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*ArcSec[c*x]))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*ArcSec[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, 5238, 12, 1267, 459, 365, 364}"
163,1,204,0,0.1870067,"\int (f x)^m \left(d+e x^2\right) \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*ArcSec[c*x]),x]","\frac{d (f x)^{m+1} \left(a+b \sec ^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \sec ^{-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 x^{m+1} \left(a+b \sec ^{-1}(c x)\right)}{m+1}+\frac{e x^{m+3} \left(a+b \sec ^{-1}(c x)\right)}{m+3}+\frac{b \sqrt{c^2 x^2-1} x^{m+2} \left(c^2 d (m+2) (m+3)+e (m+1)^2\right) \, _2F_1\left(1,\frac{m+2}{2};\frac{m+3}{2};c^2 x^2\right)}{c (m+1)^2 (m+2) (m+3) \sqrt{c^2 x^2}}-\frac{b e \sqrt{c^2 x^2-1} x^{m+2}}{c \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*ArcSec[c*x]))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*ArcSec[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",5,6,21,0.2857,0,"{14, 5238, 12, 459, 365, 364}"
164,0,0,0,0.0712152,"\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{d+e x^2} \, dx","Int[((f*x)^m*(a + b*ArcSec[c*x]))/(d + e*x^2),x]","\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{d+e x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{d+e x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSec[c*x]))/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
165,0,0,0,0.0705689,"\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcSec[c*x]))/(d + e*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSec[c*x]))/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
166,0,0,0,0.1048773,"\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]),x]","\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} (f x)^m \left(a+b \sec ^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
167,0,0,0,0.0942094,"\int (f x)^m \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","Int[(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]),x]","\int (f x)^m \sqrt{d+e x^2} \left(a+b \sec ^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} (f x)^m \left(a+b \sec ^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcSec[c*x]), x]","A",0,0,0,0,-1,"{}"
168,0,0,0,0.0957872,"\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[((f*x)^m*(a + b*ArcSec[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSec[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
169,0,0,0,0.1049031,"\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \sec ^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcSec[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
170,1,401,0,2.4835973,"\int \frac{x^{11} \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^11*(a + b*ArcSec[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\left(1-c^4 x^4\right)^{5/2} \left(a+b \sec ^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \sec ^{-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*ArcSec[c*x]))/(2*c^12) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcSec[c*x]))/(3*c^12) - ((1 - c^4*x^4)^(5/2)*(a + b*ArcSec[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, 5246, 12, 6721, 6742, 848, 50, 63, 208, 783}"
171,1,268,0,2.0175194,"\int \frac{x^7 \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^7*(a + b*ArcSec[c*x]))/Sqrt[1 - c^4*x^4],x]","\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \sec ^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \sec ^{-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 \sec ^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \sec ^{-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*ArcSec[c*x]))/(2*c^8) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcSec[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, 5246, 12, 6721, 6742, 848, 50, 63, 208, 783}"
172,1,135,0,0.2079587,"\int \frac{x^3 \left(a+b \sec ^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^3*(a + b*ArcSec[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\sqrt{1-c^4 x^4} \left(a+b \sec ^{-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 \sec ^{-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*ArcSec[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, 5246, 12, 1572, 1252, 848, 50, 63, 208}"
173,0,0,0,0.0879369,"\int \frac{a+b \sec ^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcSec[c*x])/(x*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \sec ^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"
174,0,0,0,0.0988872,"\int \frac{a+b \sec ^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcSec[c*x])/(x^5*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \sec ^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \sec ^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcSec[c*x])/(x^5*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"