1,1,143,0,0.1616768,"\int x^5 \left(a+b \sec \left(c+d x^2\right)\right) \, dx","Int[x^5*(a + b*Sec[c + d*x^2]),x]","\frac{i b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{i b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{b \text{PolyLog}\left(3,-i e^{i \left(c+d x^2\right)}\right)}{d^3}+\frac{b \text{PolyLog}\left(3,i e^{i \left(c+d x^2\right)}\right)}{d^3}+\frac{a x^6}{6}-\frac{i b x^4 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}","\frac{i b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{i b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{b \text{PolyLog}\left(3,-i e^{i \left(c+d x^2\right)}\right)}{d^3}+\frac{b \text{PolyLog}\left(3,i e^{i \left(c+d x^2\right)}\right)}{d^3}+\frac{a x^6}{6}-\frac{i b x^4 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}",1,"(a*x^6)/6 - (I*b*x^4*ArcTan[E^(I*(c + d*x^2))])/d + (I*b*x^2*PolyLog[2, (-I)*E^(I*(c + d*x^2))])/d^2 - (I*b*x^2*PolyLog[2, I*E^(I*(c + d*x^2))])/d^2 - (b*PolyLog[3, (-I)*E^(I*(c + d*x^2))])/d^3 + (b*PolyLog[3, I*E^(I*(c + d*x^2))])/d^3","A",10,6,16,0.3750,1,"{14, 4204, 4181, 2531, 2282, 6589}"
2,0,0,0,0.0154817,"\int x^4 \left(a+b \sec \left(c+d x^2\right)\right) \, dx","Int[x^4*(a + b*Sec[c + d*x^2]),x]","\int x^4 \left(a+b \sec \left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^4 \sec \left(c+d x^2\right),x\right)+\frac{a x^5}{5}",0,"(a*x^5)/5 + b*Defer[Int][x^4*Sec[c + d*x^2], x]","A",0,0,0,0,-1,"{}"
3,1,92,0,0.0877414,"\int x^3 \left(a+b \sec \left(c+d x^2\right)\right) \, dx","Int[x^3*(a + b*Sec[c + d*x^2]),x]","\frac{i b \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{2 d^2}-\frac{i b \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{2 d^2}+\frac{a x^4}{4}-\frac{i b x^2 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}","\frac{i b \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{2 d^2}-\frac{i b \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{2 d^2}+\frac{a x^4}{4}-\frac{i b x^2 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}",1,"(a*x^4)/4 - (I*b*x^2*ArcTan[E^(I*(c + d*x^2))])/d + ((I/2)*b*PolyLog[2, (-I)*E^(I*(c + d*x^2))])/d^2 - ((I/2)*b*PolyLog[2, I*E^(I*(c + d*x^2))])/d^2","A",8,5,16,0.3125,1,"{14, 4204, 4181, 2279, 2391}"
4,0,0,0,0.0152668,"\int x^2 \left(a+b \sec \left(c+d x^2\right)\right) \, dx","Int[x^2*(a + b*Sec[c + d*x^2]),x]","\int x^2 \left(a+b \sec \left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^2 \sec \left(c+d x^2\right),x\right)+\frac{a x^3}{3}",0,"(a*x^3)/3 + b*Defer[Int][x^2*Sec[c + d*x^2], x]","A",0,0,0,0,-1,"{}"
5,1,26,0,0.0226498,"\int x \left(a+b \sec \left(c+d x^2\right)\right) \, dx","Int[x*(a + b*Sec[c + d*x^2]),x]","\frac{a x^2}{2}+\frac{b \tanh ^{-1}\left(\sin \left(c+d x^2\right)\right)}{2 d}","\frac{a x^2}{2}+\frac{b \tanh ^{-1}\left(\sin \left(c+d x^2\right)\right)}{2 d}",1,"(a*x^2)/2 + (b*ArcTanh[Sin[c + d*x^2]])/(2*d)","A",4,3,14,0.2143,1,"{14, 4204, 3770}"
6,0,0,0,0.0155714,"\int \frac{a+b \sec \left(c+d x^2\right)}{x} \, dx","Int[(a + b*Sec[c + d*x^2])/x,x]","\int \frac{a+b \sec \left(c+d x^2\right)}{x} \, dx","b \text{Int}\left(\frac{\sec \left(c+d x^2\right)}{x},x\right)+a \log (x)",0,"a*Log[x] + b*Defer[Int][Sec[c + d*x^2]/x, x]","A",0,0,0,0,-1,"{}"
7,0,0,0,0.0160218,"\int \frac{a+b \sec \left(c+d x^2\right)}{x^2} \, dx","Int[(a + b*Sec[c + d*x^2])/x^2,x]","\int \frac{a+b \sec \left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\sec \left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"-(a/x) + b*Defer[Int][Sec[c + d*x^2]/x^2, x]","A",0,0,0,0,-1,"{}"
8,1,242,0,0.3702842,"\int x^5 \left(a+b \sec \left(c+d x^2\right)\right)^2 \, dx","Int[x^5*(a + b*Sec[c + d*x^2])^2,x]","\frac{2 i a b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{2 i a b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{2 a b \text{PolyLog}\left(3,-i e^{i \left(c+d x^2\right)}\right)}{d^3}+\frac{2 a b \text{PolyLog}\left(3,i e^{i \left(c+d x^2\right)}\right)}{d^3}-\frac{i b^2 \text{PolyLog}\left(2,-e^{2 i \left(c+d x^2\right)}\right)}{2 d^3}+\frac{a^2 x^6}{6}-\frac{2 i a b x^4 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}+\frac{b^2 x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{d^2}+\frac{b^2 x^4 \tan \left(c+d x^2\right)}{2 d}-\frac{i b^2 x^4}{2 d}","\frac{2 i a b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{2 i a b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{2 a b \text{PolyLog}\left(3,-i e^{i \left(c+d x^2\right)}\right)}{d^3}+\frac{2 a b \text{PolyLog}\left(3,i e^{i \left(c+d x^2\right)}\right)}{d^3}-\frac{i b^2 \text{PolyLog}\left(2,-e^{2 i \left(c+d x^2\right)}\right)}{2 d^3}+\frac{a^2 x^6}{6}-\frac{2 i a b x^4 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}+\frac{b^2 x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{d^2}+\frac{b^2 x^4 \tan \left(c+d x^2\right)}{2 d}-\frac{i b^2 x^4}{2 d}",1,"((-I/2)*b^2*x^4)/d + (a^2*x^6)/6 - ((2*I)*a*b*x^4*ArcTan[E^(I*(c + d*x^2))])/d + (b^2*x^2*Log[1 + E^((2*I)*(c + d*x^2))])/d^2 + ((2*I)*a*b*x^2*PolyLog[2, (-I)*E^(I*(c + d*x^2))])/d^2 - ((2*I)*a*b*x^2*PolyLog[2, I*E^(I*(c + d*x^2))])/d^2 - ((I/2)*b^2*PolyLog[2, -E^((2*I)*(c + d*x^2))])/d^3 - (2*a*b*PolyLog[3, (-I)*E^(I*(c + d*x^2))])/d^3 + (2*a*b*PolyLog[3, I*E^(I*(c + d*x^2))])/d^3 + (b^2*x^4*Tan[c + d*x^2])/(2*d)","A",15,11,18,0.6111,1,"{4204, 4190, 4181, 2531, 2282, 6589, 4184, 3719, 2190, 2279, 2391}"
9,0,0,0,0.0232077,"\int x^4 \left(a+b \sec \left(c+d x^2\right)\right)^2 \, dx","Int[x^4*(a + b*Sec[c + d*x^2])^2,x]","\int x^4 \left(a+b \sec \left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^4 \left(a+b \sec \left(c+d x^2\right)\right)^2,x\right)",0,"Defer[Int][x^4*(a + b*Sec[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
10,1,133,0,0.1642069,"\int x^3 \left(a+b \sec \left(c+d x^2\right)\right)^2 \, dx","Int[x^3*(a + b*Sec[c + d*x^2])^2,x]","\frac{i a b \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{i a b \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{d^2}+\frac{a^2 x^4}{4}-\frac{2 i a b x^2 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}+\frac{b^2 \log \left(\cos \left(c+d x^2\right)\right)}{2 d^2}+\frac{b^2 x^2 \tan \left(c+d x^2\right)}{2 d}","\frac{i a b \text{PolyLog}\left(2,-i e^{i \left(c+d x^2\right)}\right)}{d^2}-\frac{i a b \text{PolyLog}\left(2,i e^{i \left(c+d x^2\right)}\right)}{d^2}+\frac{a^2 x^4}{4}-\frac{2 i a b x^2 \tan ^{-1}\left(e^{i \left(c+d x^2\right)}\right)}{d}+\frac{b^2 \log \left(\cos \left(c+d x^2\right)\right)}{2 d^2}+\frac{b^2 x^2 \tan \left(c+d x^2\right)}{2 d}",1,"(a^2*x^4)/4 - ((2*I)*a*b*x^2*ArcTan[E^(I*(c + d*x^2))])/d + (b^2*Log[Cos[c + d*x^2]])/(2*d^2) + (I*a*b*PolyLog[2, (-I)*E^(I*(c + d*x^2))])/d^2 - (I*a*b*PolyLog[2, I*E^(I*(c + d*x^2))])/d^2 + (b^2*x^2*Tan[c + d*x^2])/(2*d)","A",10,7,18,0.3889,1,"{4204, 4190, 4181, 2279, 2391, 4184, 3475}"
11,0,0,0,0.023618,"\int x^2 \left(a+b \sec \left(c+d x^2\right)\right)^2 \, dx","Int[x^2*(a + b*Sec[c + d*x^2])^2,x]","\int x^2 \left(a+b \sec \left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^2 \left(a+b \sec \left(c+d x^2\right)\right)^2,x\right)",0,"Defer[Int][x^2*(a + b*Sec[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
12,1,44,0,0.0515532,"\int x \left(a+b \sec \left(c+d x^2\right)\right)^2 \, dx","Int[x*(a + b*Sec[c + d*x^2])^2,x]","\frac{a^2 x^2}{2}+\frac{a b \tanh ^{-1}\left(\sin \left(c+d x^2\right)\right)}{d}+\frac{b^2 \tan \left(c+d x^2\right)}{2 d}","\frac{a^2 x^2}{2}+\frac{a b \tanh ^{-1}\left(\sin \left(c+d x^2\right)\right)}{d}+\frac{b^2 \tan \left(c+d x^2\right)}{2 d}",1,"(a^2*x^2)/2 + (a*b*ArcTanh[Sin[c + d*x^2]])/d + (b^2*Tan[c + d*x^2])/(2*d)","A",5,5,16,0.3125,1,"{4204, 3773, 3770, 3767, 8}"
13,0,0,0,0.02204,"\int \frac{\left(a+b \sec \left(c+d x^2\right)\right)^2}{x} \, dx","Int[(a + b*Sec[c + d*x^2])^2/x,x]","\int \frac{\left(a+b \sec \left(c+d x^2\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \sec \left(c+d x^2\right)\right)^2}{x},x\right)",0,"Defer[Int][(a + b*Sec[c + d*x^2])^2/x, x]","A",0,0,0,0,-1,"{}"
14,0,0,0,0.0218362,"\int \frac{\left(a+b \sec \left(c+d x^2\right)\right)^2}{x^2} \, dx","Int[(a + b*Sec[c + d*x^2])^2/x^2,x]","\int \frac{\left(a+b \sec \left(c+d x^2\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sec \left(c+d x^2\right)\right)^2}{x^2},x\right)",0,"Defer[Int][(a + b*Sec[c + d*x^2])^2/x^2, x]","A",0,0,0,0,-1,"{}"
15,1,90,0,0.0733805,"\int x \sec ^7\left(a+b x^2\right) \, dx","Int[x*Sec[a + b*x^2]^7,x]","\frac{5 \tanh ^{-1}\left(\sin \left(a+b x^2\right)\right)}{32 b}+\frac{\tan \left(a+b x^2\right) \sec ^5\left(a+b x^2\right)}{12 b}+\frac{5 \tan \left(a+b x^2\right) \sec ^3\left(a+b x^2\right)}{48 b}+\frac{5 \tan \left(a+b x^2\right) \sec \left(a+b x^2\right)}{32 b}","\frac{5 \tanh ^{-1}\left(\sin \left(a+b x^2\right)\right)}{32 b}+\frac{\tan \left(a+b x^2\right) \sec ^5\left(a+b x^2\right)}{12 b}+\frac{5 \tan \left(a+b x^2\right) \sec ^3\left(a+b x^2\right)}{48 b}+\frac{5 \tan \left(a+b x^2\right) \sec \left(a+b x^2\right)}{32 b}",1,"(5*ArcTanh[Sin[a + b*x^2]])/(32*b) + (5*Sec[a + b*x^2]*Tan[a + b*x^2])/(32*b) + (5*Sec[a + b*x^2]^3*Tan[a + b*x^2])/(48*b) + (Sec[a + b*x^2]^5*Tan[a + b*x^2])/(12*b)","A",5,3,12,0.2500,1,"{4204, 3768, 3770}"
16,1,382,0,0.8777742,"\int \frac{x^5}{a+b \sec \left(c+d x^2\right)} \, dx","Int[x^5/(a + b*Sec[c + d*x^2]),x]","\frac{b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}+\frac{i b x^4 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a d \sqrt{b^2-a^2}}-\frac{i b x^4 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a d \sqrt{b^2-a^2}}+\frac{x^6}{6 a}","\frac{b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}+\frac{i b x^4 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a d \sqrt{b^2-a^2}}-\frac{i b x^4 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a d \sqrt{b^2-a^2}}+\frac{x^6}{6 a}",1,"x^6/(6*a) + ((I/2)*b*x^4*Log[1 + (a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) - ((I/2)*b*x^4*Log[1 + (a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) + (b*x^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) - (b*x^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) + (I*b*PolyLog[3, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - (I*b*PolyLog[3, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3)","A",13,8,18,0.4444,1,"{4204, 4191, 3321, 2264, 2190, 2531, 2282, 6589}"
17,0,0,0,0.0257448,"\int \frac{x^4}{a+b \sec \left(c+d x^2\right)} \, dx","Int[x^4/(a + b*Sec[c + d*x^2]),x]","\int \frac{x^4}{a+b \sec \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^4}{a+b \sec \left(c+d x^2\right)},x\right)",0,"Defer[Int][x^4/(a + b*Sec[c + d*x^2]), x]","A",0,0,0,0,-1,"{}"
18,1,261,0,0.5399275,"\int \frac{x^3}{a+b \sec \left(c+d x^2\right)} \, dx","Int[x^3/(a + b*Sec[c + d*x^2]),x]","\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a d^2 \sqrt{b^2-a^2}}-\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a d^2 \sqrt{b^2-a^2}}+\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a d \sqrt{b^2-a^2}}-\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a d \sqrt{b^2-a^2}}+\frac{x^4}{4 a}","\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a d^2 \sqrt{b^2-a^2}}-\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a d^2 \sqrt{b^2-a^2}}+\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a d \sqrt{b^2-a^2}}-\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a d \sqrt{b^2-a^2}}+\frac{x^4}{4 a}",1,"x^4/(4*a) + ((I/2)*b*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) - ((I/2)*b*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) + (b*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(2*a*Sqrt[-a^2 + b^2]*d^2) - (b*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(2*a*Sqrt[-a^2 + b^2]*d^2)","A",11,7,18,0.3889,1,"{4204, 4191, 3321, 2264, 2190, 2279, 2391}"
19,0,0,0,0.0249315,"\int \frac{x^2}{a+b \sec \left(c+d x^2\right)} \, dx","Int[x^2/(a + b*Sec[c + d*x^2]),x]","\int \frac{x^2}{a+b \sec \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{a+b \sec \left(c+d x^2\right)},x\right)",0,"Defer[Int][x^2/(a + b*Sec[c + d*x^2]), x]","A",0,0,0,0,-1,"{}"
20,1,66,0,0.1089821,"\int \frac{x}{a+b \sec \left(c+d x^2\right)} \, dx","Int[x/(a + b*Sec[c + d*x^2]),x]","\frac{x^2}{2 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a+b}}\right)}{a d \sqrt{a-b} \sqrt{a+b}}","\frac{x^2}{2 a}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a+b}}\right)}{a d \sqrt{a-b} \sqrt{a+b}}",1,"x^2/(2*a) - (b*ArcTanh[(Sqrt[a - b]*Tan[(c + d*x^2)/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*Sqrt[a + b]*d)","A",4,4,16,0.2500,1,"{4204, 3783, 2659, 208}"
21,0,0,0,0.0247599,"\int \frac{1}{x \left(a+b \sec \left(c+d x^2\right)\right)} \, dx","Int[1/(x*(a + b*Sec[c + d*x^2])),x]","\int \frac{1}{x \left(a+b \sec \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sec \left(c+d x^2\right)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*Sec[c + d*x^2])), x]","A",0,0,0,0,-1,"{}"
22,0,0,0,0.0136663,"\int \frac{a+b \sec \left(c+d x^2\right)}{x^2} \, dx","Int[(a + b*Sec[c + d*x^2])/x^2,x]","\int \frac{a+b \sec \left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\sec \left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"-(a/x) + b*Defer[Int][Sec[c + d*x^2]/x^2, x]","A",0,0,0,0,-1,"{}"
23,1,1092,0,2.2876992,"\int \frac{x^5}{\left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[x^5/(a + b*Sec[c + d*x^2])^2,x]","\frac{x^6}{6 a^2}+\frac{i b \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^4}{a^2 \sqrt{b^2-a^2} d}-\frac{i b^3 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^4}{2 a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{i b \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^4}{a^2 \sqrt{b^2-a^2} d}+\frac{i b^3 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^4}{2 a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{b^2 \sin \left(d x^2+c\right) x^4}{2 a \left(a^2-b^2\right) d \left(b+a \cos \left(d x^2+c\right)\right)}-\frac{i b^2 x^4}{2 a^2 \left(a^2-b^2\right) d}+\frac{b^2 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) x^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{b^2 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) x^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{2 b \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^2}-\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{2 b \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^2}+\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b-i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^3}-\frac{i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b+i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^3}+\frac{2 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^3}-\frac{i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{2 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^3}+\frac{i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^3}","\frac{x^6}{6 a^2}+\frac{i b \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^4}{a^2 \sqrt{b^2-a^2} d}-\frac{i b^3 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^4}{2 a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{i b \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^4}{a^2 \sqrt{b^2-a^2} d}+\frac{i b^3 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^4}{2 a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{b^2 \sin \left(d x^2+c\right) x^4}{2 a \left(a^2-b^2\right) d \left(b+a \cos \left(d x^2+c\right)\right)}-\frac{i b^2 x^4}{2 a^2 \left(a^2-b^2\right) d}+\frac{b^2 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) x^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{b^2 \log \left(\frac{e^{i \left(d x^2+c\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) x^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{2 b \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^2}-\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{2 b \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^2}+\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b-i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^3}-\frac{i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^2+c\right)}}{b+i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^3}+\frac{2 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^3}-\frac{i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{2 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^3}+\frac{i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^2+c\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^3}",1,"((-I/2)*b^2*x^4)/(a^2*(a^2 - b^2)*d) + x^6/(6*a^2) + (b^2*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) + (b^2*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) - ((I/2)*b^3*x^4*Log[1 + (a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) + (I*b*x^4*Log[1 + (a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + ((I/2)*b^3*x^4*Log[1 + (a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) - (I*b*x^4*Log[1 + (a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) - (I*b^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - (I*b^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - (b^3*x^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (2*b*x^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (b^3*x^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (2*b*x^2*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) - (I*b^3*PolyLog[3, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((2*I)*b*PolyLog[3, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + (I*b^3*PolyLog[3, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((2*I)*b*PolyLog[3, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + (b^2*x^4*Sin[c + d*x^2])/(2*a*(a^2 - b^2)*d*(b + a*Cos[c + d*x^2]))","A",31,12,18,0.6667,1,"{4204, 4191, 3324, 3321, 2264, 2190, 2531, 2282, 6589, 4522, 2279, 2391}"
24,0,0,0,0.0240097,"\int \frac{x^4}{\left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[x^4/(a + b*Sec[c + d*x^2])^2,x]","\int \frac{x^4}{\left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{x^4}{\left(a+b \sec \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][x^4/(a + b*Sec[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
25,1,596,0,1.2039362,"\int \frac{x^3}{\left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[x^3/(a + b*Sec[c + d*x^2])^2,x]","\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 \sqrt{b^2-a^2}}-\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a^2 d^2 \left(b^2-a^2\right)^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d^2 \sqrt{b^2-a^2}}+\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a^2 d^2 \left(b^2-a^2\right)^{3/2}}+\frac{b^2 \log \left(a \cos \left(c+d x^2\right)+b\right)}{2 a^2 d^2 \left(a^2-b^2\right)}+\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d \sqrt{b^2-a^2}}-\frac{i b^3 x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a^2 d \left(b^2-a^2\right)^{3/2}}-\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d \sqrt{b^2-a^2}}+\frac{i b^3 x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a^2 d \left(b^2-a^2\right)^{3/2}}+\frac{b^2 x^2 \sin \left(c+d x^2\right)}{2 a d \left(a^2-b^2\right) \left(a \cos \left(c+d x^2\right)+b\right)}+\frac{x^4}{4 a^2}","\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 \sqrt{b^2-a^2}}-\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a^2 d^2 \left(b^2-a^2\right)^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d^2 \sqrt{b^2-a^2}}+\frac{b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a^2 d^2 \left(b^2-a^2\right)^{3/2}}+\frac{b^2 \log \left(a \cos \left(c+d x^2\right)+b\right)}{2 a^2 d^2 \left(a^2-b^2\right)}+\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d \sqrt{b^2-a^2}}-\frac{i b^3 x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{b-\sqrt{b^2-a^2}}\right)}{2 a^2 d \left(b^2-a^2\right)^{3/2}}-\frac{i b x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d \sqrt{b^2-a^2}}+\frac{i b^3 x^2 \log \left(1+\frac{a e^{i \left(c+d x^2\right)}}{\sqrt{b^2-a^2}+b}\right)}{2 a^2 d \left(b^2-a^2\right)^{3/2}}+\frac{b^2 x^2 \sin \left(c+d x^2\right)}{2 a d \left(a^2-b^2\right) \left(a \cos \left(c+d x^2\right)+b\right)}+\frac{x^4}{4 a^2}",1,"x^4/(4*a^2) - ((I/2)*b^3*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) + (I*b*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + ((I/2)*b^3*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) - (I*b*x^2*Log[1 + (a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + (b^2*Log[b + a*Cos[c + d*x^2]])/(2*a^2*(a^2 - b^2)*d^2) - (b^3*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(2*a^2*(-a^2 + b^2)^(3/2)*d^2) + (b*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (b^3*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(2*a^2*(-a^2 + b^2)^(3/2)*d^2) - (b*PolyLog[2, -((a*E^(I*(c + d*x^2)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (b^2*x^2*Sin[c + d*x^2])/(2*a*(a^2 - b^2)*d*(b + a*Cos[c + d*x^2]))","A",22,10,18,0.5556,1,"{4204, 4191, 3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"
26,0,0,0,0.024222,"\int \frac{x^2}{\left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[x^2/(a + b*Sec[c + d*x^2])^2,x]","\int \frac{x^2}{\left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(a+b \sec \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][x^2/(a + b*Sec[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
27,1,123,0,0.2543552,"\int \frac{x}{\left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[x/(a + b*Sec[c + d*x^2])^2,x]","-\frac{b \left(2 a^2-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a+b}}\right)}{a^2 d (a-b)^{3/2} (a+b)^{3/2}}+\frac{b^2 \tan \left(c+d x^2\right)}{2 a d \left(a^2-b^2\right) \left(a+b \sec \left(c+d x^2\right)\right)}+\frac{x^2}{2 a^2}","-\frac{b \left(2 a^2-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a+b}}\right)}{a^2 d (a-b)^{3/2} (a+b)^{3/2}}+\frac{b^2 \tan \left(c+d x^2\right)}{2 a d \left(a^2-b^2\right) \left(a+b \sec \left(c+d x^2\right)\right)}+\frac{x^2}{2 a^2}",1,"x^2/(2*a^2) - (b*(2*a^2 - b^2)*ArcTanh[(Sqrt[a - b]*Tan[(c + d*x^2)/2])/Sqrt[a + b]])/(a^2*(a - b)^(3/2)*(a + b)^(3/2)*d) + (b^2*Tan[c + d*x^2])/(2*a*(a^2 - b^2)*d*(a + b*Sec[c + d*x^2]))","A",6,6,16,0.3750,1,"{4204, 3785, 3919, 3831, 2659, 208}"
28,0,0,0,0.0242544,"\int \frac{1}{x \left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[1/(x*(a + b*Sec[c + d*x^2])^2),x]","\int \frac{1}{x \left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sec \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*Sec[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
29,0,0,0,0.0244021,"\int \frac{1}{x^2 \left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[1/(x^2*(a + b*Sec[c + d*x^2])^2),x]","\int \frac{1}{x^2 \left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sec \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(a + b*Sec[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
30,0,0,0,0.0237837,"\int \frac{1}{x^3 \left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","Int[1/(x^3*(a + b*Sec[c + d*x^2])^2),x]","\int \frac{1}{x^3 \left(a+b \sec \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^3 \left(a+b \sec \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][1/(x^3*(a + b*Sec[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
31,1,476,0,0.4567526,"\int x^3 \left(a+b \sec \left(c+d \sqrt{x}\right)\right) \, dx","Int[x^3*(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{14 i b x^3 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{14 i b x^3 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{84 b x^{5/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{84 b x^{5/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{420 i b x^2 \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{420 i b x^2 \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{1680 b x^{3/2} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{1680 b x^{3/2} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{5040 i b x \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{5040 i b x \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{10080 b \sqrt{x} \text{PolyLog}\left(7,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}+\frac{10080 b \sqrt{x} \text{PolyLog}\left(7,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}-\frac{10080 i b \text{PolyLog}\left(8,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}+\frac{10080 i b \text{PolyLog}\left(8,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}+\frac{a x^4}{4}-\frac{4 i b x^{7/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}","\frac{14 i b x^3 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{14 i b x^3 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{84 b x^{5/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{84 b x^{5/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{420 i b x^2 \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{420 i b x^2 \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{1680 b x^{3/2} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{1680 b x^{3/2} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{5040 i b x \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{5040 i b x \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{10080 b \sqrt{x} \text{PolyLog}\left(7,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}+\frac{10080 b \sqrt{x} \text{PolyLog}\left(7,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}-\frac{10080 i b \text{PolyLog}\left(8,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}+\frac{10080 i b \text{PolyLog}\left(8,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}+\frac{a x^4}{4}-\frac{4 i b x^{7/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}",1,"(a*x^4)/4 - ((4*I)*b*x^(7/2)*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + ((14*I)*b*x^3*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((14*I)*b*x^3*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - (84*b*x^(5/2)*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (84*b*x^(5/2)*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 - ((420*I)*b*x^2*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((420*I)*b*x^2*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4 + (1680*b*x^(3/2)*PolyLog[5, (-I)*E^(I*(c + d*Sqrt[x]))])/d^5 - (1680*b*x^(3/2)*PolyLog[5, I*E^(I*(c + d*Sqrt[x]))])/d^5 + ((5040*I)*b*x*PolyLog[6, (-I)*E^(I*(c + d*Sqrt[x]))])/d^6 - ((5040*I)*b*x*PolyLog[6, I*E^(I*(c + d*Sqrt[x]))])/d^6 - (10080*b*Sqrt[x]*PolyLog[7, (-I)*E^(I*(c + d*Sqrt[x]))])/d^7 + (10080*b*Sqrt[x]*PolyLog[7, I*E^(I*(c + d*Sqrt[x]))])/d^7 - ((10080*I)*b*PolyLog[8, (-I)*E^(I*(c + d*Sqrt[x]))])/d^8 + ((10080*I)*b*PolyLog[8, I*E^(I*(c + d*Sqrt[x]))])/d^8","A",20,7,18,0.3889,1,"{14, 4204, 4181, 2531, 6609, 2282, 6589}"
32,1,348,0,0.3109149,"\int x^2 \left(a+b \sec \left(c+d \sqrt{x}\right)\right) \, dx","Int[x^2*(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{10 i b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{10 i b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{40 b x^{3/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{40 b x^{3/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{120 i b x \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{120 i b x \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{240 b \sqrt{x} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{240 b \sqrt{x} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{240 i b \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{240 i b \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{a x^3}{3}-\frac{4 i b x^{5/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}","\frac{10 i b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{10 i b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{40 b x^{3/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{40 b x^{3/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{120 i b x \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{120 i b x \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{240 b \sqrt{x} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{240 b \sqrt{x} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{240 i b \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{240 i b \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{a x^3}{3}-\frac{4 i b x^{5/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}",1,"(a*x^3)/3 - ((4*I)*b*x^(5/2)*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + ((10*I)*b*x^2*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((10*I)*b*x^2*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - (40*b*x^(3/2)*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (40*b*x^(3/2)*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 - ((120*I)*b*x*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((120*I)*b*x*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4 + (240*b*Sqrt[x]*PolyLog[5, (-I)*E^(I*(c + d*Sqrt[x]))])/d^5 - (240*b*Sqrt[x]*PolyLog[5, I*E^(I*(c + d*Sqrt[x]))])/d^5 + ((240*I)*b*PolyLog[6, (-I)*E^(I*(c + d*Sqrt[x]))])/d^6 - ((240*I)*b*PolyLog[6, I*E^(I*(c + d*Sqrt[x]))])/d^6","A",16,7,18,0.3889,1,"{14, 4204, 4181, 2531, 6609, 2282, 6589}"
33,1,220,0,0.1860682,"\int x \left(a+b \sec \left(c+d \sqrt{x}\right)\right) \, dx","Int[x*(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{6 i b x \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{6 i b x \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{12 b \sqrt{x} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{12 b \sqrt{x} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{12 i b \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{12 i b \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{a x^2}{2}-\frac{4 i b x^{3/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}","\frac{6 i b x \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{6 i b x \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{12 b \sqrt{x} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{12 b \sqrt{x} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{12 i b \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{12 i b \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{a x^2}{2}-\frac{4 i b x^{3/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}",1,"(a*x^2)/2 - ((4*I)*b*x^(3/2)*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + ((6*I)*b*x*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((6*I)*b*x*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - (12*b*Sqrt[x]*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (12*b*Sqrt[x]*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 - ((12*I)*b*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((12*I)*b*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4","A",12,7,16,0.4375,1,"{14, 4204, 4181, 2531, 6609, 2282, 6589}"
34,0,0,0,0.0166376,"\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])/x,x]","\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x} \, dx","b \text{Int}\left(\frac{\sec \left(c+d \sqrt{x}\right)}{x},x\right)+a \log (x)",0,"a*Log[x] + b*Defer[Int][Sec[c + d*Sqrt[x]]/x, x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0178977,"\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^2} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\sec \left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"-(a/x) + b*Defer[Int][Sec[c + d*Sqrt[x]]/x^2, x]","A",0,0,0,0,-1,"{}"
36,1,749,0,0.8602575,"\int x^3 \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[x^3*(a + b*Sec[c + d*Sqrt[x]])^2,x]","\frac{28 i a b x^3 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{28 i a b x^3 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{168 a b x^{5/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{168 a b x^{5/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{840 i a b x^2 \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{840 i a b x^2 \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{3360 a b x^{3/2} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{3360 a b x^{3/2} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{10080 i a b x \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{10080 i a b x \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{20160 a b \sqrt{x} \text{PolyLog}\left(7,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}+\frac{20160 a b \sqrt{x} \text{PolyLog}\left(7,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}-\frac{20160 i a b \text{PolyLog}\left(8,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}+\frac{20160 i a b \text{PolyLog}\left(8,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}-\frac{42 i b^2 x^{5/2} \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{105 b^2 x^2 \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{210 i b^2 x^{3/2} \text{PolyLog}\left(4,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{315 b^2 x \text{PolyLog}\left(5,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{315 i b^2 \sqrt{x} \text{PolyLog}\left(6,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^7}+\frac{315 b^2 \text{PolyLog}\left(7,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^8}+\frac{a^2 x^4}{4}-\frac{8 i a b x^{7/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{14 b^2 x^3 \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{7/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{7/2}}{d}","\frac{28 i a b x^3 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{28 i a b x^3 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{168 a b x^{5/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{168 a b x^{5/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{840 i a b x^2 \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{840 i a b x^2 \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{3360 a b x^{3/2} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{3360 a b x^{3/2} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{10080 i a b x \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{10080 i a b x \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{20160 a b \sqrt{x} \text{PolyLog}\left(7,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}+\frac{20160 a b \sqrt{x} \text{PolyLog}\left(7,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^7}-\frac{20160 i a b \text{PolyLog}\left(8,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}+\frac{20160 i a b \text{PolyLog}\left(8,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^8}-\frac{42 i b^2 x^{5/2} \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{105 b^2 x^2 \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{210 i b^2 x^{3/2} \text{PolyLog}\left(4,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{315 b^2 x \text{PolyLog}\left(5,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{315 i b^2 \sqrt{x} \text{PolyLog}\left(6,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^7}+\frac{315 b^2 \text{PolyLog}\left(7,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^8}+\frac{a^2 x^4}{4}-\frac{8 i a b x^{7/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{14 b^2 x^3 \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{7/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{7/2}}{d}",1,"((-2*I)*b^2*x^(7/2))/d + (a^2*x^4)/4 - ((8*I)*a*b*x^(7/2)*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + (14*b^2*x^3*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d^2 + ((28*I)*a*b*x^3*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((28*I)*a*b*x^3*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - ((42*I)*b^2*x^(5/2)*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (168*a*b*x^(5/2)*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (168*a*b*x^(5/2)*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 + (105*b^2*x^2*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 - ((840*I)*a*b*x^2*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((840*I)*a*b*x^2*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4 + ((210*I)*b^2*x^(3/2)*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + (3360*a*b*x^(3/2)*PolyLog[5, (-I)*E^(I*(c + d*Sqrt[x]))])/d^5 - (3360*a*b*x^(3/2)*PolyLog[5, I*E^(I*(c + d*Sqrt[x]))])/d^5 - (315*b^2*x*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^6 + ((10080*I)*a*b*x*PolyLog[6, (-I)*E^(I*(c + d*Sqrt[x]))])/d^6 - ((10080*I)*a*b*x*PolyLog[6, I*E^(I*(c + d*Sqrt[x]))])/d^6 - ((315*I)*b^2*Sqrt[x]*PolyLog[6, -E^((2*I)*(c + d*Sqrt[x]))])/d^7 - (20160*a*b*Sqrt[x]*PolyLog[7, (-I)*E^(I*(c + d*Sqrt[x]))])/d^7 + (20160*a*b*Sqrt[x]*PolyLog[7, I*E^(I*(c + d*Sqrt[x]))])/d^7 + (315*b^2*PolyLog[7, -E^((2*I)*(c + d*Sqrt[x]))])/(2*d^8) - ((20160*I)*a*b*PolyLog[8, (-I)*E^(I*(c + d*Sqrt[x]))])/d^8 + ((20160*I)*a*b*PolyLog[8, I*E^(I*(c + d*Sqrt[x]))])/d^8 + (2*b^2*x^(7/2)*Tan[c + d*Sqrt[x]])/d","A",30,10,20,0.5000,1,"{4204, 4190, 4181, 2531, 6609, 2282, 6589, 4184, 3719, 2190}"
37,1,551,0,0.6335921,"\int x^2 \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[x^2*(a + b*Sec[c + d*Sqrt[x]])^2,x]","\frac{20 i a b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{20 i a b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{80 a b x^{3/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{80 a b x^{3/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{240 i a b x \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{240 i a b x \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{480 a b \sqrt{x} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{480 a b \sqrt{x} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{480 i a b \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{480 i a b \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{20 i b^2 x^{3/2} \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{30 b^2 x \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{30 i b^2 \sqrt{x} \text{PolyLog}\left(4,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{15 b^2 \text{PolyLog}\left(5,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{a^2 x^3}{3}-\frac{8 i a b x^{5/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{10 b^2 x^2 \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{5/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{5/2}}{d}","\frac{20 i a b x^2 \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{20 i a b x^2 \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{80 a b x^{3/2} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{80 a b x^{3/2} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{240 i a b x \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{240 i a b x \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{480 a b \sqrt{x} \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{480 a b \sqrt{x} \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{480 i a b \text{PolyLog}\left(6,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{480 i a b \text{PolyLog}\left(6,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{20 i b^2 x^{3/2} \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{30 b^2 x \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{30 i b^2 \sqrt{x} \text{PolyLog}\left(4,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{15 b^2 \text{PolyLog}\left(5,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{a^2 x^3}{3}-\frac{8 i a b x^{5/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{10 b^2 x^2 \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{5/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{5/2}}{d}",1,"((-2*I)*b^2*x^(5/2))/d + (a^2*x^3)/3 - ((8*I)*a*b*x^(5/2)*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + (10*b^2*x^2*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d^2 + ((20*I)*a*b*x^2*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((20*I)*a*b*x^2*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - ((20*I)*b^2*x^(3/2)*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (80*a*b*x^(3/2)*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (80*a*b*x^(3/2)*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 + (30*b^2*x*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 - ((240*I)*a*b*x*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((240*I)*a*b*x*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4 + ((30*I)*b^2*Sqrt[x]*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + (480*a*b*Sqrt[x]*PolyLog[5, (-I)*E^(I*(c + d*Sqrt[x]))])/d^5 - (480*a*b*Sqrt[x]*PolyLog[5, I*E^(I*(c + d*Sqrt[x]))])/d^5 - (15*b^2*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^6 + ((480*I)*a*b*PolyLog[6, (-I)*E^(I*(c + d*Sqrt[x]))])/d^6 - ((480*I)*a*b*PolyLog[6, I*E^(I*(c + d*Sqrt[x]))])/d^6 + (2*b^2*x^(5/2)*Tan[c + d*Sqrt[x]])/d","A",24,10,20,0.5000,1,"{4204, 4190, 4181, 2531, 6609, 2282, 6589, 4184, 3719, 2190}"
38,1,355,0,0.4507901,"\int x \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[x*(a + b*Sec[c + d*Sqrt[x]])^2,x]","\frac{12 i a b x \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{12 i a b x \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{24 a b \sqrt{x} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{24 a b \sqrt{x} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{24 i a b \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{24 i a b \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{6 i b^2 \sqrt{x} \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{3 b^2 \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{a^2 x^2}{2}-\frac{8 i a b x^{3/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{6 b^2 x \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{3/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{3/2}}{d}","\frac{12 i a b x \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{12 i a b x \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{24 a b \sqrt{x} \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{24 a b \sqrt{x} \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{24 i a b \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{24 i a b \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{6 i b^2 \sqrt{x} \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{3 b^2 \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{a^2 x^2}{2}-\frac{8 i a b x^{3/2} \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{6 b^2 x \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^{3/2} \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^{3/2}}{d}",1,"((-2*I)*b^2*x^(3/2))/d + (a^2*x^2)/2 - ((8*I)*a*b*x^(3/2)*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + (6*b^2*x*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d^2 + ((12*I)*a*b*x*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((12*I)*a*b*x*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - ((6*I)*b^2*Sqrt[x]*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (24*a*b*Sqrt[x]*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (24*a*b*Sqrt[x]*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 + (3*b^2*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 - ((24*I)*a*b*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((24*I)*a*b*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4 + (2*b^2*x^(3/2)*Tan[c + d*Sqrt[x]])/d","A",18,10,18,0.5556,1,"{4204, 4190, 4181, 2531, 6609, 2282, 6589, 4184, 3719, 2190}"
39,0,0,0,0.0226762,"\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])^2/x,x]","\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x},x\right)",0,"Defer[Int][(a + b*Sec[c + d*Sqrt[x]])^2/x, x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.0233649,"\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])^2/x^2,x]","\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^2},x\right)",0,"Defer[Int][(a + b*Sec[c + d*Sqrt[x]])^2/x^2, x]","A",0,0,0,0,-1,"{}"
41,1,1041,0,1.4762921,"\int \frac{x^3}{a+b \sec \left(c+d \sqrt{x}\right)} \, dx","Int[x^3/(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{x^4}{4 a}+\frac{2 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a \sqrt{b^2-a^2} d}-\frac{2 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a \sqrt{b^2-a^2} d}+\frac{14 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^3}{a \sqrt{b^2-a^2} d^2}-\frac{14 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^3}{a \sqrt{b^2-a^2} d^2}+\frac{84 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a \sqrt{b^2-a^2} d^3}-\frac{84 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a \sqrt{b^2-a^2} d^3}-\frac{420 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a \sqrt{b^2-a^2} d^4}+\frac{420 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a \sqrt{b^2-a^2} d^4}-\frac{1680 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a \sqrt{b^2-a^2} d^5}+\frac{1680 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a \sqrt{b^2-a^2} d^5}+\frac{5040 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x}{a \sqrt{b^2-a^2} d^6}-\frac{5040 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x}{a \sqrt{b^2-a^2} d^6}+\frac{10080 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a \sqrt{b^2-a^2} d^7}-\frac{10080 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a \sqrt{b^2-a^2} d^7}-\frac{10080 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a \sqrt{b^2-a^2} d^8}+\frac{10080 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right)}{a \sqrt{b^2-a^2} d^8}","\frac{x^4}{4 a}+\frac{2 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a \sqrt{b^2-a^2} d}-\frac{2 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a \sqrt{b^2-a^2} d}+\frac{14 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^3}{a \sqrt{b^2-a^2} d^2}-\frac{14 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^3}{a \sqrt{b^2-a^2} d^2}+\frac{84 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a \sqrt{b^2-a^2} d^3}-\frac{84 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a \sqrt{b^2-a^2} d^3}-\frac{420 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a \sqrt{b^2-a^2} d^4}+\frac{420 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a \sqrt{b^2-a^2} d^4}-\frac{1680 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a \sqrt{b^2-a^2} d^5}+\frac{1680 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a \sqrt{b^2-a^2} d^5}+\frac{5040 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x}{a \sqrt{b^2-a^2} d^6}-\frac{5040 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x}{a \sqrt{b^2-a^2} d^6}+\frac{10080 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a \sqrt{b^2-a^2} d^7}-\frac{10080 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a \sqrt{b^2-a^2} d^7}-\frac{10080 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a \sqrt{b^2-a^2} d^8}+\frac{10080 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right)}{a \sqrt{b^2-a^2} d^8}",1,"x^4/(4*a) + ((2*I)*b*x^(7/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) - ((2*I)*b*x^(7/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) + (14*b*x^3*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) - (14*b*x^3*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) + ((84*I)*b*x^(5/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - ((84*I)*b*x^(5/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - (420*b*x^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4) + (420*b*x^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4) - ((1680*I)*b*x^(3/2)*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^5) + ((1680*I)*b*x^(3/2)*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^5) + (5040*b*x*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^6) - (5040*b*x*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^6) + ((10080*I)*b*Sqrt[x]*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^7) - ((10080*I)*b*Sqrt[x]*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^7) - (10080*b*PolyLog[8, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^8) + (10080*b*PolyLog[8, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^8)","A",23,9,20,0.4500,1,"{4204, 4191, 3321, 2264, 2190, 2531, 6609, 2282, 6589}"
42,1,781,0,1.1797632,"\int \frac{x^2}{a+b \sec \left(c+d \sqrt{x}\right)} \, dx","Int[x^2/(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{10 b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{10 b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{40 i b x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{40 i b x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{120 b x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{120 b x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^4 \sqrt{b^2-a^2}}-\frac{240 i b \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{240 i b \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{240 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^6 \sqrt{b^2-a^2}}-\frac{240 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^6 \sqrt{b^2-a^2}}+\frac{2 i b x^{5/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x^{5/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{x^3}{3 a}","\frac{10 b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{10 b x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{40 i b x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{40 i b x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{120 b x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{120 b x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^4 \sqrt{b^2-a^2}}-\frac{240 i b \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{240 i b \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{240 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^6 \sqrt{b^2-a^2}}-\frac{240 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^6 \sqrt{b^2-a^2}}+\frac{2 i b x^{5/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x^{5/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{x^3}{3 a}",1,"x^3/(3*a) + ((2*I)*b*x^(5/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) - ((2*I)*b*x^(5/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) + (10*b*x^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) - (10*b*x^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) + ((40*I)*b*x^(3/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - ((40*I)*b*x^(3/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - (120*b*x*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4) + (120*b*x*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4) - ((240*I)*b*Sqrt[x]*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^5) + ((240*I)*b*Sqrt[x]*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^5) + (240*b*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^6) - (240*b*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^6)","A",19,9,20,0.4500,1,"{4204, 4191, 3321, 2264, 2190, 2531, 6609, 2282, 6589}"
43,1,521,0,0.9661074,"\int \frac{x}{a+b \sec \left(c+d \sqrt{x}\right)} \, dx","Int[x/(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{6 b x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{6 b x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{12 i b \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{12 i b \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{12 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{12 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{2 i b x^{3/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x^{3/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{x^2}{2 a}","\frac{6 b x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{6 b x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{12 i b \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{12 i b \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{12 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{12 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{2 i b x^{3/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x^{3/2} \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{x^2}{2 a}",1,"x^2/(2*a) + ((2*I)*b*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) - ((2*I)*b*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) + (6*b*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) - (6*b*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) + ((12*I)*b*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - ((12*I)*b*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - (12*b*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4) + (12*b*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4)","A",15,9,18,0.5000,1,"{4204, 4191, 3321, 2264, 2190, 2531, 6609, 2282, 6589}"
44,0,0,0,0.0253604,"\int \frac{1}{x \left(a+b \sec \left(c+d \sqrt{x}\right)\right)} \, dx","Int[1/(x*(a + b*Sec[c + d*Sqrt[x]])),x]","\int \frac{1}{x \left(a+b \sec \left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sec \left(c+d \sqrt{x}\right)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*Sec[c + d*Sqrt[x]])), x]","A",0,0,0,0,-1,"{}"
45,0,0,0,0.0145761,"\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^2} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\sec \left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"-(a/x) + b*Defer[Int][Sec[c + d*Sqrt[x]]/x^2, x]","A",0,0,0,0,-1,"{}"
46,1,3123,0,4.117995,"\int \frac{x^3}{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[x^3/(a + b*Sec[c + d*Sqrt[x]])^2,x]","\frac{x^4}{4 a^2}+\frac{4 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \sqrt{b^2-a^2} d}-\frac{2 i b^3 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{4 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \sqrt{b^2-a^2} d}+\frac{2 i b^3 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 b^2 \sin \left(c+d \sqrt{x}\right) x^{7/2}}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}-\frac{2 i b^2 x^{7/2}}{a^2 \left(a^2-b^2\right) d}+\frac{14 b^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) x^3}{a^2 \left(a^2-b^2\right) d^2}+\frac{14 b^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) x^3}{a^2 \left(a^2-b^2\right) d^2}+\frac{28 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^3}{a^2 \sqrt{b^2-a^2} d^2}-\frac{14 b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{28 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^3}{a^2 \sqrt{b^2-a^2} d^2}+\frac{14 b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{84 i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x^{5/2}}{a^2 \left(a^2-b^2\right) d^3}-\frac{84 i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x^{5/2}}{a^2 \left(a^2-b^2\right) d^3}+\frac{168 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \sqrt{b^2-a^2} d^3}-\frac{84 i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{168 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \sqrt{b^2-a^2} d^3}+\frac{84 i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{420 b^2 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{420 b^2 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x^2}{a^2 \left(a^2-b^2\right) d^4}-\frac{840 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^4}+\frac{420 b^3 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{840 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^4}-\frac{420 b^3 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{1680 i b^2 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x^{3/2}}{a^2 \left(a^2-b^2\right) d^5}+\frac{1680 i b^2 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x^{3/2}}{a^2 \left(a^2-b^2\right) d^5}-\frac{3360 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \sqrt{b^2-a^2} d^5}+\frac{1680 i b^3 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^5}+\frac{3360 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \sqrt{b^2-a^2} d^5}-\frac{1680 i b^3 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{5040 b^2 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x}{a^2 \left(a^2-b^2\right) d^6}-\frac{5040 b^2 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x}{a^2 \left(a^2-b^2\right) d^6}+\frac{10080 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x}{a^2 \sqrt{b^2-a^2} d^6}-\frac{5040 b^3 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{10080 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x}{a^2 \sqrt{b^2-a^2} d^6}+\frac{5040 b^3 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{10080 i b^2 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) \sqrt{x}}{a^2 \left(a^2-b^2\right) d^7}-\frac{10080 i b^2 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) \sqrt{x}}{a^2 \left(a^2-b^2\right) d^7}+\frac{20160 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \sqrt{b^2-a^2} d^7}-\frac{10080 i b^3 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \left(b^2-a^2\right)^{3/2} d^7}-\frac{20160 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \sqrt{b^2-a^2} d^7}+\frac{10080 i b^3 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \left(b^2-a^2\right)^{3/2} d^7}+\frac{10080 b^2 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^8}+\frac{10080 b^2 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^8}-\frac{20160 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^8}+\frac{10080 b^3 \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^8}+\frac{20160 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^8}-\frac{10080 b^3 \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^8}","\frac{x^4}{4 a^2}+\frac{4 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \sqrt{b^2-a^2} d}-\frac{2 i b^3 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{4 i b \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \sqrt{b^2-a^2} d}+\frac{2 i b^3 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 b^2 \sin \left(c+d \sqrt{x}\right) x^{7/2}}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}-\frac{2 i b^2 x^{7/2}}{a^2 \left(a^2-b^2\right) d}+\frac{14 b^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) x^3}{a^2 \left(a^2-b^2\right) d^2}+\frac{14 b^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) x^3}{a^2 \left(a^2-b^2\right) d^2}+\frac{28 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^3}{a^2 \sqrt{b^2-a^2} d^2}-\frac{14 b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{28 b \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^3}{a^2 \sqrt{b^2-a^2} d^2}+\frac{14 b^3 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{84 i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x^{5/2}}{a^2 \left(a^2-b^2\right) d^3}-\frac{84 i b^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x^{5/2}}{a^2 \left(a^2-b^2\right) d^3}+\frac{168 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \sqrt{b^2-a^2} d^3}-\frac{84 i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{168 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \sqrt{b^2-a^2} d^3}+\frac{84 i b^3 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{420 b^2 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{420 b^2 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x^2}{a^2 \left(a^2-b^2\right) d^4}-\frac{840 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^4}+\frac{420 b^3 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{840 b \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^4}-\frac{420 b^3 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{1680 i b^2 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x^{3/2}}{a^2 \left(a^2-b^2\right) d^5}+\frac{1680 i b^2 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x^{3/2}}{a^2 \left(a^2-b^2\right) d^5}-\frac{3360 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \sqrt{b^2-a^2} d^5}+\frac{1680 i b^3 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^5}+\frac{3360 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \sqrt{b^2-a^2} d^5}-\frac{1680 i b^3 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{5040 b^2 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) x}{a^2 \left(a^2-b^2\right) d^6}-\frac{5040 b^2 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) x}{a^2 \left(a^2-b^2\right) d^6}+\frac{10080 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x}{a^2 \sqrt{b^2-a^2} d^6}-\frac{5040 b^3 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) x}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{10080 b \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x}{a^2 \sqrt{b^2-a^2} d^6}+\frac{5040 b^3 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) x}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{10080 i b^2 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) \sqrt{x}}{a^2 \left(a^2-b^2\right) d^7}-\frac{10080 i b^2 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) \sqrt{x}}{a^2 \left(a^2-b^2\right) d^7}+\frac{20160 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \sqrt{b^2-a^2} d^7}-\frac{10080 i b^3 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \left(b^2-a^2\right)^{3/2} d^7}-\frac{20160 i b \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \sqrt{b^2-a^2} d^7}+\frac{10080 i b^3 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \left(b^2-a^2\right)^{3/2} d^7}+\frac{10080 b^2 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^8}+\frac{10080 b^2 \text{PolyLog}\left(7,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right)}{a^2 \left(a^2-b^2\right) d^8}-\frac{20160 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^8}+\frac{10080 b^3 \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^8}+\frac{20160 b \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^8}-\frac{10080 b^3 \text{PolyLog}\left(8,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^8}",1,"((-2*I)*b^2*x^(7/2))/(a^2*(a^2 - b^2)*d) + x^4/(4*a^2) + (14*b^2*x^3*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) + (14*b^2*x^3*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) - ((2*I)*b^3*x^(7/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*I)*b*x^(7/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + ((2*I)*b^3*x^(7/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*I)*b*x^(7/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) - ((84*I)*b^2*x^(5/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - ((84*I)*b^2*x^(5/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - (14*b^3*x^3*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (28*b*x^3*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (14*b^3*x^3*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (28*b*x^3*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (420*b^2*x^2*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) + (420*b^2*x^2*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) - ((84*I)*b^3*x^(5/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((168*I)*b*x^(5/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((84*I)*b^3*x^(5/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((168*I)*b*x^(5/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((1680*I)*b^2*x^(3/2)*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^5) + ((1680*I)*b^2*x^(3/2)*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^5) + (420*b^3*x^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (840*b*x^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) - (420*b^3*x^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (840*b*x^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) - (5040*b^2*x*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^6) - (5040*b^2*x*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^6) + ((1680*I)*b^3*x^(3/2)*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^5) - ((3360*I)*b*x^(3/2)*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^5) - ((1680*I)*b^3*x^(3/2)*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^5) + ((3360*I)*b*x^(3/2)*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^5) - ((10080*I)*b^2*Sqrt[x]*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^7) - ((10080*I)*b^2*Sqrt[x]*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^7) - (5040*b^3*x*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^6) + (10080*b*x*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^6) + (5040*b^3*x*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^6) - (10080*b*x*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^6) + (10080*b^2*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^8) + (10080*b^2*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^8) - ((10080*I)*b^3*Sqrt[x]*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^7) + ((20160*I)*b*Sqrt[x]*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^7) + ((10080*I)*b^3*Sqrt[x]*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^7) - ((20160*I)*b*Sqrt[x]*PolyLog[7, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^7) + (10080*b^3*PolyLog[8, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^8) - (20160*b*PolyLog[8, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^8) - (10080*b^3*PolyLog[8, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^8) + (20160*b*PolyLog[8, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^8) + (2*b^2*x^(7/2)*Sin[c + d*Sqrt[x]])/(a*(a^2 - b^2)*d*(b + a*Cos[c + d*Sqrt[x]]))","A",61,11,20,0.5500,1,"{4204, 4191, 3324, 3321, 2264, 2190, 2531, 6609, 2282, 6589, 4522}"
47,1,2323,0,3.2276712,"\int \frac{x^2}{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[x^2/(a + b*Sec[c + d*Sqrt[x]])^2,x]","-\frac{2 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{10 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{10 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{40 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{40 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{120 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{120 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{240 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{240 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{240 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^6}+\frac{240 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{2 i x^{5/2} b^2}{a^2 \left(a^2-b^2\right) d}+\frac{10 x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{10 x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{40 i x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{40 i x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{120 x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{120 x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{240 i \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}+\frac{240 i \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}-\frac{240 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^6}-\frac{240 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^6}+\frac{2 x^{5/2} \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{20 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{20 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{80 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{80 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{240 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{240 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}-\frac{480 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{480 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{480 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^6}-\frac{480 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^6}+\frac{x^3}{3 a^2}","-\frac{2 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{10 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{10 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{40 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{40 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{120 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{120 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{240 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{240 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{240 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^6}+\frac{240 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{2 i x^{5/2} b^2}{a^2 \left(a^2-b^2\right) d}+\frac{10 x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{10 x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{40 i x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{40 i x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{120 x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{120 x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{240 i \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}+\frac{240 i \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}-\frac{240 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^6}-\frac{240 \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^6}+\frac{2 x^{5/2} \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x^{5/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{20 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{20 x^2 \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{80 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{80 i x^{3/2} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{240 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{240 x \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}-\frac{480 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{480 i \sqrt{x} \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{480 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^6}-\frac{480 \text{PolyLog}\left(6,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^6}+\frac{x^3}{3 a^2}",1,"((-2*I)*b^2*x^(5/2))/(a^2*(a^2 - b^2)*d) + x^3/(3*a^2) + (10*b^2*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) + (10*b^2*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) - ((2*I)*b^3*x^(5/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*I)*b*x^(5/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + ((2*I)*b^3*x^(5/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*I)*b*x^(5/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) - ((40*I)*b^2*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - ((40*I)*b^2*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - (10*b^3*x^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (20*b*x^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (10*b^3*x^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (20*b*x^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (120*b^2*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) + (120*b^2*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) - ((40*I)*b^3*x^(3/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((80*I)*b*x^(3/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((40*I)*b^3*x^(3/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((80*I)*b*x^(3/2)*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((240*I)*b^2*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^5) + ((240*I)*b^2*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^5) + (120*b^3*x*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (240*b*x*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) - (120*b^3*x*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (240*b*x*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) - (240*b^2*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^6) - (240*b^2*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^6) + ((240*I)*b^3*Sqrt[x]*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^5) - ((480*I)*b*Sqrt[x]*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^5) - ((240*I)*b^3*Sqrt[x]*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^5) + ((480*I)*b*Sqrt[x]*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^5) - (240*b^3*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^6) + (480*b*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^6) + (240*b^3*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^6) - (480*b*PolyLog[6, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^6) + (2*b^2*x^(5/2)*Sin[c + d*Sqrt[x]])/(a*(a^2 - b^2)*d*(b + a*Cos[c + d*Sqrt[x]]))","A",49,11,20,0.5500,1,"{4204, 4191, 3324, 3321, 2264, 2190, 2531, 6609, 2282, 6589, 4522}"
48,1,1523,0,2.5042201,"\int \frac{x}{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[x/(a + b*Sec[c + d*Sqrt[x]])^2,x]","-\frac{2 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{6 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{6 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{12 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{12 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{12 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{12 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{2 i x^{3/2} b^2}{a^2 \left(a^2-b^2\right) d}+\frac{6 x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{6 x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{12 i \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{12 i \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{12 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{12 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{2 x^{3/2} \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{12 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{12 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{24 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{24 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{24 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{24 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{x^2}{2 a^2}","-\frac{2 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{6 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{6 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{12 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{12 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{12 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{12 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{2 i x^{3/2} b^2}{a^2 \left(a^2-b^2\right) d}+\frac{6 x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{6 x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{12 i \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{12 i \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{12 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{12 \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{2 x^{3/2} \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{12 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{12 x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{24 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{24 i \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{24 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{24 \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{x^2}{2 a^2}",1,"((-2*I)*b^2*x^(3/2))/(a^2*(a^2 - b^2)*d) + x^2/(2*a^2) + (6*b^2*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) + (6*b^2*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) - ((2*I)*b^3*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*I)*b*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + ((2*I)*b^3*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*I)*b*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) - ((12*I)*b^2*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - ((12*I)*b^2*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - (6*b^3*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (12*b*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (6*b^3*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (12*b*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (12*b^2*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) + (12*b^2*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) - ((12*I)*b^3*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((24*I)*b*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((12*I)*b^3*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((24*I)*b*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + (12*b^3*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (24*b*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) - (12*b^3*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (24*b*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) + (2*b^2*x^(3/2)*Sin[c + d*Sqrt[x]])/(a*(a^2 - b^2)*d*(b + a*Cos[c + d*Sqrt[x]]))","A",37,11,18,0.6111,1,"{4204, 4191, 3324, 3321, 2264, 2190, 2531, 6609, 2282, 6589, 4522}"
49,0,0,0,0.0259855,"\int \frac{1}{x \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[1/(x*(a + b*Sec[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*Sec[c + d*Sqrt[x]])^2), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.0247117,"\int \frac{1}{x^2 \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[1/(x^2*(a + b*Sec[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^2 \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(a + b*Sec[c + d*Sqrt[x]])^2), x]","A",0,0,0,0,-1,"{}"
51,1,284,0,0.2480811,"\int x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right) \, dx","Int[x^(3/2)*(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{8 i b x^{3/2} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{8 i b x^{3/2} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{24 b x \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{24 b x \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{48 i b \sqrt{x} \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{48 i b \sqrt{x} \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{48 b \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{48 b \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{2}{5} a x^{5/2}-\frac{4 i b x^2 \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}","\frac{8 i b x^{3/2} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{8 i b x^{3/2} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{24 b x \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{24 b x \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{48 i b \sqrt{x} \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{48 i b \sqrt{x} \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{48 b \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{48 b \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{2}{5} a x^{5/2}-\frac{4 i b x^2 \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}",1,"(2*a*x^(5/2))/5 - ((4*I)*b*x^2*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + ((8*I)*b*x^(3/2)*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((8*I)*b*x^(3/2)*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - (24*b*x*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (24*b*x*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 - ((48*I)*b*Sqrt[x]*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((48*I)*b*Sqrt[x]*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4 + (48*b*PolyLog[5, (-I)*E^(I*(c + d*Sqrt[x]))])/d^5 - (48*b*PolyLog[5, I*E^(I*(c + d*Sqrt[x]))])/d^5","A",14,7,20,0.3500,1,"{14, 4204, 4181, 2531, 6609, 2282, 6589}"
52,1,158,0,0.1319133,"\int \sqrt{x} \left(a+b \sec \left(c+d \sqrt{x}\right)\right) \, dx","Int[Sqrt[x]*(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{4 i b \sqrt{x} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 i b \sqrt{x} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 b \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{4 b \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{2}{3} a x^{3/2}-\frac{4 i b x \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}","\frac{4 i b \sqrt{x} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 i b \sqrt{x} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 b \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{4 b \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{2}{3} a x^{3/2}-\frac{4 i b x \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}",1,"(2*a*x^(3/2))/3 - ((4*I)*b*x*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + ((4*I)*b*Sqrt[x]*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((4*I)*b*Sqrt[x]*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - (4*b*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (4*b*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3","A",10,6,20,0.3000,1,"{14, 4204, 4181, 2531, 2282, 6589}"
53,1,26,0,0.0211247,"\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{\sqrt{x}} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])/Sqrt[x],x]","2 a \sqrt{x}+\frac{2 b \tanh ^{-1}\left(\sin \left(c+d \sqrt{x}\right)\right)}{d}","2 a \sqrt{x}+\frac{2 b \tanh ^{-1}\left(\sin \left(c+d \sqrt{x}\right)\right)}{d}",1,"2*a*Sqrt[x] + (2*b*ArcTanh[Sin[c + d*Sqrt[x]]])/d","A",4,3,20,0.1500,1,"{14, 4204, 3770}"
54,0,0,0,0.0138176,"\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^{3/2}} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])/x^(3/2),x]","\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^{3/2}} \, dx","b \text{Int}\left(\frac{\sec \left(c+d \sqrt{x}\right)}{x^{3/2}},x\right)-\frac{2 a}{\sqrt{x}}",0,"(-2*a)/Sqrt[x] + b*Defer[Int][Sec[c + d*Sqrt[x]]/x^(3/2), x]","A",0,0,0,0,-1,"{}"
55,0,0,0,0.0138274,"\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^{5/2}} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])/x^(5/2),x]","\int \frac{a+b \sec \left(c+d \sqrt{x}\right)}{x^{5/2}} \, dx","b \text{Int}\left(\frac{\sec \left(c+d \sqrt{x}\right)}{x^{5/2}},x\right)-\frac{2 a}{3 x^{3/2}}",0,"(-2*a)/(3*x^(3/2)) + b*Defer[Int][Sec[c + d*Sqrt[x]]/x^(5/2), x]","A",0,0,0,0,-1,"{}"
56,1,451,0,0.5373029,"\int x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[x^(3/2)*(a + b*Sec[c + d*Sqrt[x]])^2,x]","\frac{16 i a b x^{3/2} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{16 i a b x^{3/2} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{48 a b x \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{48 a b x \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{96 i a b \sqrt{x} \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{96 i a b \sqrt{x} \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{96 a b \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{96 a b \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{12 i b^2 x \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{12 b^2 \sqrt{x} \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{6 i b^2 \text{PolyLog}\left(4,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{2}{5} a^2 x^{5/2}-\frac{8 i a b x^2 \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{8 b^2 x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^2 \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^2}{d}","\frac{16 i a b x^{3/2} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{16 i a b x^{3/2} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{48 a b x \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{48 a b x \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{96 i a b \sqrt{x} \text{PolyLog}\left(4,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{96 i a b \sqrt{x} \text{PolyLog}\left(4,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{96 a b \text{PolyLog}\left(5,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{96 a b \text{PolyLog}\left(5,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{12 i b^2 x \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{12 b^2 \sqrt{x} \text{PolyLog}\left(3,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{6 i b^2 \text{PolyLog}\left(4,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{2}{5} a^2 x^{5/2}-\frac{8 i a b x^2 \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{8 b^2 x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x^2 \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x^2}{d}",1,"((-2*I)*b^2*x^2)/d + (2*a^2*x^(5/2))/5 - ((8*I)*a*b*x^2*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + (8*b^2*x^(3/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d^2 + ((16*I)*a*b*x^(3/2)*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((16*I)*a*b*x^(3/2)*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - ((12*I)*b^2*x*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (48*a*b*x*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (48*a*b*x*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 + (12*b^2*Sqrt[x]*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 - ((96*I)*a*b*Sqrt[x]*PolyLog[4, (-I)*E^(I*(c + d*Sqrt[x]))])/d^4 + ((96*I)*a*b*Sqrt[x]*PolyLog[4, I*E^(I*(c + d*Sqrt[x]))])/d^4 + ((6*I)*b^2*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + (96*a*b*PolyLog[5, (-I)*E^(I*(c + d*Sqrt[x]))])/d^5 - (96*a*b*PolyLog[5, I*E^(I*(c + d*Sqrt[x]))])/d^5 + (2*b^2*x^2*Tan[c + d*Sqrt[x]])/d","A",21,10,22,0.4545,1,"{4204, 4190, 4181, 2531, 6609, 2282, 6589, 4184, 3719, 2190}"
57,1,255,0,0.3245278,"\int \sqrt{x} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[Sqrt[x]*(a + b*Sec[c + d*Sqrt[x]])^2,x]","\frac{8 i a b \sqrt{x} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{8 i a b \sqrt{x} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{8 a b \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{8 a b \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{2 i b^2 \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{2}{3} a^2 x^{3/2}-\frac{8 i a b x \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{4 b^2 \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x}{d}","\frac{8 i a b \sqrt{x} \text{PolyLog}\left(2,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{8 i a b \sqrt{x} \text{PolyLog}\left(2,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{8 a b \text{PolyLog}\left(3,-i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{8 a b \text{PolyLog}\left(3,i e^{i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{2 i b^2 \text{PolyLog}\left(2,-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{2}{3} a^2 x^{3/2}-\frac{8 i a b x \tan ^{-1}\left(e^{i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{4 b^2 \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}+\frac{2 b^2 x \tan \left(c+d \sqrt{x}\right)}{d}-\frac{2 i b^2 x}{d}",1,"((-2*I)*b^2*x)/d + (2*a^2*x^(3/2))/3 - ((8*I)*a*b*x*ArcTan[E^(I*(c + d*Sqrt[x]))])/d + (4*b^2*Sqrt[x]*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d^2 + ((8*I)*a*b*Sqrt[x]*PolyLog[2, (-I)*E^(I*(c + d*Sqrt[x]))])/d^2 - ((8*I)*a*b*Sqrt[x]*PolyLog[2, I*E^(I*(c + d*Sqrt[x]))])/d^2 - ((2*I)*b^2*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (8*a*b*PolyLog[3, (-I)*E^(I*(c + d*Sqrt[x]))])/d^3 + (8*a*b*PolyLog[3, I*E^(I*(c + d*Sqrt[x]))])/d^3 + (2*b^2*x*Tan[c + d*Sqrt[x]])/d","A",15,11,22,0.5000,1,"{4204, 4190, 4181, 2531, 2282, 6589, 4184, 3719, 2190, 2279, 2391}"
58,1,47,0,0.0519136,"\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{\sqrt{x}} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])^2/Sqrt[x],x]","2 a^2 \sqrt{x}+\frac{4 a b \tanh ^{-1}\left(\sin \left(c+d \sqrt{x}\right)\right)}{d}+\frac{2 b^2 \tan \left(c+d \sqrt{x}\right)}{d}","2 a^2 \sqrt{x}+\frac{4 a b \tanh ^{-1}\left(\sin \left(c+d \sqrt{x}\right)\right)}{d}+\frac{2 b^2 \tan \left(c+d \sqrt{x}\right)}{d}",1,"2*a^2*Sqrt[x] + (4*a*b*ArcTanh[Sin[c + d*Sqrt[x]]])/d + (2*b^2*Tan[c + d*Sqrt[x]])/d","A",5,5,22,0.2273,1,"{4204, 3773, 3770, 3767, 8}"
59,0,0,0,0.0224748,"\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])^2/x^(3/2),x]","\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}},x\right)",0,"Defer[Int][(a + b*Sec[c + d*Sqrt[x]])^2/x^(3/2), x]","A",0,0,0,0,-1,"{}"
60,0,0,0,0.0229092,"\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}} \, dx","Int[(a + b*Sec[c + d*Sqrt[x]])^2/x^(5/2),x]","\int \frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}} \, dx","\text{Int}\left(\frac{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}},x\right)",0,"Defer[Int][(a + b*Sec[c + d*Sqrt[x]])^2/x^(5/2), x]","A",0,0,0,0,-1,"{}"
61,1,653,0,1.0485817,"\int \frac{x^{3/2}}{a+b \sec \left(c+d \sqrt{x}\right)} \, dx","Int[x^(3/2)/(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{8 b x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{8 b x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{24 i b x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{24 i b x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{48 b \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{48 b \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^4 \sqrt{b^2-a^2}}-\frac{48 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{48 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{2 i b x^2 \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x^2 \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{2 x^{5/2}}{5 a}","\frac{8 b x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{8 b x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{24 i b x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{24 i b x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{48 b \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{48 b \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^4 \sqrt{b^2-a^2}}-\frac{48 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{48 i b \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^5 \sqrt{b^2-a^2}}+\frac{2 i b x^2 \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x^2 \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{2 x^{5/2}}{5 a}",1,"(2*x^(5/2))/(5*a) + ((2*I)*b*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) - ((2*I)*b*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) + (8*b*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) - (8*b*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) + ((24*I)*b*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - ((24*I)*b*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - (48*b*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4) + (48*b*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^4) - ((48*I)*b*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^5) + ((48*I)*b*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^5)","A",17,9,22,0.4091,1,"{4204, 4191, 3321, 2264, 2190, 2531, 6609, 2282, 6589}"
62,1,393,0,0.8264805,"\int \frac{\sqrt{x}}{a+b \sec \left(c+d \sqrt{x}\right)} \, dx","Int[Sqrt[x]/(a + b*Sec[c + d*Sqrt[x]]),x]","\frac{4 b \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{4 b \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{4 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{4 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}+\frac{2 i b x \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{2 x^{3/2}}{3 a}","\frac{4 b \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{4 b \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{4 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{4 i b \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 \sqrt{b^2-a^2}}+\frac{2 i b x \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d \sqrt{b^2-a^2}}-\frac{2 i b x \log \left(1+\frac{a e^{i \left(c+d \sqrt{x}\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d \sqrt{b^2-a^2}}+\frac{2 x^{3/2}}{3 a}",1,"(2*x^(3/2))/(3*a) + ((2*I)*b*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) - ((2*I)*b*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d) + (4*b*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) - (4*b*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2) + ((4*I)*b*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3) - ((4*I)*b*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3)","A",13,8,22,0.3636,1,"{4204, 4191, 3321, 2264, 2190, 2531, 2282, 6589}"
63,1,68,0,0.0822412,"\int \frac{1}{\sqrt{x} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)} \, dx","Int[1/(Sqrt[x]*(a + b*Sec[c + d*Sqrt[x]])),x]","\frac{2 \sqrt{x}}{a}-\frac{4 b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a+b}}\right)}{a d \sqrt{a-b} \sqrt{a+b}}","\frac{2 \sqrt{x}}{a}-\frac{4 b \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a+b}}\right)}{a d \sqrt{a-b} \sqrt{a+b}}",1,"(2*Sqrt[x])/a - (4*b*ArcTanh[(Sqrt[a - b]*Tan[(c + d*Sqrt[x])/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*Sqrt[a + b]*d)","A",4,4,22,0.1818,1,"{4204, 3783, 2659, 208}"
64,0,0,0,0.0247321,"\int \frac{1}{x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)} \, dx","Int[1/(x^(3/2)*(a + b*Sec[c + d*Sqrt[x]])),x]","\int \frac{1}{x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)},x\right)",0,"Defer[Int][1/(x^(3/2)*(a + b*Sec[c + d*Sqrt[x]])), x]","A",0,0,0,0,-1,"{}"
65,0,0,0,0.0243146,"\int \frac{1}{x^{5/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)} \, dx","Int[1/(x^(5/2)*(a + b*Sec[c + d*Sqrt[x]])),x]","\int \frac{1}{x^{5/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^{5/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)},x\right)",0,"Defer[Int][1/(x^(5/2)*(a + b*Sec[c + d*Sqrt[x]])), x]","A",0,0,0,0,-1,"{}"
66,1,1925,0,2.8584212,"\int \frac{x^{3/2}}{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[x^(3/2)/(a + b*Sec[c + d*Sqrt[x]])^2,x]","-\frac{2 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{8 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{8 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{24 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{24 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{48 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{48 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{48 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{48 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{2 i x^2 b^2}{a^2 \left(a^2-b^2\right) d}+\frac{8 x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{8 x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{24 i x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{24 i x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{48 \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{48 \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{48 i \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}+\frac{48 i \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}+\frac{2 x^2 \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{16 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{16 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{48 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{48 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{96 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{96 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}-\frac{96 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{96 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{2 x^{5/2}}{5 a^2}","-\frac{2 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{8 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{8 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{24 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{24 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{48 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{48 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{48 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{48 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{2 i x^2 b^2}{a^2 \left(a^2-b^2\right) d}+\frac{8 x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{8 x^{3/2} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{24 i x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{24 i x \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{48 \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{48 \sqrt{x} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{48 i \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}+\frac{48 i \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}+\frac{2 x^2 \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x^2 \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{16 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{16 x^{3/2} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{48 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{48 i x \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{96 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{96 \sqrt{x} \text{PolyLog}\left(4,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}-\frac{96 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{96 i \text{PolyLog}\left(5,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{2 x^{5/2}}{5 a^2}",1,"((-2*I)*b^2*x^2)/(a^2*(a^2 - b^2)*d) + (2*x^(5/2))/(5*a^2) + (8*b^2*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) + (8*b^2*x^(3/2)*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) - ((2*I)*b^3*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*I)*b*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + ((2*I)*b^3*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*I)*b*x^2*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) - ((24*I)*b^2*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - ((24*I)*b^2*x*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - (8*b^3*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (16*b*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (8*b^3*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (16*b*x^(3/2)*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (48*b^2*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) + (48*b^2*Sqrt[x]*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^4) - ((24*I)*b^3*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((48*I)*b*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((24*I)*b^3*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((48*I)*b*x*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((48*I)*b^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^5) + ((48*I)*b^2*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^5) + (48*b^3*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) - (96*b*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) - (48*b^3*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^4) + (96*b*Sqrt[x]*PolyLog[4, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^4) + ((48*I)*b^3*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^5) - ((96*I)*b*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^5) - ((48*I)*b^3*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^5) + ((96*I)*b*PolyLog[5, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^5) + (2*b^2*x^2*Sin[c + d*Sqrt[x]])/(a*(a^2 - b^2)*d*(b + a*Cos[c + d*Sqrt[x]]))","A",43,11,22,0.5000,1,"{4204, 4191, 3324, 3321, 2264, 2190, 2531, 6609, 2282, 6589, 4522}"
67,1,1125,0,2.1064322,"\int \frac{\sqrt{x}}{\left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[Sqrt[x]/(a + b*Sec[c + d*Sqrt[x]])^2,x]","-\frac{2 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{4 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{4 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{4 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{4 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{2 i x b^2}{a^2 \left(a^2-b^2\right) d}+\frac{4 \sqrt{x} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{4 \sqrt{x} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{4 i \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{4 i \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{2 x \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{8 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{8 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{8 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{8 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}+\frac{2 x^{3/2}}{3 a^2}","-\frac{2 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{4 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{4 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{4 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{4 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{2 i x b^2}{a^2 \left(a^2-b^2\right) d}+\frac{4 \sqrt{x} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}+\frac{4 \sqrt{x} \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) b^2}{a^2 \left(a^2-b^2\right) d^2}-\frac{4 i \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}-\frac{4 i \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+i \sqrt{a^2-b^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{2 x \sin \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cos \left(c+d \sqrt{x}\right)\right)}+\frac{4 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{4 i x \log \left(\frac{e^{i \left(c+d \sqrt{x}\right)} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{8 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}-\frac{8 \sqrt{x} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{8 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{8 i \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d \sqrt{x}\right)}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}+\frac{2 x^{3/2}}{3 a^2}",1,"((-2*I)*b^2*x)/(a^2*(a^2 - b^2)*d) + (2*x^(3/2))/(3*a^2) + (4*b^2*Sqrt[x]*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) + (4*b^2*Sqrt[x]*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2) - ((2*I)*b^3*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) + ((4*I)*b*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) + ((2*I)*b^3*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d) - ((4*I)*b*x*Log[1 + (a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d) - ((4*I)*b^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - ((4*I)*b^2*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3) - (4*b^3*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) + (8*b*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) + (4*b^3*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2) - (8*b*Sqrt[x]*PolyLog[2, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2) - ((4*I)*b^3*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) + ((8*I)*b*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + ((4*I)*b^3*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3) - ((8*I)*b*PolyLog[3, -((a*E^(I*(c + d*Sqrt[x])))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3) + (2*b^2*x*Sin[c + d*Sqrt[x]])/(a*(a^2 - b^2)*d*(b + a*Cos[c + d*Sqrt[x]]))","A",31,12,22,0.5455,1,"{4204, 4191, 3324, 3321, 2264, 2190, 2531, 2282, 6589, 4522, 2279, 2391}"
68,1,127,0,0.198528,"\int \frac{1}{\sqrt{x} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[1/(Sqrt[x]*(a + b*Sec[c + d*Sqrt[x]])^2),x]","-\frac{4 b \left(2 a^2-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a+b}}\right)}{a^2 d (a-b)^{3/2} (a+b)^{3/2}}+\frac{2 b^2 \tan \left(c+d \sqrt{x}\right)}{a d \left(a^2-b^2\right) \left(a+b \sec \left(c+d \sqrt{x}\right)\right)}+\frac{2 \sqrt{x}}{a^2}","-\frac{4 b \left(2 a^2-b^2\right) \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a+b}}\right)}{a^2 d (a-b)^{3/2} (a+b)^{3/2}}+\frac{2 b^2 \tan \left(c+d \sqrt{x}\right)}{a d \left(a^2-b^2\right) \left(a+b \sec \left(c+d \sqrt{x}\right)\right)}+\frac{2 \sqrt{x}}{a^2}",1,"(2*Sqrt[x])/a^2 - (4*b*(2*a^2 - b^2)*ArcTanh[(Sqrt[a - b]*Tan[(c + d*Sqrt[x])/2])/Sqrt[a + b]])/(a^2*(a - b)^(3/2)*(a + b)^(3/2)*d) + (2*b^2*Tan[c + d*Sqrt[x]])/(a*(a^2 - b^2)*d*(a + b*Sec[c + d*Sqrt[x]]))","A",6,6,22,0.2727,1,"{4204, 3785, 3919, 3831, 2659, 208}"
69,0,0,0,0.0231875,"\int \frac{1}{x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[1/(x^(3/2)*(a + b*Sec[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^{3/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x^(3/2)*(a + b*Sec[c + d*Sqrt[x]])^2), x]","A",0,0,0,0,-1,"{}"
70,0,0,0,0.0229815,"\int \frac{1}{x^{5/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[1/(x^(5/2)*(a + b*Sec[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^{5/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^{5/2} \left(a+b \sec \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x^(5/2)*(a + b*Sec[c + d*Sqrt[x]])^2), x]","A",0,0,0,0,-1,"{}"
71,0,0,0,0.0483285,"\int (e x)^m \left(a+b \sec \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^m*(a + b*Sec[c + d*x^n])^p,x]","\int (e x)^m \left(a+b \sec \left(c+d x^n\right)\right)^p \, dx","x^{-m} (e x)^m \text{Int}\left(x^m \left(a+b \sec \left(c+d x^n\right)\right)^p,x\right)",0,"((e*x)^m*Defer[Int][x^m*(a + b*Sec[c + d*x^n])^p, x])/x^m","A",0,0,0,0,-1,"{}"
72,1,44,0,0.0473253,"\int (e x)^{-1+n} \left(a+b \sec \left(c+d x^n\right)\right) \, dx","Int[(e*x)^(-1 + n)*(a + b*Sec[c + d*x^n]),x]","\frac{a (e x)^n}{e n}+\frac{b x^{-n} (e x)^n \tanh ^{-1}\left(\sin \left(c+d x^n\right)\right)}{d e n}","\frac{a (e x)^n}{e n}+\frac{b x^{-n} (e x)^n \tanh ^{-1}\left(\sin \left(c+d x^n\right)\right)}{d e n}",1,"(a*(e*x)^n)/(e*n) + (b*(e*x)^n*ArcTanh[Sin[c + d*x^n]])/(d*e*n*x^n)","A",5,4,20,0.2000,1,"{14, 4208, 4204, 3770}"
73,1,149,0,0.1135207,"\int (e x)^{-1+2 n} \left(a+b \sec \left(c+d x^n\right)\right) \, dx","Int[(e*x)^(-1 + 2*n)*(a + b*Sec[c + d*x^n]),x]","\frac{i b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{i b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{a (e x)^{2 n}}{2 e n}-\frac{2 i b x^{-n} (e x)^{2 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}","\frac{i b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{i b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{a (e x)^{2 n}}{2 e n}-\frac{2 i b x^{-n} (e x)^{2 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}",1,"(a*(e*x)^(2*n))/(2*e*n) - ((2*I)*b*(e*x)^(2*n)*ArcTan[E^(I*(c + d*x^n))])/(d*e*n*x^n) + (I*b*(e*x)^(2*n)*PolyLog[2, (-I)*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n)) - (I*b*(e*x)^(2*n)*PolyLog[2, I*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n))","A",9,6,22,0.2727,1,"{14, 4208, 4204, 4181, 2279, 2391}"
74,1,235,0,0.1898595,"\int (e x)^{-1+3 n} \left(a+b \sec \left(c+d x^n\right)\right) \, dx","Int[(e*x)^(-1 + 3*n)*(a + b*Sec[c + d*x^n]),x]","-\frac{2 b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{2 b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{2 i b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{2 i b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{a (e x)^{3 n}}{3 e n}-\frac{2 i b x^{-n} (e x)^{3 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}","-\frac{2 b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{2 b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{2 i b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{2 i b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{a (e x)^{3 n}}{3 e n}-\frac{2 i b x^{-n} (e x)^{3 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}",1,"(a*(e*x)^(3*n))/(3*e*n) - ((2*I)*b*(e*x)^(3*n)*ArcTan[E^(I*(c + d*x^n))])/(d*e*n*x^n) + ((2*I)*b*(e*x)^(3*n)*PolyLog[2, (-I)*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n)) - ((2*I)*b*(e*x)^(3*n)*PolyLog[2, I*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n)) - (2*b*(e*x)^(3*n)*PolyLog[3, (-I)*E^(I*(c + d*x^n))])/(d^3*e*n*x^(3*n)) + (2*b*(e*x)^(3*n)*PolyLog[3, I*E^(I*(c + d*x^n))])/(d^3*e*n*x^(3*n))","A",11,7,22,0.3182,1,"{14, 4208, 4204, 4181, 2531, 2282, 6589}"
75,1,79,0,0.0901147,"\int (e x)^{-1+n} \left(a+b \sec \left(c+d x^n\right)\right)^2 \, dx","Int[(e*x)^(-1 + n)*(a + b*Sec[c + d*x^n])^2,x]","\frac{a^2 (e x)^n}{e n}+\frac{2 a b x^{-n} (e x)^n \tanh ^{-1}\left(\sin \left(c+d x^n\right)\right)}{d e n}+\frac{b^2 x^{-n} (e x)^n \tan \left(c+d x^n\right)}{d e n}","\frac{a^2 (e x)^n}{e n}+\frac{2 a b x^{-n} (e x)^n \tanh ^{-1}\left(\sin \left(c+d x^n\right)\right)}{d e n}+\frac{b^2 x^{-n} (e x)^n \tan \left(c+d x^n\right)}{d e n}",1,"(a^2*(e*x)^n)/(e*n) + (2*a*b*(e*x)^n*ArcTanh[Sin[c + d*x^n]])/(d*e*n*x^n) + (b^2*(e*x)^n*Tan[c + d*x^n])/(d*e*n*x^n)","A",6,6,22,0.2727,1,"{4208, 4204, 3773, 3770, 3767, 8}"
76,1,221,0,0.1995286,"\int (e x)^{-1+2 n} \left(a+b \sec \left(c+d x^n\right)\right)^2 \, dx","Int[(e*x)^(-1 + 2*n)*(a + b*Sec[c + d*x^n])^2,x]","\frac{2 i a b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{2 i a b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{a^2 (e x)^{2 n}}{2 e n}-\frac{4 i a b x^{-n} (e x)^{2 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}+\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(\cos \left(c+d x^n\right)\right)}{d^2 e n}+\frac{b^2 x^{-n} (e x)^{2 n} \tan \left(c+d x^n\right)}{d e n}","\frac{2 i a b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{2 i a b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{a^2 (e x)^{2 n}}{2 e n}-\frac{4 i a b x^{-n} (e x)^{2 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}+\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(\cos \left(c+d x^n\right)\right)}{d^2 e n}+\frac{b^2 x^{-n} (e x)^{2 n} \tan \left(c+d x^n\right)}{d e n}",1,"(a^2*(e*x)^(2*n))/(2*e*n) - ((4*I)*a*b*(e*x)^(2*n)*ArcTan[E^(I*(c + d*x^n))])/(d*e*n*x^n) + (b^2*(e*x)^(2*n)*Log[Cos[c + d*x^n]])/(d^2*e*n*x^(2*n)) + ((2*I)*a*b*(e*x)^(2*n)*PolyLog[2, (-I)*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n)) - ((2*I)*a*b*(e*x)^(2*n)*PolyLog[2, I*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n)) + (b^2*(e*x)^(2*n)*Tan[c + d*x^n])/(d*e*n*x^n)","A",11,8,24,0.3333,1,"{4208, 4204, 4190, 4181, 2279, 2391, 4184, 3475}"
77,1,390,0,0.3962976,"\int (e x)^{-1+3 n} \left(a+b \sec \left(c+d x^n\right)\right)^2 \, dx","Int[(e*x)^(-1 + 3*n)*(a + b*Sec[c + d*x^n])^2,x]","-\frac{4 a b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{4 a b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{4 i a b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{4 i a b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{i b^2 x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(2,-e^{2 i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{a^2 (e x)^{3 n}}{3 e n}-\frac{4 i a b x^{-n} (e x)^{3 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}+\frac{2 b^2 x^{-2 n} (e x)^{3 n} \log \left(1+e^{2 i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{b^2 x^{-n} (e x)^{3 n} \tan \left(c+d x^n\right)}{d e n}-\frac{i b^2 x^{-n} (e x)^{3 n}}{d e n}","-\frac{4 a b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{4 a b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,i e^{i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{4 i a b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{4 i a b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,i e^{i \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{i b^2 x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(2,-e^{2 i \left(c+d x^n\right)}\right)}{d^3 e n}+\frac{a^2 (e x)^{3 n}}{3 e n}-\frac{4 i a b x^{-n} (e x)^{3 n} \tan ^{-1}\left(e^{i \left(c+d x^n\right)}\right)}{d e n}+\frac{2 b^2 x^{-2 n} (e x)^{3 n} \log \left(1+e^{2 i \left(c+d x^n\right)}\right)}{d^2 e n}+\frac{b^2 x^{-n} (e x)^{3 n} \tan \left(c+d x^n\right)}{d e n}-\frac{i b^2 x^{-n} (e x)^{3 n}}{d e n}",1,"(a^2*(e*x)^(3*n))/(3*e*n) - (I*b^2*(e*x)^(3*n))/(d*e*n*x^n) - ((4*I)*a*b*(e*x)^(3*n)*ArcTan[E^(I*(c + d*x^n))])/(d*e*n*x^n) + (2*b^2*(e*x)^(3*n)*Log[1 + E^((2*I)*(c + d*x^n))])/(d^2*e*n*x^(2*n)) + ((4*I)*a*b*(e*x)^(3*n)*PolyLog[2, (-I)*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n)) - ((4*I)*a*b*(e*x)^(3*n)*PolyLog[2, I*E^(I*(c + d*x^n))])/(d^2*e*n*x^(2*n)) - (I*b^2*(e*x)^(3*n)*PolyLog[2, -E^((2*I)*(c + d*x^n))])/(d^3*e*n*x^(3*n)) - (4*a*b*(e*x)^(3*n)*PolyLog[3, (-I)*E^(I*(c + d*x^n))])/(d^3*e*n*x^(3*n)) + (4*a*b*(e*x)^(3*n)*PolyLog[3, I*E^(I*(c + d*x^n))])/(d^3*e*n*x^(3*n)) + (b^2*(e*x)^(3*n)*Tan[c + d*x^n])/(d*e*n*x^n)","A",16,12,24,0.5000,1,"{4208, 4204, 4190, 4181, 2531, 2282, 6589, 4184, 3719, 2190, 2279, 2391}"
78,1,87,0,0.1469479,"\int \frac{(e x)^{-1+n}}{a+b \sec \left(c+d x^n\right)} \, dx","Int[(e*x)^(-1 + n)/(a + b*Sec[c + d*x^n]),x]","\frac{(e x)^n}{a e n}-\frac{2 b x^{-n} (e x)^n \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a+b}}\right)}{a d e n \sqrt{a-b} \sqrt{a+b}}","\frac{(e x)^n}{a e n}-\frac{2 b x^{-n} (e x)^n \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a+b}}\right)}{a d e n \sqrt{a-b} \sqrt{a+b}}",1,"(e*x)^n/(a*e*n) - (2*b*(e*x)^n*ArcTanh[(Sqrt[a - b]*Tan[(c + d*x^n)/2])/Sqrt[a + b]])/(a*Sqrt[a - b]*Sqrt[a + b]*d*e*n*x^n)","A",5,5,22,0.2273,1,"{4208, 4204, 3783, 2659, 208}"
79,1,328,0,0.5953473,"\int \frac{(e x)^{-1+2 n}}{a+b \sec \left(c+d x^n\right)} \, dx","Int[(e*x)^(-1 + 2*n)/(a + b*Sec[c + d*x^n]),x]","\frac{b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}-\frac{b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 e n \sqrt{b^2-a^2}}+\frac{i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d e n \sqrt{b^2-a^2}}-\frac{i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d e n \sqrt{b^2-a^2}}+\frac{(e x)^{2 n}}{2 a e n}","\frac{b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}-\frac{b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 e n \sqrt{b^2-a^2}}+\frac{i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d e n \sqrt{b^2-a^2}}-\frac{i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d e n \sqrt{b^2-a^2}}+\frac{(e x)^{2 n}}{2 a e n}",1,"(e*x)^(2*n)/(2*a*e*n) + (I*b*(e*x)^(2*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d*e*n*x^n) - (I*b*(e*x)^(2*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d*e*n*x^n) + (b*(e*x)^(2*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n)) - (b*(e*x)^(2*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n))","A",12,8,24,0.3333,1,"{4208, 4204, 4191, 3321, 2264, 2190, 2279, 2391}"
80,1,485,0,0.9225962,"\int \frac{(e x)^{-1+3 n}}{a+b \sec \left(c+d x^n\right)} \, dx","Int[(e*x)^(-1 + 3*n)/(a + b*Sec[c + d*x^n]),x]","\frac{2 i b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 e n \sqrt{b^2-a^2}}-\frac{2 i b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 e n \sqrt{b^2-a^2}}+\frac{2 b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}-\frac{2 b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 e n \sqrt{b^2-a^2}}+\frac{i b x^{-n} (e x)^{3 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d e n \sqrt{b^2-a^2}}-\frac{i b x^{-n} (e x)^{3 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d e n \sqrt{b^2-a^2}}+\frac{(e x)^{3 n}}{3 a e n}","\frac{2 i b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 e n \sqrt{b^2-a^2}}-\frac{2 i b x^{-3 n} (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^3 e n \sqrt{b^2-a^2}}+\frac{2 b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}-\frac{2 b x^{-2 n} (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d^2 e n \sqrt{b^2-a^2}}+\frac{i b x^{-n} (e x)^{3 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a d e n \sqrt{b^2-a^2}}-\frac{i b x^{-n} (e x)^{3 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a d e n \sqrt{b^2-a^2}}+\frac{(e x)^{3 n}}{3 a e n}",1,"(e*x)^(3*n)/(3*a*e*n) + (I*b*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d*e*n*x^n) - (I*b*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2])])/(a*Sqrt[-a^2 + b^2]*d*e*n*x^n) + (2*b*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n)) - (2*b*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n)) + ((2*I)*b*(e*x)^(3*n)*PolyLog[3, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3*e*n*x^(3*n)) - ((2*I)*b*(e*x)^(3*n)*PolyLog[3, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a*Sqrt[-a^2 + b^2]*d^3*e*n*x^(3*n))","A",14,9,24,0.3750,1,"{4208, 4204, 4191, 3321, 2264, 2190, 2531, 2282, 6589}"
81,1,157,0,0.2866466,"\int \frac{(e x)^{-1+n}}{\left(a+b \sec \left(c+d x^n\right)\right)^2} \, dx","Int[(e*x)^(-1 + n)/(a + b*Sec[c + d*x^n])^2,x]","-\frac{2 b \left(2 a^2-b^2\right) x^{-n} (e x)^n \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a+b}}\right)}{a^2 d e n (a-b)^{3/2} (a+b)^{3/2}}+\frac{b^2 x^{-n} (e x)^n \tan \left(c+d x^n\right)}{a d e n \left(a^2-b^2\right) \left(a+b \sec \left(c+d x^n\right)\right)}+\frac{(e x)^n}{a^2 e n}","-\frac{2 b \left(2 a^2-b^2\right) x^{-n} (e x)^n \tanh ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a+b}}\right)}{a^2 d e n (a-b)^{3/2} (a+b)^{3/2}}+\frac{b^2 x^{-n} (e x)^n \tan \left(c+d x^n\right)}{a d e n \left(a^2-b^2\right) \left(a+b \sec \left(c+d x^n\right)\right)}+\frac{(e x)^n}{a^2 e n}",1,"(e*x)^n/(a^2*e*n) - (2*b*(2*a^2 - b^2)*(e*x)^n*ArcTanh[(Sqrt[a - b]*Tan[(c + d*x^n)/2])/Sqrt[a + b]])/(a^2*(a - b)^(3/2)*(a + b)^(3/2)*d*e*n*x^n) + (b^2*(e*x)^n*Tan[c + d*x^n])/(a*(a^2 - b^2)*d*e*n*x^n*(a + b*Sec[c + d*x^n]))","A",7,7,22,0.3182,1,"{4208, 4204, 3785, 3919, 3831, 2659, 208}"
82,1,757,0,1.2725569,"\int \frac{(e x)^{-1+2 n}}{\left(a+b \sec \left(c+d x^n\right)\right)^2} \, dx","Int[(e*x)^(-1 + 2*n)/(a + b*Sec[c + d*x^n])^2,x]","\frac{2 b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 e n \sqrt{b^2-a^2}}-\frac{b^3 x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 e n \left(b^2-a^2\right)^{3/2}}-\frac{2 b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d^2 e n \sqrt{b^2-a^2}}+\frac{b^3 x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d^2 e n \left(b^2-a^2\right)^{3/2}}+\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(a \cos \left(c+d x^n\right)+b\right)}{a^2 d^2 e n \left(a^2-b^2\right)}+\frac{2 i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d e n \sqrt{b^2-a^2}}-\frac{i b^3 x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d e n \left(b^2-a^2\right)^{3/2}}-\frac{2 i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d e n \sqrt{b^2-a^2}}+\frac{i b^3 x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d e n \left(b^2-a^2\right)^{3/2}}+\frac{b^2 x^{-n} (e x)^{2 n} \sin \left(c+d x^n\right)}{a d e n \left(a^2-b^2\right) \left(a \cos \left(c+d x^n\right)+b\right)}+\frac{(e x)^{2 n}}{2 a^2 e n}","\frac{2 b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 e n \sqrt{b^2-a^2}}-\frac{b^3 x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 e n \left(b^2-a^2\right)^{3/2}}-\frac{2 b x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d^2 e n \sqrt{b^2-a^2}}+\frac{b^3 x^{-2 n} (e x)^{2 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d^2 e n \left(b^2-a^2\right)^{3/2}}+\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(a \cos \left(c+d x^n\right)+b\right)}{a^2 d^2 e n \left(a^2-b^2\right)}+\frac{2 i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d e n \sqrt{b^2-a^2}}-\frac{i b^3 x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d e n \left(b^2-a^2\right)^{3/2}}-\frac{2 i b x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d e n \sqrt{b^2-a^2}}+\frac{i b^3 x^{-n} (e x)^{2 n} \log \left(1+\frac{a e^{i \left(c+d x^n\right)}}{\sqrt{b^2-a^2}+b}\right)}{a^2 d e n \left(b^2-a^2\right)^{3/2}}+\frac{b^2 x^{-n} (e x)^{2 n} \sin \left(c+d x^n\right)}{a d e n \left(a^2-b^2\right) \left(a \cos \left(c+d x^n\right)+b\right)}+\frac{(e x)^{2 n}}{2 a^2 e n}",1,"(e*x)^(2*n)/(2*a^2*e*n) - (I*b^3*(e*x)^(2*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d*e*n*x^n) + ((2*I)*b*(e*x)^(2*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d*e*n*x^n) + (I*b^3*(e*x)^(2*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d*e*n*x^n) - ((2*I)*b*(e*x)^(2*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d*e*n*x^n) + (b^2*(e*x)^(2*n)*Log[b + a*Cos[c + d*x^n]])/(a^2*(a^2 - b^2)*d^2*e*n*x^(2*n)) - (b^3*(e*x)^(2*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n*x^(2*n)) + (2*b*(e*x)^(2*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n)) + (b^3*(e*x)^(2*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n*x^(2*n)) - (2*b*(e*x)^(2*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n)) + (b^2*(e*x)^(2*n)*Sin[c + d*x^n])/(a*(a^2 - b^2)*d*e*n*x^n*(b + a*Cos[c + d*x^n]))","A",23,11,24,0.4583,1,"{4208, 4204, 4191, 3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"
83,1,1384,0,2.3665318,"\int \frac{(e x)^{-1+3 n}}{\left(a+b \sec \left(c+d x^n\right)\right)^2} \, dx","Int[(e*x)^(-1 + 3*n)/(a + b*Sec[c + d*x^n])^2,x]","-\frac{2 i b^2 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b-i \sqrt{a^2-b^2}}\right) x^{-3 n}}{a^2 \left(a^2-b^2\right) d^3 e n}-\frac{2 i b^2 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b+i \sqrt{a^2-b^2}}\right) x^{-3 n}}{a^2 \left(a^2-b^2\right) d^3 e n}+\frac{4 i b (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \sqrt{b^2-a^2} d^3 e n}-\frac{2 i b^3 (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^3 e n}-\frac{4 i b (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \sqrt{b^2-a^2} d^3 e n}+\frac{2 i b^3 (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^3 e n}+\frac{2 b^2 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) x^{-2 n}}{a^2 \left(a^2-b^2\right) d^2 e n}+\frac{2 b^2 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) x^{-2 n}}{a^2 \left(a^2-b^2\right) d^2 e n}+\frac{4 b (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \sqrt{b^2-a^2} d^2 e n}-\frac{2 b^3 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^2 e n}-\frac{4 b (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \sqrt{b^2-a^2} d^2 e n}+\frac{2 b^3 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^2 e n}-\frac{i b^2 (e x)^{3 n} x^{-n}}{a^2 \left(a^2-b^2\right) d e n}+\frac{2 i b (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \sqrt{b^2-a^2} d e n}-\frac{i b^3 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \left(b^2-a^2\right)^{3/2} d e n}-\frac{2 i b (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \sqrt{b^2-a^2} d e n}+\frac{i b^3 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \left(b^2-a^2\right)^{3/2} d e n}+\frac{b^2 (e x)^{3 n} \sin \left(d x^n+c\right) x^{-n}}{a \left(a^2-b^2\right) d e n \left(b+a \cos \left(d x^n+c\right)\right)}+\frac{(e x)^{3 n}}{3 a^2 e n}","-\frac{2 i b^2 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b-i \sqrt{a^2-b^2}}\right) x^{-3 n}}{a^2 \left(a^2-b^2\right) d^3 e n}-\frac{2 i b^2 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b+i \sqrt{a^2-b^2}}\right) x^{-3 n}}{a^2 \left(a^2-b^2\right) d^3 e n}+\frac{4 i b (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \sqrt{b^2-a^2} d^3 e n}-\frac{2 i b^3 (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^3 e n}-\frac{4 i b (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \sqrt{b^2-a^2} d^3 e n}+\frac{2 i b^3 (e x)^{3 n} \text{PolyLog}\left(3,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-3 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^3 e n}+\frac{2 b^2 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b-i \sqrt{a^2-b^2}}+1\right) x^{-2 n}}{a^2 \left(a^2-b^2\right) d^2 e n}+\frac{2 b^2 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b+i \sqrt{a^2-b^2}}+1\right) x^{-2 n}}{a^2 \left(a^2-b^2\right) d^2 e n}+\frac{4 b (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \sqrt{b^2-a^2} d^2 e n}-\frac{2 b^3 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b-\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^2 e n}-\frac{4 b (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \sqrt{b^2-a^2} d^2 e n}+\frac{2 b^3 (e x)^{3 n} \text{PolyLog}\left(2,-\frac{a e^{i \left(d x^n+c\right)}}{b+\sqrt{b^2-a^2}}\right) x^{-2 n}}{a^2 \left(b^2-a^2\right)^{3/2} d^2 e n}-\frac{i b^2 (e x)^{3 n} x^{-n}}{a^2 \left(a^2-b^2\right) d e n}+\frac{2 i b (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \sqrt{b^2-a^2} d e n}-\frac{i b^3 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b-\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \left(b^2-a^2\right)^{3/2} d e n}-\frac{2 i b (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \sqrt{b^2-a^2} d e n}+\frac{i b^3 (e x)^{3 n} \log \left(\frac{e^{i \left(d x^n+c\right)} a}{b+\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \left(b^2-a^2\right)^{3/2} d e n}+\frac{b^2 (e x)^{3 n} \sin \left(d x^n+c\right) x^{-n}}{a \left(a^2-b^2\right) d e n \left(b+a \cos \left(d x^n+c\right)\right)}+\frac{(e x)^{3 n}}{3 a^2 e n}",1,"(e*x)^(3*n)/(3*a^2*e*n) - (I*b^2*(e*x)^(3*n))/(a^2*(a^2 - b^2)*d*e*n*x^n) + (2*b^2*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b - I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2*e*n*x^(2*n)) + (2*b^2*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b + I*Sqrt[a^2 - b^2])])/(a^2*(a^2 - b^2)*d^2*e*n*x^(2*n)) - (I*b^3*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d*e*n*x^n) + ((2*I)*b*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d*e*n*x^n) + (I*b^3*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2])])/(a^2*(-a^2 + b^2)^(3/2)*d*e*n*x^n) - ((2*I)*b*(e*x)^(3*n)*Log[1 + (a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2])])/(a^2*Sqrt[-a^2 + b^2]*d*e*n*x^n) - ((2*I)*b^2*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b - I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3*e*n*x^(3*n)) - ((2*I)*b^2*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b + I*Sqrt[a^2 - b^2]))])/(a^2*(a^2 - b^2)*d^3*e*n*x^(3*n)) - (2*b^3*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n*x^(2*n)) + (4*b*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n)) + (2*b^3*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^2*e*n*x^(2*n)) - (4*b*(e*x)^(3*n)*PolyLog[2, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^2*e*n*x^(2*n)) - ((2*I)*b^3*(e*x)^(3*n)*PolyLog[3, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3*e*n*x^(3*n)) + ((4*I)*b*(e*x)^(3*n)*PolyLog[3, -((a*E^(I*(c + d*x^n)))/(b - Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3*e*n*x^(3*n)) + ((2*I)*b^3*(e*x)^(3*n)*PolyLog[3, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*(-a^2 + b^2)^(3/2)*d^3*e*n*x^(3*n)) - ((4*I)*b*(e*x)^(3*n)*PolyLog[3, -((a*E^(I*(c + d*x^n)))/(b + Sqrt[-a^2 + b^2]))])/(a^2*Sqrt[-a^2 + b^2]*d^3*e*n*x^(3*n)) + (b^2*(e*x)^(3*n)*Sin[c + d*x^n])/(a*(a^2 - b^2)*d*e*n*x^n*(b + a*Cos[c + d*x^n]))","A",32,13,24,0.5417,1,"{4208, 4204, 4191, 3324, 3321, 2264, 2190, 2531, 2282, 6589, 4522, 2279, 2391}"