1,1,73,0,0.1415273,"\int x^3 \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Int[x^3*(a + b*Tan[c + d*x^2]),x]","\frac{a x^4}{4}+\frac{i b \text{Li}_2\left(-e^{2 i \left(d x^2+c\right)}\right)}{4 d^2}-\frac{b x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{2 d}+\frac{1}{4} i b x^4","\frac{a x^4}{4}+\frac{i b \text{Li}_2\left(-e^{2 i \left(d x^2+c\right)}\right)}{4 d^2}-\frac{b x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{2 d}+\frac{1}{4} i b x^4",1,"(a*x^4)/4 + (I/4)*b*x^4 - (b*x^2*Log[1 + E^((2*I)*(c + d*x^2))])/(2*d) + ((I/4)*b*PolyLog[2, -E^((2*I)*(c + d*x^2))])/d^2","A",7,6,16,0.3750,1,"{14, 3747, 3719, 2190, 2279, 2391}"
2,0,0,0,0.0179395,"\int x^2 \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Int[x^2*(a + b*Tan[c + d*x^2]),x]","\int x^2 \left(a+b \tan \left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^2 \tan \left(c+d x^2\right),x\right)+\frac{a x^3}{3}",0,"(a*x^3)/3 + b*Defer[Int][x^2*Tan[c + d*x^2], x]","A",0,0,0,0,-1,"{}"
3,1,26,0,0.0258382,"\int x \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Int[x*(a + b*Tan[c + d*x^2]),x]","\frac{a x^2}{2}-\frac{b \log \left(\cos \left(c+d x^2\right)\right)}{2 d}","\frac{a x^2}{2}-\frac{b \log \left(\cos \left(c+d x^2\right)\right)}{2 d}",1,"(a*x^2)/2 - (b*Log[Cos[c + d*x^2]])/(2*d)","A",4,3,14,0.2143,1,"{14, 3747, 3475}"
4,0,0,0,0.0045918,"\int \left(a+b \tan \left(c+d x^2\right)\right) \, dx","Int[a + b*Tan[c + d*x^2],x]","\int \left(a+b \tan \left(c+d x^2\right)\right) \, dx","b \text{Int}\left(\tan \left(c+d x^2\right),x\right)+a x",0,"a*x + b*Defer[Int][Tan[c + d*x^2], x]","A",0,0,0,0,-1,"{}"
5,0,0,0,0.0185559,"\int \frac{a+b \tan \left(c+d x^2\right)}{x} \, dx","Int[(a + b*Tan[c + d*x^2])/x,x]","\int \frac{a+b \tan \left(c+d x^2\right)}{x} \, dx","b \text{Int}\left(\frac{\tan \left(c+d x^2\right)}{x},x\right)+a \log (x)",0,"a*Log[x] + b*Defer[Int][Tan[c + d*x^2]/x, x]","A",0,0,0,0,-1,"{}"
6,0,0,0,0.0191181,"\int \frac{a+b \tan \left(c+d x^2\right)}{x^2} \, dx","Int[(a + b*Tan[c + d*x^2])/x^2,x]","\int \frac{a+b \tan \left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\tan \left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"-(a/x) + b*Defer[Int][Tan[c + d*x^2]/x^2, x]","A",0,0,0,0,-1,"{}"
7,1,126,0,0.2390838,"\int x^3 \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Int[x^3*(a + b*Tan[c + d*x^2])^2,x]","\frac{a^2 x^4}{4}+\frac{i a b \text{Li}_2\left(-e^{2 i \left(d x^2+c\right)}\right)}{2 d^2}-\frac{a b x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{d}+\frac{1}{2} i a b x^4+\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{b^2 x^4}{4}","\frac{a^2 x^4}{4}+\frac{i a b \text{Li}_2\left(-e^{2 i \left(d x^2+c\right)}\right)}{2 d^2}-\frac{a b x^2 \log \left(1+e^{2 i \left(c+d x^2\right)}\right)}{d}+\frac{1}{2} i a b x^4+\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{b^2 x^4}{4}",1,"(a^2*x^4)/4 + (I/2)*a*b*x^4 - (b^2*x^4)/4 - (a*b*x^2*Log[1 + E^((2*I)*(c + d*x^2))])/d + (b^2*Log[Cos[c + d*x^2]])/(2*d^2) + ((I/2)*a*b*PolyLog[2, -E^((2*I)*(c + d*x^2))])/d^2 + (b^2*x^2*Tan[c + d*x^2])/(2*d)","A",10,9,18,0.5000,1,"{3747, 3722, 3719, 2190, 2279, 2391, 3720, 3475, 30}"
8,0,0,0,0.0233488,"\int x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Int[x^2*(a + b*Tan[c + d*x^2])^2,x]","\int x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2,x\right)",0,"Defer[Int][x^2*(a + b*Tan[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
9,1,51,0,0.0470521,"\int x \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Int[x*(a + b*Tan[c + d*x^2])^2,x]","\frac{1}{2} x^2 \left(a^2-b^2\right)-\frac{a b \log \left(\cos \left(c+d x^2\right)\right)}{d}+\frac{b^2 \tan \left(c+d x^2\right)}{2 d}","\frac{1}{2} x^2 \left(a^2-b^2\right)-\frac{a b \log \left(\cos \left(c+d x^2\right)\right)}{d}+\frac{b^2 \tan \left(c+d x^2\right)}{2 d}",1,"((a^2 - b^2)*x^2)/2 - (a*b*Log[Cos[c + d*x^2]])/d + (b^2*Tan[c + d*x^2])/(2*d)","A",3,3,16,0.1875,1,"{3747, 3477, 3475}"
10,0,0,0,0.0048063,"\int \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","Int[(a + b*Tan[c + d*x^2])^2,x]","\int \left(a+b \tan \left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(\left(a+b \tan \left(c+d x^2\right)\right)^2,x\right)",0,"Defer[Int][(a + b*Tan[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
11,0,0,0,0.021708,"\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x} \, dx","Int[(a + b*Tan[c + d*x^2])^2/x,x]","\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x},x\right)",0,"Defer[Int][(a + b*Tan[c + d*x^2])^2/x, x]","A",0,0,0,0,-1,"{}"
12,0,0,0,0.0218076,"\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x^2} \, dx","Int[(a + b*Tan[c + d*x^2])^2/x^2,x]","\int \frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d x^2\right)\right)^2}{x^2},x\right)",0,"Defer[Int][(a + b*Tan[c + d*x^2])^2/x^2, x]","A",0,0,0,0,-1,"{}"
13,1,122,0,0.2070909,"\int \frac{x^3}{a+b \tan \left(c+d x^2\right)} \, dx","Int[x^3/(a + b*Tan[c + d*x^2]),x]","-\frac{i b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(d x^2+c\right)}}{(a+i b)^2}\right)}{4 d^2 \left(a^2+b^2\right)}+\frac{b x^2 \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d x^2\right)}}{(a+i b)^2}\right)}{2 d \left(a^2+b^2\right)}+\frac{x^4}{4 (a+i b)}","-\frac{i b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(d x^2+c\right)}}{(a+i b)^2}\right)}{4 d^2 \left(a^2+b^2\right)}+\frac{b x^2 \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d x^2\right)}}{(a+i b)^2}\right)}{2 d \left(a^2+b^2\right)}+\frac{x^4}{4 (a+i b)}",1,"x^4/(4*(a + I*b)) + (b*x^2*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*x^2)))/(a + I*b)^2])/(2*(a^2 + b^2)*d) - ((I/4)*b*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*x^2)))/(a + I*b)^2)])/((a^2 + b^2)*d^2)","A",5,5,18,0.2778,1,"{3747, 3732, 2190, 2279, 2391}"
14,0,0,0,0.0252551,"\int \frac{x^2}{a+b \tan \left(c+d x^2\right)} \, dx","Int[x^2/(a + b*Tan[c + d*x^2]),x]","\int \frac{x^2}{a+b \tan \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{a+b \tan \left(c+d x^2\right)},x\right)",0,"Defer[Int][x^2/(a + b*Tan[c + d*x^2]), x]","A",0,0,0,0,-1,"{}"
15,1,57,0,0.0779404,"\int \frac{x}{a+b \tan \left(c+d x^2\right)} \, dx","Int[x/(a + b*Tan[c + d*x^2]),x]","\frac{b \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)}{2 d \left(a^2+b^2\right)}+\frac{a x^2}{2 \left(a^2+b^2\right)}","\frac{b \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)}{2 d \left(a^2+b^2\right)}+\frac{a x^2}{2 \left(a^2+b^2\right)}",1,"(a*x^2)/(2*(a^2 + b^2)) + (b*Log[a*Cos[c + d*x^2] + b*Sin[c + d*x^2]])/(2*(a^2 + b^2)*d)","A",3,3,16,0.1875,1,"{3747, 3484, 3530}"
16,0,0,0,0.0053701,"\int \frac{1}{a+b \tan \left(c+d x^2\right)} \, dx","Int[(a + b*Tan[c + d*x^2])^(-1),x]","\int \frac{1}{a+b \tan \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{1}{a+b \tan \left(c+d x^2\right)},x\right)",0,"Defer[Int][(a + b*Tan[c + d*x^2])^(-1), x]","A",0,0,0,0,-1,"{}"
17,0,0,0,0.0250229,"\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","Int[1/(x*(a + b*Tan[c + d*x^2])),x]","\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*Tan[c + d*x^2])), x]","A",0,0,0,0,-1,"{}"
18,0,0,0,0.0242795,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","Int[1/(x^2*(a + b*Tan[c + d*x^2])),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)},x\right)",0,"Defer[Int][1/(x^2*(a + b*Tan[c + d*x^2])), x]","A",0,0,0,0,-1,"{}"
19,1,202,0,0.313916,"\int \frac{x^3}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Int[x^3/(a + b*Tan[c + d*x^2])^2,x]","-\frac{i a b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(d x^2+c\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)^2}+\frac{b \left(2 a d x^2+b\right) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d x^2\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{b x^2}{2 d \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)}+\frac{\left(2 a d x^2+b\right)^2}{8 a d^2 (a+i b) \left(a^2+b^2\right)}-\frac{x^4}{4 \left(a^2+b^2\right)}","-\frac{i a b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(d x^2+c\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)^2}+\frac{b \left(2 a d x^2+b\right) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d x^2\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{b x^2}{2 d \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)}+\frac{\left(2 a d x^2+b\right)^2}{8 a d^2 (a+i b) \left(a^2+b^2\right)}-\frac{x^4}{4 \left(a^2+b^2\right)}",1,"-x^4/(4*(a^2 + b^2)) + (b + 2*a*d*x^2)^2/(8*a*(a + I*b)*(a^2 + b^2)*d^2) + (b*(b + 2*a*d*x^2)*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*x^2)))/(a + I*b)^2])/(2*(a^2 + b^2)^2*d^2) - ((I/2)*a*b*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*x^2)))/(a + I*b)^2)])/((a^2 + b^2)^2*d^2) - (b*x^2)/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x^2]))","A",6,6,18,0.3333,1,"{3747, 3733, 3732, 2190, 2279, 2391}"
20,0,0,0,0.0253331,"\int \frac{x^2}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Int[x^2/(a + b*Tan[c + d*x^2])^2,x]","\int \frac{x^2}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][x^2/(a + b*Tan[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
21,1,94,0,0.1289347,"\int \frac{x}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Int[x/(a + b*Tan[c + d*x^2])^2,x]","-\frac{b}{2 d \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)}+\frac{a b \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)}{d \left(a^2+b^2\right)^2}+\frac{x^2 \left(a^2-b^2\right)}{2 \left(a^2+b^2\right)^2}","-\frac{b}{2 d \left(a^2+b^2\right) \left(a+b \tan \left(c+d x^2\right)\right)}+\frac{a b \log \left(a \cos \left(c+d x^2\right)+b \sin \left(c+d x^2\right)\right)}{d \left(a^2+b^2\right)^2}+\frac{x^2 \left(a^2-b^2\right)}{2 \left(a^2+b^2\right)^2}",1,"((a^2 - b^2)*x^2)/(2*(a^2 + b^2)^2) + (a*b*Log[a*Cos[c + d*x^2] + b*Sin[c + d*x^2]])/((a^2 + b^2)^2*d) - b/(2*(a^2 + b^2)*d*(a + b*Tan[c + d*x^2]))","A",4,4,16,0.2500,1,"{3747, 3483, 3531, 3530}"
22,0,0,0,0.0051947,"\int \frac{1}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Int[(a + b*Tan[c + d*x^2])^(-2),x]","\int \frac{1}{\left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][(a + b*Tan[c + d*x^2])^(-2), x]","A",0,0,0,0,-1,"{}"
23,0,0,0,0.0235792,"\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Int[1/(x*(a + b*Tan[c + d*x^2])^2),x]","\int \frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*Tan[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
24,0,0,0,0.0255948,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","Int[1/(x^2*(a + b*Tan[c + d*x^2])^2),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d x^2\right)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(a + b*Tan[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
25,1,261,0,0.3717028,"\int x^3 \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Int[x^3*(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{a x^4}{4}+\frac{7 i b x^3 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{21 b x^{5/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{105 i b x^2 \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}+\frac{105 b x^{3/2} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{315 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}-\frac{315 b \sqrt{x} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^7}-\frac{315 i b \text{Li}_8\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{4 d^8}-\frac{2 b x^{7/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{4} i b x^4","\frac{a x^4}{4}+\frac{7 i b x^3 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{21 b x^{5/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{105 i b x^2 \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}+\frac{105 b x^{3/2} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{315 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}-\frac{315 b \sqrt{x} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^7}-\frac{315 i b \text{Li}_8\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{4 d^8}-\frac{2 b x^{7/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{4} i b x^4",1,"(a*x^4)/4 + (I/4)*b*x^4 - (2*b*x^(7/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + ((7*I)*b*x^3*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (21*b*x^(5/2)*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (((105*I)/2)*b*x^2*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 + (105*b*x^(3/2)*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + (((315*I)/2)*b*x*PolyLog[6, -E^((2*I)*(c + d*Sqrt[x]))])/d^6 - (315*b*Sqrt[x]*PolyLog[7, -E^((2*I)*(c + d*Sqrt[x]))])/(2*d^7) - (((315*I)/4)*b*PolyLog[8, -E^((2*I)*(c + d*Sqrt[x]))])/d^8","A",13,8,18,0.4444,1,"{14, 3747, 3719, 2190, 2531, 6609, 2282, 6589}"
26,1,195,0,0.2754035,"\int x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Int[x^2*(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{a x^3}{3}+\frac{5 i b x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{10 b x^{3/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{15 i b x \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{15 b \sqrt{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{15 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}-\frac{2 b x^{5/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{3} i b x^3","\frac{a x^3}{3}+\frac{5 i b x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{10 b x^{3/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{15 i b x \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{15 b \sqrt{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{15 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^6}-\frac{2 b x^{5/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{3} i b x^3",1,"(a*x^3)/3 + (I/3)*b*x^3 - (2*b*x^(5/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + ((5*I)*b*x^2*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (10*b*x^(3/2)*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - ((15*I)*b*x*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 + (15*b*Sqrt[x]*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + (((15*I)/2)*b*PolyLog[6, -E^((2*I)*(c + d*Sqrt[x]))])/d^6","A",11,8,18,0.4444,1,"{14, 3747, 3719, 2190, 2531, 6609, 2282, 6589}"
27,1,135,0,0.2036538,"\int x \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Int[x*(a + b*Tan[c + d*Sqrt[x]]),x]","\frac{a x^2}{2}+\frac{3 i b x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{3 b \sqrt{x} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{3 i b \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}-\frac{2 b x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{2} i b x^2","\frac{a x^2}{2}+\frac{3 i b x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{3 b \sqrt{x} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{3 i b \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{2 d^4}-\frac{2 b x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{1}{2} i b x^2",1,"(a*x^2)/2 + (I/2)*b*x^2 - (2*b*x^(3/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + ((3*I)*b*x*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (3*b*Sqrt[x]*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - (((3*I)/2)*b*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4","A",9,8,16,0.5000,1,"{14, 3747, 3719, 2190, 2531, 6609, 2282, 6589}"
28,1,66,0,0.1028248,"\int \left(a+b \tan \left(c+d \sqrt{x}\right)\right) \, dx","Int[a + b*Tan[c + d*Sqrt[x]],x]","a x+\frac{i b \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+i b x","a x+\frac{i b \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+i b x",1,"a*x + I*b*x - (2*b*Sqrt[x]*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + (I*b*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2","A",6,5,14,0.3571,1,"{3739, 3719, 2190, 2279, 2391}"
29,0,0,0,0.0185292,"\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x} \, dx","Int[(a + b*Tan[c + d*Sqrt[x]])/x,x]","\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt{x}\right)}{x},x\right)+a \log (x)",0,"a*Log[x] + b*Defer[Int][Tan[c + d*Sqrt[x]]/x, x]","A",0,0,0,0,-1,"{}"
30,0,0,0,0.0191606,"\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x^2} \, dx","Int[(a + b*Tan[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \tan \left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"-(a/x) + b*Defer[Int][Tan[c + d*Sqrt[x]]/x^2, x]","A",0,0,0,0,-1,"{}"
31,1,402,0,0.6101958,"\int x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[x^2*(a + b*Tan[c + d*Sqrt[x]])^2,x]","\frac{a^2 x^3}{3}+\frac{10 i a b x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{20 a b x^{3/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{30 i a b x \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{30 a b \sqrt{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{15 i a b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{4 a b x^{5/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{2}{3} i a b x^3-\frac{20 i b^2 x^{3/2} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{30 b^2 x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{30 i b^2 \sqrt{x} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{15 b^2 \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\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{b^2 x^3}{3}","\frac{a^2 x^3}{3}+\frac{10 i a b x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{20 a b x^{3/2} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{30 i a b x \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{30 a b \sqrt{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}+\frac{15 i a b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}-\frac{4 a b x^{5/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+\frac{2}{3} i a b x^3-\frac{20 i b^2 x^{3/2} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{30 b^2 x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{30 i b^2 \sqrt{x} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{15 b^2 \text{Li}_5\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^6}+\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{b^2 x^3}{3}",1,"((-2*I)*b^2*x^(5/2))/d + (a^2*x^3)/3 + ((2*I)/3)*a*b*x^3 - (b^2*x^3)/3 + (10*b^2*x^2*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (4*a*b*x^(5/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d - ((20*I)*b^2*x^(3/2)*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 + ((10*I)*a*b*x^2*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 + (30*b^2*x*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 - (20*a*b*x^(3/2)*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 + ((30*I)*b^2*Sqrt[x]*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 - ((30*I)*a*b*x*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 - (15*b^2*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^6 + (30*a*b*Sqrt[x]*PolyLog[5, -E^((2*I)*(c + d*Sqrt[x]))])/d^5 + ((15*I)*a*b*PolyLog[6, -E^((2*I)*(c + d*Sqrt[x]))])/d^6 + (2*b^2*x^(5/2)*Tan[c + d*Sqrt[x]])/d","A",20,10,20,0.5000,1,"{3747, 3722, 3719, 2190, 2531, 6609, 2282, 6589, 3720, 30}"
32,1,274,0,0.46905,"\int x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[x*(a + b*Tan[c + d*Sqrt[x]])^2,x]","\frac{a^2 x^2}{2}+\frac{6 i a b x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{6 a b \sqrt{x} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{3 i a b \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{4 a b x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+i a b x^2-\frac{6 i b^2 \sqrt{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{3 b^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\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{1}{2} b^2 x^2","\frac{a^2 x^2}{2}+\frac{6 i a b x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{6 a b \sqrt{x} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}-\frac{3 i a b \text{Li}_4\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}-\frac{4 a b x^{3/2} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+i a b x^2-\frac{6 i b^2 \sqrt{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{3 b^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^4}+\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{1}{2} b^2 x^2",1,"((-2*I)*b^2*x^(3/2))/d + (a^2*x^2)/2 + I*a*b*x^2 - (b^2*x^2)/2 + (6*b^2*x*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d^2 - (4*a*b*x^(3/2)*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d - ((6*I)*b^2*Sqrt[x]*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 + ((6*I)*a*b*x*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 + (3*b^2*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 - (6*a*b*Sqrt[x]*PolyLog[3, -E^((2*I)*(c + d*Sqrt[x]))])/d^3 - ((3*I)*a*b*PolyLog[4, -E^((2*I)*(c + d*Sqrt[x]))])/d^4 + (2*b^2*x^(3/2)*Tan[c + d*Sqrt[x]])/d","A",16,10,18,0.5556,1,"{3747, 3722, 3719, 2190, 2531, 6609, 2282, 6589, 3720, 30}"
33,1,119,0,0.1768019,"\int \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2 \, dx","Int[(a + b*Tan[c + d*Sqrt[x]])^2,x]","a^2 x+\frac{2 i a b \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 a b \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+2 i a b x+\frac{2 b^2 \log \left(\cos \left(c+d \sqrt{x}\right)\right)}{d^2}+\frac{2 b^2 \sqrt{x} \tan \left(c+d \sqrt{x}\right)}{d}-b^2 x","a^2 x+\frac{2 i a b \text{Li}_2\left(-e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{4 a b \sqrt{x} \log \left(1+e^{2 i \left(c+d \sqrt{x}\right)}\right)}{d}+2 i a b x+\frac{2 b^2 \log \left(\cos \left(c+d \sqrt{x}\right)\right)}{d^2}+\frac{2 b^2 \sqrt{x} \tan \left(c+d \sqrt{x}\right)}{d}-b^2 x",1,"a^2*x + (2*I)*a*b*x - b^2*x - (4*a*b*Sqrt[x]*Log[1 + E^((2*I)*(c + d*Sqrt[x]))])/d + (2*b^2*Log[Cos[c + d*Sqrt[x]]])/d^2 + ((2*I)*a*b*PolyLog[2, -E^((2*I)*(c + d*Sqrt[x]))])/d^2 + (2*b^2*Sqrt[x]*Tan[c + d*Sqrt[x]])/d","A",10,9,16,0.5625,1,"{3739, 3722, 3719, 2190, 2279, 2391, 3720, 3475, 30}"
34,0,0,0,0.0220278,"\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","Int[(a + b*Tan[c + d*Sqrt[x]])^2/x,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x},x\right)",0,"Defer[Int][(a + b*Tan[c + d*Sqrt[x]])^2/x, x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0227265,"\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","Int[(a + b*Tan[c + d*Sqrt[x]])^2/x^2,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2}{x^2},x\right)",0,"Defer[Int][(a + b*Tan[c + d*Sqrt[x]])^2/x^2, x]","A",0,0,0,0,-1,"{}"
36,1,460,0,0.573642,"\int \frac{x^3}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Int[x^3/(a + b*Tan[c + d*Sqrt[x]]),x]","-\frac{7 i b x^3 \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{21 b x^{5/2} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{105 i b x^2 \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}-\frac{105 b x^{3/2} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}-\frac{315 i b x \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^6 \left(a^2+b^2\right)}+\frac{315 b \sqrt{x} \text{Li}_7\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^7 \left(a^2+b^2\right)}+\frac{315 i b \text{Li}_8\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{4 d^8 \left(a^2+b^2\right)}+\frac{2 b x^{7/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^4}{4 (a+i b)}","-\frac{7 i b x^3 \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{21 b x^{5/2} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{105 i b x^2 \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}-\frac{105 b x^{3/2} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}-\frac{315 i b x \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^6 \left(a^2+b^2\right)}+\frac{315 b \sqrt{x} \text{Li}_7\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^7 \left(a^2+b^2\right)}+\frac{315 i b \text{Li}_8\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{4 d^8 \left(a^2+b^2\right)}+\frac{2 b x^{7/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^4}{4 (a+i b)}",1,"x^4/(4*(a + I*b)) + (2*b*x^(7/2)*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2])/((a^2 + b^2)*d) - ((7*I)*b*x^3*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^2) + (21*b*x^(5/2)*PolyLog[3, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^3) + (((105*I)/2)*b*x^2*PolyLog[4, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^4) - (105*b*x^(3/2)*PolyLog[5, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^5) - (((315*I)/2)*b*x*PolyLog[6, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^6) + (315*b*Sqrt[x]*PolyLog[7, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/(2*(a^2 + b^2)*d^7) + (((315*I)/4)*b*PolyLog[8, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^8)","A",11,7,20,0.3500,1,"{3747, 3732, 2190, 2531, 6609, 2282, 6589}"
37,1,344,0,0.453081,"\int \frac{x^2}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Int[x^2/(a + b*Tan[c + d*Sqrt[x]]),x]","-\frac{5 i b x^2 \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{10 b x^{3/2} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{15 i b x \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^4 \left(a^2+b^2\right)}-\frac{15 b \sqrt{x} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}-\frac{15 i b \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^6 \left(a^2+b^2\right)}+\frac{2 b x^{5/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^3}{3 (a+i b)}","-\frac{5 i b x^2 \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{10 b x^{3/2} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{15 i b x \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^4 \left(a^2+b^2\right)}-\frac{15 b \sqrt{x} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}-\frac{15 i b \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^6 \left(a^2+b^2\right)}+\frac{2 b x^{5/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^3}{3 (a+i b)}",1,"x^3/(3*(a + I*b)) + (2*b*x^(5/2)*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2])/((a^2 + b^2)*d) - ((5*I)*b*x^2*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^2) + (10*b*x^(3/2)*PolyLog[3, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^3) + ((15*I)*b*x*PolyLog[4, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^4) - (15*b*Sqrt[x]*PolyLog[5, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^5) - (((15*I)/2)*b*PolyLog[6, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^6)","A",9,7,20,0.3500,1,"{3747, 3732, 2190, 2531, 6609, 2282, 6589}"
38,1,234,0,0.3369349,"\int \frac{x}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Int[x/(a + b*Tan[c + d*Sqrt[x]]),x]","-\frac{3 i b x \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b \sqrt{x} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{3 i b \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{2 b x^{3/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^2}{2 (a+i b)}","-\frac{3 i b x \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b \sqrt{x} \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{3 i b \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{2 b x^{3/2} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^2}{2 (a+i b)}",1,"x^2/(2*(a + I*b)) + (2*b*x^(3/2)*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2])/((a^2 + b^2)*d) - ((3*I)*b*x*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^2) + (3*b*Sqrt[x]*PolyLog[3, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^3) + (((3*I)/2)*b*PolyLog[4, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^4)","A",7,7,18,0.3889,1,"{3747, 3732, 2190, 2531, 6609, 2282, 6589}"
39,1,119,0,0.1747294,"\int \frac{1}{a+b \tan \left(c+d \sqrt{x}\right)} \, dx","Int[(a + b*Tan[c + d*Sqrt[x]])^(-1),x]","-\frac{i b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b \sqrt{x} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x}{a+i b}","-\frac{i b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b \sqrt{x} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x}{a+i b}",1,"x/(a + I*b) + (2*b*Sqrt[x]*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2])/((a^2 + b^2)*d) - (I*b*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)*d^2)","A",5,5,16,0.3125,1,"{3739, 3732, 2190, 2279, 2391}"
40,0,0,0,0.0253754,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","Int[1/(x*(a + b*Tan[c + d*Sqrt[x]])),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*Tan[c + d*Sqrt[x]])), x]","A",0,0,0,0,-1,"{}"
41,0,0,0,0.0253517,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","Int[1/(x^2*(a + b*Tan[c + d*Sqrt[x]])),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)},x\right)",0,"Defer[Int][1/(x^2*(a + b*Tan[c + d*Sqrt[x]])), x]","A",0,0,0,0,-1,"{}"
42,1,1147,0,2.2492132,"\int \frac{x^2}{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[x^2/(a + b*Tan[c + d*Sqrt[x]])^2,x]","\frac{4 b x^3}{3 (i a-b) (a-i b)^2}+\frac{x^3}{3 (a-i b)^2}-\frac{4 b^2 x^3}{3 \left(a^2+b^2\right)^2}+\frac{4 b \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^{5/2}}{(a-i b)^2 (a+i b) d}-\frac{4 i b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^{5/2}}{\left(a^2+b^2\right)^2 d}-\frac{4 i b^2 x^{5/2}}{\left(a^2+b^2\right)^2 d}+\frac{4 b^2 x^{5/2}}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt{x}\right)}-b\right)}+\frac{10 b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^2}{\left(a^2+b^2\right)^2 d^2}+\frac{10 b \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^2}{(i a-b) (a-i b)^2 d^2}-\frac{10 b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^2}-\frac{20 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{\left(a^2+b^2\right)^2 d^3}+\frac{20 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{(a-i b)^2 (a+i b) d^3}-\frac{20 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{\left(a^2+b^2\right)^2 d^3}+\frac{30 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^4}-\frac{30 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{(i a-b) (a-i b)^2 d^4}+\frac{30 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^4}+\frac{30 i b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{\left(a^2+b^2\right)^2 d^5}-\frac{30 b \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{(a-i b)^2 (a+i b) d^5}+\frac{30 i b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{\left(a^2+b^2\right)^2 d^5}-\frac{15 b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^6}+\frac{15 b \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{(i a-b) (a-i b)^2 d^6}-\frac{15 b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^6}","\frac{4 b x^3}{3 (i a-b) (a-i b)^2}+\frac{x^3}{3 (a-i b)^2}-\frac{4 b^2 x^3}{3 \left(a^2+b^2\right)^2}+\frac{4 b \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^{5/2}}{(a-i b)^2 (a+i b) d}-\frac{4 i b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^{5/2}}{\left(a^2+b^2\right)^2 d}-\frac{4 i b^2 x^{5/2}}{\left(a^2+b^2\right)^2 d}+\frac{4 b^2 x^{5/2}}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt{x}\right)}-b\right)}+\frac{10 b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt{x}\right)} (a-i b)}{a+i b}+1\right) x^2}{\left(a^2+b^2\right)^2 d^2}+\frac{10 b \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^2}{(i a-b) (a-i b)^2 d^2}-\frac{10 b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^2}-\frac{20 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{\left(a^2+b^2\right)^2 d^3}+\frac{20 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{(a-i b)^2 (a+i b) d^3}-\frac{20 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x^{3/2}}{\left(a^2+b^2\right)^2 d^3}+\frac{30 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^4}-\frac{30 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{(i a-b) (a-i b)^2 d^4}+\frac{30 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^4}+\frac{30 i b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{\left(a^2+b^2\right)^2 d^5}-\frac{30 b \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{(a-i b)^2 (a+i b) d^5}+\frac{30 i b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right) \sqrt{x}}{\left(a^2+b^2\right)^2 d^5}-\frac{15 b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^6}+\frac{15 b \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{(i a-b) (a-i b)^2 d^6}-\frac{15 b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^6}",1,"((-4*I)*b^2*x^(5/2))/((a^2 + b^2)^2*d) + (4*b^2*x^(5/2))/((a + I*b)*(I*a + b)^2*d*(I*a - b + (I*a + b)*E^((2*I)*(c + d*Sqrt[x])))) + x^3/(3*(a - I*b)^2) + (4*b*x^3)/(3*(I*a - b)*(a - I*b)^2) - (4*b^2*x^3)/(3*(a^2 + b^2)^2) + (10*b^2*x^2*Log[1 + ((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)])/((a^2 + b^2)^2*d^2) + (4*b*x^(5/2)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)])/((a - I*b)^2*(a + I*b)*d) - ((4*I)*b^2*x^(5/2)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)])/((a^2 + b^2)^2*d) - ((20*I)*b^2*x^(3/2)*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^3) + (10*b*x^2*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^2) - (10*b^2*x^2*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^2) + (30*b^2*x*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^4) + (20*b*x^(3/2)*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^3) - ((20*I)*b^2*x^(3/2)*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^3) + ((30*I)*b^2*Sqrt[x]*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^5) - (30*b*x*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^4) + (30*b^2*x*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^4) - (15*b^2*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^6) - (30*b*Sqrt[x]*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^5) + ((30*I)*b^2*Sqrt[x]*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^5) + (15*b*PolyLog[6, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^6) - (15*b^2*PolyLog[6, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^6)","A",28,10,20,0.5000,1,"{3747, 3734, 2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
43,1,787,0,1.7108599,"\int \frac{x}{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[x/(a + b*Tan[c + d*Sqrt[x]])^2,x]","-\frac{6 b^2 x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{6 i b^2 \sqrt{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{6 i b^2 \sqrt{x} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}+\frac{3 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 \left(a^2+b^2\right)^2}+\frac{3 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 \left(a^2+b^2\right)^2}+\frac{6 b^2 x \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{4 i b^2 x^{3/2} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d \left(a^2+b^2\right)^2}-\frac{4 i b^2 x^{3/2}}{d \left(a^2+b^2\right)^2}-\frac{2 b^2 x^2}{\left(a^2+b^2\right)^2}+\frac{4 b^2 x^{3/2}}{d (a+i b) (b+i a)^2 \left((b+i a) e^{2 i \left(c+d \sqrt{x}\right)}+i a-b\right)}+\frac{6 b x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 (-b+i a) (a-i b)^2}+\frac{6 b \sqrt{x} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 (a-i b)^2 (a+i b)}-\frac{3 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 (-b+i a) (a-i b)^2}+\frac{4 b x^{3/2} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d (a-i b)^2 (a+i b)}+\frac{2 b x^2}{(-b+i a) (a-i b)^2}+\frac{x^2}{2 (a-i b)^2}","-\frac{6 b^2 x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{6 i b^2 \sqrt{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{6 i b^2 \sqrt{x} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}+\frac{3 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 \left(a^2+b^2\right)^2}+\frac{3 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 \left(a^2+b^2\right)^2}+\frac{6 b^2 x \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{4 i b^2 x^{3/2} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d \left(a^2+b^2\right)^2}-\frac{4 i b^2 x^{3/2}}{d \left(a^2+b^2\right)^2}-\frac{2 b^2 x^2}{\left(a^2+b^2\right)^2}+\frac{4 b^2 x^{3/2}}{d (a+i b) (b+i a)^2 \left((b+i a) e^{2 i \left(c+d \sqrt{x}\right)}+i a-b\right)}+\frac{6 b x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^2 (-b+i a) (a-i b)^2}+\frac{6 b \sqrt{x} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^3 (a-i b)^2 (a+i b)}-\frac{3 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d^4 (-b+i a) (a-i b)^2}+\frac{4 b x^{3/2} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt{x}\right)}}{a+i b}\right)}{d (a-i b)^2 (a+i b)}+\frac{2 b x^2}{(-b+i a) (a-i b)^2}+\frac{x^2}{2 (a-i b)^2}",1,"((-4*I)*b^2*x^(3/2))/((a^2 + b^2)^2*d) + (4*b^2*x^(3/2))/((a + I*b)*(I*a + b)^2*d*(I*a - b + (I*a + b)*E^((2*I)*(c + d*Sqrt[x])))) + x^2/(2*(a - I*b)^2) + (2*b*x^2)/((I*a - b)*(a - I*b)^2) - (2*b^2*x^2)/(a^2 + b^2)^2 + (6*b^2*x*Log[1 + ((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)])/((a^2 + b^2)^2*d^2) + (4*b*x^(3/2)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)])/((a - I*b)^2*(a + I*b)*d) - ((4*I)*b^2*x^(3/2)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)])/((a^2 + b^2)^2*d) - ((6*I)*b^2*Sqrt[x]*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^3) + (6*b*x*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^2) - (6*b^2*x*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^2) + (3*b^2*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^4) + (6*b*Sqrt[x]*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^3) - ((6*I)*b^2*Sqrt[x]*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^3) - (3*b*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^4) + (3*b^2*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b))])/((a^2 + b^2)^2*d^4)","A",22,10,18,0.5556,1,"{3747, 3734, 2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
44,1,204,0,0.2553952,"\int \frac{1}{\left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[(a + b*Tan[c + d*Sqrt[x]])^(-2),x]","-\frac{2 i a b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{2 b \left(2 a d \sqrt{x}+b\right) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{2 b \sqrt{x}}{d \left(a^2+b^2\right) \left(a+b \tan \left(c+d \sqrt{x}\right)\right)}+\frac{\left(2 a d \sqrt{x}+b\right)^2}{2 a d^2 (a+i b) \left(a^2+b^2\right)}-\frac{x}{a^2+b^2}","-\frac{2 i a b \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{2 b \left(2 a d \sqrt{x}+b\right) \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{2 b \sqrt{x}}{d \left(a^2+b^2\right) \left(a+b \tan \left(c+d \sqrt{x}\right)\right)}+\frac{\left(2 a d \sqrt{x}+b\right)^2}{2 a d^2 (a+i b) \left(a^2+b^2\right)}-\frac{x}{a^2+b^2}",1,"(b + 2*a*d*Sqrt[x])^2/(2*a*(a + I*b)*(a^2 + b^2)*d^2) - x/(a^2 + b^2) + (2*b*(b + 2*a*d*Sqrt[x])*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2])/((a^2 + b^2)^2*d^2) - ((2*I)*a*b*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*Sqrt[x])))/(a + I*b)^2)])/((a^2 + b^2)^2*d^2) - (2*b*Sqrt[x])/((a^2 + b^2)*d*(a + b*Tan[c + d*Sqrt[x]]))","A",6,6,16,0.3750,1,"{3739, 3733, 3732, 2190, 2279, 2391}"
45,0,0,0,0.0261057,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[1/(x*(a + b*Tan[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*Tan[c + d*Sqrt[x]])^2), x]","A",0,0,0,0,-1,"{}"
46,0,0,0,0.0260402,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","Int[1/(x^2*(a + b*Tan[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(a + b*Tan[c + d*Sqrt[x]])^2), x]","A",0,0,0,0,-1,"{}"
47,1,287,0,0.4017091,"\int x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right) \, dx","Int[x^2*(a + b*Tan[c + d*x^(1/3)]),x]","\frac{a x^3}{3}+\frac{12 i b x^{7/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{42 b x^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}-\frac{126 i b x^{5/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}+\frac{315 b x^{4/3} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{945 b x^{2/3} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}+\frac{630 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}-\frac{945 i b \sqrt[3]{x} \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}+\frac{945 b \text{Li}_9\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^9}-\frac{3 b x^{8/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{3} i b x^3","\frac{a x^3}{3}+\frac{12 i b x^{7/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{42 b x^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}-\frac{126 i b x^{5/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}+\frac{315 b x^{4/3} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{945 b x^{2/3} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}+\frac{630 i b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}-\frac{945 i b \sqrt[3]{x} \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}+\frac{945 b \text{Li}_9\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^9}-\frac{3 b x^{8/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{3} i b x^3",1,"(a*x^3)/3 + (I/3)*b*x^3 - (3*b*x^(8/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d + ((12*I)*b*x^(7/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 - (42*b*x^2*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^3 - ((126*I)*b*x^(5/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^4 + (315*b*x^(4/3)*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/d^5 + ((630*I)*b*x*PolyLog[6, -E^((2*I)*(c + d*x^(1/3)))])/d^6 - (945*b*x^(2/3)*PolyLog[7, -E^((2*I)*(c + d*x^(1/3)))])/d^7 - ((945*I)*b*x^(1/3)*PolyLog[8, -E^((2*I)*(c + d*x^(1/3)))])/d^8 + (945*b*PolyLog[9, -E^((2*I)*(c + d*x^(1/3)))])/(2*d^9)","A",14,8,18,0.4444,1,"{14, 3747, 3719, 2190, 2531, 6609, 2282, 6589}"
48,1,203,0,0.2714227,"\int x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right) \, dx","Int[x*(a + b*Tan[c + d*x^(1/3)]),x]","\frac{a x^2}{2}+\frac{15 i b x^{4/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^2}-\frac{45 i b x^{2/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^4}-\frac{15 b x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{45 b \sqrt[3]{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^5}+\frac{45 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{4 d^6}-\frac{3 b x^{5/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{2} i b x^2","\frac{a x^2}{2}+\frac{15 i b x^{4/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^2}-\frac{45 i b x^{2/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^4}-\frac{15 b x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{45 b \sqrt[3]{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^5}+\frac{45 i b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{4 d^6}-\frac{3 b x^{5/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{1}{2} i b x^2",1,"(a*x^2)/2 + (I/2)*b*x^2 - (3*b*x^(5/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d + (((15*I)/2)*b*x^(4/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 - (15*b*x*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^3 - (((45*I)/2)*b*x^(2/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^4 + (45*b*x^(1/3)*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/(2*d^5) + (((45*I)/4)*b*PolyLog[6, -E^((2*I)*(c + d*x^(1/3)))])/d^6","A",11,8,16,0.5000,1,"{14, 3747, 3719, 2190, 2531, 6609, 2282, 6589}"
49,1,98,0,0.1638285,"\int \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right) \, dx","Int[a + b*Tan[c + d*x^(1/3)],x]","a x+\frac{3 i b \sqrt[3]{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 b \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^3}-\frac{3 b x^{2/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+i b x","a x+\frac{3 i b \sqrt[3]{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 b \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^3}-\frac{3 b x^{2/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+i b x",1,"a*x + I*b*x - (3*b*x^(2/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d + ((3*I)*b*x^(1/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 - (3*b*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/(2*d^3)","A",7,6,14,0.4286,1,"{3739, 3719, 2190, 2531, 2282, 6589}"
50,0,0,0,0.0174165,"\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x} \, dx","Int[(a + b*Tan[c + d*x^(1/3)])/x,x]","\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt[3]{x}\right)}{x},x\right)+a \log (x)",0,"a*Log[x] + b*Defer[Int][Tan[c + d*x^(1/3)]/x, x]","A",0,0,0,0,-1,"{}"
51,0,0,0,0.0195135,"\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x^2} \, dx","Int[(a + b*Tan[c + d*x^(1/3)])/x^2,x]","\int \frac{a+b \tan \left(c+d \sqrt[3]{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\tan \left(c+d \sqrt[3]{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"-(a/x) + b*Defer[Int][Tan[c + d*x^(1/3)]/x^2, x]","A",0,0,0,0,-1,"{}"
52,1,597,0,0.8333842,"\int x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2 \, dx","Int[x^2*(a + b*Tan[c + d*x^(1/3)])^2,x]","\frac{a^2 x^3}{3}+\frac{24 i a b x^{7/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{84 a b x^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}-\frac{252 i a b x^{5/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}+\frac{630 a b x^{4/3} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{1890 a b x^{2/3} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}+\frac{1260 i a b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}-\frac{1890 i a b \sqrt[3]{x} \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}+\frac{945 a b \text{Li}_9\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^9}-\frac{6 a b x^{8/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{2}{3} i a b x^3-\frac{84 i b^2 x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{252 b^2 x^{5/3} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}+\frac{630 i b^2 x^{4/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{1890 i b^2 x^{2/3} \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}-\frac{1260 b^2 x \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}+\frac{1890 b^2 \sqrt[3]{x} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}+\frac{945 i b^2 \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^9}+\frac{24 b^2 x^{7/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{8/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{8/3}}{d}-\frac{b^2 x^3}{3}","\frac{a^2 x^3}{3}+\frac{24 i a b x^{7/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{84 a b x^2 \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}-\frac{252 i a b x^{5/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}+\frac{630 a b x^{4/3} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{1890 a b x^{2/3} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}+\frac{1260 i a b x \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}-\frac{1890 i a b \sqrt[3]{x} \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}+\frac{945 a b \text{Li}_9\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^9}-\frac{6 a b x^{8/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+\frac{2}{3} i a b x^3-\frac{84 i b^2 x^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{252 b^2 x^{5/3} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}+\frac{630 i b^2 x^{4/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{1890 i b^2 x^{2/3} \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^7}-\frac{1260 b^2 x \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^6}+\frac{1890 b^2 \sqrt[3]{x} \text{Li}_7\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^8}+\frac{945 i b^2 \text{Li}_8\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^9}+\frac{24 b^2 x^{7/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{8/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{8/3}}{d}-\frac{b^2 x^3}{3}",1,"((-3*I)*b^2*x^(8/3))/d + (a^2*x^3)/3 + ((2*I)/3)*a*b*x^3 - (b^2*x^3)/3 + (24*b^2*x^(7/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d^2 - (6*a*b*x^(8/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d - ((84*I)*b^2*x^2*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^3 + ((24*I)*a*b*x^(7/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 + (252*b^2*x^(5/3)*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^4 - (84*a*b*x^2*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^3 + ((630*I)*b^2*x^(4/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^5 - ((252*I)*a*b*x^(5/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^4 - (1260*b^2*x*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/d^6 + (630*a*b*x^(4/3)*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/d^5 - ((1890*I)*b^2*x^(2/3)*PolyLog[6, -E^((2*I)*(c + d*x^(1/3)))])/d^7 + ((1260*I)*a*b*x*PolyLog[6, -E^((2*I)*(c + d*x^(1/3)))])/d^6 + (1890*b^2*x^(1/3)*PolyLog[7, -E^((2*I)*(c + d*x^(1/3)))])/d^8 - (1890*a*b*x^(2/3)*PolyLog[7, -E^((2*I)*(c + d*x^(1/3)))])/d^7 + ((945*I)*b^2*PolyLog[8, -E^((2*I)*(c + d*x^(1/3)))])/d^9 - ((1890*I)*a*b*x^(1/3)*PolyLog[8, -E^((2*I)*(c + d*x^(1/3)))])/d^8 + (945*a*b*PolyLog[9, -E^((2*I)*(c + d*x^(1/3)))])/d^9 + (3*b^2*x^(8/3)*Tan[c + d*x^(1/3)])/d","A",26,10,20,0.5000,1,"{3747, 3722, 3719, 2190, 2531, 6609, 2282, 6589, 3720, 30}"
53,1,408,0,0.5745652,"\int x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2 \, dx","Int[x*(a + b*Tan[c + d*x^(1/3)])^2,x]","\frac{a^2 x^2}{2}+\frac{15 i a b x^{4/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{45 i a b x^{2/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{30 a b x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{45 a b \sqrt[3]{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}+\frac{45 i a b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^6}-\frac{6 a b x^{5/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+i a b x^2+\frac{45 b^2 x^{2/3} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{30 i b^2 x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{45 i b^2 \sqrt[3]{x} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{45 b^2 \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^6}+\frac{15 b^2 x^{4/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{5/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{5/3}}{d}-\frac{1}{2} b^2 x^2","\frac{a^2 x^2}{2}+\frac{15 i a b x^{4/3} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{45 i a b x^{2/3} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{30 a b x \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{45 a b \sqrt[3]{x} \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}+\frac{45 i a b \text{Li}_6\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^6}-\frac{6 a b x^{5/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+i a b x^2+\frac{45 b^2 x^{2/3} \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^4}-\frac{30 i b^2 x \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{45 i b^2 \sqrt[3]{x} \text{Li}_4\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^5}-\frac{45 b^2 \text{Li}_5\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{2 d^6}+\frac{15 b^2 x^{4/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{5/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{5/3}}{d}-\frac{1}{2} b^2 x^2",1,"((-3*I)*b^2*x^(5/3))/d + (a^2*x^2)/2 + I*a*b*x^2 - (b^2*x^2)/2 + (15*b^2*x^(4/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d^2 - (6*a*b*x^(5/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d - ((30*I)*b^2*x*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^3 + ((15*I)*a*b*x^(4/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 + (45*b^2*x^(2/3)*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^4 - (30*a*b*x*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^3 + ((45*I)*b^2*x^(1/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^5 - ((45*I)*a*b*x^(2/3)*PolyLog[4, -E^((2*I)*(c + d*x^(1/3)))])/d^4 - (45*b^2*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/(2*d^6) + (45*a*b*x^(1/3)*PolyLog[5, -E^((2*I)*(c + d*x^(1/3)))])/d^5 + (((45*I)/2)*a*b*PolyLog[6, -E^((2*I)*(c + d*x^(1/3)))])/d^6 + (3*b^2*x^(5/3)*Tan[c + d*x^(1/3)])/d","A",20,10,18,0.5556,1,"{3747, 3722, 3719, 2190, 2531, 6609, 2282, 6589, 3720, 30}"
54,1,206,0,0.3548063,"\int \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2 \, dx","Int[(a + b*Tan[c + d*x^(1/3)])^2,x]","a^2 x+\frac{6 i a b \sqrt[3]{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 a b \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}-\frac{6 a b x^{2/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+2 i a b x-\frac{3 i b^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{6 b^2 \sqrt[3]{x} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{2/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{2/3}}{d}-b^2 x","a^2 x+\frac{6 i a b \sqrt[3]{x} \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}-\frac{3 a b \text{Li}_3\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}-\frac{6 a b x^{2/3} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d}+2 i a b x-\frac{3 i b^2 \text{Li}_2\left(-e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^3}+\frac{6 b^2 \sqrt[3]{x} \log \left(1+e^{2 i \left(c+d \sqrt[3]{x}\right)}\right)}{d^2}+\frac{3 b^2 x^{2/3} \tan \left(c+d \sqrt[3]{x}\right)}{d}-\frac{3 i b^2 x^{2/3}}{d}-b^2 x",1,"((-3*I)*b^2*x^(2/3))/d + a^2*x + (2*I)*a*b*x - b^2*x + (6*b^2*x^(1/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d^2 - (6*a*b*x^(2/3)*Log[1 + E^((2*I)*(c + d*x^(1/3)))])/d - ((3*I)*b^2*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^3 + ((6*I)*a*b*x^(1/3)*PolyLog[2, -E^((2*I)*(c + d*x^(1/3)))])/d^2 - (3*a*b*PolyLog[3, -E^((2*I)*(c + d*x^(1/3)))])/d^3 + (3*b^2*x^(2/3)*Tan[c + d*x^(1/3)])/d","A",14,11,16,0.6875,1,"{3739, 3722, 3719, 2190, 2531, 2282, 6589, 3720, 2279, 2391, 30}"
55,0,0,0,0.0222086,"\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x} \, dx","Int[(a + b*Tan[c + d*x^(1/3)])^2/x,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x},x\right)",0,"Defer[Int][(a + b*Tan[c + d*x^(1/3)])^2/x, x]","A",0,0,0,0,-1,"{}"
56,0,0,0,0.0230776,"\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x^2} \, dx","Int[(a + b*Tan[c + d*x^(1/3)])^2/x^2,x]","\int \frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2}{x^2},x\right)",0,"Defer[Int][(a + b*Tan[c + d*x^(1/3)])^2/x^2, x]","A",0,0,0,0,-1,"{}"
57,1,511,0,0.5934752,"\int \frac{x^2}{a+b \tan \left(c+d \sqrt[3]{x}\right)} \, dx","Int[x^2/(a + b*Tan[c + d*x^(1/3)]),x]","-\frac{12 i b x^{7/3} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{42 b x^2 \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{126 i b x^{5/3} \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^4 \left(a^2+b^2\right)}-\frac{315 b x^{4/3} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}+\frac{945 b x^{2/3} \text{Li}_7\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^7 \left(a^2+b^2\right)}-\frac{630 i b x \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^6 \left(a^2+b^2\right)}+\frac{945 i b \sqrt[3]{x} \text{Li}_8\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^8 \left(a^2+b^2\right)}-\frac{945 b \text{Li}_9\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^9 \left(a^2+b^2\right)}+\frac{3 b x^{8/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^3}{3 (a+i b)}","-\frac{12 i b x^{7/3} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{42 b x^2 \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}+\frac{126 i b x^{5/3} \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^4 \left(a^2+b^2\right)}-\frac{315 b x^{4/3} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^5 \left(a^2+b^2\right)}+\frac{945 b x^{2/3} \text{Li}_7\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^7 \left(a^2+b^2\right)}-\frac{630 i b x \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^6 \left(a^2+b^2\right)}+\frac{945 i b \sqrt[3]{x} \text{Li}_8\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^8 \left(a^2+b^2\right)}-\frac{945 b \text{Li}_9\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^9 \left(a^2+b^2\right)}+\frac{3 b x^{8/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^3}{3 (a+i b)}",1,"x^3/(3*(a + I*b)) + (3*b*x^(8/3)*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2])/((a^2 + b^2)*d) - ((12*I)*b*x^(7/3)*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^2) + (42*b*x^2*PolyLog[3, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^3) + ((126*I)*b*x^(5/3)*PolyLog[4, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^4) - (315*b*x^(4/3)*PolyLog[5, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^5) - ((630*I)*b*x*PolyLog[6, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^6) + (945*b*x^(2/3)*PolyLog[7, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^7) + ((945*I)*b*x^(1/3)*PolyLog[8, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^8) - (945*b*PolyLog[9, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/(2*(a^2 + b^2)*d^9)","A",12,7,20,0.3500,1,"{3747, 3732, 2190, 2531, 6609, 2282, 6589}"
58,1,352,0,0.4137574,"\int \frac{x}{a+b \tan \left(c+d \sqrt[3]{x}\right)} \, dx","Int[x/(a + b*Tan[c + d*x^(1/3)]),x]","-\frac{15 i b x^{4/3} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{45 i b x^{2/3} \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{15 b x \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}-\frac{45 b \sqrt[3]{x} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^5 \left(a^2+b^2\right)}-\frac{45 i b \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{4 d^6 \left(a^2+b^2\right)}+\frac{3 b x^{5/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^2}{2 (a+i b)}","-\frac{15 i b x^{4/3} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{45 i b x^{2/3} \text{Li}_4\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{15 b x \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^3 \left(a^2+b^2\right)}-\frac{45 b \sqrt[3]{x} \text{Li}_5\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^5 \left(a^2+b^2\right)}-\frac{45 i b \text{Li}_6\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{4 d^6 \left(a^2+b^2\right)}+\frac{3 b x^{5/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x^2}{2 (a+i b)}",1,"x^2/(2*(a + I*b)) + (3*b*x^(5/3)*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2])/((a^2 + b^2)*d) - (((15*I)/2)*b*x^(4/3)*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^2) + (15*b*x*PolyLog[3, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^3) + (((45*I)/2)*b*x^(2/3)*PolyLog[4, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^4) - (45*b*x^(1/3)*PolyLog[5, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/(2*(a^2 + b^2)*d^5) - (((45*I)/4)*b*PolyLog[6, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^6)","A",9,7,18,0.3889,1,"{3747, 3732, 2190, 2531, 6609, 2282, 6589}"
59,1,176,0,0.276943,"\int \frac{1}{a+b \tan \left(c+d \sqrt[3]{x}\right)} \, dx","Int[(a + b*Tan[c + d*x^(1/3)])^(-1),x]","-\frac{3 i b \sqrt[3]{x} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^3 \left(a^2+b^2\right)}+\frac{3 b x^{2/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x}{a+i b}","-\frac{3 i b \sqrt[3]{x} \text{Li}_2\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b \text{Li}_3\left(-\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{2 d^3 \left(a^2+b^2\right)}+\frac{3 b x^{2/3} \log \left(1+\frac{\left(a^2+b^2\right) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{(a+i b)^2}\right)}{d \left(a^2+b^2\right)}+\frac{x}{a+i b}",1,"x/(a + I*b) + (3*b*x^(2/3)*Log[1 + ((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2])/((a^2 + b^2)*d) - ((3*I)*b*x^(1/3)*PolyLog[2, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/((a^2 + b^2)*d^2) + (3*b*PolyLog[3, -(((a^2 + b^2)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)^2)])/(2*(a^2 + b^2)*d^3)","A",6,6,16,0.3750,1,"{3739, 3732, 2190, 2531, 2282, 6589}"
60,0,0,0,0.0248469,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","Int[1/(x*(a + b*Tan[c + d*x^(1/3)])),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*Tan[c + d*x^(1/3)])), x]","A",0,0,0,0,-1,"{}"
61,0,0,0,0.0258066,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","Int[1/(x^2*(a + b*Tan[c + d*x^(1/3)])),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)},x\right)",0,"Defer[Int][1/(x^2*(a + b*Tan[c + d*x^(1/3)])), x]","A",0,0,0,0,-1,"{}"
62,1,1691,0,2.8885143,"\int \frac{x^2}{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Int[x^2/(a + b*Tan[c + d*x^(1/3)])^2,x]","\frac{4 b x^3}{3 (i a-b) (a-i b)^2}+\frac{x^3}{3 (a-i b)^2}-\frac{4 b^2 x^3}{3 \left(a^2+b^2\right)^2}+\frac{6 b \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{8/3}}{(a-i b)^2 (a+i b) d}-\frac{6 i b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{8/3}}{\left(a^2+b^2\right)^2 d}-\frac{6 i b^2 x^{8/3}}{\left(a^2+b^2\right)^2 d}+\frac{6 b^2 x^{8/3}}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt[3]{x}\right)}-b\right)}+\frac{24 b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{7/3}}{\left(a^2+b^2\right)^2 d^2}+\frac{24 b \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{7/3}}{(i a-b) (a-i b)^2 d^2}-\frac{24 b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{7/3}}{\left(a^2+b^2\right)^2 d^2}-\frac{84 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^3}+\frac{84 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{(a-i b)^2 (a+i b) d^3}-\frac{84 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^3}+\frac{252 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{\left(a^2+b^2\right)^2 d^4}-\frac{252 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{(i a-b) (a-i b)^2 d^4}+\frac{252 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{\left(a^2+b^2\right)^2 d^4}+\frac{630 i b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{\left(a^2+b^2\right)^2 d^5}-\frac{630 b \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{(a-i b)^2 (a+i b) d^5}+\frac{630 i b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{\left(a^2+b^2\right)^2 d^5}-\frac{1260 b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^6}+\frac{1260 b \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{(i a-b) (a-i b)^2 d^6}-\frac{1260 b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^6}-\frac{1890 i b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{\left(a^2+b^2\right)^2 d^7}+\frac{1890 b \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{(a-i b)^2 (a+i b) d^7}-\frac{1890 i b^2 \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{\left(a^2+b^2\right)^2 d^7}+\frac{1890 b^2 \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{\left(a^2+b^2\right)^2 d^8}-\frac{1890 b \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{(i a-b) (a-i b)^2 d^8}+\frac{1890 b^2 \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{\left(a^2+b^2\right)^2 d^8}+\frac{945 i b^2 \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^9}-\frac{945 b \text{Li}_9\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{(a-i b)^2 (a+i b) d^9}+\frac{945 i b^2 \text{Li}_9\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^9}","\frac{4 b x^3}{3 (i a-b) (a-i b)^2}+\frac{x^3}{3 (a-i b)^2}-\frac{4 b^2 x^3}{3 \left(a^2+b^2\right)^2}+\frac{6 b \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{8/3}}{(a-i b)^2 (a+i b) d}-\frac{6 i b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{8/3}}{\left(a^2+b^2\right)^2 d}-\frac{6 i b^2 x^{8/3}}{\left(a^2+b^2\right)^2 d}+\frac{6 b^2 x^{8/3}}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt[3]{x}\right)}-b\right)}+\frac{24 b^2 \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) x^{7/3}}{\left(a^2+b^2\right)^2 d^2}+\frac{24 b \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{7/3}}{(i a-b) (a-i b)^2 d^2}-\frac{24 b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{7/3}}{\left(a^2+b^2\right)^2 d^2}-\frac{84 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^3}+\frac{84 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{(a-i b)^2 (a+i b) d^3}-\frac{84 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^2}{\left(a^2+b^2\right)^2 d^3}+\frac{252 b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{\left(a^2+b^2\right)^2 d^4}-\frac{252 b \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{(i a-b) (a-i b)^2 d^4}+\frac{252 b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{5/3}}{\left(a^2+b^2\right)^2 d^4}+\frac{630 i b^2 \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{\left(a^2+b^2\right)^2 d^5}-\frac{630 b \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{(a-i b)^2 (a+i b) d^5}+\frac{630 i b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{4/3}}{\left(a^2+b^2\right)^2 d^5}-\frac{1260 b^2 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^6}+\frac{1260 b \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{(i a-b) (a-i b)^2 d^6}-\frac{1260 b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x}{\left(a^2+b^2\right)^2 d^6}-\frac{1890 i b^2 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{\left(a^2+b^2\right)^2 d^7}+\frac{1890 b \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{(a-i b)^2 (a+i b) d^7}-\frac{1890 i b^2 \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) x^{2/3}}{\left(a^2+b^2\right)^2 d^7}+\frac{1890 b^2 \text{Li}_7\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{\left(a^2+b^2\right)^2 d^8}-\frac{1890 b \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{(i a-b) (a-i b)^2 d^8}+\frac{1890 b^2 \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) \sqrt[3]{x}}{\left(a^2+b^2\right)^2 d^8}+\frac{945 i b^2 \text{Li}_8\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^9}-\frac{945 b \text{Li}_9\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{(a-i b)^2 (a+i b) d^9}+\frac{945 i b^2 \text{Li}_9\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{\left(a^2+b^2\right)^2 d^9}",1,"((-6*I)*b^2*x^(8/3))/((a^2 + b^2)^2*d) + (6*b^2*x^(8/3))/((a + I*b)*(I*a + b)^2*d*(I*a - b + (I*a + b)*E^((2*I)*(c + d*x^(1/3))))) + x^3/(3*(a - I*b)^2) + (4*b*x^3)/(3*(I*a - b)*(a - I*b)^2) - (4*b^2*x^3)/(3*(a^2 + b^2)^2) + (24*b^2*x^(7/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a^2 + b^2)^2*d^2) + (6*b*x^(8/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a - I*b)^2*(a + I*b)*d) - ((6*I)*b^2*x^(8/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a^2 + b^2)^2*d) - ((84*I)*b^2*x^2*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^3) + (24*b*x^(7/3)*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^2) - (24*b^2*x^(7/3)*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^2) + (252*b^2*x^(5/3)*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^4) + (84*b*x^2*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^3) - ((84*I)*b^2*x^2*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^3) + ((630*I)*b^2*x^(4/3)*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^5) - (252*b*x^(5/3)*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^4) + (252*b^2*x^(5/3)*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^4) - (1260*b^2*x*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^6) - (630*b*x^(4/3)*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^5) + ((630*I)*b^2*x^(4/3)*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^5) - ((1890*I)*b^2*x^(2/3)*PolyLog[6, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^7) + (1260*b*x*PolyLog[6, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^6) - (1260*b^2*x*PolyLog[6, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^6) + (1890*b^2*x^(1/3)*PolyLog[7, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^8) + (1890*b*x^(2/3)*PolyLog[7, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^7) - ((1890*I)*b^2*x^(2/3)*PolyLog[7, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^7) + ((945*I)*b^2*PolyLog[8, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^9) - (1890*b*x^(1/3)*PolyLog[8, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^8) + (1890*b^2*x^(1/3)*PolyLog[8, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^8) - (945*b*PolyLog[9, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^9) + ((945*I)*b^2*PolyLog[9, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^9)","A",37,10,20,0.5000,1,"{3747, 3734, 2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
63,1,1155,0,2.0827039,"\int \frac{x}{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Int[x/(a + b*Tan[c + d*x^(1/3)])^2,x]","-\frac{2 x^2 b^2}{\left(a^2+b^2\right)^2}-\frac{6 i x^{5/3} b^2}{\left(a^2+b^2\right)^2 d}+\frac{6 x^{5/3} b^2}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt[3]{x}\right)}-b\right)}-\frac{6 i x^{5/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b^2}{\left(a^2+b^2\right)^2 d}+\frac{15 x^{4/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b^2}{\left(a^2+b^2\right)^2 d^2}-\frac{15 x^{4/3} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^2}-\frac{30 i x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^3}-\frac{30 i x \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^3}+\frac{45 x^{2/3} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^4}+\frac{45 x^{2/3} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^4}+\frac{45 i \sqrt[3]{x} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^5}+\frac{45 i \sqrt[3]{x} \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^5}-\frac{45 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{2 \left(a^2+b^2\right)^2 d^6}-\frac{45 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{2 \left(a^2+b^2\right)^2 d^6}+\frac{2 x^2 b}{(i a-b) (a-i b)^2}+\frac{6 x^{5/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b}{(a-i b)^2 (a+i b) d}+\frac{15 x^{4/3} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(i a-b) (a-i b)^2 d^2}+\frac{30 x \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(a-i b)^2 (a+i b) d^3}-\frac{45 x^{2/3} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(i a-b) (a-i b)^2 d^4}-\frac{45 \sqrt[3]{x} \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(a-i b)^2 (a+i b) d^5}+\frac{45 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{2 (i a-b) (a-i b)^2 d^6}+\frac{x^2}{2 (a-i b)^2}","-\frac{2 x^2 b^2}{\left(a^2+b^2\right)^2}-\frac{6 i x^{5/3} b^2}{\left(a^2+b^2\right)^2 d}+\frac{6 x^{5/3} b^2}{(a+i b) (i a+b)^2 d \left(i a+(i a+b) e^{2 i \left(c+d \sqrt[3]{x}\right)}-b\right)}-\frac{6 i x^{5/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b^2}{\left(a^2+b^2\right)^2 d}+\frac{15 x^{4/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b^2}{\left(a^2+b^2\right)^2 d^2}-\frac{15 x^{4/3} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^2}-\frac{30 i x \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^3}-\frac{30 i x \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^3}+\frac{45 x^{2/3} \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^4}+\frac{45 x^{2/3} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^4}+\frac{45 i \sqrt[3]{x} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^5}+\frac{45 i \sqrt[3]{x} \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{\left(a^2+b^2\right)^2 d^5}-\frac{45 \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{2 \left(a^2+b^2\right)^2 d^6}-\frac{45 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b^2}{2 \left(a^2+b^2\right)^2 d^6}+\frac{2 x^2 b}{(i a-b) (a-i b)^2}+\frac{6 x^{5/3} \log \left(\frac{e^{2 i \left(c+d \sqrt[3]{x}\right)} (a-i b)}{a+i b}+1\right) b}{(a-i b)^2 (a+i b) d}+\frac{15 x^{4/3} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(i a-b) (a-i b)^2 d^2}+\frac{30 x \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(a-i b)^2 (a+i b) d^3}-\frac{45 x^{2/3} \text{Li}_4\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(i a-b) (a-i b)^2 d^4}-\frac{45 \sqrt[3]{x} \text{Li}_5\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{(a-i b)^2 (a+i b) d^5}+\frac{45 \text{Li}_6\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right) b}{2 (i a-b) (a-i b)^2 d^6}+\frac{x^2}{2 (a-i b)^2}",1,"((-6*I)*b^2*x^(5/3))/((a^2 + b^2)^2*d) + (6*b^2*x^(5/3))/((a + I*b)*(I*a + b)^2*d*(I*a - b + (I*a + b)*E^((2*I)*(c + d*x^(1/3))))) + x^2/(2*(a - I*b)^2) + (2*b*x^2)/((I*a - b)*(a - I*b)^2) - (2*b^2*x^2)/(a^2 + b^2)^2 + (15*b^2*x^(4/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a^2 + b^2)^2*d^2) + (6*b*x^(5/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a - I*b)^2*(a + I*b)*d) - ((6*I)*b^2*x^(5/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a^2 + b^2)^2*d) - ((30*I)*b^2*x*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^3) + (15*b*x^(4/3)*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^2) - (15*b^2*x^(4/3)*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^2) + (45*b^2*x^(2/3)*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^4) + (30*b*x*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^3) - ((30*I)*b^2*x*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^3) + ((45*I)*b^2*x^(1/3)*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^5) - (45*b*x^(2/3)*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^4) + (45*b^2*x^(2/3)*PolyLog[4, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^4) - (45*b^2*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/(2*(a^2 + b^2)^2*d^6) - (45*b*x^(1/3)*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^5) + ((45*I)*b^2*x^(1/3)*PolyLog[5, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^5) + (45*b*PolyLog[6, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/(2*(I*a - b)*(a - I*b)^2*d^6) - (45*b^2*PolyLog[6, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/(2*(a^2 + b^2)^2*d^6)","A",28,10,18,0.5556,1,"{3747, 3734, 2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
64,1,610,0,1.4030472,"\int \frac{1}{\left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Int[(a + b*Tan[c + d*x^(1/3)])^(-2),x]","-\frac{6 b^2 \sqrt[3]{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{3 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{3 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}+\frac{6 b^2 \sqrt[3]{x} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{6 i b^2 x^{2/3} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d \left(a^2+b^2\right)^2}-\frac{6 i b^2 x^{2/3}}{d \left(a^2+b^2\right)^2}-\frac{4 b^2 x}{\left(a^2+b^2\right)^2}+\frac{6 b^2 x^{2/3}}{d (a+i b) (b+i a)^2 \left((b+i a) e^{2 i \left(c+d \sqrt[3]{x}\right)}+i a-b\right)}+\frac{6 b \sqrt[3]{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 (-b+i a) (a-i b)^2}+\frac{3 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 (a-i b)^2 (a+i b)}+\frac{6 b x^{2/3} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d (a-i b)^2 (a+i b)}+\frac{4 b x}{(-b+i a) (a-i b)^2}+\frac{x}{(a-i b)^2}","-\frac{6 b^2 \sqrt[3]{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{3 i b^2 \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}-\frac{3 i b^2 \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 \left(a^2+b^2\right)^2}+\frac{6 b^2 \sqrt[3]{x} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{6 i b^2 x^{2/3} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d \left(a^2+b^2\right)^2}-\frac{6 i b^2 x^{2/3}}{d \left(a^2+b^2\right)^2}-\frac{4 b^2 x}{\left(a^2+b^2\right)^2}+\frac{6 b^2 x^{2/3}}{d (a+i b) (b+i a)^2 \left((b+i a) e^{2 i \left(c+d \sqrt[3]{x}\right)}+i a-b\right)}+\frac{6 b \sqrt[3]{x} \text{Li}_2\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^2 (-b+i a) (a-i b)^2}+\frac{3 b \text{Li}_3\left(-\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d^3 (a-i b)^2 (a+i b)}+\frac{6 b x^{2/3} \log \left(1+\frac{(a-i b) e^{2 i \left(c+d \sqrt[3]{x}\right)}}{a+i b}\right)}{d (a-i b)^2 (a+i b)}+\frac{4 b x}{(-b+i a) (a-i b)^2}+\frac{x}{(a-i b)^2}",1,"((-6*I)*b^2*x^(2/3))/((a^2 + b^2)^2*d) + (6*b^2*x^(2/3))/((a + I*b)*(I*a + b)^2*d*(I*a - b + (I*a + b)*E^((2*I)*(c + d*x^(1/3))))) + x/(a - I*b)^2 + (4*b*x)/((I*a - b)*(a - I*b)^2) - (4*b^2*x)/(a^2 + b^2)^2 + (6*b^2*x^(1/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a^2 + b^2)^2*d^2) + (6*b*x^(2/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a - I*b)^2*(a + I*b)*d) - ((6*I)*b^2*x^(2/3)*Log[1 + ((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b)])/((a^2 + b^2)^2*d) - ((3*I)*b^2*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^3) + (6*b*x^(1/3)*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((I*a - b)*(a - I*b)^2*d^2) - (6*b^2*x^(1/3)*PolyLog[2, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^2) + (3*b*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a - I*b)^2*(a + I*b)*d^3) - ((3*I)*b^2*PolyLog[3, -(((a - I*b)*E^((2*I)*(c + d*x^(1/3))))/(a + I*b))])/((a^2 + b^2)^2*d^3)","A",19,11,16,0.6875,1,"{3739, 3734, 2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391}"
65,0,0,0,0.0241474,"\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Int[1/(x*(a + b*Tan[c + d*x^(1/3)])^2),x]","\int \frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*Tan[c + d*x^(1/3)])^2), x]","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0245027,"\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","Int[1/(x^2*(a + b*Tan[c + d*x^(1/3)])^2),x]","\int \frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \tan \left(c+d \sqrt[3]{x}\right)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(a + b*Tan[c + d*x^(1/3)])^2), x]","A",0,0,0,0,-1,"{}"